Material properties of n-type silicon and n-type UMG solar ...... · As n-type silicon can tolerate...

Material properties of n-type silicon and n-type

UMG solar cells

Peiting Zheng

A thesis submitted for the degree of

Doctor of Philosophy

of

The Australian National University

Research School of Engineering

College of Engineering and Computer Science

The Australian National University

April 2016

i

Declaration

I certify that this thesis does not incorporate, without acknowledgement any material

previously submitted for a degree or diploma in any university, and that, to the best of

my knowledge, it does not contain any material previously published or written by

another person except where due reference is made in the text. The work in this thesis is

my own, except for the contributions made by others as described in the

Acknowledgements.

Peiting Zheng

April 2016

iii

Acknowledgements

I would like to extend my gratitude to many people, who contributed to the creation of

this thesis.

First of all, I would like to express my deepest gratitude to my supervisor, Assoc.

Prof. Daniel Macdonald, for giving me support, encouragement, and valuable advice on

my research, for always contributing his time to share his knowledge and discuss the

problems encountered in the experiments, for his motivation, patience and enthusiasm.

Also, I am extremely grateful for his private time he took to give valuable feedbacks on

this thesis and other papers. Without those, I could not have completed these

publications during my PhD. I would also like to thank my co-supervisor, Dr. Fiacre

Rougieux, for being so generous with his time to share knowledge and discuss the

experiment results with me, for giving me support and precious experience in my

experiments and data analysis, for contributing his time to help me measuring samples

and solar cells. Moreover, I really appreciate his feedbacks on this thesis and papers

during my PhD. I would also like to show my gratitude to my co-supervisor Prof.

Andres Cuevas, for being so generous with his time, knowledge and ideas and for

enriching my knowledge with his brilliant knowledge about the fundamentals of silicon

solar cells.

I would like to thank Dr. Julien Degoulange and Dr. Roland Einhaus of Apollon Solar

for providing brilliant UMG materials and important information and measurements of

these materials. Without these excellent materials, I would not have achieved high

efficiency solar cells.

I am thankful to Chris Samundsett for his assistance in the labs and for taking the

time to induct me into the different clean-room processes and various solar cell

processes. Thank you to Maureen Brauers, Nina De Caritat, Josephine Anne McKeon,

Dr. Beatriz Velasco and Teng Kho for giving me helps in the labs and processes. I am

deeply thankful to the technical staff James Cotsel, Mark Saunders and Bruce Condon

for their brilliant expertise in electronics. Without them, the experiments would not

have been completed successfully.

iv

I am grateful to Dr. Pheng Phang for his help with the boron and phosphorus

diffusions and extensive discussions about the cell fabrication processes. Also, I

appreciate his help in designing new photolithography mask for the cell processes. I

would like to thank Di Yan for his help with PECVD deposition in ANFF, diffusions

and other characterizations. I would like to thank Tom Allen and Dr. Yimao Wan for

helping me out with ALD and PECVD depositions. I would like to thank Dr. Xinbo

Yang for giving me advices on the solar cell processes. Also, I would like to thank Dr.

Er-Chien Wang for giving me help with ECV and spectrophotometer measurements. I

want to acknowledge Dr Nicholas Grant for his extensive discussions with the

experiment and train me with HF passivation. I would like to thank Hieu Nguyen for his

enthusiastic discussion and measurements in PL spectroscopy. I am also deeply grateful

to James Bullock for his collaboration and contribution in the PRC solar cell and for

being generous to share his knowledge and ideas with me.

I am grateful to my fellow office mate and group mate, Dr. Anyao Liu, Dr. Jie Cui,

Dr. Xinyu Zhang, Dr. Lujia Xu, Chang Sun, Kelvin Sio, Teck Kong Chong, Wensheng

liang, Azul Osorio Mayon, Young Han, Siewyee lim and Mohsen Goodarzi. Thank you

for all the exciting discussions and good laughs we had. I would also like to thank Dr.

Heping Shen, The Duong and Jun Peng for sharing their valuable knowledge on

Perovskite solar cells. I am grateful to all the other PhD students who also made this

time very enjoyable, Xiao Fu, Tom Ratcliff, Lachlan Black, Simeon Baker-Finch, Chog

Barugkin.

Finally, I would like to thank my partner Chengdi Xiang for her support,

encouragement and patience throughout this entire journey. Without her support, I

would not complete my PhD and this thesis. I am also deeply grateful to my family,

their support and encouragement allow me to overcome many challenges.

v

Abstract

This thesis focuses on understanding the electrical properties of n-type mono-crystalline

silicon. Such material has been widely used for high efficiency solar cells and has the

potential to be used for low-cost high-efficiency devices and ultra-high efficiency

devices. However, the fundamental properties of n-type silicon, such as the mobility of

electrons and holes as well as the influence of growth and feedstock related defects on

the minority carrier lifetime remains unclear. This thesis clarifies these issues and brings

new understanding regarding the influence of excess carrier density and temperature on

the mobility in n-type silicon, the influence of grown-in defects on the minority carrier

lifetime in n-type silicon and the influence of feedstock related defects in n-type UMG

silicon. In addition, this thesis also demonstrates the applicability of n-type upgraded

metallurgical grade silicon as an alternative source of feedstock for high efficiency

crystalline silicon solar cells.

We experimentally measured the carrier mobility sum in n-type silicon as a function

of doping density, injection level and temperature. Based on the measurements, an

empirical model is derived over a temperature range from 150K to 450K. The empirical

model shows good agreement with the existing mobility models, for instance,

Klaassen’s mobility model. The model is then further extended to include data from p-

type silicon and shows good agreement. This model provides experimental confidence

for the use of existing mobility models in modelling highly injected bulk regions of high

efficiency solar cells.

We also investigate the impact of intrinsic-related lifetime-limiting defects in n-type

as-grown Czochralski (Cz) silicon. The thermal stability and annihilation activation

energy of the defects are measured based on minority carrier lifetime measurements. It

is found that these defects in as-grown silicon can significantly reduce the minority

carrier lifetime in n-type Cz silicon by several hundreds of microseconds and thus affect

the performance of high efficiency solar cells. However, we demonstrate that these

defects can be thermally annihilated at low temperature between 150oC to 300oC. Based

on the annealing characteristics of the defects, it is found that these defects could be

vi

related to vacancies and are identified to be vacancy-phosphorus (VP) and vacancy-

oxygen (VO), pairs by comparing to studies in irradiated silicon by Electron

Paramagnetic Resonance (EPR) measurements.

As n-type silicon can tolerate more impurities than p-type silicon, n-type solar grade

silicon is a potential candidate for low cost high-efficiency solar cells. In this thesis, we

used 100% upgraded metallurgical grade silicon (UMG) purified from a metallurgical

route to fabricate silicon solar cells. We showed that the bulk lifetime is significantly

affected by the boron diffusion and can be recovered by the phosphorus diffusion. An

etch-back approach is applied to the cell fabrication process to maintain a relatively

high bulk lifetime in the final state of the cells. A record efficiency of 21.6% is achieved

using this process. However, UMG silicon is compensated, thus, the presence of boron

still leads to the formation of boron-oxygen defects in n-type UMG silicon. The effect

of light-induced degradation due to boron-oxygen defects is quantified and strategies for

permanent deactivation of boron-oxygen defects in cell level are investigated. We

demonstrate that the boron-oxygen defects in the cell level can be partially permanently

deactivated through annealing under illumination. Moreover, simulation and loss

analysis reveals that the lower mobility in UMG material due to material compensation

does not lead to significant losses in the cell. With the current structure and material,

UMG solar cells with efficiencies above 22% are achievable.

vii

Contents

Acknowledgements iii

Abstract v

Introduction

Thesis Motivation ............................................................................................................. 1

Thesis Outline ................................................................................................................... 5

Chapter 1 Measurement and Parameterization of Carrier Mobility Sum in Silicon

1.1 Introduction ............................................................................................................ 7

1.2 Carrier mobility ...................................................................................................... 8

1.2.1 Mean free time ................................................................................................ 8

1.2.2 Drift current .................................................................................................... 9

1.2.3 Diffusion current ........................................................................................... 10

1.2.4 Total charge current ...................................................................................... 11

1.3 Scattering mechanisms ......................................................................................... 12

1.3.1 Lattice scattering ........................................................................................... 12

1.3.2 Impurity scattering ........................................................................................ 13

1.3.2.1 Ionized impurity scattering ....................................................................... 13

1.3.2.2 Neutral impurity scattering ....................................................................... 14

1.3.3 Carrier-carrier scattering ............................................................................... 14

1.3.4 Matthiesen’s rule........................................................................................... 14

1.4 Carrier mobility sum measurement ...................................................................... 15

1.4.1 Dannhauser’s method ................................................................................... 15

1.4.2 Neuhaus’s method......................................................................................... 16

1.4.3 Contactless photoconductance method ......................................................... 17

1.5 Carrier mobility models ....................................................................................... 19

1.5.1 Semi-empirical mobility models ................................................................... 19

viii

1.5.1.1 Arora’s mobility model ............................................................................. 19

1.5.1.2 Dorkel –Leturcq’s mobility model ............................................................ 20

1.5.1.3 Klaassen’s unified mobility model ........................................................... 21

1.5.2 Empirical mobility model ............................................................................. 22

1.5.2.1 Caughey and Thomas’s mobility model ................................................... 22

1.5.2.2 WCT-100 parameterization ....................................................................... 23

1.5.3 Summary of the existing mobility models .................................................... 23

1.6 Empirical model based on photoconductance technique ..................................... 24

1.6.1 Experimental method .................................................................................... 25

1.6.2 Empirical mobility sum model ..................................................................... 26

1.6.2.1 Experimental results .................................................................................. 26

1.6.2.2 Derivation of the empirical mobility sum model ...................................... 28

1.6.3 Comparison to other models ......................................................................... 34

1.6.3.1 Applicability as a function of carrier injection ......................................... 34

1.6.3.2 Applicability as a function of dopant density ........................................... 36

1.6.3.3 Applicability as a function of temperature ................................................ 37

1.7 Summary .............................................................................................................. 38

Chapter 2 Vacancy-related recombination active defects in as-grown n-type

Czochralski Silicon

2.1 Introduction .......................................................................................................... 39

2.2 Review of Crystallographic Defects in Silicon .................................................... 40

2.2.1 Point defects .................................................................................................. 41

2.2.1.1 Intrinsic point defects ................................................................................ 41

2.2.1.2 Extrinsic point defects ............................................................................... 41

2.2.2 Line defects ................................................................................................... 42

2.2.3 Planar defects ................................................................................................ 42

2.2.4 Bulk defects .................................................................................................. 43

2.3 Review of crystal growth ..................................................................................... 45

2.3.1 Dislocation free silicon crystal growth ......................................................... 45

2.3.2 Influence of v and G on crystal growth ........................................................ 46

2.3.2.1 Voronkov’s theory .................................................................................... 46

2.3.2.2 Radial non-uniformity of G ....................................................................... 48

2.3.3 Defects incorporated in vacancy mode crystal growth ................................. 49

ix

2.3.3.1 Voids ......................................................................................................... 50

2.3.3.2 Vacancy-oxygen agglomerates ................................................................. 50

2.3.3.3 Binding of vacancies by oxygen ............................................................... 52

2.3.4 Defects incorporated in interstitial mode crystal growth .............................. 52

2.3.4.1 A/B-defects ............................................................................................... 52

2.3.5 Perfect Silicon ............................................................................................... 53

2.4 Vacancy-impurity pairs in irradiated Silicon ....................................................... 53

2.4.1 Various types of vacancy-impurity pairs complexes .................................... 54

2.4.2 Vacancy-phosphorus pair ............................................................................. 55

2.4.3 Vacancy-oxygen pair .................................................................................... 56

2.5 Recent studies on vacancy-related defects in as-grown silicon ........................... 57

2.5.1 Review of lifetime limiting defects in high-purity Cz silicon crystals ......... 57

2.5.2 Review of lifetime limiting defects in high-purity FZ silicon crystals ......... 59

2.6 Investigation of vacancy-related defects in Cz n-type as-grown silicon .............. 60

2.6.1 Experimental method .................................................................................... 60

2.6.2 Impact of vacancy-related defects on lifetime .............................................. 62

2.6.3 Temperature dependent defect deactivation ................................................. 64

2.6.4 Activation energy of stage 1 defect .............................................................. 66

2.6.5 Discussion and conclusion ............................................................................ 70

2.7 Summary .............................................................................................................. 72

Chapter 3 High Efficiency Upgraded Metallurgical Grade Silicon Solar Cells:

Fabrication and Analysis

3.1 Introduction .......................................................................................................... 75

3.2 Silicon feedstock .................................................................................................. 75

3.2.1 Metallurgical grade silicon ........................................................................... 76

3.2.2 Electronic grade silicon feedstock ................................................................ 77

3.2.2.1 The Siemens process ................................................................................. 77

3.2.2.2 Other processes ......................................................................................... 78

3.2.3 Solar grade silicon feedstock ........................................................................ 80

3.2.3.1 SoG-Si purified through chemical routes .................................................. 82

3.2.3.2 SoG-Si purified through metallurgical routes ........................................... 84

3.2.3.2.1 Directional solidification ................................................................... 84

3.2.3.2.2 Acid Leaching .................................................................................... 85

x

3.2.3.2.3 Plasma refining .................................................................................. 86

3.2.3.2.4 Slag treatment .................................................................................... 87

3.2.3.2.5 Electron beam melting ....................................................................... 88

3.2.3.2.6 State of the art of SoG-Si purified by metallurgical routes ............... 89

3.3 Impact of compensation on material properties ................................................... 89

3.3.1 Net doping and compensation ratios ............................................................. 90

3.3.2 Impact of compensation on mobility and resistivity ..................................... 91

3.3.3 Impact of compensation on recombination ................................................... 93

3.3.4 Impact of compensation on JSC ..................................................................... 94

3.3.5 Impact of compensation on Voc .................................................................... 94

3.3.6 Impact of compensation on fill factor ........................................................... 95

3.3.7 Impact of compensation on efficiency .......................................................... 96

3.4 Evolution of UMG-Si solar cells ......................................................................... 97

3.5 Permanent deactivation of boron oxygen defect in compensated silicon ............ 99

3.5.1 Deactivation of BO defect in p-type silicon wafers and cells ...................... 99

3.5.2 Deactivation of BO defect in n-type silicon wafers .................................... 100

3.6 High efficiency UMG-Si solar cell: fabrication and analysis ............................ 101

3.6.1 Bulk lifetime studies after high temperature process ................................. 102

3.6.2 Cell fabrication process .............................................................................. 105

3.6.3 UMG-Si solar cell batch A ......................................................................... 107

3.6.3.1 Material properties for batch A ............................................................... 108

3.6.3.2 Control parameter measurements............................................................ 109

3.6.3.2.1 Diffusion profiles ............................................................................. 109

3.6.3.2.2 Bulk lifetime measurements ............................................................ 110

3.6.3.2.3 J0 measurements .............................................................................. 111

3.6.3.2.4 Contact resistivity measurements .................................................... 114

3.6.3.2.5 Summary of control parameters....................................................... 116

3.6.3.3 Batch A cell results ................................................................................. 117

3.6.3.3.1 I-V measurements ............................................................................ 117

3.6.3.3.2 EQE and reflectance measurements ................................................ 119

3.6.3.3.3 Rsh measurements ............................................................................ 120

3.6.3.3.4 Rs measurements .............................................................................. 122

3.6.3.4 Permanent deactivation of BO defects at the cell level .......................... 124

3.6.3.5 UMG-Si solar cells batch B .................................................................... 126

xi

3.6.3.5.1 Material properties for batch B ........................................................ 127

3.6.3.5.2 Control parameters for batch B ........................................................ 127

3.6.3.5.3 Batch B cell results .......................................................................... 129

3.6.3.5.4 Statistical distribution ...................................................................... 133

3.6.3.6 Simulation of PERL cells made from UMG silicon ............................... 136

3.6.3.6.1 Simulation of optics ......................................................................... 137

3.6.3.6.2 Electrical properties ......................................................................... 139

3.6.3.6.3 Simulation results ............................................................................ 139

3.6.3.6.4 Free energy loss analysis ................................................................. 142

3.7 Summary ............................................................................................................ 144

Chapter 4 Conclusion and Further Work

4.1 Carrier mobility sum .......................................................................................... 147

4.2 Intrinsic-related defect ....................................................................................... 148

4.3 High efficiency UMG solar cell ......................................................................... 148

4.4 Further work ....................................................................................................... 149

List of Symbols 151

List of Publications 155

Bibliography 159

1

Introduction

Thesis Motivation

The photovoltaics (PV) industry has experienced outstanding growth in the past decades.

The cumulative installed PV capacity reached 180GWp in 2014, a tenfold increase in

capacity since 2008 [1]. The International Energy Agency (IEA) has forecast the

cumulative installed capacity for PV to reach 1.7TWp by 2030 and 4.7TWp by 2050 [2].

Such a forecast implies capacity additions of over 120GWp/year. However, the PV

industry still faces many difficulties. Although the price of electricity generated by PV

has dramatically dropped in recent years, mainly due to fast scaling up of solar cell

manufacturing, and the oversupply of modules, the price of PV is still high compared to

the wholesale price for most conventional power generation technologies. The levelized

cost of electricity (LCOE) of PV is approximately 0.12 US$/kWh in the USA. In

comparison to about 0.09 US$/kWh for conventional coal and 0.07 US$/kWh for

natural gas, PV is still 30% to 70% more expensive [3, 4].

The disadvantage in price has forced PV to rely on government subsidies, which are

strongly dependent on government policies and economics. This affects the stability of

PV industries and has caused some industry players, including some leading

manufacturers, to make large losses, and even close, in the past few years due to the

reduction in subsidies and prices.

In addition, potential shortages in the supply of raw materials is an issue for the

growing PV industries. Such issues arose previously, for example in 2008 when a

shortage in polycrystalline silicon feedstock production caused the price to drastically

increase from 20 US$/kg to 450 US$/kg ,with a subsequent return to 20 US$/kg [5-7].

Although the price of silicon feedstock has been stable in recent years, it is possible that

a new polysilicon shortage could happen in the future. This is reinforced by the fact that

in order to achieve the fast growth predicted by the IEA (TWp installation capacity by

2030), significant investment will be required in polysilicon production to prevent

further polysilicon shortages and subsequent fluctuations in price. In order to become

subsidy-free and achieve high and sustainable growth rates, the PV industry has to

2

reduce both operational costs and Capital Expenditure (CapEx). Considering that

polysilicon is one of the highest CapEx components of module production, seeking

alternative lower CapEx feedstock supplies exclusively for PV will allow greater

growth rates for the PV industries, and greater immunity from the volatility of the

feedstock price.

A key approach to reduce module costs is to increase the efficiency at the cell and

module level. The choice of wafer polarity can play a role in the efficiency of silicon

solar cells. p-type silicon has been the dominant material in the PV industry and

commercial market over several decades. The main reasons for this are historical as p-

type silicon was proven to be more resistant to space irradiation [8] than n-type silicon

wafer. It was proven that p-type silicon has a superior end-of-life performance, although

the beginning-of-life performance is superior in n-type silicon. In addition, p-type

silicon has a minority carrier mobility 3 times higher than in n-type silicon, which is

beneficial for carrier collection in a solar cell. p-type silicon has other advantages over

n-type silicon in terms of processing techniques, such as the phosphorus diffusion which

requires lower temperature to form the emitter of solar cells, and which can also have

gettering effects to remove unwanted metallic impurities in the bulk material [9]. Also

aluminium can be easily used to both contact the rear and form a p+ surface.

However, the vast majority of commercial silicon solar cell production today is for

terrestrial applications, where degradation due to high-energy radiation is not an issue.

Furthermore, the wafers used for high-efficiency commercial silicon solar cells are

becoming thinner and with improved material quality. Therefore the light-generated

current is dominated more by optics and surface passivation instead of the minority

carrier mobility. Moreover, n-type silicon is immune to the negative impact of the

boron-oxygen (BO) defect, which is known to significantly reduce the device

performance [10-12]. Also, it has been demonstrated that defects, for instance, diffusion

induced misfit dislocations, laser induced dislocations, and many common metallic

impurities such as Fe, Ti, Cr, Mo and Co lead to a lower lifetime in p-type silicon

compared to n-type silicon [13-15]. Thus, n-type silicon wafers usually have higher

minority carrier lifetimes than p-type silicon wafers. Several groups have reported high

pre- and post-processing lifetimes in both cast multi-crystalline and Czochralski grown

n-type silicon [16-18]. The world record efficiency crystalline silicon (c-Si) solar cell

with 25.6% is an interdigitated back contact (IBC) heterojunction structure from

Panasonic [19], and is based on an n-type silicon substrate. In addition, the recently

3

announced n-type silicon front junction device from Fraunhofer ISE with efficiency

25.1% and recent IBC cell from SunPower of efficiency 25.2% are also based on n-

type c-Si substrates [20]. Large industrial players such as SunPower, and Yingli Green

Energy [21, 22] are already manufacturing high efficiency commercialized solar cell

modules using n-type c-Si substrates.

Although efficiencies above 25% have been achieved using n-type c-Si wafers, the

efficiency is still somewhat below the ideal case [23]. Material quality is one of the

limiting factors to obtain ideal efficiency for solar cells. Figure 0.1(a) illustrates the

simulated material quality required to achieve very high efficiency with Quokka using

the input parameters in [24]. It is seen that the required lifetime increases exponentially

with increase in target efficiency. Even when the highest quality n-type silicon wafers

available, with 9 nine purity (9N electronic grade) and effectively free of metallic

impurities are used, the effective lifetime is usually still below the intrinsic limit [25], as

shown for example in Figure 0.1(b). There must therefore be some residual defects in

the material that limits the minority carrier lifetime. These defects are not necessarily

related to metallic impurities or oxygen (O). They could be related to complexes of

intrinsic defects and light elements, such as carbon (C), nitrogen (N).

(a) (b)

Figure 0.1: (a) Lifetime required to achieve very high efficiency silicon solar cells [24].

(b) Measured injection dependence of the lifetime for a 4.7Ω.cm n-type FZ wafer, the

lines are fits using the SRH, Auger and recombination parameter equations [26].

In order to further improve the efficiency of c-Si solar cells, understanding of the

electrical properties of n-type c-Si, such as, mobility, minority carrier lifetime, and

4

understanding and identifying the properties of defects in very pure electronic grade

(EG) n-type c-Si is crucial.

As discussed previously, using cheaper feedstock exclusive for PV industries can also

reduce the costs and avoid large price fluctuations due to the imbalance between supply

and demand in the market. The Siemens process is the conventional process to produce

very pure silicon feedstock via gas phase distillation (called EG-Si). This process is

relatively expensive, and very energy consuming (~200kWh/kg) [27]. Moreover,

Siemens purification plants require long construction lead times (~ 3 years) and a large

capital expenditure (CapEx). As mentioned previously, the large oversupply has driven

the feedstock price to 20 US$/kg. At this low selling price, EG-Si manufacturers make

little profit that could feed future investments to expand their production capacity.

Therefore, the EG-Si market is likely to experience a shortage in supply leading to

further price hikes to allow further investments and expansions. This price fluctuation is

of minor impact on the semiconductor industry, since Si feedstock only accounts for a

very small portion of the cost of integrated circuits. However, Si feedstock contributes

an important cost component of solar modules (~20% of the total module costs) [28].

Thus, volatility in the feedstock price can potentially limit the reductions in module

costs and in the long term has a negative impact for PV to become more competitive

with conventional energy resources.

Upgraded metallurgical-grade silicon (UMG-Si) has raised interest as an alternative

feedstock supply to secure the availability of silicon feedstock at low price for PV

industries in the recent years. Instead of using gas phase purification, it is obtained

using an improved metallurgical refinement techniques [29-32], and as such, during

purification the silicon only goes through solid or liquid phases. As a result, the

purification process is generally less energy consuming (~20-30kWh/kg) [33]. Also, it

requires less CapEx. Most of the UMG-Si producers aim at selling feedstock for around

15 US$/kg [33, 34]. Compared to the current polycrystalline silicon price (~20 US$/kg),

this amounts to a 25% reduction in price, which can be translated to a 5% reduction in

total module costs. However, metallurgical refinement techniques are less efficient at

removing impurities than the conventional Siemens process and hence UMG-Si usually

contains more impurities than EG-Si. These impurities can affect the efficiency of solar

cells in different ways depending on their electrical properties and concentrations. The

reduction in efficiency can directly increase the cost of the total PV systems, thus any

significant reduction in efficiency is not tolerable, even if the feedstock cost can be

5

reduced. The challenge for UMG-Si to be applied in PV industries is to make solar cells

with comparable efficiency to EG-Si solar cells despite the presence of more impurities.

n-type silicon, as discussed above, can in general tolerate more impurities. Therefore,

using n-type UMG-Si can potentially lead to higher efficiencies than p-type UMG-Si,

perhaps even comparable to EG-Si for PV applications. However, the difficulties of

removing dopant atoms, such as boron (B), phosphorus (P) and aluminium (Al) during

the purification of UMG-Si makes this material compensated. The presence of B atoms

still leads to the well-known boron-oxygen (BO) defects [35-38] in n-type UMG-Si,

thus, significantly impacting the device performance. The highest efficiency solar cell

reported to date based on 100% UMG-Si is 19.8% on n-type UMG substrates with a

passivated emitter rear totally diffused (PERT) cell structure [39]. Can we use n-type

UMG-Si to break the 20% efficiency barrier? Is there any way to permanently solve the

BO issue in n-type UMG-Si at the cell level? This thesis aims to answer these specific

questions.

In summary, the broader aim of the present thesis is to understand and characterize

the electrical properties of n-type silicon from a material perspective in order to

contribute to the advancement for high efficiency and low cost solar cells.

Thesis Outline

Chapter 1 reports on measurements of the carrier mobility sum in n-type

monocrystalline silicon (mono-Si) as a function of injection level, doping density and

temperature based on a recently developed technique from 150K to 450K. The results

are then used to derive an empirical relationship for the carrier mobility sum in n-type

silicon in terms of doping density, injection and temperature. This is the first mobility

sum model that is derived solely based on measured data that has simultaneous injection

and temperature dependences. The model is then extended to p-type silicon in a

narrower resistivity range. The applicability of the new mobility model is assessed and

compared with existing mobility models.

In Chapter 2, we investigate recombination active defects in very high lifetime n-type

as-grown Cz mono-Si wafers. The thermal stabilities and annihilation activation energy

of the defects are measured based on photoconductance minority carrier lifetime

measurements. Two types of defects are identified in the experiments that can be

thermally deactivated at 150oC and 350 oC, respectively. Both defects are found to

6

significantly degrade the lifetime of millisecond-range Cz grown n-type silicon wafers:

a material widely used for high efficiency solar cells. The observed deactivation

temperature suggests that the first defect may be caused by vacancy-phosphorus (VP)

pairs. The deactivation temperature of the second defect is consistent with the presence

of vacancy-oxygen (VO) pairs.

In Chapter 3, we present solar cells fabricated with n-type Cz mono-Si wafers grown

with strongly compensated 100% upgraded metallurgical-grade feedstock. The

fabricated cells have efficiencies above 20%. The cells have a passivated boron-diffused

front surface, and a rear locally phosphorus-diffused structure fabricated using an etch-

back process. The local heavy phosphorus diffusion on the rear helps to maintain a high

bulk lifetime in the substrates via phosphorus gettering, whilst also reducing

recombination under the rear-side metal contacts. The impact of high temperature

processes on the minority carrier lifetime in the wafers is investigated. Cell results from

two separate batches (Batch A and B) are presented with an independently confirmed

efficiency of 20.9% for the best UMG-Si cell and 21.9% for a control device made with

EG FZ silicon in batch A. In batch B, a 21.6% efficiency UMG cell (in-house

measurement) is achieved. The statistical distribution of the cell results is also shown

for batch B. In addition, the presence of BO related defects in the cells are also studied,

and we demonstrate that these defects can be partially deactivated permanently by

annealing under illumination. At the end of this chapter, we provide modelling results

using 3D simulation tools for the best UMG-Si and EG control cells for both batch A

and B. Through a power loss analysis, we quantify material related losses in the UMG-

Si cells.

7

Chapter 1

Measurements and Parameterization of Carrier

Mobility Sum in Silicon

1.1 Introduction

Carrier mobility is a key parameter to characterize the fundamental properties of silicon

as well as devices like solar cells and transistors. Numerous experimental data on the

minority and majority carrier mobility in both p- and n-type silicon over a range of

temperatures have been published, mostly as a function of the dopant concentration [40-

45]. However, data for the electron and hole mobility sum as a function of excess carrier

density, as opposed to the dopant density, have only been measured at room temperature

[46-49]. Experimental evidence regarding the simultaneous impact of excess carrier

injection and temperature does not exist, to our knowledge.

In this chapter, we determine the sum of the electron and hole mobilities as a function

of both excess carrier density and temperature in p- and n-type silicon. Based on the

measurements, we then derive a comprehensive empirical model that includes injection,

doping and temperature dependences for the carrier mobility sum in silicon. This model

is useful for modelling the mobility in silicon solar cells with different doping under a

wide range of injections levels and temperatures. This model is also well suited to allow

accurate photoconductance-based lifetime spectroscopy of defects in silicon, where

knowledge of the mobility sum is required. This empirical model is also compared to

various existing mobility models, e.g. Klaassen’s and Dorkel-Leturcq. The applicability

of this model for both p- and n-type silicon will also be validated.

Measurements and Parameterization of Carrier Mobility Sum in Silicon

8

1.2 Carrier mobility

Under thermal equilibrium, carriers in silicon diffuse in all directions and are scattered

by different scattering centres, resulting in zero net displacement over a sufficiently

long time. However, when there is an electric field or carrier gradient, the random

thermal motion still occurs, but in addition, there is on average a net motion along the

direction of the electric field or concentration gradient. Therefore, the carrier mobility

determines how quickly electron or hole concentration change through silicon when an

electric field or concentration gradient appear [50]. In this section, the basic definition

of carrier mobility will be reviewed and different scattering mechanisms that affect the

carrier mobility will be discussed.

1.2.1 Mean free time

The mean free time of carriers is an important parameter to characterize carrier mobility

under thermal equilibrium. As carriers move through the silicon crystal lattice with

random thermal motion, they will collide with lattice atoms, impurities or defects in the

crystal structure, leading to different capture and scattering mechanisms. The mean free

time is the average time travelled by a carrier between successive impacts (collisions or

scattering) and will be introduced in this section.

Figure 1.1: Cylindrical representation of a carrier travelling through a volume

containing collision centers at a thermal velocity of vth over a time t.

Figure 1.1 shows a carrier travelling through a volume containing collisions centers

with a cylinder of cross section area of A with a thermal velocity vth which in thermal

equilibrium is given by:


9

𝑣𝑡ℎ = √3𝑘𝐵𝑇

𝑚∗

(1.1)

Where kB is the Boltzmann constant, T is the temperature and m* is the effective mass of

a particle, in this case electron or hole [50]. Over a period of time t, the carrier will

travel through a volume of Avtht. If we let the collision center density be N centers per

cm-3, the total number of centers in this volume will be NAvtht. Let the radius of the

center be r cm, and then the collision cross section of the center is given by:

𝜎 = 𝜋𝑟2

(1.2)

Therefore the total area covered by the centers is NAvthtσ and the fraction of the area

covered by the centers is NAvthtσ/A = Nvthtσ, and the number of scattering events per

second is

𝑁𝑣𝑡ℎ𝜎𝑡/𝑡 = 𝑁𝑣𝑡ℎ𝜎

(1.3)

Hence, the mean free time τc between collisions or scattering is given by:

𝜏𝑐 =1

𝑁𝑣𝑡ℎ𝜎

(1.4)

1.2.2 Drift current

Carrier transport in silicon is mainly caused by two physical mechanisms, carrier drift

and carrier diffusion. In this section, the relationship between the drift current and

mobility will be introduced. Under an externally applied electric filed, electrons and

holes are accelerated by the electrostatic force, however, due to the different scattering

mechanisms which resist further acceleration, they reach a constant velocity 𝑣 .

Therefore, based on the mean free time, the momentum gained by the carrier between

successive collisions is given by [51]

−𝑞𝜀𝜏𝑐 = 𝑚𝑛𝑣𝑛

(1.5)


10

Where 𝑣𝑛 is the drift velocity of electrons and 𝑚𝑛 is the electron effective mass, and 𝜀

is the electric field strength. If equation (1.5) is rearranged, it gives:

𝑣𝑛 = −(𝑞𝜏𝑐

𝑚𝑛)𝜀

(1.6)

𝑣𝑛 = −𝜇𝑛𝜀

(1.7)

It is seen from equations (1.6) and (1.7), carrier mobility is a proportionality constant

between the electric field strength and the drift velocity, the corresponding drift current

for electrons and holes is given by: [51]

𝐽𝑛 = −𝑞𝑛𝑣𝑛 = 𝑞𝑛𝜇𝑛𝜀

(1.8)

𝐽𝑝 = 𝑞𝑝𝑣𝑝 = 𝑞𝑝𝜇𝑝𝜀

(1.9)

The total drift current is the sum of equation (1.8) and (1.9).

𝐽 = 𝐽𝑛 + 𝐽𝑝 = (𝑞𝑛𝜇𝑛 + 𝑞𝑝𝜇𝑝)𝜀

(1.10)

Using the fact that the electric field is the gradient of the electrical potential φ

𝜀 = −𝑔𝑟𝑎𝑑(𝜑)

(1.11)

We obtain:

𝐽 = −(𝑛𝜇𝑛 + 𝑝𝜇𝑝)𝑔𝑟𝑎𝑑(𝑞𝜑)

(1.12)

1.2.3 Diffusion current

In addition to carrier drift, a carrier concentration gradient in silicon can also drive

carrier flow and produce a current. The corresponding diffusion current is described by:


11

𝐽𝑛 = 𝑞𝐷𝑛𝑔𝑟𝑎𝑑(𝑛) = 𝑞𝐷𝑛𝑛𝑔𝑟𝑎𝑑(𝑛)

𝑛

(1.13)

𝐽𝑝 = −𝑞𝐷𝑝𝑔𝑟𝑎𝑑(𝑝) = −𝑞𝐷𝑝𝑝𝑔𝑟𝑎𝑑(𝑝)

𝑝

(1.14)

These become:

𝐽𝑛 = 𝑞𝑛𝐷𝑛

𝑘𝑇𝑔𝑟𝑎𝑑(𝜗)

(1.15)

𝐽𝑝 = − 𝑞𝑝𝐷𝑝

𝑘𝑇𝑔𝑟𝑎𝑑(𝜗)

(1.16)

Where ϑ is the chemical potential and 𝐷𝑛 and 𝐷𝑝 are the diffusion constants for

electrons and holes respectively. By using the Einstein relations, the relationship

between the diffusion constant and mobility is given by: [51]

𝐷𝑛 =𝑘𝑇

𝑞𝜇𝑛

(1.17)

𝐷𝑝 =𝑘𝑇

𝑞𝜇𝑝

(1.18)

One obtains:

𝐽𝑛 = (𝑛𝜇𝑛)𝑔𝑟𝑎𝑑(𝜗)

(1.19)

𝐽𝑝 = −(𝑝𝜇𝑝)𝑔𝑟𝑎𝑑(𝜗)

(1.20)

1.2.4 Total charge current

In practice, the drift and diffusion current do not exist separately. The total charge

current can be expressed by combining equations (1.8), (1.9), (1.11), (1.19) and

equations (1.20) for electron and hole:


12

𝐽𝑛 = (𝑛𝜇𝑛)[𝑔𝑟𝑎𝑑(𝜗) + 𝑔𝑟𝑎𝑑(𝑞𝜑)]

(1.21)

𝐽𝑝 = −(𝑝𝜇𝑝)[𝑔𝑟𝑎𝑑(𝜗) + 𝑔𝑟𝑎𝑑(𝑞𝜑)]

(1.22)

This becomes:

𝐽𝑛 = (𝑛𝜇𝑛)𝑔𝑟𝑎𝑑(𝐸𝐹𝐶)

(1.23)

𝐽𝑝 = −(𝑝𝜇𝑝)𝑔𝑟𝑎𝑑(𝐸𝐹𝑉)

(1.24)

Where EFC = ϑ+qφ is the quasi Fermi energy (electrochemical potential).

1.3 Scattering mechanisms

Carrier mobility is affected by a number of scattering mechanisms in silicon. When an

electric field or carrier concentration gradient occurs, free electrons or holes travel

through the bulk and are scattered in different ways. From equation (1.6), it is seen that

the carrier mobility is proportional to the mean free time, hence, the less scattering, the

higher the mobility. In this section, three of the most important scattering mechanisms

will be introduced, namely lattice scattering, impurity scattering, and carrier-carrier

scattering.

1.3.1 Lattice scattering

Lattice scattering is caused by the vibrations of lattice atoms. At any temperature above

absolute zero, there are thermal vibrations of the lattice atoms, and the vibrations disturb

the periodic potential of the lattice and hence allow energy transfer between the lattice

and carriers. The vibration of the lattice atoms is strongly affected by the temperature,

the higher the temperature the stronger the vibrations. Therefore, lattice scattering

becomes dominant at high temperatures and thus the mobility decreases. Theoretical


13

analysis [52] shows that the relationship between the mobility component due to lattice

scattering and the temperature is given by:

𝜇𝐿 ∝ 𝑇−3/2

(1.25)

Where 𝜇𝐿 is the mobility component due to lattice scattering. The relation shows that

the mobility due to acoustic phonons, which is a quantized lattice vibration wave,

decreases with temperature as 𝑇−3/2.

1.3.2 Impurity scattering

In addition to lattice scattering, impurity scattering is another mechanism that can

significantly affect the carrier mobility in silicon. Impurities which cause carrier

scattering are typically charged (ionised) or neutral donor or acceptor species

1.3.2.1 Ionized impurity scattering

Ionized impurity scattering involves ionized particles. At elevated temperature, all the

donors and acceptors in silicon are ionized and possess either a positive or negative

charge. When charge carriers travel through the lattice and pass near ionized particles,

they experience a Coulombic force. The positive hole is attracted by the negative donor

and repelled by the positive acceptor. The path of the carrier is deflected by the

Coulombic attraction or repulsion. Hence the mobility decreases with greater ionized

impurity scattering. The probability that carriers are affected by ionized impurities is

directly related to the concentration of ionized impurities, which itself depends on the

dopant concentration and the temperature. The theoretical relationship between the

mobility component due to impurity scattering and the temperature and dopant

concentration is given by: [52, 53]

𝜇𝐼 ∝𝑇−3/2

𝑁𝐼

(1.26)

Where, 𝑁𝐼 = 𝑁𝐷+ + 𝑁𝐴

−, which is the total ionized impurities concentration in the silicon

and 𝜇𝐼 is the mobility component due to impurities scattering. From equation (1.26), the

mobility increases with increasing temperature and decreases with higher impurity


14

concentration. In silicon at room temperature ionized impurities become influential on

the mobility when the dopant concentration reaches the 1015 to 1016 cm-3 range.

1.3.2.2 Neutral impurity scattering

Besides ionized impurities, other impurities such as carbon and oxygen may remain

neutral, but can also scatter carriers in silicon. Additionally, dopants can become neutral

at low temperatures or when compensated or under very high injection. However, due to

the relatively small scattering cross section of neutral particles, they have less impact on

the mobilities.

1.3.3 Carrier-carrier scattering

Carrier-carrier scattering [54] can occur between carriers of different charge, that is

between electrons and holes in silicon. It can also occur between the same kind of

carrier, namely electron-electron scattering and hole-hole scattering. For electron-hole

scattering, electrons in the conduction band can interact with holes in the valence band

through a Coulombic force. When the concentration of majority carriers is much higher

than minority carriers, electron-hole scattering mainly affects minority carriers. The

scattering mechanism between the same kinds of carriers (eg. electron-electron

scattering and hole-hole scattering) is a second order scattering, and does not affect and

will not alter the total momentum and energy of the carriers, but redistributes the

momentum [55].

1.3.4 Matthiesen’s rule

In this section, three main scattering mechanisms have been introduced. The effective

mobility can then be computed based on the individual scattering components. If the

energy dependence for all the scattering components is the same, the effective mobility

sum can be calculated using Matthiesen’s rule:

1

𝜇𝑡𝑜𝑡𝑎𝑙= ∑

1

𝜇𝑖𝑖

(1.27)


15

Matthiesen’s rule is expected to be vaild under the following conditions [56]: (1) There

is only one dominant scattering mechanism, or (2) All scattering mechanisms have the

same energy dependence.

1.4 Carrier mobility sum measurement

There are a number of ways to measure the carrier mobility sum in silicon. Some of the

methods are complicated and/or destructive to the sample. In this section, techniques

that can measure the carrier mobility sum in silicon will be introduced.

1.4.1 Dannhauser’s method

Dannhauser’s method is applied to measure the mobility sum as a function of injection

level Δn at room temperature by utilizing a p-i-n (p+pn+) structure. Figure 1.2 shows

the structure of the p+pn+ diode [46, 47] . In this method, the diode is initially forward

biased. Charge is stored in the weakly doped p middle region under the forward bias.

The mobility sum is calculated by measuring the voltage step when the diode is

switched form the forward into reverse direction. The equation that used to calculate the

mobility sum is given below:

𝜇𝑠𝑢𝑚 =𝑖𝐹(2𝑑)2

𝑄𝑈𝑚𝑂𝐻𝑀𝑔(

𝑑

𝐿)

(1.28)

Where 𝑖𝐹 is the forward current applied to the diode, 𝑄 is the stored charge in the

weakly doped p region during the forward bias. 𝑈𝑚𝑂𝐻𝑀 is the voltage drop across the

ohmic resistive p region and can be calculated from the measured voltage step when

changing from forward to reverse bias given in equation (1.29). 2𝑑 is the thickness of

the middle region. L is the diffusion length of the minority carriers. 𝑔(𝑑

𝐿) is the

correction factor.

∆𝑈 = (1 +𝑖𝑅

𝑖𝐹) 𝑈𝑚𝑂𝐻𝑀

(1.29)

𝑔 (𝑑

𝐿) =

sinh (𝑑𝐿)

(𝑑𝐿)

2

√[1 − 𝐵2𝑡𝑎𝑛ℎ2 (𝑑𝐿)]

𝑡𝑎𝑛−1√[1 − 𝐵2𝑡𝑎𝑛ℎ2 (𝑑

𝐿)] sinh (

𝑑

𝐿)

(1.30)


16

Where B is 0.5 for silicon with µn = 3µp [57]

Figure 1.2: p+pn+ structure for Dannhauser mobility sum measurement [58]

1.4.2 Neuhaus’s method

Neuhaus’s method [48] measures mobility utilizing both the contactless quasi-steady-

state photoconductance (QSS-PC) and the quasi-steady-state open-circuit voltage (QSS-

Voc) measurements. For both QSS-PC and QSS-Voc methods, excess carriers Δn are

generated by a slowly decaying flash lamp. In the QSS-PC method, the conductance Δσ

increase with increasing Δn. The decaying Δσ is measured with a calibrated coil

inductively coupled to the Δn in the wafer and is given by:

∆𝜎 = 𝑞𝑊∆𝑛𝑎𝑣𝜇𝑠𝑢𝑚

(1.31)

Where q is the electric charge, W is the thickness of the wafer, and 𝜇𝑠𝑢𝑚 is the mobility

sum to be calculated. It is seen from equation (1.31), to calculate 𝜇𝑠𝑢𝑚 requires

knowledge of the average excess carrier density ∆𝑛𝑎𝑣 in the wafer. This quantity is

obtained from the QSS-Voc method applied to a solar cell. Again, a slowly decaying

flashlight is used to generate excess carriers in the cells. The open circuit voltage across

the terminals of the junction is then measured. The excess carrier density at the edge of

the space charge region ∆𝑛𝑠𝑐𝑟 can be calculated from 𝑉𝑜𝑐 according to

(𝑛0 + ∆𝑛𝑠𝑐𝑟)(𝑝0 + ∆𝑛𝑠𝑐𝑟) = 𝑛𝑖.𝑒𝑓𝑓2 exp (

𝑞𝑉𝑜𝑐

𝑘𝑇) (1.32)


17

In order to calculate the injection dependence of the mobility 𝜇𝑠𝑢𝑚(∆𝑛), we assume

that ∆𝑛𝑎𝑣 = ∆𝑛𝑠𝑐𝑟 . However, this requires that (1) the bulk lifetime in the sample is

sufficiently high, that is, the minority carrier diffusion length in the bulk is much larger

than its thickness; and (2) the device has a low effective surface recombination velocity

at both the front and rear surfaces. Neuhaus’s method therefore requires a full solar cell

structure and identical photoconductance test structure to measure the injection

dependence of the mobility sum in silicon in the mid- to high injection range.

1.4.3 Contactless photoconductance method

In section 1.4.1 and 1.4.2, we have reviewed the methods proposed by Dannhauser and

Neuhaus. Dannhauser’s method uses a p-i-n diode and Neuhaus’s method combines the

QSS-PC and QSS-Voc measurements and requires a full solar cell and lifetime test

structure. Both methods therefore require complicated and destructive device structures.

Moreover, they both need contacting to apply current or measure the voltage in the

devices. In this section, a contactless technique [59] that is used to obtain the mobility

sum to derive the empirical model in this chapter is introduced. This method is also

based on photoconductance measurements and as its name implies, it does not require

any physical contact and only requires a single, simple test structure.

This technique combines two common methods that are used to determine effective

carrier lifetimes in silicon. The first method, which is referred to as the transient

photoconductance decay (PCD) method, uses an inductive coil [51, 60] to measure the

decay rate of the photoconductance and thus the rate at which carriers recombine after

flashing the sample. The lifetime is extracted by:

𝜏𝑃𝐶𝐷 = −∆𝑛

(𝑑∆𝑛/𝑑𝑡)

(1.33)

Where 𝜏𝑃𝐶𝐷 is the transient lifetime, ∆𝑛 is the excess carrier density, and 𝑑∆𝑛/𝑑𝑡 is the

decay rate of the execss carrier density in the sample. The second method is the Quasi-

Steady-State photoconductance (QSSPC) method, which measures the balance between

generation and recombination, thus, the effective carrier lifetime in the sample under a

slowly decaying flash. The generalized carrier lifetime under the QSS illumination is

given by: [61]


18

𝜏𝑄𝑆𝑆𝑃𝐶 = ∆𝑛

𝐺𝑄𝑆𝑆𝑃𝐶 −𝑑∆𝑛𝑑𝑡

(1.34)

where 𝜏𝑄𝑆𝑆𝑃𝐶 is the quasi-static lifetime and 𝐺𝑄𝑆𝑆𝑃𝐶 is the generation rate in the sample.

Assuming that at the same excess conductance the transient lifetime 𝜏𝑃𝐶𝐷 and the QSS

lifetime 𝜏𝑄𝑆𝑆𝑃𝐶 are equal, which will be true for uniform carrier profiles throughout the

wafer thickness [62, 63], the mobility sum can be obtained from equations (1.33) and

(1.34) together with equation (1.35) that relates the excess conductance Δσ to the excess

carrier concentration Δn.

∆𝑛 = ∆𝜎

𝑞𝑊𝜇𝑠𝑢𝑚

(1.35)

By combining equations (1.33), (1.34) and (1.35), we can arrive at:

𝑞𝑊(𝜇𝑛 + 𝜇𝑝)2

𝐺𝑄𝑆𝑆𝑃𝐶(∆𝜎)

+(𝜇𝑛 + 𝜇𝑝) (𝑑∆𝜎𝑃𝐶𝐷

𝑑𝑡−

𝑑∆𝜎𝑄𝑆𝑆𝑃𝐶

𝑑𝑡) (∆𝜎)

+ (∆𝜎𝑄𝑆𝑆𝑃𝐶

𝑑(𝜇𝑛 + 𝜇𝑝)𝑄𝑆𝑆𝑃𝐶

𝑑𝑡) (∆σ)

− (∆𝜎𝑃𝐶𝐷

𝑑(𝜇𝑛 + 𝜇𝑝)𝑃𝐶𝐷

𝑑𝑡) (∆σ) = 0

(1.36)

Where 𝜇𝑛 and 𝜇𝑝 are the electron and hole mobility, respectively, q is the electronic

charge, W is the thickness of the sample, and 𝑑∆𝜎𝑃𝐶𝐷/𝑑𝑡 and 𝑑∆𝜎𝑄𝑆𝑆𝑃𝐶/𝑑𝑡 are the

variation of conductance with time for transient and quasi-steady state excitation.

However, as the mobility varies only very slightly compared with the other time-

dependent quantities, the final two terms on the left-hand side of equation (1.36) can be

neglected. Thus, the expression can be simplified to extract the mobility sum (𝜇𝑛 +

𝜇𝑝) as:

𝜇𝑛 + 𝜇𝑝 = 1

𝑞𝑊𝐺𝑄𝑆𝑆𝑃𝐶(

𝑑∆𝜎𝑃𝐶𝐷

𝑑𝑡−

𝑑∆𝜎𝑄𝑆𝑆𝑃𝐶

𝑑𝑡)

(1.37)


19

1.5 Carrier mobility models

There are a number of models that can describe minority and majority carrier mobilities

in silicon. The mobility models can be mainly divided into three categories: Theoretical,

semi-empirical and empirical. Theoretical models are derived solely from physical laws

and theories. Semi-empirical models are also based partly on physical law and theories,

but in addition, experimental data are used to extract some parameters in the model.

Finally, empirical models are solely based on experimental data. They are derived by

fitting the experimental data with a mathematical expression to describe the trend of the

data under different conditions. In this section, different kinds of existing mobility

models are reviewed.

1.5.1 Semi-empirical mobility models

As mentioned above, theoretical models are physically based. The coefficients and

power-law dependences of these models are based on first principle calculations. Due to

the simplifications and assumptions inherent in them, they rarely agree with

experimental data. However, if the coefficients in the models are allowed to vary, and

the power-law dependences are preserved, the resulting model is called a semi-empirical

model. Currently, there is no theoretical model which adequately describes carrier

mobilities in silicon. In this sub-section, semi-empirical mobility models are reviewed.

1.5.1.1 Arora’s mobility model

Arora presented an analytical expression for electron and hole mobility in silicon based

on modified Brooks-Herring theory [64] of mobility and experimental data. The

resulting expression can allow one to calculate electron and hole mobility as a function

of doping concentration up to 1020 cm-3 and over a temperature range of 200 to 500K

within an error of ±13% of the experimental values.

Arora’s model is actually based on fitting data with the Fermi-Dirac function (or

hyperbolic tangent), which can be expressed in the form:


20

𝜇 = 𝜇𝑚𝑖𝑛 +

𝜇𝑚𝑎𝑥 − 𝜇𝑚𝑖𝑛

1 + (𝑁

𝑁𝑟𝑒𝑓)𝛼

(1.38)

However, Arora [65] adopted electron and hole mobility data from both analytical

calculation and experiments and as such is a semi-empirical model. For concentration

up to 5×1018 cm-3, theoretical calculations for different scattering mechanisms have been

taken into account. For the lattice scattering term, Arora adopted Lang [66], Norton et al.

[67] and Li’s [68] experimental data over a temperature range of 150 to 500K. For

impurity scattering, a modified Brooks-Herring formulation was used. Finally, Arora

took the electron-electron scattering and hole-hole scattering mechanism into account

for the calculation of the electron and hole mobility respectively based on Li and

Thurber [64]. Since Matthiesen’s rule is restricted to a number of conditions and proved

not to be generally true. To seek for more precise modelling of carrier mobility Debye

and Conwell’s [69] formula was used to combine different scattering mechanisms in

Arora’s formulations.

For concentrations above 5×1018 cm-3, various experimental data from the literature

are taken and results in the final expression for electron and hole mobility respectively:

𝜇𝑛 = 88(

𝑇

300)−0.57 +

7.4 × 108𝑇−2.33

1 + 0.88 (𝑇

300)−0.146

(𝑁

1.26 × 1017 (𝑇

300)2.4)

(1.39)

𝜇𝑝 = 54.3(

𝑇

300)−0.57 +

1.36 × 108𝑇−2.33

1 + 0.88 (𝑇

300)−0.146

(𝑁

2.35 × 1017 (𝑇

300)2.4)

(1.40)

1.5.1.2 Dorkel –Leturcq’s mobility model

Dorkel and Leturcq [70] proposed an approximate calculation based on theory and

published experimental data to arrive at a simple and accurate formula which allows

manual calculation and a short time of execution for computers, which saved

computation time in the early 1980s.


21

Dorkel and Lecturcq used a similar formulation to the model of Arora. The lattice

scattering was adopted from the data of Norton et al.,[67] and the impurity scattering

term was the Brooks-Herring formulation. Thurber et al. [64] and Luong et al.’s [71]

data were taken into account to evaluate the coefficient in the Brooks-Herring

formulation. In addition to lattice and impurity scattering, Dorkel and Leturcq adopted

the carrier-carrier scattering term from Choo [72], which was different from Arora’s

mobility model. Finally, Debye and Conwell’s formula was used to combine different

scattering terms. To simplify the calculation, Dorkel and Leturcq confined the doping,

temperature and injection levels to certain ranges. The final formula can be simplified

into:

𝜇 = 𝜇𝐿(1.025

1 + (𝑥

1.68)1.43 − 0.025)

(1.41)

𝑥 = √6𝜇𝐿(𝜇𝐼 + 𝜇𝑐𝑐𝑠)

𝜇𝑐𝑐𝑠𝜇𝐼

(1.42)

Where μL, μI and μccs are lattice, impurity and carrier-carrier scattering terms,

respectively. This simplified formula is very close to the form of Fermi-Dirac function.

1.5.1.3 Klaassen’s unified mobility model

The model proposed by Klaassen provides a physically-based unified description of

majority and minority carrier mobilities. Klaassen’s model [73-75] includes a number of

scattering effects which are not taken into account in Arora and Dorkel’s mobility

models in the previous sub-sections. The additional scattering effects considered in

Klaassen’s model are impurity scattering with screening from charged carriers, and

impuritiy clustering effects at high concentration.

In addition, Klaassen’s model also accounts for the presence of both acceptors and

donors as scattering centers, which is not fully considered in the models of Arora and

Dorkel. Therefore, Klaassen’s model is more accurate in predicting mobility in

compensated silicon, for example, silicon obtained from low cost purification routes

like upgraded metallurgical-grade silicon (UMG-Si).


22

Recently, Schindler et al. [45] suggested that Klaassen’s mobility model predicted

significantly lower mobilities with increasing compensation level and proposed that the

compensation-related reduction of screening was not taken into account sufficiently in

Klaassen’s mobility model. Schindler et al. suggested a modification of Klaassen’s

model for compensated silicon.

Overall, the unified mobility model from Klaassen accounts for temperature, dopant

concentration and injection level dependences. Together with the modification from

Schindler et al., it can model the mobility for compensated silicon. The use of Masetti’s

[76] model as a starting point, allows Klaassen’s mobility model to calculate both

majority and minority carrier mobility for dopant concentrations above 1020 cm-3.

1.5.2 Empirical mobility model

In contrast to semi-empirical models, empirical models are not based on physical

theories and are simply parameterisations of experimental data. Therefore, they simply

describe the behaviour and trend of the measurement results and merely implies any

physical meaning behind it. In this section, a few empirical mobility models are

introduced.

1.5.2.1 Caughey and Thomas’s mobility model

Caughey and Thomas’s mobility model is an empirical model that uses published

experimental data [77] to fit the Fermi-Dirac function as shown in equation (1.38). The

final form of Caughey and Thomas’s mobility model is:

𝜇 = 𝜇𝑚𝑖𝑛 (𝑇

300)𝛼 +

𝜇𝑚𝑎𝑥(𝑇

300)𝛽 − 𝜇𝑚𝑖𝑛 (𝑇

300)𝛽

1 + (𝑇

300)𝛾(𝑁

𝑁𝑟𝑒𝑓)𝜎

(1.43)

The simplicity of this equation has meant Caughey and Thomas’s mobility model has

been widely used in device simulation and modelling.


23

1.5.2.2 WCT-100 parameterization

The parameterisation of the mobility sum 𝜇𝑠𝑢𝑚 used in the Sinton WCT-100 software

[78] is derived from Dannhauser and Krause’s data [46, 47], who measured the mobility

sum as a function of carrier injection at room temperature using the p-i-n structure

mentioned before. The expression is given by:

ref

DA

ref

DA

sum

N

nNN

N

nNN

1

1

max

(1.44)

This parameterization gives the mobility sum as a function of injection level and

dopant concentration. It is used to evaluate electrical properties of silicon material or

silicon devices, for instance, effective minority carrier lifetime, emitter saturation

current J0e and implied open circuit voltage (i-Voc) of a solar cell. It is only valid at room

temperature.

1.5.3 Summary of the existing mobility models

Some of the existing mobility models have been briefly reviewed in section 1.5.1 and

1.5.2. In addition to these models, there are a number of other mobility models

published in the literature to evaluate mobilities in silicon across different temperature,

dopant concentration and injection level ranges. Some of these models, together with

those presented above, are summarized in Table 1.1 in terms of their temperature,

dopant concentration and injection level dependences.

From Table 1.1, it is seen that only Klaassen and Dorkel-Leturcqs’ models include all

three dependences, and there is no empirical model (and no experimental data) that

describes the mobility as a function of temperature and injection dependence

simultaneously. In the next section, mobility sum data measured using the contactless

photoconductance technique introduced in section 1.4.3 are presented. The derivation of

a new empirical model based on those measurement results and the comparison with

some of the mobility models in Table 1.1 will be shown.


24

Table 1.1: Summary of the existing mobility models

Model Doping

Dependence

Temperature

Dependence

Injection

Dependence

Klaassen [73-75] Yes Yes Yes

Dorkel-Leturcq [70] Yes Yes Yes

Reggiani [79-81] Yes Yes

Arora [65] Yes Yes

Masetti [76] Yes

Thurber [82, 83] Yes

Caughey-Thomas [77] Yes

WCT-100

Parameterization [78] Yes Yes

Fischetti [84] Yes

1.6 Empirical model based on photoconductance technique

In the previous sections, various techniques measuring mobility sum in silicon have

been introduced. Among all these techniques, the contactless photoconductance

technique has the advantage of using a non-destructive and simple test structure,

allowing the simultaneous measurement of the mobility sum as a function of

temperature and injection level. Based on the summary in Table 1.1of section 1.5.3, we

see that only Klaassen and Dorkel-lecturcqs’ models include temperature, doping and

injection level dependences and these models are semi-empirical models. To our

knowledge, the measurement data for electron and hole mobility sum as a function of

excess carrier density available to date have only been measured at room temperature

[46-49]. Hence, there is no experimental validation of the existing semi-empirical

mobility models as a function of excess carrier density at temperatures other than room

temperature.

Based on contactless photoconductance measurements of silicon wafers we have

determined the sum of the electron and hole mobilities as a function of doping, excess


25

carrier concentration and temperature. By separately analysing those three functional

dependences, we then developed a simple mathematical expression to describe the

mobility sum as a function of carrier injection, wafer doping and temperature from

150K to 450K. This new parameterization also provides experimental validation of

Klaassen’s and Dorkel-Lecturcq’s mobility models over a range of temperatures.

1.6.1 Experimental method

In this experiment, the initial focus was on n-type crystalline phosphorus doped silicon

wafers. The samples used in this study were three Float Zone (FZ) wafers of resistivity

1.0Ω.cm, 10Ω.cm, 100Ω.cm and two Czochralski (Cz)-grown wafers of resistivity

0.5Ω.cm and 5Ω.cm. In order to apply a high quality passivation to the samples, the

samples were prepared by damage etching and RCA cleaning, followed by surface

passivation at 400oC with plasma-enhanced chemical vapour-deposited (PECVD)

silicon nitride films. In order to validate the applicability of the mobility model for p-

type silicon, the experiment was then extended to p-type silicon wafers. Two Cz wafers

of resistivity 0.75Ω.cm and 10Ω.cm were included. The p-type wafers went through the

same sample preparation steps as the n-type wafers.

The effective minority carrier lifetime of the samples was measured using a

calibrated photoconductance lifetime tester from Sinton Instruments. In order to

measure the simultaneous temperature and injection dependence of the mobility sum,

we used a purpose-built, temperature controlled inductive coil photoconductance

instrument [85]. The mobility sum was then determined by comparing transient

Photoconductance Decay (PCD) and Quasi-steady-state Photoconductance (QSSPC)

measurements of the excess conductance (Δσ) for every sample. The detail of the

method has been introduced in section 1.4.3. To obtain accurate measurements using

this technique, the excess carrier profile in the samples has to be uniform. Therefore, a

sufficiently low surface recombination velocity (SRV) is required. The values of SRV,

calculated using the Auger limit from Richter et al.[25], ranged from 16cm.s-1 to

39cm.s-1 for all samples. Based on the measured SRV, simulations [86] show that the

difference in excess carrier density between the front and back surfaces is less than 10%

for all the samples, which is sufficient to ensure the accuracy of the extracted mobility

sums. The uncertainty of the calculated mobility sum using equation (1.37) is estimated

by assuming a ±3% uncertainty in the measurement of the generation rate (required for


26

the QSSPC method) and an uncertainty of ±5% in the measurement of the

photoconductance Δσ [87].

1.6.2 Empirical mobility sum model

In this section, the experimental data measured by contactless photoconductance

technique is presented. The data are measured on the five different resistivity n-type

samples and the two different resistivity p-type samples ranging from -120oC to 180oC.

The injection level is from 3×1015cm-3 to 3×1016cm-3.

1.6.2.1 Experimental results

The mobility sum 𝜇𝑠𝑢𝑚 = 𝜇𝑛 + 𝜇𝑝 at 30oC as a function of excess carrier density for

the five n-type samples of different dopant concentration ranging from 4×1013cm-3 to

1×1016cm-3 is plotted in Figure 1.3 (a). At a given excess carrier density, the mobility

sum decreases with the dopant density. This is consistent with the expectation that

ionized impurity scattering is higher in the more highly doped samples.

Figure 1.3: (a) Measured mobility sum as a function of excess carrier density at 30˚C for

five n-type samples of different doping. (b) Measured mobility sum as a function of the

sum of excess carrier density and the ionized doping density at 30˚C.


27

However, as shown in Figure 1.3 (b), when 𝜇𝑠𝑢𝑚 is plotted as a function of the sum

of excess carrier density and the ionized dopant concentration (that is, as a function of

the total concentration of majority carriers), the curves for the highly doped samples are

shifted to the right and align themselves with the lowly doped samples. This indicates

that majority carriers arising from the dopant atoms have a similar impact on the

mobility as excess carriers generated by light. This interesting observation will be

discussed in more detail in the next section.

As mentioned above, in order to assess the applicability of this model to p-type

silicon, two Cz p-type samples were also studied. The mobility sum at 30oC as a

function of excess carrier density for the 0.75Ω.cm and 10Ω.cm p-type samples is

plotted in Figure 1.4 (a). The mobility sum for the p-type samples shows the same trend

as the n-type samples in Figure 1.3 (a), the higher dopant density sample gives lower

mobility sum due to the higher ionized impurities scattering effect. By plotting the

mobility sum for p-type sample as a function of the sum of excess carrier density and

the ionized dopant concentration in Figure 1.4 (b), the p-type samples agree well with

the n-type samples and form a continuous curve.

Figure 1.4: Measured mobility sum as a function of excess carrier density at 30˚C for

five n-type samples from the previous study and two different resistivity p-type samples

plotted as a function (a) of the excess carrier density (b) of the sum of excess carrier

density and the ionized doping density at 30˚C.


28

(a) (b)

Figure 1.5: (a) Measured mobility sum as a function of the sum of excess carrier

density and the ionized doping density at -120˚C, -60˚C, 0˚C, 60˚C, 120˚C and 180˚C

for both n- samples. (b) Measured mobility sum for p-type.

The measurement results for other temperatures, ranging from -120˚C to 180˚C, are

shown in Figure 1.5. The results for n-type samples are shown in Figure 1.5 (a). As

above, the mobility sum forms a continuous curve when plotted against the sum of

excess carrier density and the ionized dopant concentration. The p-type samples align

themselves with the n-type samples for all temperatures shown in Figure 1.5 (b).

Moreover, Figure 1.5 also shows that increased phonon (lattice) scattering produces a

reduction of the mobility as temperature increases. This causes the mobility sum to

become less dependent on carrier injection and doping.

1.6.2.2 Derivation of the empirical mobility sum model

From the above experimental results, we can derive an empirical mobility sum model as

a function of temperature, ionized dopant density and carrier injection level. In this

section, the derivation of this empirical model will be shown and the assumptions that

are made will be discussed.

As a starting point, we adopt the parameterization of 𝜇𝑠𝑢𝑚 in the WCT-100 software

used in the analysis of QSSPC lifetime measurements [78]. As mentioned in the

previous sections, this expression is based on Danhauser and Krause’s data, who

measured the mobility sum as a function of carrier injection at room temperature.

Therefore, this expression only has doping and injection dependences. The expression is


29

given in equation (1.44), where NA is the acceptor concentration, ND is the donor

concentration, Δn is the excess carrier density, µmax = 1800 cm2·V-1·s-1, β = 8.36, α

=0.8431 and Nref = 1.2×1018cm-3. This simple formula takes carrier density and dopant

concentration into account, but it does not include the temperature. The expression can

be rearranged as follows:

nNN

N

DA

ref

sum

11

maxminmax

(1.45)

Where µmin = µmax/β, equation (1.45) can be further transformed into the following

linearized form:

)1

log(log

loglogmax

min

ref

DA

sum

sum

N

nNN

(1.46)

The mobility sum in equation (1.45) depends on n ( n = p ) rather than 2× n .

Indeed, only electron-hole scattering reduces the mobility (electron-electron and hole-

hole scattering redistribute momentum, but do not reduce it, and are therefore second

order scattering mechanisms as mentioned in section 1.3.3. The dopant concentrations

in equation (1.45) have been replaced by the ionized dopant concentrations for both

donors and acceptors [88, 89]. This is essential in our model, since the dopants are not

completely ionized at low temperatures, therefore ionized doping density should be

used to account for impurity scattering due to Coulombic effects of the ionized dopants

at low temperature. Having both acceptor and donor densities incorporated in this way

assumes the scattering cross-section of both donors and acceptors to be similar, which is

not necessarily valid [90]. Similarly having both dopant density and excess carrier

density in the same variable assumes that the scattering cross section of two moving

particles (an electron and a hole) is the same as the scattering cross section of a static

dopant and a moving particle (e.g. donor and hole), which is not always valid in

principle [90]. However, such physical considerations were not found to negatively

affect the fitting of the experimental data in the injection range covered by this work, as


30

can be observed in Figure 1.6. We therefore conclude that the impact of such

assumptions is not significant.

As shown above, equation (1.46) is a linear transformation from equation (1.45),

achieved by taking its logarithm. Hence, in equation (1.46), -α is the slope and

αlog(Nref)+log(1/β) is the intercept of the linear relationship. The parameters µmax and β

can be optimized by maximizing the correlation coefficient of log ((μ-μmin)/(μmax-μ)) and

log(NA-+ND

++Δn). The parameters α and Nref are calculated from a least squares fit to

the experimental data, where α is the slope of the straight line and Nref can be obtained

from the intercept.

The model has four fitting parameters as seen in equation (1.46), µmin depends on

both µmax and β. Since our experimental data are scarce in the high injection range, there

are a number of parameter combinations that can be derived at each temperature.

However, two reasonable assumptions can be made to arrive at a unique set of

parameters that fit all the experimental data. They are:

1) The range of the experimental data available for this mobility sum model span

from Δn + ND+ = 3×1015 cm-3 to 3×1016 cm-3 (see Figure 1.5). It is important to

note that µmin only has a significant impact in the high injection range and has a

minor influence on the fitting of the model in the range available. Therefore, we

can make a reasonable assumption that µmin and µmax have the same temperature

dependence and are related through the same β at each temperature. The value β

= 8.36 from equation (1.44) above is used in the following.

2) With Known µmax and β, it is found that the slope (-α) of the experimental curve

at each temperature lies between -0.95 and -1 and does not show any

temperature dependence. Therefore, we assume that α is independent of

temperature with an average value of 0.97.

Based on the assumptions made above, we can fit the data shown in Figure 1.5 with

the linearized equation (1.46) at each temperature. From the fitting, we can calculate

parameters µmax and Nref for each temperature. Figure 1.6 plots the linearized mobility

sum data used in the fitting of the model. The solid lines are calculated from the right

hand side of equation (1.46) by adjusting the reference dopant density (Nref). The

symbols are obtained from the experimental data with µmax that gives the best

correlation coefficient to the data. An excellent agreement between fit and the

experimental data is found at every temperature for both n- and p-type samples.


31

Figure 1.6: Fitting of measured mobility sum using equation (1.46) at -120˚C, -60˚C, 0˚C,

30˚C, 60˚C, 120˚C and 180˚C. The symbols are calculated based on the left hand side of

equation (1.46), the solid lines are the fitting using the right hand side of equation (1.46)

by adjusting Nref and α.


32

Based on the linear fitting using equation (1.46) to the data, we have obtained a set of

µmax and Nref from Figure 1.6. As µmax is derived from the experimental data at each

temperature, all the µmax values are plotted in Figure 1.7 and the temperature

dependence can be derived with the well-known power dependence used for the lattice

scattering terms in a number of mobility models as (see e.g. Refs [65, 91]):

300)( 300maxmax

TT K

(1.47)

Figure 1.7: Temperature dependence of the fitting parameter µmax. This parameter is

extracted from the experimental data and subsequently fitted using equation (1.47).

Where µmax300K is the maximum mobility sum at 300K and γ is the power factor to fit the

µmax curve. The values of µmax300K and γ are listed in Table 1.2. The resulting fit is

plotted in Figure 1.7, showing an excellent agreement between measured and modelled

µmax. Physically, µmax accounts for the lattice scattering mechanism. The decrease of

µmax with increase of temperature is mainly due to the increase of lattice vibrations at

high temperature.

In addition to the fitting of µmax with temperature, the data for Nref are plotted in a

similar fashion in Figure 1.8. Like µmax, the fitting for Nref can be described by the same

temperature dependence relationship:

28.2

max300

1800)(

TT


33

300)( 300

TNTN Krefref

(1.48)

Where Nref300K is the total reference carrier concentration at 300K that takes the dopant

impurity and carrier-carrier scattering into consideration and affects the mobility sum

mainly in the range of NA-+ND

++Δn that is comparable to it. θ is the power factor to fit

the Nref curve, and α is from equation (1.45). The values obtained are Nref300K

=4.65×1017cm-3 and θ = 3.09. The resulting fit is plotted in Figure 1.8, showing again an

excellent agreement between measured and modelled Nref. Nref increases with increasing

temperature because at high temperature, lattice scattering becomes dominant compared

to impurity and carrier-carrier scattering.

Figure 1.8: Temperature dependence of the fitting parameter Nref .This parameter is

extracted from the experimental data and subsequently fitted using equation (1.48)

Once we have obtained the temperature dependence of both Nref and µmax based on

the fitting of equations (1.47) and (1.48) to the data shown in Figure 1.7 and Figure 1.8,

we can insert them into equation (1.45) to have the complete form of the empirical

mobility sum model in terms of temperature, ionized dopant density and carrier

injection level:


34

300

11

300

300

300

300max300min

300max

T

nNN

N

T

T

DA

Kref

KK

Ksum

(1.49)

Where µmin300K = µmax300K/β, the parameters in equation (1.49) are summarized in Table

1.2

Table 1.2: Parameters for mobility sum model

Parameters Values

µmax300K 1800 cm2·V-1·s-1

Nref300K 4.65×1017cm-3

β 8.36

α 0.97

γ -2.28

θ 3.09

1.6.3 Comparison to other models

In sections 1.6.1 and 1.6.2, the experimental method and the derivation of the empirical

models have been shown. We have obtained an empirical model that can describe the

mobility sum in silicon as a function of temperature, doping density and injection level.

In this section, the applicability of this new empirical model will be assessed. This

model will be compared to a few existing models shown in Table 1.1 in terms of

temperature, doping density and injection level separately. The validity of this model as

a function of carrier injection is assessed firstly.

1.6.3.1 Applicability as a function of carrier injection

In this section, the empirical model is compared to other mobility models in order to

assess its validity for both n- and p-type silicon. Firstly, a comparison is made as a

function of carrier injection level. Figure 1.9 (a) shows the resulting mobility sum from


35

this study for n-type silicon and the mobility models from the WCT-100

parameterization [78], Klaassen’s [73-75] and Dorkel-Leturcq’s [70] with a doping

density of 4×1013cm-3 (100Ω.cm sample) at 300K in the 1×1014cm-3 to 3×1016cm-3

carrier injection range. The empirical model derived here from the photoconductance

measurements is in good agreement with the existing injection dependence mobility

models, especially in the range of injection levels relevant for the characterization of

silicon wafers by photoconductance measurements, that is, from approximately

1×1015cm-3 to 3×1016cm-3. In this range, equation (1.49) gives intermediate values

relative to the other models. For injection levels below 1×1015cm-3, equation (1.49)

coincides with the WCT-100 parameterization, but is about 10% lower than the Klassen

and Dorkel-Leturcq models. equation (1.49) predicts a lower mobility sum than

Klassen’s and WCT-100 parameterization beyond an injection level of 1×1015cm-3, but

it is close to the model of Dorkel-Leturcq up to an injection level of 3×1016cm-3.

(a) (b)

Figure 1.9: Comparison of the empirical mobility sum from this study for (a) n-type

silicon with the existing mobility models from WCT-100 parameterization, Klaassen

and Dorkel-Leturcq as a function of injection at 300K at a doping density of 4×1013cm-3.

(b) p-type silicon at doping density of 1×1015cm-3 at 300K as a function on injection

level.

In addition to the n-type silicon, the validity of this empirical model to p-type silicon

is also compared. The empirical model is compared to the same mobility models used in

n-type silicon comparison with a doping density of 1×1015cm-3 (10Ω.cm p-type sample)

at 300K in the same injection level range. The comparison is shown in Figure 1.9 (b).

As in the n-type case, the model derived from the photoconductance measurements is in


36

good agreement in the range shown. The empirical model predicts lower mobility than

all three models for injection level below 1×1015cm-3. In the injection level between

1×1015cm-3 to 3×1016cm-3, the model predicts intermediate values to the other models

and a stronger injection dependence close to 3×1016cm-3. Overall, the empirical model is

in good agreement with the existing models for both n- and p-type silicon as a function

of injection in the range where the experimental data is available.

1.6.3.2 Applicability as a function of dopant density

In addition to the influence of injection dependence, the applicability of this empirical

model in terms of dopant density is also validated. Figure 1.10 (a) shows the doping

dependence of the mobility sum computed at 300K at an injection level of 1×1016cm-3

for n-type silicon. The mobility models from Klaassen, Dorkel-Lecturcq and WCT-100

parameterization are included for comparison. The mobility predicted from our

empirical model lies within the mobilities from other models and is in reasonable

agreement with them, even if it is slightly lower at high dopant concentrations. The

most heavily doped sample used in this experiment is ND=1×1016cm-3. Therefore the

empirical model of equation (1.49) may not be valid for samples doped more than

1×1016cm-3.

(a) (b)


silicon with the existing mobility models from WCT-100 parameterization, Klaassen

and Dorkel-Leturcq as a function of doping density at 300K and injection level of

1×1016cm-3. (b) p-type silicon as a function of doping density at 300K and injection

level of 1×1016cm-3 silicon.


37

The comparison for the p-type silicon in terms of dopant density is shown in Figure

1.10 (b). The mobility sum is computed at 300K and at an injection level of 1×1016cm-3.

The mobility predicted from our empirical model lies within the mobilities from other

models and is in reasonable agreement with them, even if it is slightly lower at high

dopant concentrations. The most heavily doped sample used in this experiment is

NA=2×1016cm-3. Therefore the empirical model of equation (1.49) may not be valid for

samples doped more than 2×1016cm-3.

1.6.3.3 Applicability as a function of temperature

In this section, the last variable temperature in equation (1.49) is accessed. Figure 1.11

(a) shows the modelled temperature dependence of the mobility sum from the empirical

model together with the mobility models from Klaassen and Dorkel-Leturcq. WCT-100

parameterization is not included as it does not include temperature dependence. The

mobility sum is computed at a doping density of 1×1016cm-3 and an injection level of

1×1016cm-3. The empirical model is in good agreement with both Klaassen’s and

Dorkel-Leturcq’s models, especially at high temperatures, while the discrepancy to

these models increases with decreasing temperature. The model may not be valid at

temperature below 150K where the experimental data is not available.

(a) (b)


silicon with the existing mobility models from Klaassen and Dorkel-Leturcq as a

function of temperature at doping density of 1×1016cm-3 and injection level of

1×1016cm-3. (b) p-type silicon as a function of temperature at doping density of

1×1016cm-3 and injection level of 1×1016 cm-3.


38

Figure 1.11 (b) shows the comparison to p-type silicon as a function of temperature.

The mobility sum is computed at an doping density of 1×1015 cm-3 and an injection level

of 1×1015 cm-3. The empirical model is in good agreement with both Klaassen’s and

Dorkel-Leturcq’s models especially at high temperature. The empirical model may not

be valid at temperature below 150K.

1.7 Summary

In summary, the carrier mobility is an important parameter that determines the electrical

properties of silicon material and the performance of silicon devices. Over the years,

there has been a number of techniques and models developed to measure and calculate

electron and hole mobilities in silicon effectively. However, the lack of simultaneous

temperature and injection level control has resulted in scarce experimental data having

simultaneous doping density, temperature and injection dependences. The existing

mobility models that have all three dependences were derived semi- empirically and

there has been no direct experimental validation of how these factors are combined. In

this chapter, a new contactless photoconductance technique that can measure the

mobility sum in silicon as a function of temperature and injection level is used to

measure such dependences. The experimental data on five n-type from 0.5Ω.cm to

100Ω.cm and two p-type sample from 0.75Ω.cm to 10Ω.cm from -120 oC to 180oC are

obtained based on this technique. The data shows good self-consistency and an

empirical mobility sum model is derived. The new empirical model uses a form of the

Fermi-Dirac equation and has doping density, temperature and injection dependences.

This empirical model is then compared with the existing mobility models in terms of

different dependences. The model shows good agreement with other semi-empirical in

the ranges where experimental data are available for both n- and p-type silicon. The

model may not be valid outside the range. This empirical model is useful for lifetime

spectroscopy measurements. In addition, the experimental results presented here also

validate the use of Klaassen’s model to calculate the carrier diffusion length and the

resistivity in moderately injected bulk regions of high efficiency silicon solar cells [92].

39

Chapter 2

Vacancy-related recombination active defects in

as-grown n-type Czochralski Silicon

2.1 Introduction

For decades, p-type silicon has been the dominant material for silicon solar cells.

However, metallic-related impurities such as iron, and the boron-oxygen defect, have

been found to significantly degrade the performance of p-type silicon solar cells. By

contrast, the same defects in n-type silicon have been shown to have little impact on its

electronic quality [13-15, 35, 36, 93, 94]. However, other defects related to the presence

of silicon vacancies, self-interstitials, and complexes formed with dopant atoms or light

elements, such as, oxygen, carbon and nitrogen could potentially limit the performance

of n-type solar cells. In particular, Czochralski (Cz) silicon ingots grown for

photovoltaics are generally pulled relatively rapidly, leading to vacancy-rich conditions

along much of the ingots [95-99]. It is therefore plausible that vacancy-related centres

could play a role in terms of recombination in these materials. However, to date there

have been few studies on these types of defects in terms of their impact on carrier

lifetimes.

The thermal stability and energy level of vacancy or interstitial related defects in

silicon have been extensively studied and are well known from Deep Level Transient

Spectroscopy (DLTS) [100-102], Electron Paramagnetic Resonance (EPR), Positron

Annihilation and Localized Vibrational Mode (LVM) spectroscopy [103-105]. The

defects in these studies were intentionally created using electron and proton irradiation,

leading to much higher concentrations of defects than generally occur in as-grown

silicon wafers. The impact of such intrinsic point defects on the minority carrier lifetime

remains unclear.

Vacancy-related recombination active defects in as-grown n-type Czochralski Silicon

40

In this chapter, we investigate the thermal stability and recombination activity of

grown-in point defects in the as grown state of high lifetime Cz n-type silicon wafers

using minority carrier lifetime measurements. The impact of these defects on minority

carrier lifetime is studied systematically. The deactivation temperature range and

annihilation activation energy are also determined.

2.2 Review of Crystallographic Defects in Silicon

A perfect crystalline solid has a periodic crystal structure. The atoms are situated in a

periodic array over large atomic distances, that is, long-range order exists. Silicon for

instance has a diamond cubic structure consisting of two interpenetrating face-

centered-cubic (FCC) lattices. Figure 2.1 shows such a lattice structure. However, such

an idealized solid does not exist in the real world. The regular patterns are often

interrupted by crystallographic defects, that is, imperfections or lattice irregularities

having one or more of its dimensions on the order of an atomic diameter. Classification

of crystalline defects is frequently made according to geometry or dimensionality of

the defect, including point defects, one-dimensional linear defects, two-dimensional

planar defects and three-dimensional volume defects [106]. In this section, these four

categories of defects in silicon are briefly reviewed.

(a) (b)

Figure 2.1: (a) Silicon lattice unit cell with tetrahedral interstitial site. (b) Silicon lattice

unit cell with hexagonal interstitial site. [107]


41

2.2.1 Point defects

Point defects occur only at or around a single lattice point. They are not extended in

space in any dimension, meaning they are zero dimensional defects. Point defects can

be mainly divided into two categories: Intrinsic and extrinsic point defects. Extrinsic

point defects involve impurities, whereas intrinsic point defects do not involve any

foreign impurities, but only crystallographic imperfections. In this section, the different

types of point defects, both intrinsic and extrinsic are introduced.

2.2.1.1 Intrinsic point defects

The two most basic point defects in silicon crystals are vacancies and self-interstitials.

These are the fundamental building unit to form more complex point defects, such as

divacancies. Vacancies and self-interstitials are intrinsic point defects inherent to the

material whose occurrence in the lattice arises from thermodynamic equilibrium and

incorporated into the growing crystal at the melt-crystal interface. Vacancy defects [107]

are simply lattice sites that would be occupied in a perfect crystal, but are vacant. In

addition to vacancies, self-interstitials is another type of intrinsic point defect. A self-

interstitial is a silicon atom that occupies a tetrahedral or hexagonal interstitial site in

the silicon lattice.

2.2.1.2 Extrinsic point defects

As mentioned previously, unlike intrinsic point defects, extrinsic point defects involve

foreign impurities atoms. Silicon crystals can never be 100% pure due to the

fundamental limitations of material purification methods and impurities incorporated

during the crystal growth. The material used for Integrated Circuit (IC) industries are

99.9999999% (9 nines) pure [108]. Thus, some of the impurities will exist as crystalline

point defects in silicon. Common impurities in silicon are dopants, such as boron and

phosphorus, various metallic impurities and light elements, like carbon and oxygen.

Extrinsic point defects usually occupy either substitutional and or interstitial sites in the

lattice crystal lattice. Substitutional impurities replace or substitute the host atoms.

Interstitial impurities fill the sites within the host lattice.

Moreover, impurities, such as dopant atoms and oxygen, can interact with vacancy-

type defects [104, 107, 109] to form vacancy-impurity pairs. The vacancy-type defects


42

can pair with both substitutional and interstitial impurities. These vacancy-impurities

type defects have been studied extensively with irradiation damage experiments [103,

110, 111].

2.2.2 Line defects

In addition to point defects, which are considered as zero dimensional, the second

category of defects is linear or one-dimensional. Dislocations are a typical type of line

defects, in which some of the atoms of the crystal lattice are misaligned. Two basic

types of dislocations are edge and screw dislocations. Dislocations appear in silicon

mainly due to stress generated by high temperature operations during the manufacturing

of the ingots. Today, Cz silicon crystals are grown in dislocation-free mode.

2.2.3 Planar defects

In silicon, two typical planar or two-dimensional defects are grain boundaries and

stacking faults (SF). Grain boundaries occur where the crystallographic direction of the

lattice abruptly changes. The grain boundaries appear in multi-crystalline silicon.

Another important planar defect in silicon is stacking faults, SFs occur where the

crystallographic planes are disordered, and are bound at each end by dislocations. SFs

are generally distinguished as intrinsic or extrinsic faults. Intrinsic SFs occur by missing

atomic planes. Extrinsic SFs are formed by excess atomic planes. In silicon, SFs are

always of extrinsic nature [112]. SFs originate from the condensation of silicon self-

interstitials [113] and will form preferentially on suitable nucleation sites, for instance,

oxide precipitates, metal precipitates and damaged locations in the lattice. A common

stacking fault that can be observed in Cz silicon wafers is the oxidation induced

stacking faults ring (OISFs ring) [114-116]. It can appear in silicon wafers after

oxidation. The stacking faults are caused by the coalescence of supersaturated self-

interstitials during the oxidation of silicon wafers. These surplus interstitials tend to

agglomerate at the nucleation site, which are oxygen particles in the ring-shaped

Particle (P)-band. The P-band and various micro defects will be discussed in later

sections.

The various type of defects discussed above are illustrated schematically in the 2D

representation in Figure 2.2.


43

Figure 2.2: 2D representation of crystal defects in silicon. (a) Vacancy, (b) Self-

interstitial, (c) Edge dislocation, (d) Interstitial impurity, (e) Substitutional impurity

atom of larger atomic radius, (f) Substitutional impurity atom of smaller atomic radius,

(g) Extrinsic stacking fault [117]

2.2.4 Bulk defects

The last category of defects is the category of three-dimensional defects, in other words,

bulk or volume defects. Typical scale of the bulk defect is ~100nm, several hundred of

nm to ~10μm for line and planner defects and less than 1nm for point defects [118].

These include pores, cracks, foreign particles and inclusions, and other phases. In this

section, the most influential bulk defects in monocrystalline silicon are reviewed. These

include voids, A and B swirls defects and oxide precipitates.

Voids are common defects in vacancy rich silicon crystals. As the name implies,

voids are small regions where there are no atoms, and can be thought of as clusters of

vacancies. Therefore, it is a vacancy-type defect. They are also known as D-defects.

Voids have an octahedral shape with eight (111) facets. At high temperature

supersaturated free vacancies present in the silicon crystal agglomerate into voids [119].

A typical void density in the crystals is about 106 cm-3. If a void intersects with the

wafer surface it creates a pit. This pit is referred to as the crystal-originated particle

(COP) [120].


44

Two common types of interstitial-type bulk defects are the A- and B- swirl defects.

In analogy with the void case, A- and B- swirl defects are formed by an agglomerate of

supersaturated silicon self-interstitials. B-swirl defects are coherent globular clusters

and A-swirl defects are large dislocation loops [121, 122]. Therefore B-type clusters are

smaller in size than A-type clusters, but are present in higher density. The difference

between the A- and B- swirl defects can be easily distinguished using an optical

microscope. Figure 2.3 shows the etch-pits or hillocks by Sirtl .etch [123].

Figure 2.3: (a) A swirl band containing A- and B- swirl defect. A-swirls show large

hillocks; B-swirls appear as small shallow etch-pits. (b) A/B-swirl band. No A-swirls

are present in this region. [121]

Oxygen is a common impurity in Cz silicon and will affect the electronic properties

of silicon device in many different ways. Oxide precipitates are another type of bulk

defect in Cz silicon. They are formed during the cooling after ingot growth. Due to the

rapid decrease of oxygen solubility as the temperature decreases and the rather high

oxygen concentration in Cz silicon crystals, oxygen in silicon is usually at a

supersaturated state at most common process temperature. The precipitation of oxygen

interstitials then leads to the formation of oxide particles or oxide precipitates [124].

The oxide precipitates are in the form of amorphous SiOx. The shape varies from rod-

like, square platelet, truncated octahedral, polyhedral to spherical and depends on the

formation temperature and degree of supersaturation [125]. The presence of oxide

precipitate will result in other type of defects, such as OISF rings mentioned above.


45

2.3 Review of crystal growth

In section 2.2, some important types of defects in silicon have been briefly reviewed in

terms of their different dimensions. In this section, the focus moves to the formation

mechanisms of these defects during crystal growth.

2.3.1 Dislocation free silicon crystal growth

As discussed above, dislocations are one-dimensional. The presence of dislocations in

silicon crystals is un-favorable for photovoltaic applications as it will introduce

recombination and in turn reduce the efficiency of silicon solar cells. Dislocations can

occur in silicon growth whether by the Cz technique from a quartz crucible, or from a

silicon pedestal to avoid oxygen contamination [126]. The growth of dislocation-free

crystals is attractive for both photovoltaics and IC industries. In 1959, Dash [127]

introduced a new technique allowing the growth of dislocation-free silicon ingots.

Based on the investigation of the origin of dislocations using preferential etching and

copper decoration techniques, Dash concluded that the dislocations formed during the

crystal growth mainly originated from the following sources: (1) The dislocations

initially present in the seed can grow and propagate in the crystals. (2) New dislocations

can also be generated by thermal stresses in the seed from the dislocations already

present and propagate during the crystal growth. (3) New dislocations can also be

generated by thermal stress from the residual surface damage in the seed. (4) Poor

epitaxy of the newly crystallized material from the seed. (5) Impurities segregation at

the tail end of the crystal can affect dislocations further up the crystal due to the

difference in thermal contraction. (6) Dislocations generated plastically in the bulk of

the crystal by thermal stresses and expand down to the growing interface. It is seen that

the sources of dislocations mainly come from the imperfection in the seed crystal.

Based on these sources, the following procedure can be applied to grow dislocation-

free silicon crystals. (1) The seed has to be etched and polished to remove surface

damages from the seed including severe cracks from saw damage. (2) The seed needs to

have a small diameter over all or a long taper to a small diameter at the tip of the seed to

minimize thermal stress and the total number of dislocations at the interface. (3) To

avoid defect generation by plastic deformation , <111> orientation is preferred, but

<100> is also acceptable. (4) The seed has to stay for a sufficiently long time and high


46

temperature when inserted into the melt to remove surface damage and possible

contaminants, prior to the commencement of crystal pulling. (5) The diameter of the

initial crystal growth should be kept as small as possible to let the dislocations grow out,

that is, the necking process. Based on the above procedure, dislocation-free crystals are

achievable by seeding and necking.

2.3.2 Influence of v and G on crystal growth

In section 2.3.1, the growth of dislocation-free crystals has been discussed. The material

quality has dramatically been improved without dislocations. The switch to industrial

production of dislocation-free silicon crystals removed all the problems created by

dislocations-but opened a Pandora’s box of new problems related to intrinsic point

defects. In crystals containing dislocations, the dislocations behave as sinks for intrinsic

point defects, however, in the absence of these sinks, different types of grown-in

intrinsic point defects are inherited from the crystallization and form agglomerates (also

called grown-in microdefects) upon cooling of the crystals.

Based on different experimental observations, several theories and models [128-131]

have been devised to understand the distribution of grown-in intrinsic point defects and

microdefects in silicon ingots. In this section, we will introduce Voronkov and Falter’s

theory of crystal growth, which is a generally accepted theory. The theory is based on

two process parameters: v (The growth rate of the crystal) and G (The near interface

axial temperature gradient).

2.3.2.1 Voronkov’s theory

In Voronkov’s theory [129], the microdefect formation in dislocation-free crystals

depends on both v and G. A silicon crystal can be grown with vacancies or interstitials

as the dominant type of native defects. The dominant type is found to be controlled by

the v/G ratio as shown inFigure 2.4.

From Figure 2.4, it is clear that the vacancy type agglomerate D-defect in both Cz

and FZ crystals are separated from the interstitial type A/B defects by a constant v/G

ratio. In 1982, Voronkov [129] proposed a detailed quantitative equilibrium model to

describe this v/G dependence phenomenon. This model is based on the assumption that

both vacancies and self-interstitials exist at crystallization temperature. The equilibrium


47

concentration at the crystallization front (the crystal-melt interface) of vacancies Cv0 and

self-interstitials Ci0 are comparable, but Cv0 is slight higher than Ci0. The defect

formation is also based on the recombination and diffusion of vacancies and self-

interstitials in the vicinity of the crystallization front. The type of defects grown in the

crystal is determined by the competition between convection and diffusion. The self-

interstitial has higher diffusivity than that of vacancies. As a consequence of this

inequality, self-interstitials are formed in the growing crystals when the diffusion flux

dominates over the convection flux and vacancies formed otherwise. The diffusion

fluxes of point defects are proportional to the temperature gradient G resulting from the

faster recombination rate of point defects moving away from the crystal-melt interface.

The convection fluxes are proportional to the growth rate v of the crystal [132]. As

shown in Figure 2.4, the constant ratio that separate the D-defects and A/B-defects is

defined as the critical ratio ξt [99].

Figure 2.4: reported microdefect type plotted in dependence of combination of growth

rate v and the near interface axial temperature gradient G. The open symbols correspond

to D-defects and the filled ones to A/B- swirl defects. Circles represent FZ crystals and

squares are Cz crystals. [95]

For v/G > ξt, that is, the convection flux dominates over diffusion flux, vacancies are

incorporated into the crystal. The grown crystal is of vacancy type. Vacancies can


48

agglomerate into vacancy type microdefects, such as three-dimensional voids, oxide

particles, P-band, H-band and L-band, upon subsequent cooling. For v/G < ξt, the

reverse will happen, interstitials are incorporated into the grown crystal due to the

higher diffusion flux. A/B-swirls defects will be formed from the agglomeration of self-

interstitials upon cooling of the crystals. The critical ratio ξt determined experimentally

are scattered and equals to 0.16±0.04 mm2/min-K, however, 0.13 mm2/min-K is

believed to be more reliable [95, 97]. Figure 2.5 shows a typical microdefect pattern in

a Cz crystal grown with a ramped pull rate. The banded structure is revealed by a

subsequent oxygen precipitation cycle, at 800oC + 1000oC. In vacancy-rich regions this

creates high concentration of precipitates, and in interstitial-rich region this creates a

low concentration of oxygen precipitates (vacancy enhanced oxygen precipitation).

Following etching, an optical image of the sample reveals the vacancy-rich and

interstitial rich region. This particular image was taken with a varying pull rate and

shows that the type of incorporated microdefects change from vacancy type to

interstitial type when varying the pull rate.

Growth Rate

Figure 2.5: A typical grown-in microdefects pattern in a Cz crystal grown with a

ramped pull rate [133].

2.3.2.2 Radial non-uniformity of G

As shown in Figure 2.5, different v/G ratios result in different types of defects in the

silicon crystals. The growth rate v is easily controlled to be uniform across the radial

direction of the crystal during the growth, but the near interface the temperature gradient

Vacancy rich region Interstitial rich

region


49

G varies. Therefore, in the radial direction, v/G ratio is mainly dependent on G. A

typical radial cross section wafer in the defect transition region has a defect distribution

shown in Figure 2.6 (a) and (b). In the next section, the various agglomerated

microdefects shown in Figure 2.6 (a) and (b) will be discussed in more detail.

(a) (b)

Figure 2.6: (a) Schematic spatial distribution of grown in microdefects in a crystal

grown at gradually increasing growth rate [97]. (b) Sequence of microdefect bands in

wafer cut from a mixed-type crystal represented by the dashed line in Figure 2.6 (a)

[133].

2.3.3 Defects incorporated in vacancy mode crystal growth

At a relatively high pull rate, when the v/G ratio exceeds ξt, the crystal grown is of

vacancy-type. During the cooling stage of the crystal, the vacancy concentration

becomes strongly supersaturated as the temperature decreases. The vacancies tend to

agglomerate into microdefects, such as bulk defect voids, at a progressively increasing

rate. Due to the fast increase of the nucleation rate upon cooling, appreciable nucleation

occurs only within a narrow range of temperature around a certain nucleation

temperature Tn [97]. A typical nucleation temperature is around 1100oC [134] for a Cz

silicon crystal grown under typical conditions. In this section, the various vacancy-type

agglomerates shown in Figure 2.6 (b) will be discussed.


50

2.3.3.1 Voids

Voids are common bulk defects that form by the aggregation of vacancies during the

cooling of crystals grown in vacancy mode from a supersaturated vacancy solution [119,

135]. The density of voids is proportional to the factor q1.5CV-0.5 [97], where q is the

cooling rate at the temperature at which the nucleation occurs, and CV is the local

concentration of vacancies. The nucleation temperature of voids depends on CV. The

range lies at about 1100 oC as mentioned above. The nucleation occurs over a narrow

temperature range of ΔT~5K. The voids have energetically favored octahedral shape.

Various techniques have been used to characterize this type of defect. Therefore

different names are given according to the technique used before people come to the

conclusion that they are characterizing the same defect, for instance, D-defects, COPs,

Flow Pattern Defects (FPDs), Light Scattering Tomography Defects (LSTDs) and Gate

Oxide Integrity (GOI) [120, 136-138].

2.3.3.2 Vacancy-oxygen agglomerates

In addition to self-agglomerates of vacancies to form voids, vacancies forms complex

with oxygen or can be involved in oxygen precipitation process to accommodate the

requested extra volume. In Figure 2.6 (b), at the periphery of the central voids region

there are three bands: H-band, P-band and L-band [132, 133]. The middle one is called

the P-band, that is, particle-band. In this band, large oxide particles are formed with

typical density of 108 cm-3 [132]. Vacancies and oxygen atoms are two crucial

constituent to produce oxide particles. As the oxide particles become twice as large in

volume after adding oxygen atoms, the role of vacancies is to provide space for an oxide

particle and to release the significant strain energy created. The formation of oxide

particles is actually in competition with the formations of voids. The nucleation rate of

voids and oxide particles decreases dramatically upon reducing CV. However, the

reduction of the particle nucleation rate is of smaller extent. Since vacancies are not the

only constituent involved in the oxide particle formation, the particle nucleation rate is

not as sensitive to vacancy concentration as that of void formation. Therefore, at

sufficiently low CV, the dominant agglomeration path is switched from voids to oxide

particles. The formation of oxide particles consumes a large number of vacancies and

the residual vacancy density in the P-band is very low. The well-known OISFs-ring in


51

the wafer after oxidation is a result of the oxide particle in the P-band, which is a

stacking fault formed at those oxide particles by nucleating interstitials injected from

the growth of a surface oxide [112, 114].

Besides the P-band, there are another two bands in Figure 2.6 (b), the L-band and H-

band. The L-band appears when the initially incorporated CV is even lower than in the

P-band. L stands for low CV. Instead of producing large oxide particles, very small high

density oxide particles are formed [139]. The nucleation temperature in the L-band is

shifted to a lower temperature T. Thus, the oxygen diffusivity is reduced and the oxide

particles grow very slowly, meaning that vacancy consumption becomes insignificant.

The vacancy concentration remaining in the L-band is therefore much higher than in the

P-band, and close to the originally incorporated value.

At a slightly higher initially incorporated CV than that in the P-band, the vacancies

agglomerate mostly into voids, but this occurs at relatively low T. This band is called

the H-band (H refers to the peak in Figure 2.7 located at the side of higher initially

incorporated vacancy concentration). Due to the formation of voids, the vacancy

consumption is limited and the remaining vacancy concentration in the H-band is

comparable to the value in the L-band. The oxide particle formation is similar to the L-

band and results in high density of very small oxide particles. The difference from the

L-band is that the oxide particles in the H-band coexist with small voids.

Figure 2.7: Residual (normalized) vacancy concentration versus the starting vacancy

concentration, solid Curve: combined effect of voids and oxide particles; dashed curve:

negligible particle contribution [139]

The residual vacancy concentrations in the P-band, L-band and H-band can be

summarized in Figure 2.7. The two peaks corresponds to the L-band and H-band


52

respectively, L and H also represents the lower and higher peaks, the P-band is located

at zero residual vacancy concentration. The residual concentration above the higher

peak decreases due to the formation of voids.

2.3.3.3 Binding of vacancies by oxygen

Another important effect of vacancies is a reversible trapping of oxygen into Vacancy-

Oxygen (VO) and VO2 Defects. The binding occurs below some binding temperature Tb,

which is estimated around 1050oC [140].The binding of vacancies with oxygen reduces

the effective diffusivity of vacancies, thus, preventing vacancies from complete

consumption by voids.

2.3.4 Defects incorporated in interstitial mode crystal growth

As a counterpart of vacancy-type crystals, the interstitial type crystal can be grown with

decreasing growth rate as shown in Figure 2.5. If the growth rate is low enough and v/G

ratio is lower than the critical ratio, interstitial type microdefects can be formed. In this

section, the mainly interstitial type microdefects are introduced.

2.3.4.1 A/B-defects

There are two types of interstitial type defects: A-swirl defects and B-swirl defects.

They are the agglomeration of self-interstitials and formed at higher incorporated

interstitial concentration CIs. The A-swirls defect is an extrinsic dislocation loop [121]

of micron or sub-micron size. The loop has much larger size than voids but in

considerably less density. Moreover, B-swirls defect are small agglomerates of self-

interstitials. They reveal as large and small etch pits after preferential etch. The A/B-

defects have been shown in Figure 2.3 previously. The competition between the

formation of A- and B- defects in interstitial-rich silicon is comparable to the

competition between voids and oxide particles in vacancy-rich silicon. A-swirls defects

are formed at lower self-interstitial concentration than B-swirls defects. Accordingly,

the region containing A-defects is surrounded by a band of B-defects. The A-swirls

defects are known to cause serious catastrophic shorts in the p-n junction due the large

size of dislocation loop and nature. The structure of B-defects and their impact on the


53

devices is still unclear presently (may be joint agglomerates of self-interstitials and

residual impurities such as carbon or oxygen) [141].

2.3.5 Perfect Silicon

As shown in Figure 2.6, A/B-defects are surrounded by a defect-free zone that is the I-

perfect in Figure 2.5. The defect-free zone occurs at the transition from vacancy-type to

interstitial type crystal. Hence, the P-band is an indicator of V/I boundary, that is the I-

perfect zone in a mixed type crystal. The I-perfect zone is formed by suppressing the

formation of microdefects. This is achieved by keeping both the vacancies and

interstitials at low concentration during the cooling of the crystal to prevent microdefect

nucleation. The low concentrations of both vacancies and interstitials can be achieved

by controlling the v/G ratio within 10% around the critical ratio ξt at both axial and

radial direction [96].

In this section, two different crystal growth modes were reviewed: vacancy and

interstitial mode. Different v/G ratios can result in different dominating defect types in

the crystal, including mixed vacancy interstitial growth. Since, interstitials are more

harmful to silicon devices, such as, the shorts in p-n junction due to A-swirls defect,

most silicon crystals today are grown in the vacancy mode with v/G ratios well above ξt.

Therefore, vacancies, vacancies-impurity complexes, and the microdefects formed by

the agglomeration of vacancies, are of primary technological interest. In the following

sections, the focus will therefore be on vacancy-type defects.

2.4 Vacancy-impurity pairs in irradiated Silicon

As shown in section 2.3, dislocation-free crystals contain various types of intrinsic point

defects and their agglomerates. These point defects and microdefects will affect the

performance of silicon devices in many different ways. Understanding the structures

and properties of these defects is important for silicon technology. Lattice vacancies

and interstitials are the fundamental building blocks of vacancies and interstitials

aggregates. Therefore, understanding the individual vacancy and interstitial defects is

the first logical step toward unraveling the structures and properties of the many

complex grown-in and process-induced defects involved in crystalline silicon. Since

electron irradiation can produce isolated single vacancies and interstitials for study, the


54

study of irradiated silicon has been crucial. Watkins [103] used electron irradiation ~1-

3MeV at cryogenic temperatures to displace lattice atoms by Rutherford scattering of

the high-energy electrons. The advantage of that is, the low mass of the electron will

assure simple damage, since the recoiling nucleus only obtains a small amount of excess

kinetic energy, preventing further displacements of lattice atoms by it. The cryogenic

temperature will freeze out the displacement products. In addition, electrons are not an

impurity and only results in the displacement of the host atoms, but do not cause any

contamination. In this section, the various types of vacancies and vacancy-impurity

pairs studied in irradiated silicon are reviewed. These results will be the guideline for

the investigation of vacancy-related as-grown defects studied later in this chapter.

2.4.1 Various types of vacancy-impurity pairs complexes

Vacancies can be trapped by different types of impurities to form complexes. For

example, interstitial oxygen, isoelectronic substitutional impurities (Ge,Sn),

substitutional donors (P, As, Pb), substitutional acceptors (B, Al) and other vacancies to

produce divacancies, 3-Vacancies and 4-Vacancies [142-144]. The EPR and LVM

methods have been used to investigate the chemical constituents and their atomic lattice

structures. Watkins [103] summarized the energy and charge state of different types of

vacancies and vacancy complexes, which is shown in Figure 2.8 below.

Figure 2.8: Charge state and energy level of trapped vacancies with impurities [103]


55

Watkins also investigated the stability of the vacancy and several of the vacancy-

defect pairs in ~15-30 min isochronal annealing studies. Figure 2.9 shows the results

from this study, revealing that most vacancy and vacancy-defect pairs are unstable and

can be annihilated below 500oC.

Figure 2.9: Schematic of vacancy and vacancy-impurity pair annealing in ~15 – 30min

isochronal conditions [103]

The samples used for the studies in this chapter are Cz n-type silicon, therefore, if

any vacancy defect pairs limit the lifetime phosphorus and oxygen vacancy complexes

are the most likely candidates. The possible configuration of vacancy-phosphorus (PV)

and vacancy-oxygen pairs are briefly discussed next.

2.4.2 Vacancy-phosphorus pair

Phosphorus is used as dopant atoms in n-type silicon due to its high segregation

coefficient and low cost. In section 2.4.1, it has been shown that dopant atoms like

phosphorus can actually be trapped by vacancies to form VP pairs, which has an energy

level about 0.47eV below the conduction band. It also has two charge states: negative

and neutral [145]. The VP complexes in silicon were first identified by Watkins and

Corbett [146] using EPR and electron nuclear double resonance. However, due to the

lack of conclusive experimental observations, the formation mechanism is still unclear.

Phosphorus atoms occupy substitutional lattice sites in silicon. Chen et al. [109]

suggested that vacancy and phosphorus form clusters in silicon and has the form of PnV,


56

denoting a vacancy pairing with n of its nearest phosphorus neighbors (1 ≤ n ≤ 4).

Figure 2.10 illustrates the structure of a P4V cluster.

Figure 2.10: Schematic of a P4V cluster containing 4 phosphorus atoms (pink/dark) and

a vacancy (grey/light). Yellow spheres denote silicon atoms [109].

2.4.3 Vacancy-oxygen pair

Oxygen is the main residual impurity in Cz silicon crystals. As mentioned in section

2.3.3.3, oxygen can be trapped by vacancies easily and form vacancy-oxygen (VO)

complexes, these complexes are also called silicon A-centers. As shown in Figure 2.8

above, the VO complex has an energy level of 0.17eV below the conduction band and

has two charge states: negative and neutral. As in the case of VP, VO complexes can

have different atomic configurations, which can be written as VOn (1 ≤ n ≤ 4) [147].

Figure 2.11 (a) and (b) shows two types of VO complexes. In both case, the vacancy is

trapped by interstitial oxygen in silicon to form VO complex.

In this section, different vacancy-impurity pairs have been briefly illustrated. It is

seen that both VP and VO pairs can introduce deep levels, which may significantly

contribute to recombination in n-type silicon. In the experimental section, evidence will

be provided to validate the presence of these defects in as-grown n-type Cz silicon.


57

(a) (b)

Figure 2.11: (a) Schematic representation of VO defect. (b) Schematic representation of

VO2 defect [147].

2.5 Recent studies on vacancy-related defects in as-grown

silicon

As illustrated in section 2.4, silicon vacancy pairs have been studied extensively in the

past using deep level transient spectroscopy (DLTS), EPR and LVM spectroscopy. The

energy levels, charge states and thermal stability are well known and shown in Figure

2.8 and Figure 2.9 previously. For silicon power devices used in micro electronics

industry, it has been demonstrated that intrinsic-related defects created by high-energy

electron, proton, alpha-particle or ion irradiation [148] can effectively reduce the

minority carrier lifetime to improve the switching characteristics. However, the impact

of grown-in intrinsic point defects and their agglomerates in as-grown crystals, which

are in much lower concentration than in irradiated silicon, on the minority carrier

lifetime, is still unclear. Recently, studies on these defects in as-grown silicon have

been carried out by direct minority carrier lifetime measurements. The results indicate

the negative effect of these defects on carrier lifetime, thus, the performance of solar

cells. In this section, the most recent results on both Cz and Float Zone (FZ) wafers

will be included.

2.5.1 Review of lifetime limiting defects in high-purity Cz

silicon crystals

Recent study from Rougieux et al. [149] has shown that grown-in intrinsic defects in n-

type Cz silicon have a significant impact on the minority carrier lifetime in high-lifetime


58

wafers, and can be thermally deactivated above 360oC. In that study, n-type Cz silicon

wafers with resistivity ranging from 3.6Ωcm to 4.1 Ωcm were used. The samples went

through 30 minutes isochronal anneal at different temperature ranging from 150oC to

650oC as in the case of Watkins [103] shown in Figure 2.9. The effective lifetime was

then measured by a WCT-120 setup. The effective defect density was calculated by the

inverse of minority carrier lifetime relative to control wafers. Rougieux et al. showed

that the carrier lifetime in samples for annealing temperature above 360oC increased

dramatically from 1.6±0.4 ms to 4.7±0.4 ms at an injection level of 1×1015 cm-3. The

annealed lifetime is about 3 times the as-cut lifetime. However, the lifetime did not

show much improvement below 300 oC. The summarized results based on the effective

defect density are shown in Figure 2.12 together with Watkins’ EPR results for

comparison.

Figure 2.12: (a) Remaining defect density after 30 min isochronal anneal measured by

lifetime measurements. (b) Remaining defect density after 30 min isochronal anneal

measured by EPR from Watkins [149]

By comparing the results from Waktins, Rougieux et al. suggested that the observed

defects are likely VO pairs due to the similar annealing characteristics. Rougieux et al.

also suggested that upon annealing above 360oC, different vacancy-impurity complexes

are dissociated, such as, VP,VO,V2. However, during the subsequent rapidly cooling,

the portion of vacancies paired with other less recombination active point defects

increases. Hence, the effective lifetime increases upon annealing.


59

2.5.2 Review of lifetime limiting defects in high-purity FZ

silicon crystals

FZ silicon is more expensive to produce than Cz silicon. The advantage of FZ silicon is

a lower oxygen concentration and thus, fewer oxygen-related defects, for instance,

vacancy-oxygen pairs, oxygen precipitates and boron-oxygen defects. However, the

lifetime of most FZ silicon still does not reach the intrinsic limit [25]. Thus, there must

be other types of defects in the crystals. Recent works by Rougieux and Grant [150-152]

have shown that intrinsic-related defects in both n- and p- type FZ silicon can

significantly reduce the bulk lifetime from several milliseconds down to several

hundreds of microseconds.

Rougieux and Grant [150, 151] have studied the thermal stability of the lifetime

limiting defects in n-type FZ silicon and show that the defects can be

deactivated >1000oC isochronally over 30 minutes in both nitrogen and oxygen

atmosphere. The minority carrier lifetime can be improved from 450µs to 4.8ms for a

1.5Ωm n-type FZ wafer. The spatial distribution of the effective lifetime by

photoluminescence (PL) imaging shows that the defects are in the center region of the

wafer, which matches the distribution of vacancies in the silicon crystal under mixed

growth conditions. The nitrogen concentration measured by secondary ion mass

spectrometry (SIMS) is 3×1014 cm-3 to 5×1014 cm-3. Based on the nitrogen concentration

and the distribution of the defects, Rougieux [150] suggested that Vacancy and

nitrogen-related defects VXNY are the potential defects involved.

In addition to the defects found in n-type, Grant [152] reported defects which can be

deactivated between 150 oC to 250 oC in p-type FZ silicon wafers. The bulk lifetime can

be improved from 500µs to 1.5ms. The deactivated defects are not stable under 0.2 sun

illumination for 24h or phosphorus gettering at 880 oC. However, SIMS did not reveal

any detectable oxygen in the wafers. Based on the SIMS and the gettering results, it was

concluded that the defect is not related to BO or other fast diffusing metal impurities.

Grant suggested that the defect is either lattice-impurity or an impurity-impurity

metastable defect which is not identified based on the results from his study.

From section 2.2 to 2.5, we have shown that different types of intrinsic point defects

and their agglomerates can be formed during crystal growth in a dislocation-free silicon

crystal. The types of defects are vacancy or self-interstitial dominant, depending on the

control of the growth conditions. In section 2.5, recent studies have shown that vacancy-


60

type defects exist in the as-grown state can significantly affect the minority carrier

lifetime in the wafer, and in turn, the efficiency of silicon solar cells in both Cz and FZ

wafers. In the later section of this chapter, focus will be on the investigation of the

impact of intrinsic-related defects on carrier lifetime in Cz n-type silicon with lower

resistivity than the samples used by Rougieux and Grant.

2.6 Investigation of vacancy-related defects in Cz n-type as-

grown silicon

In section 2.5.1, Rougieux et al. has demonstrated that intrinsic-related defects in the as-

grown state of Cz n-type silicon, which appears as much lower concentrations than

irradiated silicon, can significantly reduce the minority carrier lifetime. The defect can

be deactivated between 300oC to 350oC. It was suggested that the defect involved was

possibly vacancy-oxygen (VO) pairs.

In this section, we further investigate the thermal stability of grown-in point defects

in the as-grown state of high lifetime Cz n-type silicon wafers using minority carrier

lifetime measurements. In addition to the defect observed by Rougieux et al., we also

observe a second defect, which is thermally deactivated at even lower temperatures. We

have determined the deactivation temperature range and annihilation activation energy

of this second lower temperature defect.

2.6.1 Experimental method

The samples used in this study were three n-type Cz grown monocrystalline

phosphorous-doped silicon wafers. All wafers had a diameter of 4 inch and thickness of

1000µm and were not subject to any thermal treatment after being sawn from the ingot.

Two wafers had a resistivity of 0.4Ωcm, and one wafer had a resistivity of 0.75Ωcm.

All wafers were diced into quarters. The study of the annihilation mechanism of the

defects was performed at temperatures between 100oC and 450oC. For temperatures

below 250oC, wafers were annealed in a conventional oven in air. For temperatures

higher than 250oC, the samples were annealed in a quartz tube furnace in nitrogen

ambient. The annealing was followed by rapid cooling in air.

The thermal stability of grown-in defects was then investigated using minority carrier

lifetime measurements with a room temperature surface passivation technique [153]. In


61

this technique, silicon wafers were immersed into a container filled with 150ml of 20

wt.% hydrofluoric acid (HF) (90 ml of H2O, 60ml of 48% HF) and centered over an

inductive coil for transient photoconductance (PC) measurements. The activation of the

surface passivation was done by subsequently illuminating under 0.2 suns for 1 minute

using a halogen lamp, the light source was switched off, and a lifetime measurement

was immediately performed [153]. The setup used in this experiment is shown in Figure

2.13 below.

Figure 2.13: setup used for minority carrier lifetime measurement using HF passivation

[153].

However, to consistently achieve very low surface recombination velocity (S<1 cm/s)

with the HF passivation setup shown in Figure 2.13, the surface preparation of the

samples was critical. In this technique, silicon wafers were prepared by etching the

samples for 10 minutes in 25 wt% tetramethylammonium hydroxide (TMAH) at 60-

70oC and, subsequently, cleaning using RCA1 at ~70oC for 10 min [153]. This etch and

clean procedure was performed before each passivation round in order to remove

surface defect and any contamination prior to surface passivation. The method allows

bulk lifetimes well above 1 ms to be reliably measured. To account for possible

variations in surface recombination after each chemical treatment step, an n-type FZ

monocrystalline silicon wafer of resistivity 1.5 Ωcm was used as a control. The same


62

samples were reused for subsequent anneals at a given temperature. Each time,

approximately 10 µm of silicon was removed by etching prior to each HF passivation.

2.6.2 Impact of vacancy-related defects on lifetime

The impact of defects on the minority carrier lifetime was analyzed first. The samples

were annealed at different temperatures to assess the thermal stability of the defects.

Figure 2.14 (a) plots the injection dependence of the effective minority carrier lifetime,

where the hollow symbols correspond to the 0.4 Ωcm samples annealed at 200oC for

0,7,30 and 80 minutes. Following the 200oC anneal, the samples were annealed at

400oC for 30 minutes. The graph shows an increase of lifetime from 600 µs (at Δn =0.1

× n0) in the as-grown state, to 850 µs after 7 minutes annealing. The lifetime increase to

1ms after a further 23 minutes (30 minutes in total) annealing and remains at 1 ms after

a total of 80 minutes, indicating longer annealing times would not further improve the

lifetime. However, when the samples were subject to a 400oC anneal for 30 minutes, τeff

improves again from 1 to 1.5 ms.

Figure 2.14: Injection dependence of the measured lifetime for (a) 0.4 Ωcm Cz samples

annealed at 200oC for different lengths of time (total of 80 minutes), followed by a

400oC annealing furnace for 30 minutes. (b) FZ control wafer annealed at 200oC for a

total 80 minutes, followed by a 400oC annealing for 30 minutes.


63

Figure 2.15: Injection dependence of the measured lifetime for 0.75 Ωcm Cz samples

annealed at 185oC for a total of 180 minutes, followed by a 450oC annealing for 30

minutes.

To ascertain whether the improvements in τeff were due to a reduction in bulk or

surface recombination, the FZ control wafer underwent the same annealing sequence as

the Cz samples. In contrast to the Cz samples, the lifetime of the FZ control remained

stable, as represented by the solid symbols in Figure 2.14 (b).

The lifetime of the 0.75 Ωcm sample behaved similarly to the 0.4 Ωcm sample, where

the lifetime improved from 2.1 to 2.6 ms after 30 minutes annealing at 185oC and did

not show any further significant change over a total of 3 hours annealing at 185oC. The

lifetime was then found to increase further to 3.4 ms after a 450oC anneal for 30 minutes.

The lifetime data for the 0.75 Ωcm material is shown in Figure 2.15. From these

observations, it is found that the defects are recombination active and undergo a two-

stage annihilation mechanism. In addition, the temperature range of the first stage defect

is similar to the well-known boron-oxygen defect [11, 94]. However, it is important to

note that the only dopant species in the samples is phosphorus (no boron); hence, the

observed defect is not related to the boron-oxygen defect. In addition, we do not observe

any lifetime degradation after 24 hours illumination at room temperature for these


64

samples when passivated by amorphous silicon a-Si:H, providing further evidence that

the defect is not the boron-oxygen defect.

2.6.3 Temperature dependent defect deactivation

Based on the investigation on minority carrier lifetime in the previous section, it is clear

that the defects appear as two annihilation stages. One at low temperature around 200oC,

another one is at higher temperature approximately 400oC. In order to investigate the

two-stage defect annihilation mechanism and the characteristics of the defects, we have

determined the threshold temperature, at which the defect annihilation begins and the

temperature at which it is complete. The samples were annealed for a fixed time of 30

minutes at different temperatures ranging from 100 to 450oC. To determine the change

of defect concentration in the samples, the normalized effective defect density is

calculated by [149]

effeff

effannealeff

t

annealt

N

N

11

11

0

*

0.

*

.

(2.1)

Where τeff0 is the measured effective lifetime in the as-grown state, τeff-anneal is the

annealed effective lifetime at any given temperature after 30 minutes annealing, and τeff∞

is the maximum lifetime where all metastable defects were suppressed. For practical

purpose, we obtain τeff∞ by taking the average value of effective data of the wafers after

an anneal of at least 2 hours at 400 and 450 oC to ensure that the effective lifetime has

reached a stable value. In this section, the normalized effective defect concentration was

determined at an injection level of 10% of the net doping Δn =0.1 × n0.

Figure 2.16 shows the remaining defect density after isochronal annealing of 30

minutes for temperatures ranging from 100 to 450 oC. Data for both resistivities of 0.4

and 0.75 Ωcm are shown. The uncertainty of the normalized effective defect density is

estimated by assuming ±5% uncertainty in the measurement of carrier lifetime [87]. The

graph shows two annealing stages, the normalized effective defect concentration remain

flat below 150oC, and starts to decrease sharply between 150 and 200oC. The

normalized effective defect concentration stabilizes between 200 and 300oC and starts

to decrease again beyond that. For a 30 minutes anneal, the second annealing stage


65

occurs between 300 and 350oC. The defect concentration then remains stable up to

450oC. The two annealing stages could involve two forms of the same defect, or two

entirely different species of defect. This will be discussed in more detail in the

following sections.

Figure 2.16: Normalized effective defect density for (a) 0.4Ωcm wafers and 0.75 Ωcm

wafers after 30 minutes annealing over a temperature range of 100 to 450oC. The line is

a guide to the eye. (b) 30 minutes isochronal anneal for temperatures ranging from 0 to

600oC measured by EPR from Watkins [103].


66

Similar results for the remaining defect density after isochronal annealing have been

presented previously by Watkins [103] using EPR shown in Figure 2.16 (b). The lower

temperature defect in our samples is deactivated over a temperature range of 150 to

200oC, similar to the vacancy-phosphorus (VP) pairs, as observed by Watkins. The

higher temperature defect we observe is deactivated over temperature ranging between

300 and 350oC, a similar range to the defect recently observed by Rougieux et al. [149]

In comparison with Watkins’s data, this result lies closest to the VO pairs.

The defect observed by Rougieux et al. using the same minority carrier lifetime and

passivation techniques was observed in n-type Cz wafers of lower phosphorus

concentration, with deactivation occurring over a temperature range of 300 to 350oC.

However, in that study, no change of lifetime was observed in the lower temperature

range that corresponds to the lower temperature defect reported in this section. A

possible reason for this is that the phosphorus concentration in the samples from the

earlier study is approximately an order of magnitude less than in the samples used in

this study. The fact that the samples with higher doping have higher effective defect

densities supports the hypothesis that the lower temperature defect is caused by VP

pairs.

2.6.4 Activation energy of stage 1 defect

In an attempt to identify the defects found in this study more clearly, further

characteristics of the defects have to be studied. An alternative way to identify the

defect is through its characteristic annihilation energy. Thus, we have determined the

annihilation activation energy Eann for the lower temperature defect, and compare it with

the Eann values from the literature for known defects.

By monitoring τeff versus the annealing time t, the effective defect concentration N*

can be extracted from [11]

effeff t

TtN

1

)(

1),(*

(2.2)

where τeff (t) is the effective lifetime of the sample after t minutes annealing at any given

temperature. Figure 2.17 shows the isothermal evolution of τeff for five different

temperatures ranging from 170 to 235oC. Note that the wafer used for the annealing at

185oC has a resistivity of 0.75Ωcm, while the remaining wafers have a resistivity of


67

0.4Ωcm, hence the lower starting defect concentration. The normalized effective defect

concentration N* follows an exponential decay during the annihilation process

])([exp(),( *

0

* tTRNTtN ann

(2.3)

Where N0* corresponds to the value of N* at t = 0, where the wafers are in the as-grown

state. Thus, by fitting the isothermal experimental N* data with equation (2.3) above, the

annihilation rate Rann(T) at each temperature can be determined. As the annihilation

mechanism of the defect is thermally activated, the annihilation activation energy Eann

can then be obtained from an Arrhenius plot of the variation of Rann with temperature

according to the following expression [154], where k0 is a scaling constant and kB is

Boltzmann’s constant.

)exp()( 0Tk

EkTR

B

annann

(2.4)

Figure 2.17: Effective defect concentration (N*) versus annealing time, where the wafer

used for 185oC is 0.75Ωcm, and the others are 0.4Ωcm wafers. The lines are fitting to

the data using equation (2.3).


68

From Figure 2.17, we can see a clear exponential decay trend of the normalized

defect concentration at five different temperatures. At 185oC, the exponential decay

starts with a lower normalized defect concentration than others. For this temperature, a

wafer of higher resistivity was used; however, the resistivity does not appear to have an

impact on the annihilation rate. From these results, we then evaluate the Rann at each

temperature. To determine Rann, we take the logarithm of both sides of equation (2.3).

We then obtain a linearized equation of the form

)ln()()],(ln[ *

0

* NtTRTtN ann

(2.5)

Figure 2.18: Least square fits for ln(N*) as a function of annealing time using equation

(2.5) for different temperatures. The lines are fitting to data using equation (2.5).

As shown in equation (2.5), we can determine Rann by taking the slope of the

linearized relationship using a least squares fit. However, if we use the N* data of close

to 0, a large error in ln(N*) results, and the slope of the linear regression is affected

significantly. Therefore in the following calculations, data which has reached ±5% of

the maximum value of the lifetime is ignored in the calculation. The uncertainty of the

activation energy is estimated by assuming a ±5% uncertainty in the measurement of


69

carrier lifetime. Figure 2.18 shows the least squares fit for the data from Figure 2.17.

The linear regression fits well with the data and results in a good correlation of 0.98–

0.993. Note that the large error bars for some of the data results from the value of N*

approaching zero.

Using the Rann(T) computed using equation (2.3) and (2.5), the variation of Rann with

T is plotted in Figure 2.19. Rann is found to follow an Arrhenius law. We use a statistical

method to calculate the prediction interval for ln(N*), and estimate a confidence interval

from the slope of the linear regression, thus, we can estimate the error in Eann. It gives a

value of 0.57±0.16 eV. However, the accuracy of the statistical method may be

somewhat limited by the relatively small data sets in some cases, and may therefore

somewhat underestimate the final uncertainty.

Figure 2.19: Arrhenius plot with least square fit for Rann(T) as a function of Temperature

using equation (2.4)

The annihilation activation energy calculated using a more conservative error tracing

method is 0.64±0.44 eV. In this case, the large uncertainty in Eann results from the

amplification of the error in N* after taking the logarithm. It can be considered as

yielding a conservative upper and lower bound for Eann.


70

2.6.5 Discussion and conclusion

In section 2.6.2 to 2.6.4, it has been shown that there are two types of defects in as-

grown Cz n-type silicon wafers. The two defects are associated with two different

annihilation temperature intervals. By comparing to the data from Watkins in irradiated

silicon and the results by Rougieux et al., the defects are tentatively identified as VP

and VO pairs. In order to provide further evidence for the constituents of the defects, the

annihilation activation energy for the first stage defect with lower annihilation

temperature is investigated. In this section, the activation energy for the first stage

defect is compared with the data from literatures in irradiated silicon.

Various studies have reported the annealing behaviour of VP pairs around 150 oC.

Hirata et al. [155] and Kimerling et al. [156] created VP pairs by irradiating lightly

doped FZ n-type wafers using a Co60 gamma-ray source at room temperature, thus

allowing them to investigate the annealing characteristics of the VP defect. Dannefaer et

al. [104] utilized the same approach to create vacancies, however they used n-type Cz

wafers with an oxygen concentration of 1×1018 cm-3. The activation energy values from

the literature are summarized in Table 2.1.

Table 2.1: Activation energy values from the literature for annihilation of intrinsic-

defect related complexes in silicon

Authors

Activation

Energy (Eann)

eV

Characterization

Method

Type of

Defects

Phosphorus Doping

Concentration (cm-3)

Hirata et

al. 0.93±0.05 Lifetime measurement VP0 1×1014

Kimerling

et al. 0.95±0.05

Junction Capacitance

Transient Technique VP0 5×1015

Kimerling

et al. 1.25±0.05

Junction Capacitance

Transient Technique VP- 5×1015

Dannefaer

et al. 0.8±0.2 Positron annihilation VP0 5 ×1015 to 5 × 1018

This Study 0.57±0.16 Lifetime measurement — 6.6 ×1015 to 1.3 ×

1016


71

It has also previously been shown that the annihilation activation energy of VP pairs

depends on the charge state. In order to compare the activation energy calculated in this

study, we have to determine the charge state of VP pairs. The charge state of the VP

pair depends on the Fermi level of the wafer, thus, the doping density in the wafer and

the energy level of the defect in the band-gap. Various studies have shown that VP pairs

have an acceptor level in the band-gap at EC-0.4 eV determined by Hall effect

measurements [146, 157, 158] (EC is the conduction band edge). The VP pairs are

negatively charged while the Fermi level is above the defect energy level and neutral

otherwise, as suggested by Kimerling et al. and Watkins [103, 156]. In this study, the

doping density of the samples is approximately 6.6×1015 cm-3 to 1.3×1016 cm-3. The VP

pairs in these samples are negatively charged at room temperature, however, in the

temperature range of 150oC to 200oC, the Fermi level shifts down to a value below or

similar to the defect energy level (About EC-0.44 eV for 200oC and EC-0.39 eV for

150oC). Therefore, the VP pairs are neutral during annealing. We compare our Eann

result with VP0 in Table 2.1. Our result lies in or close to the range of activation energy

values reported above and best matches Dannefaer’s data (with similar sample

conditions to ours). Dannefaer et al. also reported a second annealing stage and

suggested the annealing is associated with the phosphorus-vacancy-oxygen (PV-O)

complex, which is stable at 250oC for at least 250 hours, but unstable at 300oC or above.

Therefore, the defect found in the second annealing stage in this study may involve both

phosphorus and vacancies, not simply VO pairs.

A possible scenario has been suggested by Rougieux et al. regarding the formation of

recombination active defects during ingot growth. Rougieux et al. suggested that during

ingot cool down, free vacancies pair with oxygen around 360oC, other vacancies at

around 270oC and potentially phosphorus near 140oC. In this case, the lifetime was

limited by what appears to be the vacancy-oxygen defect. In such a scenario, the

vacancy-oxygen defect would correspond to defect 2 observed here, while defect 1

would be vacancy-phosphorus pairs. Note that, in general, comparison between ingots

and even within one ingot is not straightforward, as the vacancy concentration could

potentially be significantly different, which strongly depends on the control of the

growth conditions [139].

Finally, we note that DLTS measurements are unlikely to detect the defects studied here,

due to their very low concentrations. Based on typical values of carrier capture cross

sections of 10-14 cm2 and the lifetimes measured with full defect activation, we estimate


72

that the defect concentrations are below 1010 cm-3, which is below the sensitivity limit

of conventional DLTS systems for wafers of the resistivities used here.

Overall, we have studied a lifetime limiting grown-in defect in high-lifetime n-type

Cz grown silicon wafers. We also confirm the existence of another recently measured

recombination active defect in n-type Cz grown silicon wafers. The defects can be

thermally deactivated in two different annealing stages. The first stage occurs between

150oC and 200oC and the second stage between 300oC and 350oC. We observe a

threefold increase in the lifetime from 0.5 ms to 1.5 ms for the 0.45 Ωcm samples and

from 2 ms to 3.4 ms for the 0.75 Ωcm sample at an injection level of Δn =0.1 × n0. The

annihilation activation energy measured for the first stage defect is estimated to be

0.57±0.16 eV. A potential candidate for the first stage defect could be VP pairs, which

are known to anneal out in the temperature range observed by Watkins. VO pairs are a

possible candidate for the second stage defect investigated in this study. The suggestion

that VP pairs are responsible for the first defect is also supported by the heavier doping

in the samples studied here, in comparison to the previous study in which they were not

observed. However the relatively weak agreement between measured annihilation

activation energy and the values from literature indicates that the identification of the

first stage defect is speculative and other defect (maybe not seen in previous studies)

could also be responsible. Together with a previous study, our results indicate that

grown-in vacancy-related point defects formed during ingot growth can significantly

affect the bulk lifetime of high quality n-type silicon wafers.

2.7 Summary

In summary, this chapter discussed different crystallographic defects and the type of

defects formed during the silicon crystal growth. In 1959, Dash suggested the

procedures to growth dislocation-free silicon crystal based on the detailed analysis of

dislocations in the different parts of silicon ingots. He demonstrated that by a controlled

seeding and necking process, a dislocation-free silicon ingot can be grown nearly over

the entire length of the ingot. Voronkov found that even though the ingot became free of

dislocations, the crystal was still not perfect. Indeed removing dislocations opened a

Pandora’s Box of new problems related to intrinsic point defects. Even though the

dislocations were unwanted in the silicon crystal lattice, they were also sinks for

intrinsic point defects. The lack of sinks then caused intrinsic point defects, such as


73

vacancies and self-interstitials, to propagate during crystal growth and form various

agglomerates during the cooling of the crystal. Voronkov proposed a theory that

explains the formation mechanisms of intrinsic point defects and agglomerates in

crystalline silicon ingots. It is an equilibrium theory based on two parameters, the

growth rate of the crystal v and the near interface temperature gradient G. Two types of

crystals can be grown based on the critical v/G ratio: Vacancy-type and self-interstitial

type. Self-interstitial type defects are more harmful to devices than vacancy type defects,

hence most of the crystals grown today are vacancy-rich. Thus, it became critical to

understand the electrical properties of vacancy-related defects. The fundamental

properties of vacancy-related defects were studied in irradiated silicon, which contains

much higher vacancy concentrations than in as-grown silicon. However, the electronic

properties of these defects in as-grown silicon are not well known, especially in relation

to minority carrier lifetime. Recent studies by Rougieux and Grant have shown that the

intrinsic-related defects in as-grown silicon can significantly affect the minority carrier

lifetime in silicon. They conducted various experiments on the spatial distribution and

thermal stabilities of these defects. They concluded that these defects can potentially be

VO pairs in Cz silicon and VXNY defects in FZ silicon.

In this study, n- type Cz silicon wafers with higher phosphorus concentrations were

used. It is found that the defects observed were associated with two annihilation stages,

one at lower temperature around 150oC and another at 300oC, and that the annihilation

of these defects can significantly improve the minority carrier lifetime in silicon wafers.

The annihilation activation energy for the lower temperature defects was also measured.

Based on a comparison with the results from irradiated silicon, the defects were

tentatively identified to be VP and VO pairs. The mitigation of these defects during

solar cell processing will improve the solar cell efficiency, especially for solar cells

processed at low temperature such as heterojunction solar cells [19]. An improved

awareness of the presence and properties of these low temperature defects should also

allow better correlation between lifetimes measured in the as-grown state, and final

device performance.


74

75

Chapter 3

High Efficiency Upgraded Metallurgical Grade

Silicon Solar Cells: Fabrication and Analysis

3.1 Introduction

Upgraded Metallurgical-Grade (UMG) silicon has raised interest as a low cost

alternative material for high efficiency silicon solar cells [159-165]. UMG silicon

(UMG-Si) feedstock is purified using a liquid phase purification process. As a result, it

contains more impurities, especially shallow acceptors and donors (B, Al and P), and

the minority carrier lifetime is usually lower in the as-grown state. In addition, due to

dopant compensation, the carrier mobility is reduced, and the presence of boron leads to

the formation of the boron-oxygen (BO) defect, even in n-type compensated UMG-Si

wafers [37, 38, 154]. Recent improvements in the UMG purification process have led to

an improvement in feedstock quality.

In this Chapter, we will review the different techniques used in silicon feedstock

purification, the effects of dopant compensation on the performance of UMG-Si solar

cells and the influence of BO defects at the cell level. In addition to the review, we

present the first reported efficiency above 20% for a solar cell based on 100% UMG-Si

feedstock, using n-type Cz wafers.

3.2 Silicon feedstock

Silicon feedstock is the raw material used to grow crystalline silicon ingots for micro-

electronic and photovoltaics (PV) applications. The quality of different feedstocks can

vary significantly according to its purity. Different techniques have been developed to

purify the feedstocks in order to achieve high purity and low cost materials, namely the

chemical route or the metallurgical route. The chemical route requires higher energy

High Efficiency Upgraded Metallurgical Grade Silicon Solar Cells: Fabrication and Analysis

76

consumption than metallurgical routes, but results in higher purities. In this section, we

will review the different grades of silicon produced and the purification techniques

developed.

3.2.1 Metallurgical grade silicon

Metallurgical grade silicon (MG-Si), also called silicon metal, is normally used as the

starting material for both the chemical purification route like the Siemens process, and

the metallurgical route that produces the solar-grade silicon (SOG-Si). Silicon metal is

produced by the carbothermic reduction of silica, which is a process developed at the

beginning of the twentieth century. The process has been greatly improved with larger

arc furnaces, efficient material handling and improved control of operations through the

years. The carbothermic reduction is basically achieved by reaction in a furnace

consisting of a crucible filled with quartz and carbon materials. The overall reaction is

given by

SiO2 + 2C = Si + 2CO

(3.1)

Generally, the production of 1 ton of MG-Si requires 2.9 to 3.1 ton of quartz, 1.2 to 1.4

ton of coke, 1.7 to 2.5 ton of charcoal, 0.12 to 1.4 ton of graphite (electrodes). The

electricity consumption is about 12.5 to 14 MWh [166]. The purity of the MG-Si varies

from 98.5% up to 99.5% and the average price is 1.5 to 2.5 €/kg [167]. The MG-Si

contains different types of impurities, for instance, dopant elements like B and P, light

elements like O and C and different metallic impurities. The chemical quality of

commercial metallurgical grade silicon is shown in Table 3.1

Table 3.1: Chemical characteristics of commercial metallurgical grade silicon [168]

Element O Fe Al Ca C Mg Ti Mn V B P

Low (ppm) 100 300 300 20 50 5 100 10 1 5 5

High (ppm) 5000 25000 5000 2000 1500 200 1000 300 300 70 100

Element Cu Cr Ni Zr Mo

Low (ppm) 5 5 10 5 1

High (ppm) 100 150 100 300 10


77

The high impurity concentrations in MG-Si listed in Table 3.1 are not suitable for

applications in PV industries and micro-electronic industries. Further purification is

needed, especially for the various metallic impurities, which will introduce deep energy

levels in the silicon band-gap to create Shockley-Read-Hall recombination in the bulk

of a silicon device [169-171], and hence reduce the efficiency of solar cells. The typical

purity requirement of silicon feedstock for application in PV is above 99.9999% (6

nines, 6N) and for micro-electronic industries, 9N is the minimum requirement [172]. A

direct application of MG-Si is to produce the aluminium-silicon alloys for aluminium

parts casts used in the automotive industry.

3.2.2 Electronic grade silicon feedstock

As mentioned above, the chemical characteristics in Table 3.1 prevents MG-Si from

being applied in the semiconductor industry. The impurity requirement of silicon for

semiconductor applications is in the range of ppb to ppt. Therefore, electronic grade

(EG) or semiconductor grade silicon is required for such devices. In this sub-section,

different purification techniques developed to produce EG-Si will be briefly reviewed.

All techniques require chemical treatment of the MG-Si to synthesise the volatile silicon

hydride. Therefore, they are normally categorized as the chemical routes. The feedstock

produced is often called polysilicon, due to the micro-crystalline nature of the silicon

produced by the Siemens process.

3.2.2.1 The Siemens process

Among various purification techniques, the Siemens process [173] is the most well-

known and the most common technique. This process was developed in the late 1950’s.

In 2001, this process still accounted for at least 60% of the worldwide production of EG

polycrystalline silicon (poly-Si). As for all chemical route purifications, the Siemens

process starts with preparing volatile silicon hydride from MG-Si in a fluidised bed

reactor (FBR), the reaction is given by

Si(s) + 3HCl = HSiCl3 + H2

(3.2)

Si(s) + 4HCl = SiCl4 + 2H2 (3.3)


78

Trichlorosilane HSiCl3 from reaction (3.2) is the main component required in the

further purification steps. Equation (3.3) is the competing reaction, which forms the

unwanted tetrachlorosiliane in molar proportion of 10% to 20%. Followed by two

fractional distillation treatments of HSiCl3, hyper pure HSiCl3 is produced. Finally

HSiCl3 is decomposed onto the surface of heated U-shape silicon seed rods, electrically

heated to about 1100oC to grow large rods of hyper-pure silicon. This reaction involves

high-purity hydrogen and is represented by

HSiCl3 + H2 = Si + 3HCl

(3.4)

The schematic representation of the whole Siemens process is illustrated in Figure

3.1, which clearly shows the different purification stages and the recycling of by-

products.

Figure 3.1: Schematic representation of the Siemens process [173]

3.2.2.2 Other processes

Besides the Siemens process, there are other processes that produce EG poly-Si

feedstock. Two typical processes are the Union Carbide Process and The Ethyl

Corporation process. Research on these two processes was initiated after the

international oil crisis in 1976. The original objective for both processes was to develop


79

a route to produce inexpensive solar grade poly-Si. However, both processes ended up

as new commercial EG poly-Si processes. In this sub-section, the two processes will be

introduced.

The Union Carbide Process [174] –The main differences between the Siemens process

and the Union Carbide process are the starting reaction of the trichlorosilane (TCS)

production in the FBR and the final compound used in the pyrolysis treatment. As in the

Siemens process, there is a significant amount of by-product tetrachlorosilane (TET) left

in the gas mixture in Figure 3.1. The utilization of TET became an environmental and

economic issue. The Union Carbide Process used a hydrogenation process to convert

TET into TCS and developed a closed-loop production process. The hydrogenation

involves TET and MG-Si and is given by

3SiCl4 + 2H2 + Si(s) = 4HSiCl3

(3.5)

As in the Siemens process, the TCS is then purified by distillation. Contrary to the

Siemens process, the purified TCS is then redistributed in two separate steps to produce

silane. The two separate reactions are given by

2HSiCl3= H2SiCl2 + SiCl4

(3.6)

3H2SiCl2 = SiH4 + 2HSiCl3

(3.7)

The silane produced is then further purified by distillation and then pyrolysed to

produce poly silicon onto heated silicon seed rods mounted in a metal bell-jar reactor.

The advantage of the process compared to the Siemens process is that this process

operated as a closed-loop process and silane can be pyrolysed at lower temperature and

higher efficiency without the formation of any corrosive compounds.

The Ethyl Corporation Process [168] – Unlike the Siemens and the Union Carbide

Process, the reaction to produce EG poly-Si is not based on MG-Si. The idea of the

Ethyl Corporation Process is to utilize tens of thousands of tonnes of silicon fluoride

that are produced as a waste by-product from the huge fertiliser industry, which is a


80

very low cost starting material. The main reactions of the Ethyl Corporation Process are

shown in the equations below

2H + M + Al = AlMH4

(3.8)

SiF4 + AlMH4 = SiH4 + AlMF4

(3.9)

Where M being lithium (Li) or sodium (Na). After producing the monosilane, the

purification is done by distillation similar to the Union Carbide Process. Another radical

change of this process is the utilizing of FBR instead of bell-jar reactor. The FBR has

lower energy consumption and continuous operation, which are advantages over the

Siemens batch process.

3.2.3 Solar grade silicon feedstock

The photovoltaics industry has different requirements than the semiconductor industry

in terms of impurities. Therefore, low cost feedstock can provide an attractive

alternative to maintain the rapid growth of the photovoltaics industry. SoG-Si feedstock

which can potentially replace EG poly-Si has been researched and developed for many

years. There is no unequivocal definition for SoG-Si. Based on various investigations,

Wakefield et al. [175, 176] provided guidelines for the drafting of SoG-Si specifications.

They proposed that silicon feedstock containing a total impurity concentration of up to

120 ppm of various common impurities is a material acceptable for solar cells. They

also listed the individual maximum impurity levels as follows: Al, 25ppm; B and P,

0.01ppm; others less than 5ppm. In addition to this general definition of SoG-Si, Davis

et al. [177] presented the effect of individual impurities grown into Cz ingots on the

conversion efficiency of solar cells. The results are shown in Figure 3.2 and Figure 3.3

below.


81

Figure 3.2: Solar cell efficiency versus impurity concentration for 4 Ωcm p-base devices

[177]

Figure 3.3: Solar cell efficiency versus impurity concentration for 1.5Ωcm n-base

devices [177]

From Figure 3.2 and Figure 3.3, it is seen that different impurities have significantly

different effects on the final conversion efficiency. Note that these estimations were

made for solar cells with higher recombination parameters than current structures.

Hence this represents a best case scenario, for modern cells the efficiency will begin to

drop at lower impurity concentrations. Moreover, the effect of combinations of

impurities on the efficiency is rather complex and is not necessarily simply an additive

degradation. Therefore, a simple number of nines (N) may not be adequate to fully

describe the quality of solar grade silicon. Moreover, for many of the metal impurities


82

shown in Figure 3.2 and Figure 3.3, n-type substrates can tolerate higher impurity

concentrations than p-type wafers. Overall, the strict impurity tolerance limits of SoG-Si

is difficult to establish, mainly due to the fact that silicon purification, crystallization

and solar cell processing technologies are still improving towards tolerating higher

concentrations of residual impurities in the feedstock.

In the following sub-sections, SoG-Si produced by both the chemical and

metallurgical routes will be reviewed.

3.2.3.1 SoG-Si purified through chemical routes

SoG-Si that is produced by chemical routes is also called solar grade poly-Si. As the

name implies, the SoG-Si purified through chemical routes still involves the synthesis

of volatile silicon compounds and utilizes the EG polysilicon process, such as, the

Siemens process. Various industries [33, 178-182] have invested in the purification of

silicon through chemical routes, but none of them have resulted yet in establishing a

new polysilicon route devoted to solar cells and completely decoupled from the

semiconductor feedstock. Most of the process is based on either a down-graded

Siemens-type process or a modified FBR. The following sub-sections discuss the state

of the art in the development of silicon purification technologies to obtain low-cost

material through the chemical routes.

Table 3.2 summarizes the state of art in the industries that produce low-cost solar

grade poly-Si feedstock. From the table, it can be seen that all processes involve volatile

silicon hydride compounds as the starting material. The only difference in these

processes from the traditional EG polysilicon process is the use of a modified or

different decomposition reactor. The reduction of feedstock cost is mainly obtained by

increasing the production rate and in turn the purity is also reduced. In addition,

simplifying and relaxing the production procedures and quality control [168] can also

further reduce the cost.

Even though the chemical route purification can achieve acceptable purity feedstock

at relatively lower cost to fulfil a portion of the PV demand, there are still some

disadvantages. The major disadvantage of the chemical route is the production of

chlorosilanes and reactions with hydrochloric acid. These compounds are toxic and

corrosive, causing irritations of the skin and mucous membranes [183]. Moreover, their

handling requires extreme care, since they are explosive in the presence of water and


83

hydrochloric acid. The chlorine emission through chemical routes is estimated to

amount to 0.02kg of chlorine per square meter of cells [172]. In addition to the emission

in poly-Si production, the energy consumption is also relatively high.

The disadvantages discussed above have been the driving force for the development

of metallurgical processes for SoG-Si feedstock production in the recent years.

Table 3.2: State of the art in the development of low-cost solar grade polysilicon

through chemical purification routes

Developer Processes involved

Waker Chemie

AG [178]

1) Traditional Siemens process is utilized.

2) Fluidised-bed reactor is used to decompose the gaseous mixture

of trichlorosilane and hydrogen to produce granular polysilicon.

3) FBR can increase the production rate and reduce the cost of

feedstock.

Bayer AG

[179, 180]

1) The cost-effective synthesis of silane in the Union Carbide

process is used.

2) The FBR from the Ethyl Corporation process is used to deposit

polysilicon.

Tokuyama

Corporation

[181]

1) Vapour-to-liquid deposition, which is based on the chlorosilane

decomposition on a silicon liquid film.

2) This process can result in 10-fold higher deposition rate than in

the Siemens process, thus reducing the cost.

REC Group [33]

1) Using an inverse U-shape hot filament chemical vapour

deposition (CVD) reactor to decompose SiH4 thermally.

2) The increase of polysilicon production rate reduces the cost

Chisso

Corporation

[182]

1) Reduction of silicon tetrachloride by zinc to produce 6N grade

polysilicon.

2) Closed loop system that cyclically utilizes zinc chloride, which is

a by-product, thus, reduces the cost and the production of by-

product.


84

3.2.3.2 SoG-Si purified through metallurgical routes

Metallurgical routes involve obtaining SoG-Si directly from MG-Si through a

combination of metallurgical techniques. The metallurgical routes have the potential to

be five times more energy efficient than the conventional Siemens approach [184]. In

this sub-section, some of the metallurgical techniques developed will be reviewed.

3.2.3.2.1 Directional solidification

Many metallic impurities introduce deep energy levels in the band-gap of silicon and

thus act as effective recombination centres. Recombination can greatly reduce the

efficiency of crystalline silicon solar cells, as shown in Figure 3.2 and Figure 3.3.

Therefore, the removal of metallic impurities in the feedstock is the first priority to

achieve high quality SoG-Si. Directional solidification is known to be a key step in the

various metallurgical refining technologies. Purification by directional solidification is

based on segregating impurities into the last fraction solidified of the ingot. The last

fraction solidified is then removed and the remaining ingot is purer. The segregation of

impurities between the solid and molten silicon is defined by the equilibrium

segregation coefficient, given by

𝑘0 =𝑋𝑠

𝑋𝑙

(3.10)

Where Xs and Xl are the equilibrium impurity concentrations in the solid and liquid

phases respectively. From equation (3.10), it is clear that impurities with low

segregation coefficient are more easily removed. The equilibrium segregation

coefficient for various elements [185-187] in silicon is listed in Table 3.3 and Table 3.4.

Most metallic impurities have very low segregation coefficient, thus can be effectively

removed in this refining process. However, Boron (B) and Phosphorus (P), which are

two key elements that affect the performance of silicon solar cells, have relatively high

segregation coefficient and thus are difficult to remove through directional solidification.

Various other techniques can be used to remove B and P to meet SoG-Si purity

requirements.


85

Table 3.3: Equilibrium segregation coefficient for dopants and light elements in silicon

at the melting point

Element k0 Element k0

B 0.8 P 0.35

Al 0.002 As 0.3

Ga 0.008 N 7×10-4

C 0.07 O 0.25-1.25

Table 3.4: Equilibrium segregation coefficient for metallic impurities in silicon at the

melting point

Element k0 Element k0

Co 8×10-6 Ti 3.6×10-4

Ni 8×10-6 Cr 1.1×10-5

Cu 4×10-4 Mn 1×10-5

Zn 1×10-5 Fe 8×10-6

3.2.3.2.2 Acid Leaching

In addition to directional solidification, acid leaching is another way to remove metallic

impurities in MG-Si. Acid leaching is based on the fact that, during the solidification of

molten MG-Si, metallic impurities tend to precipitate at the grain boundaries, forming

intermetallic phases with silicon, mostly made of silicides and silicates [168, 172].

Upon grinding the MG-Si, breakage occurs mainly at grain boundaries, thus exposing

the impurities to the surface of the pulverised MG-Si, and thus allowing purification by

acid leaching [32, 188]. Different acids or mixtures can then be applied to remove the

impurities (HNO3, H2SO4, HCl and HF). The main advantage of acid leaching is that it

is a low temperature process and has a lower energy requirement. The leaching

efficiency depends on the particle size, time, temperature and the type of leaching

agents [188-190]. Various authors [188, 191-195] have demonstrated the use of aqua

regia or HF to obtain purity around 99.9% from MG-Si. Many of them [188, 189, 192,

195] reported that HF is quicker and more efficient than aqua regia in removing


86

impurities. Table 3.5 represents the chemical analysis of impurities in silicon feedstock

before and after acid leaching with HF/H2SO4 solution over 20 hours at 80oC by Hunt el

al. [192].

It is seen from Table 3.5, most of the metallic impurities can be effective removed

after acid leaching, however, B and P is still difficult to remove. It has been reported

that leaching is not effective for B, C and O [172]. However, addition of Ca to the

silicon alloy can remove P by a factor of 5 down to relatively low concentrations of less

than 5 ppmw, probably due to the dissolution of P in calcium silicide [172].

Table 3.5: Chemical characteristic of MG-Si before and after acid leaching

Impurity MGS (ppma) Leached (ppma)

B 37 28

P 27 17

Al 1200 220

Fe 1600 100

Ti 200 <5

Cr 110 <5

V 120 <5

Mn 80 <5

Ni 70 <5

Cu 24 17

3.2.3.2.3 Plasma refining

As shown above, metallic impurities can be effectively removed by directional

solidification and acid leaching. However, elements such as, B, P, C and Al have

relatively higher segregation coefficient and are therefore more difficult to remove. In

this sub-section, the metallurgical process that is designed to remove B from the

feedstock is reviewed. Plasma treatment is considered as an effective way to remove B

in the MG-Si.

The principle of plasma treatment is to form volatile compounds of B [196-199] ,

such as boron oxides (BO, B2O, BO2, B2O2, B2O3) or boron hydrates (BHO, BH2, BH2,


87

BH2O2 etc.). Different reactive gases have been explored, for example, Ar/H2O, Ar/O2

and Ar/CO2 as reported by Suzuki et al. [197, 200], and O2, HCl, Cl2 and water as

demonstrated by Alexis et al. [198]. Since the boron-containing compounds are more

volatile than molten silicon, they can be transported through the gas blown by the

plasma torch away from the surface. The effectiveness of this method depends on the

vapour pressure of the compounds. The compounds are more volatile with higher

vapour pressure. It has been shown that BOH is ten times more volatile than BO, thus,

B can be more efficiently removed with hydrogen or water plasmas rather than pure

oxygen plasma [198, 199]. Moreover, carbon can also be eliminated as carbon

monoxide in the presence of oxygen or water. Experimental results have shown a

reduction of B in MG-Si from 35.7 to 0.4ppmw with a Ar/H2O plasma within 25

minutes. The disadvantages of plasma refining are: (1) Complicated technology and

process control. (2) Dramatic reduction of volatilization rate due to the formation of a

silica layer at the molten silicon surface [201].

3.2.3.2.4 Slag treatment

Even though plasma treatment can effectively remove B from MG-Si, the plasma

equipment and operation requires a large initial investment. Researches have therefore

focused on finding a simpler solution. Slagging is one solution that is in principle

simpler and can be done in large scale in high capacity metallurgical vessels.

The slag refining method is based on the distribution between two different phases:

molten silicon phase and the slag phase. The distribution of B in two phases is mainly

achieved by the oxidation of B to form boron oxides, such as, B2O3. The efficiency of

slag refining is characterized by the distribution coefficient, given by: [172]

𝐿𝐵 =(%𝐵)𝑠𝑙𝑎𝑔

[𝐵]𝑆𝑖

(3.11)

Where (%B)slag is the boron concentration in the slag phase, and [B]Si is the

concentration in the silicon phase. Different compositions of slags have been

investigated in the literature [202-207] and these slags include binary CaO-SiO2 and

Na2O-SiO2 systems, and ternary systems CaO-SiO2-Y, with Y being Al2O3, MgO, TiOx


88

or CaF2. It has been shown that the basicity of the slags can significantly affect the

effectiveness of the refining, that is, the ratio of CaO to SiO2 in a CaO-SiO2 system for

example. Wu et al. [202] and Teixeira et al. [204] have demonstrated that LB is not a

monotonic function of the CaO concentration. Typical ranges of LB are between 0.5 to

3.5 [203, 204, 206, 208]. Wu et al. [202] and Khattak et al. [207] have shown a

reduction of B concentration by an order of magnitude with the CaO-SiO2 system.

Although slagging can remove B quite effectively, this process still suffers some

disadvantages: (1) the purity of the slag is critical and requires careful preparation. (2)

larger volume of slag compared to silicon are required to remove B from typical

concentrations of 20 ppmw down to 0.5 ppmw.

3.2.3.2.5 Electron beam melting

We have illustrated four techniques that can effectively remove metallic impurities and

boron. Phosphorus has a lower segregation and higher vapour pressure than boron and

can be partly removed in some of the techniques above. However, the purity still does

not meet the SoG-Si requirements. Therefore, techniques specifically designed to

remove P have been developed. The high vapour pressure of P gives the advantages of

using simple technologies with ease of control and operations. High frequency vacuum

melting and electron beam (EB) melting [30, 159, 209, 210] have been considered as

potential technologies. However, vacuum melting is shown to be slow and the final P

content does not meet the target requirement [30, 159]. In this sub-section, the more

effective approach, EB melting is reviewed.

EB purification uses an electron beam to melt silicon and effectively removes

elements with higher vapour pressure than Si. Pires et al.[210] demonstrated that P

content can be reduced from 38 ppmw to 0.39 ppmw with an extraction efficiency of

98.97%. Hanazawa et al. [30] also reported similar effectiveness to purify P from 25

ppmw to <0.1 ppmw. In addition, other elements with relatively high vapour pressure

can also be removed, such as Al, Ca, Cu, Fe, Mg, Na etc. [172, 209] The simplicity and

effectiveness makes the EB melting a successful process candidate for SoG-Si.


89

3.2.3.2.6 State of the art of SoG-Si purified by metallurgical

routes

In addition to the techniques reviewed above, there are also other techniques that have

been developed, for example, Alloying of Si with aluminium to form Si-Al alloys [211,

212] and ladle treatment [168]. The different metallurgical technologies are generally

combined to achieve the overall target for SoG-Si. In this chapter, to distinguish

between SoG-Si from chemical routes and metallurgical routes, the SoG-Si purified by

metallurgical routes are termed upgraded metallurgical grade (UMG) Silicon. The state

of the art of UMG feedstock is summarized in Table 3.6. All starting material is MG-Si.

Table 3.6: State of the art of UMG feedstock purification

Developer Processes involved

Kawasaki Steel Corporation

NEDO Project [213]

(1) EB melting (2) Directional solidification

(3) Plasma treatment (4) Directional solidification

Apollon Solar

PHOTOSIL Project [34, 214-216]

(1) Directional solidification (2) Plasma treatment

(3) Directional solidification

Elkem ASA [167, 217]

Heliotronic [167]

(1) Slag treatment (2) Acid leaching

(3) Directional solidification

Bayer AG [167] (1) Acid leaching (2)Reactive gas blowing

(3) Vacuum treatment (4) Directional solidification

University of Campinas [210] (1) Acid leaching (2) EB melting

SOLSILC Project [218] (1)Plasma treatment (2) Directional solidification

3.3 Impact of compensation on material properties

In the previous sections, different purification routes to obtain SoG-Si have been

reviewed. It is seen that among various impurities in UMG feedstock, B and P are

relatively difficult to remove due to the relatively higher segregation coefficients.

Therefore, ingots and wafers produced from UMG feedstock are compensated, that is,

both type of dopants are simultaneously present in the materials. In this section, the

effects of compensation on the material properties are reviewed.


90

3.3.1 Net doping and compensation ratios

In compensated Si, both donor and acceptor species coexist. If donors are more

numerous than acceptors (ND > NA), the wafer is n-type and electrons are majority

carriers. Otherwise, the wafer is p-type and holes majority carriers. The majority carrier

concentration nmaj at equilibrium is generally written as;

𝑛𝑚𝑎𝑗 = 𝑛0 = 𝑁𝐷+ − 𝑁𝐴

− ≈ 𝑁𝐷 − 𝑁𝐴

(3.12)

𝑛𝑚𝑎𝑗 = 𝑝0 = 𝑁𝐴− − 𝑁𝐷

+ ≈ 𝑁𝐴 − 𝑁𝐷

(3.13)

Equation (3.12) is for n-type Si and (3.13) for p-type. Where n0 and p0 are the

equilibrium electron and hole densities, ND and NA represent the concentrations of

substitutional donors and acceptors, while ND+ and NA

- are the ionized dopant

concentrations. The dopants are assumed to be completely ionized at room temperature

and at low dopant concentration (<1×1017 cm-3).

It is often useful to quantify compensation when studying the electrical properties of

compensated Si. The most widely used metric in the literature is the compensation ratio

defined as: [219]

𝑅𝑐 =𝑁𝑚𝑖𝑛

𝑁𝑚𝑎𝑗

(3.14)

Where Nmin is the minority dopant concentration and Nmaj is the majority dopant

concentration. The advantage of this ratio is its simplicity, and the fact that it does not

diverge. It is often used to study moderate compensation (Rc <0.9). However, it is not

able to provide a clear distinction between extreme compensation levels. At extreme

compensation, diverging ratios [220, 221] are required. For such cases, the ratio defined

by Libal et al. [220] is:

𝐾𝑐 =𝑁𝑚𝑎𝑗 + 𝑁𝑚𝑖𝑛

𝑁𝑚𝑎𝑗 − 𝑁𝑚𝑖𝑛

(3.15)


91

3.3.2 Impact of compensation on mobility and resistivity

As demonstrated in Chapter 1, carrier mobility is an important parameter to characterize

silicon material and the performance of silicon solar cells. It is affected by various types

of scattering mechanism in silicon and strongly affected by dopant concentrations due

to ionized impurity scattering. Moreover, the majority carrier mobility is directly related

to the resistivity ρ. In compensated Si, it is given by:

𝜌 =1

𝑛𝑚𝑎𝑗 × 𝑞 × 𝜇𝑚𝑎𝑗=

1

(𝑁𝑚𝑎𝑗 − 𝑁𝑚𝑖𝑛) × 𝑞 × 𝜇𝑚𝑎𝑗(𝑁𝑚𝑎𝑗 , 𝑁min)

(3.16)

Carrier mobility shown in equation (3.16) is affected by both the majority and

minority dopant concentrations. Compensation will increase the concentration of

scattering centers (that is the ionized boron and phosphorus atoms). In addition, Lim et

al.[222] and Schindler et al. [45] have proposed that the mobility in compensated

silicon could be further reduced due to the reduction of the screening of scattering

centers by free carriers, of which the concentration is reduced by compensation.

(a) (b)

Figure 3.4: (a) Resistivity as a function of acceptor and donor concentrations in

compensated Si [223]. (b) Compensation ratio as a function of resistivity in n-type

compensated Si for three fixed minority dopant concentrations (NA)

Cuevas [223] has calculated the resistivity of compensated Si, as a function of the

concentration of acceptor and donor dopants, Thurber’s [82] and Arora’s [65] mobility


92

models are used in this calculation. Figure 3.4 (a) shows the calculation results, it shows

that for a given resistivity value, there is an infinite number of possible acceptor and

donor concentration couples. Figure 3.4 (b) shows the compensation ratio Kc as a

function of resistivity in n-type compensated silicon at three fixed minority dopant

concentrations (NA). It is shown that at the same resistivity, there is more than one

compensation ratio. In other words, at the same net doping (nmaj) in compensated silicon,

there are an infinite number of possible resistivities.

(a) (b)

Figure 3.5: (a) Electron mobility as a function of resistivity in n-type compensated Si at

different NA (b) Hole mobility as a function of resistivity in n-type compensated Si at

different NA

Figure 3.5 (a) and (b) shows the electron and hole mobility as a function of resistivity

for uncompensated Si and three n-type compensated cases with a fixed minority dopant

concentration, as a function of resistivity. The mobility is calculated using Schindler’s

mobility model [45]. It shows that both electron and hole mobilities are lower than in

the uncompensated Si at the same resistivity. From Figure 3.5, it can be seen that the

mobility in compensated silicon increases with resistivity. However, it is not always

true, as it depends on which type of dopant is fixed. If we fix the majority dopant

concentration, then, the mobility will decrease with resistivity. Moreover, the mobility

also decreases with increasing NA due to the increasing effect of minority dopant

scattering at a fixed resistivity. Overall, the mobility in compensated Si is always lower

than the uncompensated counterpart at the same resistivity or net doping.


93

3.3.3 Impact of compensation on recombination

Carrier recombination is a key parameter determining the performance of silicon solar

cells. There are three important recombination mechanisms in silicon: intrinsic

recombination via Auger and radiative mechanisms, [224, 225], and Shockley-Read-

Hall (SRH) recombination through defect states [170, 171]. In this sub-section, the

impact of dopant compensation on recombination is reviewed.

Over the years, various groups have reported an increase of effective lifetime τeff in

highly-compensated regions of multi- and mono-crystalline Si ingots and wafers [220,

226-228]. Experimental results by Veirman et al. [228] reported an increase of effective

lifetime in the highly-compensated center region of a heterogeneously-doped multi-

crystalline compensated silicon wafer. The wafer is uniformly doped with [B] =2.6×1017

cm-3 across the wafer whereas the phosphorus concentration increased from [P]

=1.6×1017 cm-3 from the edges to [P] =2.1×1017 cm-3 in the center. The highest lifetime

occurs in the most compensated region, despite the fact that this region contains the

highest total concentration of dopants.

(a) (b)

Figure 3.6:(a) Variation of the intrinsic recombination lifetime with donor concentration

for fixed acceptor concentrations. (b) Variation of the effective recombination lifetime

with donor concentration for fixed acceptor concentrations [229].

Macdonald [229] modelled the impact of compensation on the carrier lifetime. Figure

3.6 (a) and (b) shows the modelling results, it shows that an increase in compensation

level can actually increase of effective lifetime. The modelling shows that the

equilibrium majority carrier concentration nmaj plays the most important role in the

recombination mechanisms instead of the total concentration of dopants. These results


94

explain the increase of effective lifetime in Veirman et al.’s study. In summary, the

dopants themselves do not act as recombination centers. Recombination is identical in

compensated Si as in uncompensated Si with the same net doping.

3.3.4 Impact of compensation on JSC

In a short base device, the material quality of the base of a solar cell determines the

short circuit current Jsc, which is defined by the minority carrier diffusion length, given

by:

𝐿𝑚𝑖𝑛 = √𝜏𝑒𝑓𝑓 × 𝐷𝑚𝑖𝑛 = √𝜏𝑒𝑓𝑓 × 𝜇𝑚𝑖𝑛 ×𝑘𝑇

𝑞

(3.17)

From equation (3.17), it is clear that Lmin is subjected to a compromise between the

carrier lifetime and minority carrier mobility. As mentioned in the previous two sub-

sections, compensation will reduce the minority carrier mobility but increase the

recombination lifetime. The question is which parameter can outweigh another as the

compensation ratio increase. Xiao et al. [230] and Macdonald et al.[229] modelled the

impact of compensation on the Jsc and found that Jsc increases monotonically with

compensation. However, their modelling is based on Klaassen’s model, which is known

to overestimate μmin in highly compensated Si. However, various experimental studies

[221, 231] also report the increase of Lmin with compensation and Jsc measured by

various groups [226, 232] shows a monotonic increase with compensation.

3.3.5 Impact of compensation on Voc

Besides Jsc, the open circuit voltage Voc is another important parameter governing the

efficiency of silicon solar cells. Voc across a front-junction n+pp+ device can be defined

by the following expression:

𝑉𝑜𝑐 =𝑘𝑇

𝑞ln [

(𝑛0 + ∆𝑛𝑓𝑟𝑜𝑛𝑡)(𝑝0 + ∆𝑛𝑏𝑎𝑐𝑘)

𝑛𝑖2 ]

(3.18)


95

Where ni is the intrinsic carrier concentration, ∆𝑛𝑓𝑟𝑜𝑛𝑡 and ∆𝑛𝑏𝑎𝑐𝑘 are the excess carrier

concentrations at the edges of the space charge regions of the front n+p junction and the

rear pp+ high-low junction, respectively. Equation (3.18) shows a competing effect

between ∆𝑛 and the net doping. Compensation leads to a reduction of the net doping,

while increasing the effective carrier lifetime and thus ∆𝑛 . Macdonald et al.[229]

calculated the impact of compensation on Voc for the particular case of iron

contamination. The results are shown in Figure 3.7. The results do not show a

monotonic increase of Voc with compensation for all three fixed acceptor concentrations

on the p-type side, however, the Voc still shows a drastic increase in the highly

compensation region for NA = 1×1017 cm-3. Xiao et al. [230] also reported similar

trends as Figure 3.7. Moreover, Veirman et al.[232] experimentally validated this

theoretical finding using UMG-Si containing very large boron concentrations (2 -

4×1017 cm-3).On the n-type side, τeff is not injection dependent and compensation leads

to a reduction of Voc due to the decrease of net doping.

Figure 3.7: Calculated Voc as a function of donor concentration for fixed acceptor

concentrations [229].

3.3.6 Impact of compensation on fill factor

The fill factor (FF) is generally affected by various factors, for example, series and

shunt resistances, injection-dependence carrier lifetimes and recombination currents

within various parts of a device [233, 234]. With increasing compensation, the majority

and minority carrier concentration decreases, leading to a reduction in both majority and

minority carrier conductivity, hence the FF decreases due to increased bulk resistive


96

losses. Moreover, if the effective lifetime exhibits a strong injection dependence, it will

lead to a reduction in the voltage at maximum power point (Vmpp) and thus reduce the

FF. Macdonald et al. [229] calculated the impact of compensation on the FF. The

results show a reduction of FF in the moderate compensation range and the FF then

recovers until extreme compensation is reached, as the base reaches high injection.

3.3.7 Impact of compensation on efficiency

The impact of compensation on the cell efficiency is based on the three parameters

shown in the previous sub-sections. We showed that these three parameters are strongly

dependent on the equilibrium majority carrier concentration, which can be adjusted by

compensation, and the type of defects in the material that can cause different injection

dependence of the effective carrier lifetime. Macdonald et al [229]. have shown that for

effective lifetime with strong injection dependence, such as the condition used in the

modelling of Figure 3.6(b) and Figure 3.7 with interstitial iron concentration of [Fei] =

5×1011 cm-3 in p-type compensated Si, compensation can increase the efficiency with

extreme compensation resulting in the improvement of all three parameters. However,

for the same condition in n-type compensated Si, interstitial iron has little impact on the

recombination of minority carriers, that is, holes. The efficiency will firstly improve

with compensation at moderate compensation level due to the improvement in Jsc. At

extreme compensation close to the intrinsic point, the efficiency will decrease due to the

reduction of all three parameters.

UMG-Si is not as pure as EG-Si and is compensated. To keep the low cost and low

energy advantages of this material, the lesser the purification steps involved the better.

The above discussions show that for an overall improvement in solar cell conversion

efficiency, the degree of compensation has to be strong. Therefore, in practice, to

achieve a reasonable UMG-Si solar cell performance, instead of including additional

purification steps, compensation engineering can be another route to success. Moreover,

as shown in Figure 3.2 and Figure 3.3, n-type Si can tolerate more impurities level than

p-type Si, that is, the injection level dependence of defects has less impact in n-type Si.

Hence, silicon solar cells made of n-type UMG-Si may in principle achieve higher

efficiencies for a large range of compensation level, except for extreme compensation

close to intrinsic point, as discussed above.


97

3.4 Evolution of UMG-Si solar cells

UMG-Si purification technologies have been developed for many years. As these

technologies progress, the efficiency of UMG-Si solar cells have also improved over the

years with different cell structures and processing techniques. Various companies and

institutes have reported UMG-Si solar cell efficiencies over the years based on different

solar cell structure in both industrial and laboratorial scales. Table 3.7 summarizes the

reported efficiency of solar cells based on UMG-Si from year 2001 to 2015 [39, 163-

165, 213-215, 227, 235-238]. In this section, the evolution of UMG-Si solar cells is

illustrated.

According to the data shown in Table 3.7, the record efficiencies have been

summarized in Figure 3.8. The progress of UMG-Si cell efficiency is mainly based on

p-type multi-crystalline silicon from 2001 up to year 2011 and achieved 18.5% by Q-

cells in year 2011 based on a PERC structure. Afterwards, the record efficiency was

overtaken by n-type mono-crystalline silicon and achieved 19% efficiency by Apollon

solar in the year 2012 based on a heterojunction solar cell and 19.8% from ANU with a

PERT small area solar cell. For p-type mono-crystalline and n-type multi-crystalline,

the data is scarce. The highest overall efficiency reported to date is 19.8% from ANU.

In this chapter, we will present the first solar cell with efficiency above 20% based on

100% UMG-Si.

Figure 3.8: Evolution of the record efficiency of solar cells based on UMG-Si for

various type of ingot growth.


98

Table 3.7: progress of silicon solar cells based on UMG-Si feedstock

Company/Institute Type Efficiency Year Area Structure

Kawasaki Steel multi p-type 14.1% 2001 100×100 (mm2) Industrial Screen

Print

EPM multi p-type 12.38% 2002 102 (cm2) Industrial Screen

Print

Konstanz

University multi p-type 16.2% 2009 125×125 (mm2)

Industrial Screen

Print

CaliSolar multi p-type 16.73% 2009 156×156 (mm2) Laser-grooved

Contact

PHOTOSIL multi p-type 16.2%

2010 125×125 (mm2) Industrial Screen

Print mono p-type 17.6%

PHOTOSIL multi p-type 16.7% 2011 125×125 (mm2) Industrial Screen

Print

CEA INES multi p-type 15.9% 2011 125×125 (mm2) Industrial Screen

Print

Q-Cells multi p-type 18.5% 2011 243 (cm2) PERC*

CEA INES multi n-type 15% 2012 125×125 (mm2) Industrial Screen

Print

PHOTOSIL mono n-type 19% 2012 149 (cm2) Heterojunction

Chinese

Academy

of Science

multi p-type 16.68% 2013 156×156 (mm2) Industrial Screen

Print

Konstanz

University mono n-type 19% 2013 125×125 (mm2)

Industrial

Standard

ANU mono n-type 19.8% 2015 4 (cm2) PERT**

*PERC stands for Passivated Emitter and Rear Cell structure

**PERT stands for Passivated Emitter Rear Totally-diffused cell structure


99

3.5 Permanent deactivation of boron oxygen defect in

compensated silicon

The boron-oxygen (BO) related defect has been studied extensively in p-type boron

doped and compensated silicon, as well as in n-type compensated silicon for several

years [10, 38, 154, 239]. It is known to significantly reduce the minority carrier lifetime

in silicon wafers, and thus, the efficiency of crystalline silicon solar cells. Recently, the

focus has moved to the permanent deactivation of the BO defects, first reported by

Herguth et al. [240-245] by annealing under illumination or bias. In this section, the

results on the permanent deactivation of BO defects in both n- and p-type silicon wafers

are reviewed.

3.5.1 Deactivation of BO defect in p-type silicon wafers and

cells

The presence of oxygen in Cz silicon leads to the formation of BO defects in p-type

silicon. Light-induced-degradation (LID) due to the formation of recombination active

BO defects is un-favourable for silicon in PV applications. The international effort to

permanently deactivate this defect has recently ramped up. In this sub-section, recent

advances on the permanent deactivation of BO defects in p-type silicon wafers and cells

are summarised.

Lim et al. [246] investigated the permanent deactivation of BO defects in p-type Cz-

Si wafers. Instead of annealing the wafers in the dark, the permanent deactivation is

done with annealing with illumination. Figure 3.9 (a) shows the results of a B-doped 1.4

Ω.cm Cz-si annealed on hotplate under illumination. It is shown that the lifetime

recovers dramatically after 150 hours anneal and stable for at least 300 hours under

subsequent illumination at room temperature.

In addition to the experiments done on p-type silicon wafer, Munzer and Herguth et

al. [240, 241] conducted experiments on the p-type silicon solar cells. The results from

Herguth et al. [241] are shown in Figure 3.9 (b). It is clear that the Voc of the cells

degraded after 50 hours of illumination with the permanent recovery of the Voc back to

its initial value. The Voc is shown to be stable under subsequent illumination at room

temperature for at least 192 hours. The regeneration condition is not mentioned in the

text. In addition, Munzer [240] also reported regeneration of the Voc for p-type silicon


100

solar cells, the deactivation is performed under 50oC and 75oC with illumination. The

results show that regeneration occurs with Plasma Enhanced Chemical Vapour

Deposition (PECVD) films, and does not with Low Pressure Chemical Vapour

Deposition (LPCVD) film. The recovery is potentially related to hydrogen in the film.

The Voc can be completely recovered back to its initial value.

(b)

Figure 3.9: (a) Time dependence of the lifetime of two P-diffused (open symbols) and

one undiffused (closed circles) p-type Cz-Si samples which are illuminated at 135oC

and 165oC, respectively, at a light intensity of 70mW/cm2 [246]. (b) Degradation and

regeneration of Voc on p-type silicon solar cells [241].

3.5.2 Deactivation of BO defect in n-type silicon wafers

In the previous sub-section, the permanent deactivation of BO defects in p-type silicon

at both wafer and cell level are reviewed. It shows that BO defects can be deactivated

with a regeneration process which is stable under illumination afterwards. In this sub-

section, the permanent deactivation of BO defects in n-type compensated silicon is

reviewed.

In n-type compensated silicon, for example, UMG-Si, the presence of boron still

leads to the formation of BO defects and causes LID [37, 38, 154]. Niewelt et al. [242]

utilized a similar regeneration procedure as used in the p-type silicon to permanently

deactivate BO defects. The results are shown in Figure 3.10. It shows that the minority

carrier lifetime in the wafer does not recover back to the initial carrier lifetime after 350

hours regeneration at 110oC with an illumination intensity of 100mW/cm2 for all 6


101

samples. Niewelt et al. also shows that the regenerated samples are mostly stable under

illumination at room temperature. On the other hand, Sondena et al.[245] also reported

the permanent deactivation of BO in n-type compensated silicon wafers, the wafers

were annealed under 1 sun illumination at 140oC. The lifetime showed a partial

recovery as in the study by Niewelt et al. However, the lifetime showed slight

degradation under 1 sun illumination at room temperature and stabilized afterwards. The

stabilized lifetime is higher than the degraded lifetime. Although there is data on the

impact of BO defects at the wafer level, data at the cell level is scarce. In this chapter,

the permanent deactivation of BO defects in completed n-type compensated silicon

solar cells will be investigated.

Figure 3.10: Lifetime evaluation of the investigated n-type compensated samples [242].

3.6 High efficiency UMG-Si solar cell: fabrication and

analysis

UMG-Si feedstock is a low cost and low energy consumption candidate for PV

applications. As reviewed in section 3.2.3.2, there are a number of technologies

available to purify MG-Si into UMG-Si via the metallurgical routes. Each technology is

developed for a certain type of impurity in the feedstock. The higher impurity content in

UMG-Si feedstock can potentially lead to lower bulk lifetime than EG silicon purified

via the Siemens process. As shown in the evolution of UMG-Si solar cell in Figure 3.8,

the highest efficiency of UMG-Si solar cell reported in the literature up to date is 19.8%


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with a PERT structure. In this chapter, we will illustrate a more sophisticated cell

structure to maintain a high bulk lifetime in UMG-Si solar cells to achieve efficiency

above 20%.

Among various batches of cells fabricated for this study, the initial batches failed for

a number of reasons, for example, breakage of wafers, non-optimized processing

conditions and techniques resulting in low shunt resistance and high series resistance,

and failure in the passivation. The final two batches of cells were more successful. In

this chapter, the results for these two final batches of cells are presented. We call them

batch A and batch B in this chapter.

Batch A does not give a statistical distribution analysis of the cell parameters due to

the smaller number of completed cells. The best cell in this batch has been

independently measured and confirmed. For Batch B, which produced a much larger

number of cells, we will show the statistical distribution of different cell parameters.

3.6.1 Bulk lifetime studies after high temperature process

As mentioned previously, the bulk lifetime is an important parameter affecting the

efficiency of solar cells fabricated on UMG-Si wafers. In order to achieve high

efficiency or comparable efficiency to the same cell structure fabricated on EG silicon,

the bulk lifetime in UMG-Si has to be maintained or improved during the processing.

Boron and phosphorus diffusion are high temperature steps widely used in n-type solar

cell fabrication processing to form the emitter and back surface field (BSF). The bulk

lifetime can be affected significantly after these high temperature processes. Therefore,

it is worth investigating the impact of individual high temperature processes on the bulk

lifetime in the UMG-Si before determining the solar cell structure and fabrication

procedure to be used afterwards.

In this section, the bulk lifetime in the UMG-Si after each high temperature process,

or a combination of the processes, is investigated. In order to monitor possible

contamination during the process, n-type FZ EG and Cz EG control wafers were

included. In addition, two n-type UMG-Si wafers cut from the same ingot but different

locations are used, UMG-S1 stands for the seed position of the ingot with solidification

fraction fs=0.06 and UMG-T1 from the tail of the ingot with fs=0.59. The seed wafer and

tail wafer had different resistivity of 13Ω.cm and 0.82 Ω.cm respectively. The FZ EG

and Cz EG had resistivity of 2.75Ω.cm and 8 Ω.cm. Two sets of these wafers were used


103

in this experiment. The first set of wafers went through a boron diffusion followed by

phosphorus diffusion. The second set of wafers went through phosphorus diffusion (a

pre-gettering), followed by boron diffusion and then another phosphorus diffusion. The

boron diffusion was done at 940oC deposition for 17 minutes and followed by 25

minutes oxidation and 25 minutes nitrogen annealing and cooled in oxygen. The

phosphorus diffusion was done at 790 oC deposition for 25 minutes followed by 900 oC

oxidation and cooled in oxygen. After each process, the samples were etched by

tetramethylammonium hydroxide (TMAH) to remove the boron or phosphorus

diffusions, and then passivated with PECVD SiNx. The same sample was used during

the subsequent process. The bulk lifetime was measured with a Sinton WCT-120

lifetime tester [247].

The measured minority carrier lifetime after each process is shown in Figure 3.11

below for the 4 types of wafers used. The as-cut lifetime is in the millisecond range for

the EG control wafers. For the UMG-Si wafers, the as-cut lifetime is about 300µs, much

lower than the EG controls.

For the first processing sequence, the wafers went through boron diffusion, which is

indicated by B Diff in Figure 3.11. It is obvious that the minority carrier lifetime for all

4 wafers degraded. For the EG wafers, the carrier lifetime dropped from the millisecond

range to several hundreds of microseconds. For the UMG-Si wafers, the lifetime

degraded about 15 times to 10 to 20 µs. The reduction of bulk lifetime after boron

diffusion in both UMG and EG controls indicates some process contamination. In

addition to process contamination, the dramatically lower lifetime in UMG wafers

indicates the additional presence of residual impurities in these wafers that were

activated during the boron diffusion. After the boron diffusion, the samples were then

subjected to phosphorus diffusion, as required to allow ohmic contact to the rear side of

the devices. It is seen that the phosphorus diffusion improves the carrier lifetime

significantly for all 4 wafers, indicated by B Diff-P Diff in the Figure. The minority

carrier lifetime in the EG wafers recovered back to about 1 ms. For UMG-T1, the

lifetime improve to above 100 µs and even above 1 ms for UMG-S1. The recovered

lifetime after phosphorus diffusion is still lower than the as-cut lifetime, except for

UMG-S1.

For the second processing sequence, the wafers were firstly subjected to phosphorus

diffusion prior to boron diffusion, which can be viewed as a pre-gettering step, indicated

by Pre P Diff in the Figure. It is seen that the carrier lifetime improved dramatically


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after the pre-gettering step except for the FZ EG wafer. The lifetime improved to

approximately 10 ms for the Cz EG and 4 ms for the UMG-S1 and 1 ms for UMG-T1. It

shows that UMG-Si has the potential to achieve millisecond range lifetime after

gettering of mobile impurities in the wafers. The data for the pre-gettered wafer after

subsequent boron and phosphorus diffusion is also shown in Figure 3.11, it shows

similar final lifetime compared to process sequence 1 (without pre-gettering). Thus, the

advantage gained from pre-gettering is mostly lost during the subsequent boron

diffusion. Therefore, including pre-gettering in the cell process does not give much

advantage, and complicates the process.

Figure 3.11: Evolution of bulk lifetime in two EG wafers and two UMG-Si wafers after

different combinations of processing sequencing.

Based on the results from the two processing sequences above, it was concluded that

due to gettering of mobile impurities introduced during the boron diffusion or inherent

in the wafer, a process with phosphorus gettering after the boron diffusion is important

for UMG-Si wafers. To maintain a high bulk lifetime in the UMG cells, a relatively

heavy and full area phosphorus diffusion was chosen for the cell process. However, a

heavy phosphorus diffusion will significantly increase recombination on the non-

metallized portion of the rear side, for a device with a full rear-side diffusion, such as


105

the Passivated Emitter and Rear Totally diffused (PERT) cells we have reported

previously on similar material [39]. Therefore, a Passivated Emitter and Rear Locally

diffused (PERL) structure was selected to minimize the area of the diffused regions to

achieve high efficiency UMG-Si solar cells. Crucially, the localization of the diffusion

at the rear is achieved by an etch-back process, instead of being diffused locally into the

contact area, in order to maintain full-area gettering effect. In addition, the heavy local

phosphorus diffusion has the benefit of reducing recombination under the metal contacts,

in comparison to the lighter diffusions usually required for an efficient PERT device.

3.6.2 Cell fabrication process

In the previous sub-section, we have demonstrated the importance of phosphorus

diffusion in the cell process to maintain a high bulk lifetime in UMG-Si wafers. An

etch-back approach is chosen to fabricate PERL cell structure in order to obtain high

efficiency. In this sub-section, the detailed cell fabrication process is discussed. The

schematic representation of the summary of fabrication sequence for PERL cells is

illustrated in Figure 3.12.

The fabrication process starts with a bare n-type silicon wafer as shown in step (1),

during this step, the as-cut silicon wafers are cleaned by standard RCA clean (RCA1

and RCA2), followed by a saw-damage etch using an 85oC, 50% v/v TMAH solution to

remove approximately 5 to 10 µm from each wafer surface. It is then followed by a

random pyramid texturing process (step (2)), the random pyramids are formed in a

TMAH/isopropyl alcohol (IPA) texturing solution. The bare silicon wafers are double-

side textured after this step. A standard RCA clean is performed before the formation of

the boron emitter in step (3). The boron emitter is formed via conventional BBr3 tube

diffusion (step (3)) with the same conditions mentioned in sub-section 3.6.1 for the bulk

lifetime studies. The boron emitter was formed by a full-area boron diffusion with sheet

resistance of approximately 120 Ω/. As well as the texturing, the boron emitter is also

double sided. Therefore, it is important to remove one side of the boron diffusion from

the cells. In order to do so, masking layers are applied to the wafers and one side of the

wafers is protected and the other side of the wafer is left out without protection. The

wafers are then subjected to TMAH etching with the same conditions for the saw-

damage etch to remove approximately 5 µm of silicon on the side without protection.


106

As a result, the boron emitter and texturing are both removed from the rear side as

shown in step (4).

The masking layers are left on the side with the boron diffusion in preparation for the

full-area phosphorus diffusion in step (5). Prior to phosphorus diffusion, the wafers are

RCA cleaned again. Phosphorus diffusion is done via a conventional tube furnace

POCl3 diffusion, with the same conditions as in sub-section 3.6.1. This recipe yields a

sheet resistance of approximately 70 Ω/. In order to pattern the rear side phosphorus

diffusion via photolithography to obtain localized diffusions, masking layers are applied

to the phosphorus diffusion side. In step (6) both the boron emitter side and rear

phosphorus sides are patterned via photolithography. The cell area is defined on the

front surface and is 2 × 2 cm2 in size. The rear localized diffusions were 75 µm diameter

dots with a hexagonal pitch of 300 µm, which was formed by a full-area phosphorous

diffusion and etch back in TMAH solution as shown step (6).

After the patterning in step (6), the masking layers on the front and rear sides are

removed. The front side of the cells is passivated with a SiNx/Al2O3 stack. The Al2O3

film is deposited by Atomic Layer Deposition (ALD) at 200oC and SiNx by PECVD at

400oC. The Al2O3 film is deposited first with thickness of 20 nm and followed by a SiNx

capping layer of about 65 nm as shown in step (7). The passivated cells are then

subjected to a 400oC anneal for 30 minutes in forming gas (FGA) to activate the

passivation of Al2O3 film. The rear passivation layer is a single SiNx film of about 75nm

deposited by PECVD at 400oC in step (8).

Figure 3.12: Schematic representation of the summary of PERL cell fabrication process


107

In step (9), photolithography is utilized again to form the contact openings on both

the front and rear surfaces of the cells. In this case, the SiNx/Al2O3 stack on the front

and the single SiNx layer on the rear work as the masking/patterning layer. The front

finger contact openings were 10 µm wide prior to plating, with a spacing of 1.3 mm.

The rear contact openings were 30 µm in diameter and had the same pitch as the

localized diffusion. The patterned cells are then metallized. The front and rear contacts

are formed by thermal evaporation of Cr/Pd/Ag stacks. The rear side is then thickened

by another run of evaporation of 1.5 µm Ag as shown in step (10). The front fingers are

thickened by Ag electro plating in step (11). The final thickness of the front fingers is

about 35 to 45 µm. The cells are then sintered in FGA at 350oC to form better contact

between the metal-silicon interfaces.

3.6.3 UMG-Si solar cell batch A

Based on the cell fabrication process shown in Figure 3.12 and discussed in sub-section

3.6.2, UMG-Si PERL cells are fabricated. A schematic diagram representing the

structure and different layers of the cell is shown in Figure 3.13 below. In this sub-

section, the results for UMG-Si solar cell batch A are presented.

Figure 3.13: Schematic diagram of n-type UMG silicon solar cell with full front boron

diffusion and rear localized phosphorus diffusion, Al2O3/SiNx stack at the front and

SiNx at the rear side and with Cr/Pd/Ag stacks for both the front and rear metallization.


108

3.6.3.1 Material properties for batch A

For this batch, we have used two different types of n-type monocrystalline silicon

wafers. The first type was from a 9.5kg Czochralski-grown ingot with a diameter of 6

inch, grown with 100% UMG silicon feedstock without adding any electronic-grade

polysilicon feedstock. The second type was from a FZ grown ingot using standard

electronic grade (EG) silicon feedstock. The UMG feedstock was produced by

FerroPem in the framework of the PHOTOSIL project. The wafers had resistivities of 4

Ω.cm (solidified fraction fs=20%) for the UMG material and 1 Ω.cm for the EG wafers.

Table 3.8: Impurities concentration in UMG-Si ingot, all concentrations are in ppb wt.

Element fs = 0,06 fs = 0,32 Element fs = 0,06 fs = 0,32

Na <0,456 <0,442 As <0,074 <0,071

Mg <0,939 <0,909 Sr <0,012 <0,012

Al <1,438 <1,392 Zr <0,014 <0,014

K <0,958 <0,928 Nb <0,002 <0,002

Ca <2,136 <2,068 Mo <0,016 <0,015

P 167.143 204.550 Pd <0,017 <0,017

Ti <0,247 <0,247 Ag <0,118 <0,115

V <0,183 <0,183 Cd <0,042 <0,040

Cr <0,108 <0,105 In <0,004 <0,008

Mn <0,014 <0,013 Sn <0,314 <0,304

Fe <0,487 <0,471 Sb <0,010 <0,010

Co <0,007 <0,007 Ta <0,003 <0,003

Ni <0,069 <0,067 W <0,157 <0,157

Cu <0,225 <0,218 Pt <0,111 <0,107

Zn <0,323 <0,313 Au <0,014 <0,013

Ga 0.041 0.058 Pb <0,013 <0,012

Ge 47.428 51.466

The doping density of both phosphorus and boron within the UMG wafers was

measured by Secondary Ion Mass Spectrometry (SIMS) analysis, showing that the

UMG wafers had a boron concentration [B] = 1.27×1016cm-3 and phosphorus

concentration of [P] = 1.42×1016 cm-3, which results in a net doping of n0 = 1.4×1015cm-


109

3. The oxygen and carbon concentrations of the UMG wafers were [O] = 6.6×1017cm-3

and [C] = 6.1×1016cm-3 respectively. The metallic impurity concentrations were below

the detection limit of Inductively Coupled Plasma Mass Spectrometry (ICPMS) and the

chemical analysis is shown in Table 3.8. The fs of the UMG-Si wafers used in this batch

of cells is in between the fs in Table 3.8 and the impurity concentration is assumed to be

within that range as well. The EG wafers were non-compensated and had a majority

carrier concentration of n0 = [P] = 4.8×1015cm-3, as determined by dark conductance

measurements.

3.6.3.2 Control parameter measurements

Process monitoring is an important part in the fabrication of silicon solar cells, and can

aid in the trouble-shooting if the batch of cells failed or gives unexpected results. The

parameters measured during the fabrication process are also useful in device simulations.

In this sub-section, the control parameters measured for batch A are introduced.

The control parameters we measured were: (1) the diffusion profiles (2) bulk lifetime

of the UMG-Si, since the wafers used in this batch of cell are different from those

studied in sub-section 3.6.1. (3) recombination parameter J0 of the front textured boron

emitter and the J0 for the un-diffused rear side passivated with SiNx. (4) contact

resistivity of the front and rear contacts. In the following sub-sections, the techniques

used for these measurements and the results are discussed.

3.6.3.2.1 Diffusion profiles

It is important to control the diffusion profile accurately. The surface concentration of

the diffusion and the junction depth are critical parameters and affect the efficiency of

silicon solar cells. The surface concentration can affect the passivation and contact

resistivity of the cells. A resonable junction depth is normally required to prevent metal

spiking through the junction, creating an unwanted shunt or other losses. In additon, the

junction depth can also affect the carrier collection efficiency towards the front surface.

In this sub-section, the diffusion profiles for both the boron emitter and the phosphorus

diffusion are measured. The electrochemical capacitance-voltage (ECV) [248]

technique is used.


110

Figure 3.14: Diffusion profiles for the boron and phosphorus diffusions used in the cell

fabrication process.

Figure 3.14 shows the diffusion profile for the front boron diffusion and rear

phosphorus diffusion of the cells on two types of control wafers. To measure the boron

diffusion profile, a planar n-type 100Ω.cm wafer is used. A planar surface is necessary

to ensure the accuracy of ECV measurement. For the phosphorus diffusion, a planar p-

type 100Ω.cm wafer is used. The same control wafers are used again in the contact

resistivity measurements in the later section. The sheet resistance calculated from the

profiles shown in Figure 3.14 are 121.7 Ω/ for boron diffusion and 72.5 Ω/ for

phosphorus diffusion, which are in excellent agreement with the target sheet resistance

we are aiming for this cell structure (120 and 70 Ω/ respectively). The relatively high

surface concentrations from the profiles imply relatively low contact resistance can be

achieved from the metal-silicon interface for both front and rear contacts.

3.6.3.2.2 Bulk lifetime measurements

In order to investigate the impact of high temperature processing (boron and phosphorus

diffusion) on the minority carrier lifetime of the UMG-Si wafers, we used sister wafers

(fs=23%) to the cell wafers (fs =20%). FZ EG control wafers from the same ingot as the

EG cell of resistivity 1 Ω.cm were also included. The samples were TMAH etched after

processing to remove the boron and phosphorus diffusions, and then passivated by

PECVD SiNx. The bulk lifetimes of both samples before and after processing are


111

shown in Figure 3.15. The UMG sample had an initial as-cut lifetime above 1 ms, while

the EG control wafer had an initial as-cut lifetime of several milliseconds. The samples

then underwent boron diffusion. The bulk lifetimes degraded to around 100 µs and 200

µs after boron diffusion for the UMG and EG wafers respectively. The minority carrier

lifetime in both EG control and UMG-Si wafers shows exactly the same behavior as

discussed previously in sub-section 3.6.1. The phosphorus diffusion results in an

increase of the minority carrier lifetime in the UMG-Si wafer close to 1 ms, comparable

to the EG control wafer, showing the advantage of the PERL cell structure with etch-

back for this material.

Figure 3.15: Injection dependent minority carrier bulk lifetime (a) n-type EG 1 Ω.cm

control wafer and (b) n-type UMG Cz silicon wafers in the as-cut state, after boron

diffusion, and after both boron and phosphorus diffusions

3.6.3.2.3 J0 measurements

In order to measure the recombination parameter J0e of the front textured boron emitter

we used 100 Ω.cm n-type control wafers. High resistivity wafers were used to ensure

high injection conditions and low bulk injection dependence during measurement. To

measure the J0 for the un-diffused rear side passivated with SiNx we used sister wafers

to those used for cells. The equation to extract J0 is given by [249]:


112

1

𝜏𝑒𝑓𝑓=

1

𝜏𝑏𝑢𝑙𝑘+ 2𝐽0

𝑛

𝑞𝑛𝑖2𝑊

+ 𝐶𝐴𝑛2

(3.19)

Where CA is the auger coefficient, which is 1.66×10-30 s-1cm6 [250] used in the Sinton

lifetime tester, W is the thickness, ni is the intrinsic carrier concentration. n is the total

carrier concentration. Equation (3.19) can be transformed into:

1

𝜏𝑒𝑓𝑓− 𝐶𝐴𝑛2 = 2𝐽0

𝑛

𝑞𝑛𝑖2𝑊

+1

𝜏𝑏𝑢𝑙𝑘

(3.20)

It is seen that by subtracting the auger term from the inverse effective lifetime in

equation (3.19), J0 can be extracted from the slope when plotting against the total carrier

concentration that is the sum of base doping Ndop and excess carrier density Δn. For

relatively lightly doped samples, the J0 can be measured in high injection, therefore,

Ndop + Δn ≈ Δn.

Figure 3.16: J0e measurement and fitting for the front textured boron emitter


113

The emitter saturation current J0e for the front boron diffusion is measured by the

photoconductance decay technique with a Sinton lifetime tester [247, 251]. The 100

Ω.cm n-type control wafers used went through the same texturing and diffusion steps as

in the cell process to replicate the real cell conditions. The control wafer is diffused on

both sides and passivated with the same SiNx/Al2O3 stack as for the cells. The results

and the fitting are shown in Figure 3.16. The 2J0e obtained from the slope in Figure 3.16

is 91.5 fA.cm-2, which is for double side diffusion. Thus, the emitter saturation current

J0e for the diffusion in the cells is 45.8 fA.cm-2. The J0e measured on the control wafer

gives the expected value for Al2O3 passivation on the boron emitter formed with the

recipe used. It indicates that the passivation qualities on the cells are within our

expectations. This value is also important for the cell simulation that will be discussed

in the later sections.

In addition to the J0e fitting shown above, the recombination parameter for the rear

un-diffused surface is also measured. Sister wafers with similar resistivity to the cells

are used in this measurement. Figure 3.17 (a) and (b) shows the recombination

parameters for both the FZ EG control wafer and Cz UMG-Si wafer, respectively. The

fittings shown in Figure 3.17 give J0 surface of 3.3 fA.cm-2 and 3 fA.cm-2 for the FZ EG

control wafer and the Cz UMG-Si wafer. The measured J0 values indicate excellent

passivation achieved with SiNx on n-type surfaces. The passivation on the cells is

expected to be of high quality. These values will also be used in the cell simulations

presented below.

(a) (b)

Figure 3.17: J0 measurement and fitting (a) for the rear side un-diffused surface of FZ

EG control cell. (b) for the rear side un-diffused surface of Cz UMG-Si cell


114

3.6.3.2.4 Contact resistivity measurements

Contact resistivity, quantifies resistive losses at the metal-silicon interface. The contact

resistivity ρc, also called the specific contact resistance, is defined by [252]:

𝜌𝑐 = (𝜕𝐽

𝜕𝑉)

−1

|𝑉=0

(3.21)

The contact resistance will contribute to the lumped series of the solar cell and influence

the FF through resistive losses. Thus, it is an important parameter to control and

measure during the cell fabrication process. For heavily doped surfaces, for instance the

phosphorus diffused rear side and boron emitter, the contact resistivity is governed by

tunnelling effects rather than thermal emission of carriers, which depends on the work

function of the metal [252, 253]. Therefore, the contact resistivity on heavily doped

silicon surfaces is expected to be very low with minimal impact on the lumped series

resistance. In this sub-section, the contact resistivity for the front fingers and the rear

side dot contact is measured by the Transfer Length Method (TLM) [252, 254].

Figure 3.18: Schematic representation of the test structure used to measure ρc

The TLM structure used in this experiment is shown in Figure 3.18 . For contact

resistivity on the boron emitter, an n-type 100Ω.cm control wafer is used. The wafer is

planar, which ensures the width (W) in Figure 3.18 is measured correctly and we do not

underestimate ρc resulting from any uncertainty of the area under the metal pads. The

wafer is diffused with boron to form the same emitter as the cells. Resistance between


115

the pads is measured using a Keithley 2400 source meter. For the ρc measurement on the

boron emitter, a 100Ω.cm n-type wafer is used. for the ρc on the phosphorus diffusion,

a p-type 100Ω.cm control wafer is used. The metallization is performed by thermal

evaporation of a Cr/Pd/Ag stack to replicate the real cell conditions.

The ρc is calculated by plotting the measured resistances between the metal pads

against the spacing between the pads, that is, L1, L2 etc. in Figure 3.17. The calculation

of ρc is given by:

𝜌𝑐 = 𝐿𝑇

2 × 𝑠𝑙𝑜𝑝𝑒 × 𝑊

(3.22)

Where LT is called the transfer length calculated by the intercept of a fitted line with the

x-axis (y=0). The measurement results are shown in Figure 3.19.

The ρc measured for the front and rear contacts are 0.06 mΩ.cm2 and 0.024 mΩ.cm2,

respectively. These low contact resistivity values are expected on the heavily diffused

surfaces. It is therefore concluded that if the diffusion in the cell batch is uniform and

also uniform on every cell, the contact resistance will be negligible in its impact on the

lumped series resistance.

Figure 3.19: Contact resistivity for both front and rear contact on boron and phosphorus

diffusions respectively


116

3.6.3.2.5 Summary of control parameters

The control parameters measured for batch A are introduced through sub-section

3.6.3.2.1 to sub-section 3.6.3.2.3 , and are summarized in Table 3.9.

Table 3.9: Summary of control parameters measured during the cell fabrication process

Parameters Values Control

Wafers Process involved

Surface

Conditions

Boron

Diffusion

Profile

- n-type

100Ω.cm BBr3 Planar

Phosphorus

Diffusion

Profile

- p-type

100Ω.cm POCl3 Planar

τbulk for FZ

EG 856.64 µs Sister

Wafers

BBr3 followed by POCl3

(Diffusions are removed

after each process)

Planar with

PECVD SiNx τbulk for Cz

UMG-Si 703 µs

J0e 45.8 fA.cm-2 n-type

100Ω.cm

Texturing followed by

BBr3 (Diffusion is not

removed)

Textured with

SiNx/Al2O3 stack

J0-undiffused for

FZ EG 3.3 fA.cm-2 Sister

Wafers

As-cut Planar with

PECVD SiNx J0-undiffused for

UMG-Si 5 fA.cm-2

ρc for front

contact 0.06 mΩ.cm2

n-type

100Ω.cm

BBr3 followed by

metallization

Planar with p+

diffused surface

ρc for rear

contact 0.024 mΩ.cm2

p-type

100Ω.cm

POCl3 followed by

metallization

Planar with n+

diffused surface


117

3.6.3.3 Batch A cell results

In the previous sections, the material properties for the wafers used in batch A and the

control parameters measured to monitor the fabrication process have been discussed.

The measured control parameters are within our expectations. In this section, the cell

results for Batch A are presented. Only the results for the best cell from both the FZ EG

control group and Cz UMG-Si group are shown. The statistical analysis of the cells

efficiency and cell parameters is not included due to the small number of completed

cells.

The light I-V measurements, external quantum efficiency (EQE), reflectance and

internal quantum efficiency (IQE) will be presented. In addition, other cell parameters,

for example, shunt resistance (Rsh) and lumped series resistance (Rs) at maximum power

point are also analysed by dark IV with the two diode model [255, 256] and Suns-Voc

measurements [257, 258], respectively.

3.6.3.3.1 I-V measurements

The efficiencies as well as the illuminated current-voltage characteristics of the best n-

type Cz UMG-Si cell and the best n-type FZ EG cell were independently measured at

Fraunhofer CalLab. The confirmed efficiencies are 20.96% and 21.91% for the UMG

and EG cells, respectively. This is the highest efficiency reported to date for a cell made

from 100% UMG silicon. The I-V curves measured are plotted in Figure 3.20. The

thickness, dopant concentrations, and net doping n0 (n0 = [P] – [B] for UMG material)

of the cells and the details of the extracted cell parameters from the I-V curves are

shown in Table 3.10.

From the I-V curves shown in Figure 3.20 and the extracted cell parameters shown in

Table 3.10, the higher efficiency from the FZ EG cell is mainly contributed from the

higher Voc and FF. The higher Voc in the EG cell is expected considering its higher net

doping density compared to the UMG-Si wafer as shown in Table 3.10 .


118

Figure 3.20: Illuminated I-V measurements of the best n-type Cz UMG-Si and FZ EG

cells, measured at Fraunhofer CalLab

Table 3.10: Summary of the cell parameters for the best n-type Cz UMG-Si and FZ EG

cells

Parameters n-type Cz UMG-Si n-type FZ EG

[P] (cm-3) 1.42×1016 4.8×1015

[B] (cm-3) 1.27×1016 -

n0(cm-3) 1.4×1015 4.8×1015

W (µm) 150 170

Finger spacing (mm) 1.3 1.3

Finger opening (µm) 10 10

Finger width (µm) 40 40

Rear Diffusion dot diameter (µm) 75 75

Rear Contact opening diameter (µm) 30 30

Jsc (mA.cm-2) 40.23 39.89

Voc (mV) 672.6 686.2

FF (%) 77.5 80.1

Jmpp (mA.cm-2) 37.03 37.03

Vmpp (mV) 566.1 591.69

η (%) 20.96 21.91


119

3.6.3.3.2 EQE and reflectance measurements

The Quantum Efficiency (QE) is a useful measurement to understand the origin of

losses in cells. The External Quantum Efficiency (EQE) is the ratio of the number of

carriers collected by the solar cell to the number of photons of a given energy incident

on the solar cell. The Internal Quantum Efficiency (IQE) is the ratio between collected

carriers to the number of photons absorbed by the cell. Therefore, EQE and IQE are

related by the reflectance of the solar cells. One can be corrected by the reflectance

measurements to obtain the other. In this sub-section, the EQE, reflectance and IQE for

the cells are discussed together with the Jsc to show that the lower minority carrier

mobility and lower lifetime does not affect the current of the UMG-Si solar cell in this

batch.

The EQE, IQE and reflectance data for both the UMG and EG cells are shown in

Figure 3.21 below. The EQE data is independently measured by Fraunhofer CalLab and

the reflectance data is measured by a spectrophotometer. The IQE is calculated based on

the EQE and front reflectance (The escape reflectance is subtracted from the front

reflectance for this calculation) according to:

𝐼𝑄𝐸 =𝐸𝑄𝐸

1 − 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑎𝑛𝑐𝑒𝑓𝑟𝑜𝑛𝑡

(3.23)

The EQE and reflectance measurements for the best cells are shown in Figure 3.21

(a). These reveal a slightly higher EQE for the UMG cell in the wavelength range from

300 to 900nm, especially in the range from 300nm to 600nm. This difference results

from a slight difference in the random texturing at the front surface and minor variations

in the thickness of the SiNx capping layer on the front surface. To confirm this, the

reflectance of both cells was measured. Figure 3.21 shows the reflectance measurements

for both UMG and EG cells. It confirms that the reflectance for the EG cell is slightly

higher than the UMG cell in the range from 300nm up to 900 nm. Of particular note is

the fact that the UMG and EG cells are almost identical in their EQE in the long

wavelength range between 900nm to 1200nm. This indicates that the minority carrier

diffusion length is significantly larger than the wafer thickness for both the UMG and

EG cells, despite the expected impact of the strong dopant compensation on the carrier

mobilities in the UMG material. Based on the carrier lifetimes in Figure 3.15, the


120

minority carrier diffusion lengths for the UMG and EG cells are estimated to be 695 µm

and 1018 µm, with minority carrier mobilities estimated using Schindler’s model [45] of

372 cm2V-1s-1 and 399 cm2V-1s-1. These diffusion lengths are more than three times the

device thickness, resulting in almost complete carrier collection at the front junction.

(a) (b)

Figure 3.21: (a) EQE measurements of the best n-type UMG Cz and EG FZ cells

(measured at Fraunhofer CalLab) also shown is the Reflectance for both cells. (b) IQE

calculated based on EQE and reflectance for both cells.

Figure 3.21 (b) shows the IQE calculated from the EQE and front reflectance data for

both cells. It shows that, by neglecting the difference in reflectance between the two

cells, the IQE of the UMG and EG cells are identical between 400nm to 600nm. It

further confirms the fact that the difference in currents between the cells is related to the

optics of the front surface, either from the SiNx capping layer or a difference in random

pyramid texturing. The compensation of the UMG-Si does not affect the current of the

solar cell in this case.

3.6.3.3.3 Rsh measurements

A shunt resistance provides an alternate current path for the light-generated current.

This type of diversion reduces the amount of current flowing through the solar cell

junction and thus reduces the voltage from the solar cell and the fill factor. The presence

of a shunt resistance can cause significant power losses, which is normally modelled as

a resistor parallel to the diodes and current source in a two diode model. Therefore, the


121

impact of a shunt resistance is large at lower voltages where the effective resistance of

the solar cell is high. In this sub-section, Rsh is obtained by fitting the dark-IV curve

with the two diode model for both cells. A schematic representation of the two diode

model is shown in Figure 3.22.

Figure 3.22: Schematic representation of the two diode model

In Figure 3.22, the components denoted by J01 and J02 are diodes with ideality factor

of 1 and 2 respectively. Rsh is the shunt resistor and Rs is the series resistor. JL is the

light-generated current. The component of a resistor denoted by RH in series with a

diode titled J0H is defined as the region of high recombination [255]. From a real solar

cell point of view, J0H represents the high recombination that occurs at the edge of the

solar cell, and the resistor RH represents the resistance between the peripheral fingers

and the edge. Using this two diode model, the shunt resistance can be simply obtained at

the low voltage part of the dark-IV curve.

Figure 3.23 (a) and Figure 3.23 (b) show the fitting of the dark-IV curve with this

model for the EG and UMG cells.

(a) (b)

Figure 3.23: (a) Fitting the two diode model with dark-IV curve for n-type FZ EG solar

cell. (b) Fitting of two diodes model with Dark-IV curve for n-type Cz UMG-Si solar

cell.


122

For the EG cells, the two diode model can fit the dark-IV in the voltage range

provided, which is the range for a normal silicon solar cell. The shunt resistance mainly

affects the lower voltage part of the curve, which is about 0 to 0.2V. The shunt

resistance obtained from the fitting the EG cell is about 5000 Ω.cm2, which is large

enough to have no effect on the FF of the cell. Figure 3.23 (b) shows the fitting for the

UMG cell, the shunt resistance is approximately 8000 Ω.cm2. Again, the shunt

resistance in this cell is large enough to have no effect on the FF. However, the edge

recombination components denoted by H is dominating both cells from low voltage up

to 500mV, which can potentially affect the FF.

Overall, the high shunt resistance obtained for both cells means that they have

negligible impact on the FF. The lower FF in the UMG cell compared to the EG cell is

not due to shunt resistance. In the next sub-section, the lumped series resistance at the

maximum power point of the cells is calculated.

3.6.3.3.4 Rs measurements

The lumped series resistance quantifies resistive losses in silicon solar cells. A high

series resistance reduces the voltage at maximum power point and thus decreases the FF,

hence it is a critical parameter. Rs can come from different sources in the solar cell: the

base resistance, the lateral resistance in the emitter (sheet resistance), the resistive losses

between the metal-silicon interfaces for the front and rear contacts, as well as the

resistance of the front and rear contact themselves. In this sub-section, Rs in the cells is

calculated by a combination of Suns-Voc measurements and I-V measurements. The

potential sources of series resistance for batch A are discussed.

There are numerous methods to calculate the lumped series resistance at maximum

power point [258]. In this section, the lumped Rs is calculated by comparing the series

resistance from Suns-Voc measurement, also called the Jsc-Voc measurement [255, 257],

with the actual light I-V curve of the solar cells at maximum power point. The series

resistance can be extracted as:

𝑅𝑠 =∆𝑉

𝐽𝑚𝑝𝑝

(3.24)


123

Where ΔV is the difference in voltage of the Suns-Voc curve and actual I-V curve at

maximum power point. This method is also illustrated in Figure 3.24 below.

(a) (b)

Figure 3.24: Suns-Voc and light I-V curve for lumped series resistance calculation at the

maximum power point for n-type (a) FZ EG cell And (b) Cz UMG cell

Based on the method introduced above, the lumped Rs can be extracted from the light

I-V curves shown in Figure 3.24 for both EG and UMG cells. It is clear from the figure

that the difference between the Suns-Voc curve and actual I-V curve is small for the EG

cell, however, for the UMG cell, the difference is obvious. Another important parameter

that can be extracted from the Suns-Voc curve is the pseudo fill factor (PFF), which

accounts for all the recombination in the solar cell as well as shunt resistance, but

excludes series resistance. The PFF measured by Suns-Voc is 81.5% for EG cell and

82.2% for UMG cell. The much lower FF on UMG cell indicates a relatively large Rs in

the cell. The lumped Rs calculated is 0.35 and 0.77 Ω.cm2 for EG and UMG cells,

respectively. As expected, Rs is two times higher in UMG than EG cells and greatly

reduces the FF. The base resistivity of the cells is unlikely to contribute such difference

in Rs between the UMG and EG cells. The front and rear side diffusions of the EG and

UMG cells are processed in the same batch and should not result in much variation. The

contact formation is also done in the same batch. One potential source of the series

resistance in this batch of cells is from the Ag electro-plating of the cells. Peeling off of

fingers was observed after plating in some of the cells in this batch. It indicates that the

surface condition of the fingers before Ag electro-plating may not have been well

controlled. Residues from the previous photolithography step can potentially affect the

plating quality. In the next batch of cells (Batch B), an optimized process before Ag


124

electro-plating is developed. The results show a significant improvement in FF leading

to an efficiency above 21%. The detailed results will be shown in later sections. The

shunt resistance, series resistance and PFF calculated for Batch A are summarized in

Table 3.11.

Table 3.11: Shunt resistance, series resistance and PFF for EG and UMG cells

Parameters For n-type Cz UMG-Si n-type FZ EG

Shunt resistance (Rsh) 8000 Ω.cm2 5000 Ω.cm2

Lumped series resistance (Rs) 0.77 Ω.cm2 0.35 Ω.cm2

PFF 82.2% 81.5%

3.6.3.4 Permanent deactivation of BO defects at the cell level

As reviewed in section 3.5, BO defects have been studied on both p-type and n-type

compensated silicon for several years. In compensated n-type, LID still exists.

Deactivation in the dark can recover the minority carrier lifetime, however, it is not

stable subjected to further illumination. Hence there is a strong interest in finding

approaches to permanently deactivate BO defects in compensated n-type silicon. Stable

permanent deactivation has been demonstrated in p-type silicon at the wafer and cell

level. For n-type compensated silicon, studies have so far only been conducted on

lifetime samples, and there is no data available on BO defects at the cell level. In this

section, we present the permanent deactivation of BO defects on the high efficiency

UMG-Si solar cells fabricated in batch A.

The Voc evolution of the cells is shown in Figure 3.25. For the defect activation stage,

the Voc of the UMG cells degraded by approximately 17 mV over 200 hours

illumination at an intensity of 1 sun, while the EG control cell did not experience any

degradation, as expected. The regeneration was then performed at four different

temperatures ranging from 130oC to 200oC under an illumination intensity of 3 suns.

The Voc improvements increased with increasing temperature. The cell annealed at

130oC (Cell 3) did not see significant improvement. However, Cell 3 showed fast

improvement during subsequent annealing at 200oC. The same control cell was used

for all the processes and only experienced slight degradation during the final 200oC

annealing. The stability of the regenerated cells was then tested under 1 sun light


125

intensity over 200 hours. Cell 3, which was regenerated at 200oC, showed fast

degradation back to the level of the degraded cells under illumination. Cell 1, which

was regenerated at 150oC, did not show any degradation and remained at approximately

655mV. Cell 2 degraded slightly and saturated at the same level as Cell 1.

Figure 3.25: The Voc evolution due to the boron-oxygen related defect of 3 investigated

UMG Cz Cells through 3 different stages: First light soaking at room temperature

(activation stage), Light soaking at elevated temperature (regeneration stage) and

second light Soaking at room temperature (stability test).

As shown in section 3.5, Munzer [240] and Herguth et al. [241] reported regeneration

of the BO defect in p-type silicon solar cells at 50 to 75 oC, and showed that the

regenerated cells had similar Voc and efficiencies as the cells before degradation. The

cells were stable under illumination of 1 sun intensity over 200 hours. However, from

Figure 3.25, it can be seen that the Voc of the regenerated cells cannot be recovered to

the initial value. Niewelt et al. [242] used n-type compensated wafers with similar

oxygen, boron and phosphorus concentrations for a regeneration experiment, and

showed on lifetime structures that the regeneration cannot recover the bulk lifetime to

the initial level with non-optimized curing conditions. The non-optimized temperature

and illumination intensity could therefore explain the partial recovery of Voc in this

study. The slight degradation of Cell 2 and complete degradation of Cell 3 during the

stability test agrees with the study by Sondena et al. [245] and could also be related to

the non-optimized curing conditions. As suggested by Wilking et al. [243], when


126

starting from a fully degraded state, the reactions creating the annealed state and

permanently deactivated state of the BO defect are competing reactions. Their kinetics

depends on the temperature. If the temperature is too high, the kinetics of the reaction

creating the annealed state will be faster than the reaction producing the permanently

deactivated state. Hence most of the BO defect will transform into the annealed state

rather than the permanently deactivated state. This is likely to be the reason that Cell 2

and Cell 3 degraded during the final stability test. The reason for the much faster

degradation rate of Cell 3 during the light soaking after permanent deactivation

compared to the initial light soaking is still unclear.

Various authors have proposed physical explanations of the regeneration process,

Voronkov et al. [259] suggested the regeneration process was due to a loss of interstitial

boron to boron nano-precipitates during simultaneous annealing and illumination. Upon

subsequent illumination no interstitial boron is present and therefore no recombination

active BO can form. In contrast, Hallam et al. [244] and Munzer [240] proposed that the

regeneration is caused by the hydrogenation of BO defects, and controlled by the charge

state of hydrogen, which is strongly related to temperature and illumination intensity, as

also proposed by Sun et al. [260]. Whichever model is correct, our results indicate that

the permanent deactivation of the defect can be partially achieved at the cell level on

compensated n-type devices, and we expect with further optimisation of the curing

conditions, more complete deactivation can be achieved.

3.6.3.5 UMG-Si solar cells batch B

Previously, we have shown the cell results for Batch A. The best UMG cell and EG cell

were 20.96% and 21.91% respectively. The efficiency of the UMG cell was strongly

affected by the FF. From various control data and analysis on the cell, it is found a non-

optimal Ag electro-plating potentially plays a role in the increased series resistance and

lower FF measured. In this section, we present results of subsequent batch of n-type Cz

UMG-Si solar cells, which uses the same design and recipe in batch A. In addition, the

metal surface before-electro plating is optimized with a careful cleaning process to

avoid finger peeling and reduce the series resistance. A UMG cell above 21% is

achieved with an improved FF. The statistical distribution of the cells in this batch will

also be discussed.


127

3.6.3.5.1 Material properties for batch B

As in batch A, we have used two different types of n-type monocrystalline silicon

wafers in this batch. The first type was from 100% UMG silicon feedstock without

adding electronic grade polysilicon feedstock using the Czochralski process. The second

type was from a Float-Zone (FZ) grown ingot using standard electronic grade (EG)

silicon feedstock. The UMG feedstock was produced by FerroPem in the framework of

the PHOTOSIL project. The wafers had resistivities of 0.6 Ω.cm (Middle of the ingot,

solidified fraction fs=60%) and 4 Ω.cm for the UMG materials. The UMG wafers with

0.6 Ω.cm resistivity used in this batch are from a different ingot used in batch A. The 4

Ω.cm wafers are sister wafers to the wafers used in batch A. The FZ EG wafers used in

this batch are sister wafers to the 1 Ω.cm wafers from batch A. However, there was only

a limited number of these wafers left. In order to avoid the risk of breakage, FZ EG

wafers from a different ingot with resistivity of 3.5 Ω.cm were also included. These

wafers were used as a backup for the 1 Ω.cm FZ control cells.

The doping density of both phosphorus and boron was measured by Secondary Ion

Mass Spectrometry (SIMS) analysis, showing that the UMG wafers had a boron

concentration [B] = 1.0×1016cm-3 and phosphorus concentration of [P] = 2.1×1016 cm-3,

which results in a net doping of n0 = 1.1×1016cm-3. The oxygen and carbon

concentrations of the UMG wafers were [O] = 5.4×1017cm-3 and [C] = 1.4×1017cm-3.

The EG wafers were non-compensated and had a majority carrier concentration of n0 =

[P] = 1.29×1015cm-3 for 3.5 Ω.cm, as determined by dark conductance measurements.

3.6.3.5.2 Control parameters for batch B

The control parameters for this batch of cells were measured. The same recipes for

boron and phosphorus diffusions were used in this batch. The resulting doping profiles

were very close to the ones shown in Figure 3.14. The evolution of minority carrier

lifetime after each high temperature process for 0.6 Ω.cm n-type Cz UMG-Si wafer is

shown in Figure 3.26 below.

The evolution of the injection dependent minority carrier lifetime in Figure 3.26

shows similar behaviour as shown previously. The final lifetime after phosphorus

diffusion is slightly higher than the as-cut state at a doping density of 0.1×n0. The

evolution of the lifetime for this type of UMG wafers were performed in the same time


128

as the wafers used in batch A. Therefore, the lifetime control experiments were not

performed for batch B. The data for the evolution of minority carrier lifetime for the FZ

EG 3.5 Ω.cm wafers is not available. The rear side J0 for the un-diffused surface of the

0.6 Ω.cm UMG wafers is about 7 fA.cm-2 and for the boron emitter is 60 fA.cm-2, which

are slightly higher than in batch A. The contact resistivity measured for the boron and

phosphorus diffused surfaces are 0.04 mΩ.cm2 and 0.05 mΩ.cm2, which is in the same

order of magnitude as measured in batch A. All the measured cell parameters are

summarized in Table 3.12.

Figure 3.26: Injection dependent minority carrier bulk lifetime for n-type UMG Cz 0.6

Ω.cm silicon wafers in the as-cut state, after boron diffusion, and after both boron and

phosphorus diffusions

Table 3.12: Summary of control parameters measured during the cell fabrication process

Parameters Values

τbulk for Cz UMG-Si 300 µs

J0e 60 fA.cm-2

J0-undiffused for UMG-Si 7 fA.cm-2

ρc for front contact 0.04 mΩ.cm2

ρc for rear contact 0.05 Ω.cm2


129

3.6.3.5.3 Batch B cell results

The efficiency of the best UMG solar cell is higher than the best FZ EG cell. Hence,

only the result for the best UMG solar cell is shown. The best UMG solar cell is based

on the 0.6 Ω.cm n-type Cz UMG-Si wafer. The results for the rest of the cells in this

batch including both UMG and EG cells will be shown in the later sections when

discussing the statistical distributions.

Figure 3.27: In-house illuminated I-V measurements of the best n-type 0.6 Ω.cm Cz

UMG-Si in Batch B

The efficiency as well as the illuminated I-V curve for the best n-type Cz UMG-Si

solar cell is done via in-house measurement. The efficiency for the best UMG cell

measured is 21.64%, which is the best cell we fabricated among various batches. The I-

V characteristic of this cell is shown in Figure 3.27. The extracted cell parameters from

the I-V curve are shown in Table 3.13, the higher efficiency from this cell is mainly due

to the higher FF. The higher FF will be analysed in the following sections from dark-IV

and Suns-Voc measurements.

The cell parameters for the best UMG solar cell from batch A are also included for

comparison. It is seen that the 21.64% cell has higher net doping than the 20.96% cell


130

from Batch A. However, the Voc are very similar to each other. This may result from

the slightly higher J0 and the lower bulk lifetime and thus lower Δn in this wafer, which

is about 2.5 times less in the 0.6 Ω.cm UMG. These factors will be evaluated in the

simulation of these cells in the later sections.

The EQE, IQE and reflectance for the best UMG cell from batch B are shown in

Figure 3.28. The best UMG cell from the previous batch is also included for comparison.

It is clear from Figure 3.28 (a), that the measured reflectance is identical between the

best UMG cells from batch A and B. The measured EQE for the 0.6 Ω.cm UMG cell

(in-house measurement) is slightly higher in the wavelength between 300 nm to 400 nm

and slightly lower at 400 nm to 500nm. The slight variation of EQE in the short

wavelength indicates that the emitter boron diffusion may differ slightly given identical

reflectance measurements between the two cells. The main difference in EQE is at

800nm to 1050nm, the IQE for 0.6 Ω.cm UMG cell is much lower than the 4 Ω.cm

UMG cell, which is the main reason for the lower current in this batch. The lower EQE

in this range is mainly due to the lower minority carrier diffusion length 530µm for

batch B UMG cell comparing to 695µm for batch A UMG cell. The diffusion length is

3.3 and 4.6 times of the thickness of the cells, respectively. In addition, the slightly

higher rear side J0 surface can also contribute to this reduction. The lower EQE directly

translated into the lower IQE shown in Figure 3.28 (b).

(a) (b)

Figure 3.28: (a) EQE measurements of the best n-type 4 Ω.cm UMG Cz and 0.6 Ω.cm

also shown is the Reflectance for both cells. (b) IQE calculated based on EQE and

reflectance for both cells.


131

Series and shunt resistances of the 21.64% UMG cell are analyzed using the Suns-Voc

and Dark-IV measurements. The two diodes model fit to the dark IV is shown in Figure

3.28 and the Suns-Voc data is shown in Figure 3.29. Rsh, Rs and PFF obtained from the

measurements are summarized in Table 3.13.

The fit of the Dark-IV in Figure 3.29 reveals that the shunt dominates as opposed to

the region of high recombination. The shunt resistance obtained in this case is large

enough to have very little influence on the FF.

The Suns-Voc curve is shown in Figure 3.30. The illuminated I-V curve is almost

identical to the Suns-Voc curve, the lumped series resistance at maximum power point

obtained is 0.05 Ω.cm2.

Table 3.13: Summary of the cell parameters for the best n-type Cz UMG-Si from batch

A (Independently confirmed) and batch B (In-house measurement)

Parameters Batch B best UMG Batch A best UMG

[P] (cm-3) 2.1×1016 1.42×1016

[B] (cm-3) 1.0×1016 1.27×1016

n0(cm-3) 1.1×1016 1.4×1015

W (µm) 160 150

Jsc (mA.cm-2) 39 40.23

Voc (mV) 671 672.6

FF (%) 82.7 77.5

Jmpp (mA.cm-2) 37.39 37.03

Vmpp (mV) 578.8 566.1

η (%) 21.64 20.96

Shunt resistance Rsh (Ω.cm2) 7000 8000

Lumped series resistance Rs (Ω.cm2) 0.05 0.77

PFF 83.1% 82.2%


132

Figure 3.29: Fitting of two diodes model with Dark-IV curve for n-type 0.6 Ω.cm Cz

UMG-Si solar cell from batch B.

Figure 3.30: Suns-Voc and actual illuminated I-V curve for lumped series resistance

calculation at the maximum power point for n-type 0.6 Ω.cm Cz UMG-Si solar cell

from batch B.


133

3.6.3.5.4 Statistical distribution

In this section, we present a statistical analysis of the distribution of cell parameters for

batch B. The analysis for each parameter is categorized according to the type of wafers

used and the resistivity of the wafers. Therefore, there are four categories in total: n-type

0.6 Ω.cm Cz UMG-Si, n-type 4 Ω.cm Cz UMG-Si, n-type 3.5 Ω.cm FZ EG-Si and n-

type 1 Ω.cm FZ EG-Si. The analysis is based on box plots, which show the maximum,

minimum, and mean values for each category. In addition, the median, 25% percentile,

and 75% percentile are also shown. There are 12 cells in total for the UMG 0.6 Ω.cm

category, 27 cells for UMG 4 Ω.cm, 8 cells for EG 3.5 Ω.cm and 10 cells for EG 1

Ω.cm. The box plots for Voc, Jsc, FF and efficiency are shown in Figure 3.31 below.

(a) (b)

(c) (d)

Figure 3.31: Box plots for the statistical distribution of n-type 0.6 Ω.cm Cz UMG-Si, n-

type 4 Ω.cm Cz UMG-Si, n-type 3.5 Ω.cm FZ EG Si and n-type 1 Ω.cm FZ EG Si. (a)

Analysis for Voc. (b) Analysis for Jsc. (c) Analysis for FF. (d) Analysis for Efficiency.


134

Figure 3.31 (a) illustrates the distribution of Voc for the four different categories of

cells. Where IQR stands for the inter quantile range, that is, the difference between 75%

percentile and 25% percentile. The whisker of the box plot is extended to the largest

data within 1.5 times IQR. Thus, any data point out of that range is considered as

outliers. It is seen that the IQR for the Voc plot has large spread in the categories of

UMG 4 Ω.cm, EG 3.5 Ω.cm and EG 1 Ω.cm than UMG 0.6 Ω.cm. The larger spread

can be explain by the net doping of these three categories, the net doping is in the range

of 1.29×1015 cm-3 to 5×1015 cm-3 range for these three categories (≥ 1 Ω.cm cells) and

the 0.6 Ω.cm UMG wafer has higher net doing in the order of 1016 cm-3. Moreover,

according to equation (3.18), the Voc is determined by the combination effect of net

doping n0 and excess carrier density Δn. By using equation (3.18), we can calculate Δn

in these cells from the known n0 at Voc. It is found that Δn is in the range of 1×1015 cm-3

to 3×1015 cm-3 for all the four categories, which is very close to the doping density of

these three categories (≥ 1 Ω.cm cells) of cells. Therefore, the dependence of Voc on Δn

is in the form of (Δn)2 instead of Δn in the case of 0.6 Ω.cm UMG. It indicates that Voc

is sensitive to the change in the recombination activities. A slight difference between the

bulk lifetime or J0 of the emitter or rear surface will lead to the change in the effective

carrier lifetime and thus affect Δn. It will then be translated into the large spread in Voc.

Overall, the EG 1 Ω.cm cells have higher average Voc than the three other cell categories.

For the distribution of short circuit current Jsc, the EG 3.5 Ω.cm category has lower

spread. The rest of the categories have similar and larger spread. The difference

between the EG 3.5 Ω.cm cell to the rest of the cells is the thickness, 240 µm comparing

to 150 to 170 µm. This can be the potential reason that this category has higher average

current than the rest of the categories.

As explained above, the FF can be affected by various factors, for instance, series

resistance, shunt resistance, injection dependence of minority carrier lifetime and

recombination activities in the cell. If the outliers are excluded in the box plot, the IQR

range for the UMG cells and EG 3.5 Ω.cm is similar. EG 1 Ω.cm category has slightly

wider spread in FF.

Overall, the distributions of the efficiency for the three categories expect EG 1 Ω.cm

category has similar and narrow spread. The long whisker in the EG 1 Ω.cm category is

caused by the outliers. The statistics of the distribution for these parameters above are

summarized in Table 3.14.


135

Table 3.14: Statistics of the distribution of cell parameters

n-type 0.6

Ω.cm Cz

UMG

n-type 4

Ω.cm Cz

UMG

n-type 3.5

Ω.cm FZ

EG

n-type 1

Ω.cm FZ

EG

n-type 1

Ω.cm FZ

EG

(without

outlier)

Voc

(V)

Mean 0.669 0.659 0.664 0.678 0.681

s* 0.003 0.01 0.003 0.011 0.007

Max 0.673 0.674 0.668 0.692 0.692

Min 0.665 0.641 0.661 0.652 0.675

Jsc

(mA/cm2)

Mean 38.74 38.89 39.61 38.69 38.93

s 0.45 0.35 0.13 0.58 0.39

Max 39.33 39.45 39.75 39.32 39.32

Min 37.81 38.31 39.41 37.4 38.43

FF

(%)

Mean 80.5 78.1 79.5 74.9 78.8

s 1.7 1.8 1.4 8.0 2.0

Max 82.7 80.9 81.2 80.7 80.7

Min 76.9 73.3 76.8 58.0 74.6

Efficiency

(%)

Mean 20.8 20.02 20.9 19.67 20.92

s 0.55 0.5 0.37 2.26 0.72

Max 21.64 20.76 21.46 21.57 21.57

Min 19.8 18.9 20.35 15.22 19.38

*s stands for sample standard deviation

From Table 3.14, it is seen that the average FF has been improved above 78% for all

four categories of cells comparing to batch A when discarding the outliers. The short

circuit current on average is lower than batch A (average of 39 mA/cm2), which is about

1 mA/cm2 less than batch A. the average Voc is close to batch A for 1 Ω.cm FZ EG cells,

but 10 mV lower than the best UMG cell in batch A for 4 Ω.cm UMG cell. This

difference is mainly due to either the bulk lifetime or the slightly worse surface

passivation in this batch. The average efficiencies for both UMG cell categories are

above 20%, with an average efficiency of 20.8% for 0.6 Ω.cm UMG category. This

average efficiency is slightly lower than the best UMG cell in batch A owing to the

dramatic improvement in FF. For the EG categories, the average efficiency is 1% lower


136

than the best EG cell in batch A, mainly caused by the lower average Jsc. In the next

section, 3D cell simulations will be performed to perform a free energy loss analysis

(FELA) in both UMG and EG cells.

3.6.3.6 Simulation of PERL cells made from UMG silicon

In this section, the best UMG cells and EG cell from batch A and B are presented. The

cells are modelled using a 3D semiconductor simulation tool, Quokka [261]. The cell

parameters measured on control wafers from batch A and B are used in Quokka. The

control parameters are listed in Table 3.9 and Table 3.12 in the previous sections. The

parameters used are summarized in Table 3.15 below for a clearer comparison between

batch A and B. The dimensions of the cells are also summarized in Table 3.15.

Table 3.15: Simulation parameters used in Quokka simulation of the cells from both

batch A and batch B

Side Properties Batch A Batch B

Front

Sheet Resistance 120 Ω/ 120 Ω/

ρc 0.06 mΩ.cm2 0.04 mΩ.cm2

J0-diffused 45 fA/cm2 60 fA/cm2

J0-contacted 1800 fA/cm2 1800 fA/cm2

Contact width 10 µm fingers 10 µm fingers

Contact spacing 1300 µm 1300 µm

Rear

Sheet Resistance 70 Ω/ 70 Ω/

ρc 0.024 mΩ.cm2 0.05 mΩ.cm2

J0-undiffused 3 fA/cm2 7 fA/cm2

J0-diffused 70 fA/cm2 70 fA/cm2

J0-contacted 700 fA/cm2 700 fA/cm2

Diffusion size 75 µm dot 75 µm dot

Contact size 30 µm dot 30 µm dot

Contact Spacing 300 µm 300 µm

Quokka 3D simulation utilizes the conductive boundary approximation. Thus, the

recombination parameters J0 measured on control wafers for the front and rear surfaces


137

are used to account for the recombination at these boundaries [261]. These parameters

are listed in Table 3.15. The J0-contacted for the front and rear and the J0-diffused for the rear

side are taken from typical values from literatures for a 70Ω/ phosphorus diffusion

[262] and for a 120Ω/ boron diffusion [263]. The values are also summarized in Table

3.15.

3.6.3.6.1 Simulation of optics

To simulate the Jsc accurately in the cells, it is critical to accurately model the wafer

optical properties. The optics are modelled using the wafer ray tracer software from PV

lighthouse [264]. The front optics of the cell are modelled with a random textured

surface with a Al2O3/SiNx stack with thickness of 15nm/52nm and 15nm/55nm for the 4

Ω.cm UMG and EG cells from batch A. Thicknesses of 15nm/54nm are used to

simulate for the 0.6 Ω.cm UMG from batch B. Note that the deposition rate of

Al2O3/SiNx stack on textured surface is slower than planar, therefore the thickness used

in the simulation is less than the target thickness mentioned in the fabrication process,

which is measured on planar test structures. Slightly different SiNx thickness are used

to match the small variation of the reflectance measured at short wavelength.

(a) (b)

Figure 3.32: (a) Measured and simulated reflectance of the cells for the best UMG cells

from batch A and batch B. (b) Measured and simulated reflectance of the best EG cell

from batch A. The reflectance of the fingers is subtracted from the measurement results.


138

The rear side is modelled with a rear reflector, 0.96 Lambertian fraction, with

95.5%/96% for UMG (both batch A and B)/EG cells. The rear reflectance is adjusted

until the escape reflectance matches the measured reflectance. Figure 3.32 shows the

measured and simulated reflectance of the cells. The reflectance from the fingers has

been subtracted by assuming a constant reflection from the fingers across the whole

wavelength range shown in the figure.

The simulated reflectance for all the cells agrees with the measurement results. Based

on the simulated reflectance, the EQE of the cells are simulated and shown in Figure

3.33. The simulated EQE matches with the measured EQE in the wavelength range

shown in the figure. As discuss before, the best UMG cell and best EG cell from batch

A are identical in their EQE in the long wavelength range between 900nm to 1200nm.

This indicates that the minority carrier diffusion length is significantly larger than the

wafer thickness, and is estimated to be 695µm and 1018µm respectively from lifetime

measurements combined with mobility simulation. This is 4.6 and 6.8 times of the cell

thicknesses respectively. However, the best UMG cell from batch B, the diffusion

length is 530 µm due to the lower lifetime and lower mobility owing to the higher net

doping. It is only 3.3 times the thickness. In addition, the rear J0 is also higher in this

batch as mentioned previously. The simulation results also reveals this reduction in

EQE as shown in Figure 3.33 (a). Therefore, it is reasonable to say that the reduction in

Jsc is mainly due to bulk losses.

(a) (b)

Figure 3.33: (a) Measured and simulated EQE of the cells for the best UMG cells from

batch A and batch B. (b) Measured and simulated EQE of the best EG cell from batch A.

The reflectance of the fingers is subtracted from the measurement results.


139

3.6.3.6.2 Electrical properties

In addition to the recombination pre-factor listed in Table 3.15 for both front and rear

surfaces of the cells, the bulk lifetime is another important electric property in the

simulation. As mentioned before, the as-cut lifetime is not representative of the final

bulk lifetime. According to the bulk lifetime study in the previous studies on the control

wafers for both batch A and batch B, we are able to use the bulk lifetime post high

temperature processing in the simulation. The injection dependent minority carrier

lifetime shown in Figure 3.15 and Figure 3.26 are modelled in Quokka using two

defects via the SRH model to fit the measured lifetime for the EG FZ and UMG Cz

samples. Table 3.16 shows the SRH parameters extracted from the lifetime test

structures and used in the simulation of the cells. The majority and minority carrier

mobility are also listed in Table 3.16.

Table 3.16: SRH parameters used in the simulation to reflect the minority carrier

lifetime measured in Figure 3.15 and Figure 3.26.

EC-ET

(eV) σn (cm-2) σp (cm-2) Nt (cm-3) µn (cm2V-1s-1) µp (cm2V-1s-1)

UMG Cz 4Ω.cm

(Batch A)

0.5 1×10-18 5×10-17 1×1012 948.7 372.5

1 9×10-15 3×10-16 2×1012

EG FZ 1Ω.cm

(Batch A)

0.5 4×10-19 2×10-17 1×1012 1263 439

1 3×10-15 9×10-17 2×1012

UMG Cz

0.6Ω.cm

(Batch B)

0.5 1×10-18 5×10-17 1×1012

912 361 1 8×10-15 8×10-16 2×1012

3.6.3.6.3 Simulation results

Simulation of the I-V characteristics of the cells is shown in Figure 3.34, and is in good

agreement with the measured light I-V curves for both EG FZ and UMG Cz cells in

terms of Jsc and Voc from batch A. However, the simulated Jsc for the 0.6Ω.cm UMG

cell is about 0.7mA.cm-2 higher than the measurement results. Considering the

measured EQE for this cell agrees with the simulation results. This variation is due to

the actual cell area. It is important to note here, the actual size of the cells from the


140

independent measurements by Fraunhofer ISE is 3.96cm2. Therefore, it is 1% less than

the designed area (4cm2). However, the results for 0.6Ω.cm cell is obtained from in-

house measurement, the actual area of the cell is not corrected. If taking the area of 3.96

cm2, the actual current density in the cell is 39.4, which is very close to the simulation

results.

The simulated FF is not in good agreement with the measurements for the 4Ω.cm

UMG and 1Ω.cm EG cells. The simulated FF is much larger than the actual

measurements. Quokka simulation only takes the contact resistivity and bulk electric

properties into account. Any non-ideal processing conditions that may cause resistive

losses elsewhere will not be included. It also does not consider the reduction of FF from

edge recombination. The Suns-Voc measurements indicate that series resistance affects

the FF in the cells in this case. The PFF is closer to the simulated FF. For the 0.6Ω.cm

UMG, the simulated FF matches with the measurements. It indicates that any resistive

losses or edge recombination losses from the non-ideal processing is small enough to

not affect the FF. This is the outcome from the optimized process control for batch B.

The measured and simulated I-V curves for all three cells are shown in Figure 3.34. The

device parameters extracted from the simulated light I-V are shown in Table 3.17

together with the measurements for comparison.

(a) (b)

Figure 3.34: (a) Measured and simulated I-V curves of the cells for the best UMG cells

from batch A and batch B. (b) For the best EG cell from batch A.


141

Table 3.17, Device parameters extracted from the simulated light I-V for the best UMG

and EG from batch A and B

Parameters

UMG Cz

4Ω.cm

simulated

UMG Cz

4Ω.cm

measured

EG FZ

1Ω.cm

simulated

EG FZ

1Ω.cm

measured

UMG Cz

0.6Ω.cm

simulated

UMG Cz

0.6Ω.cm

measured

Jsc

(mA.cm-2) 40.36 40.23 40.17 39.89 39.8 39

Voc (mV) 672.75 672.6 687.27 686.2 667.6 671

Jmpp

(mA.cm-2) 38.42 37.03 38.41 37.03 38.05 37.39

Vmpp (mV) 577.11 566.1 597.19 591.7 578.03 578.8

FF (%) 81.7 77.5

(PFF 82.2) 83.1

80.1

(PFF 81.5) 82.8

82.7

(PFF 83.1)

η (%) 22.22 20.96 22.98 21.91 22.04 21.64

Δnmpp(cm-3) 4.4×1014 - 3×1014 - 1.1×1014 -

Δnoc(cm-3) 3.8×1015 - 4×1015 - 1.6×1015 -

no(cm-3) 1.4×1015 - 4.8×1015 - 1.1×1016 -

(no+ Δnoc)×

Δnoc (cm-6) 2×1031 - 3.5×1031 - 2×1031 -

It has been shown previously in Table 3.13 that the [B] concentrations in the 4Ω.cm

UMG and 0.6Ω.cm UMG cells are similar. Therefore, it is interesting to compare the

effect of compensation on the solar cell performance. The compensation ration Rc and

Kc according to equation (3.14) and (3.15) for the 4Ω.cm UMG and 0.6Ω.cm UMG

materials are 0.89/0.48 and 179/2.82, respectively. The 4Ω.cm UMG cell is more

compensated than the 0.6Ω.cm UMG cell. Section 3.3 discussed the impact of

compensation on various cell parameters. The impact of compensation on

recombination is obvious, the 4Ω.cm UMG has higher as-cut and post-processing bulk

lifetime due to the lower net doping. The Jsc is also higher in the 4Ω.cm UMG cell due

to the higher diffusion length as discussed previously, the compensation improves the

current due to higher bulk lifetime and minority carrier mobility. The Voc does not show

significant improvement from compensation. Even though the net doping is about 8

times higher, the excess carrier density at open circuit as shown in Table 3.17 is lower.

According to equation (3.18), the Voc scales with the natural logarithm of the product of


142

the net doping plus excess carrier density, and excess carrier density. As shown in Table

3.17 the lower Δnmpp is balanced by a higher net doping, and therefore the 4Ω.cm UMG

cell and the 0.6Ω.cm UMG cell have similar Voc. The compensation does not seem to

provide an obvious advantage in this case. For the FF, as discussed in section 3.3.6, at

moderate compensation, the FF will reduce due to resistive loss. The results here show

this reduction in FF for the 4Ω.cm UMG cell. The simulated FF is also lower. This is

mainly due to the resistive loss from the lower majority carrier mobility and lower net

doping in the bulk, which will be discussed in the free energy loss analysis (FELA) in

the next sub-section. Based on the simulation results from Table 3.17, compensation

does not lead to much improvement in cell efficiency given the cell structure and bulk

properties used in this simulation.

3.6.3.6.4 Free energy loss analysis

The simulation results for the best UMG and FZ cells from batch A and B agree well

with the measurements in terms of Jsc and Voc. It indicates that the parameters measured

on test structures reflect the conditions in the real cells. In this sub-section, the

breakdown of power losses simulated at maximum power point (MPP) using the FELA

[265] for all three cells is presented. Note that, FELA is based on the volume integral of

photogeneration rate multiplied by the splitting of the quasi-Fermi levels at MPP. Even

though all the simulated cells have the same thickness and optical properties, the FELA

contributions do not add up to the same efficiency value. A reduced bulk lifetime in the

cell results in a smaller quasi-Fermi level splitting and hence lower FELA contributions.

Figure 3.35 shows the FELA for the cells used in this study. The higher efficiency of

the EG cell reflects its higher doping and bulk lifetime, leading to a greater quasi-Fermi

levels splitting at MPP. A greater Fermi level splitting at MPP also means that losses

due to SRH recombination are less significant (they are a smaller fraction of the total

power loss) as shown in Figure 3.35. For the UMG cells, the main loss in the device is

the SRH loss for both 4Ω.cm UMG and 0.6Ω.cm UMG cells. SRH loss in the UMG

cells is much greater than the EG cell. Even though the 0.6Ω.cm UMG cell has higher

net doping than the EG, however, the lower Δn at MPP shown in Table 3.17 results in

lower efficiency.


143

Figure 3.35: Power losses using free energy loss analysis (FELA) for the best UMG and

EG cells from batch A and B at MPP.

Figure 3.35 also shows that majority electrons resistive losses are greater in the UMG

4Ω.cm cell compared to the EG cell. However, with these two simulations (with

different doping) one cannot clearly conclude if this loss is due to lower doping or lower

mobility (or both) of the UMG material. To allow a fair and meaningful comparison

between UMG and EG cells we add a third scenario where the net doping of the EG cell

is adjusted to be the same level as the UMG cell. With this new scenario the UMG cell

and EG cell have similar simulated efficiency 22.2% to 22.28%, respectively. The

difference in efficiency is mainly caused by an increase in bulk electron resistive loss in

the UMG cell. This reflects the lower mobility in UMG material leading to a lower

electron conductivity in the bulk. Contrary to the previous study by Rougieux et al. [39],

this effect is apparently due to the fact that the full-area rear-diffusion is absent in this

cell structure and hence cannot assist with majority carrier conduction. All in all

however, this effect has a minor influence on the efficiency (0.08% drop). In the case of

the 0.6Ω.cm UMG cell, the electron resistive loss is much smaller and mainly due to the

increase of net doping density in this cell.


144

3.7 Summary

In summary, this chapter discussed the feedstocks used in PV industries and the

potential feedstock candidates for lower energy consumption during purification. The

PV industry is still dominated by polycrystalline silicon feedstocks from the Siemens

process these days. The high energy consumption of the Siemens process due to the gas

phase purification and the emission of toxic gases are disadvantageous factors for PV.

However, it is clear that solar cells have different requirements than the semiconductor

industries, especially for n-type silicon. UMG-Si purified via the solid or liquid phases

can significantly lower the energy consumption, and have raised interest in the PV

industry. There are various types of purification technologies developed to purify MG-

Si through the metallurgical route, for example, directional solidification, acid leaching,

plasma treatment, slag treatment and electron-beam melting. Each process is designed

for removing specific types of elements. The purity of UMG-Si and especially the

presence of both donor and acceptor atoms (compensation) are the biggest issues. Both

industries and laboratories have made efforts over the last decade to demonstrate the

potential of UMG-Si on solar cells, and up to 2015, the best UMG-Si solar cell reported

was 19.8% efficient. In this chapter, we demonstrate a process designed to maintain a

high post processing bulk lifetime in the cell (a PERL structure with an etch-back

process). We achieve UMG-Si solar cells with efficiencies above 20%. An

independently confirmed result of 20.96% for a solar cell based on 100% UMG-Si, and

21.91% for an EG FZ cell, fabricated using the same process are presented. The results

show that with an optimized fabrication process, the bulk lifetime and minority carrier

diffusion length are not strongly limiting factors for UMG material to achieve high

efficiency devices. The BO defects due to material compensation reduces the efficiency

of n-type UMG Cz solar cells, however, they can be partially recovered with annealing

under illumination. With an optimized illumination intensity and temperature, a more

complete deactivation of this defect should be possible.

Although 20.96% UMG-Si solar cell has been achieved, the efficiency is limited by

the lower FF, which results from non-optimized process control and not the UMG

material itself. With a better process control, a 21.64% UMG-Si solar cell has been

fabricated (in-house measurement). This cell has a relatively high FF of 82.7%,

however, its lower diffusion length leads to a lower current. 3D simulation of the cells

has shown that the lower majority and minority carrier mobilities in the cells do not lead


145

to significant efficiency losses (<0.1%) in this cell structure. The main loss for UMG-Si

solar cell is SRH recombination loss, reducing the cell voltage. Simulations show that

with this structure and the measured bulk properties of UMG material, UMG-Si solar

cells with efficiencies above 22% are potentially achievable.


146

147

Chapter 4

Conclusion and Further Work

In this thesis we have presented a thorough study of some key properties of n-type

monocrystalline silicon wafers and solar cells. This thesis describes the properties of n-

type silicon, from the influence of dopant, temperature and excess carrier density on the

mobility, and the impact of intrinsic defects on the lifetime, to the impact of

compensation on high efficiency solar cells. We show the potential of using n-type

UMG-Si to fabricate solar cells with efficiency above 21% and demonstrate permanent

partial deactivation of the boron oxygen defect at the cell level.

The main outcome and contributions of this thesis are summarized below, together with

an outlook for further related work.

4.1 Carrier mobility sum

This thesis presents the first experimentally based model for dopant, injection and

temperature dependence of the mobility sum. We have measured the carrier mobility

sum in n-type mono-Si using photoconductance measurements over a wide range of

temperature, dopant density and injection. We show and quantify the reduction of the

mobility with increasing temperature, dopant and injection density. The result of chapter

1 is a novel model to describe the mobility sum as a function of carrier injection, doping

and temperature. The model is then extended to p-type mono-Si. Good agreement is

found between this model and the model of Klaassen, validating the use of Klaassen’s

model in device simulation, especially in the highly injected region, where Klaassen’s

model lacked experimental validation.


148

4.2 Intrinsic-related defect

It is shown in chapter 2 that non-metallic defects can significantly limit the lifetime of

high lifetime n-type Cz mono-Si wafers. These intrinsic defects are shown to be

thermally deactivated at temperatures of 150oC and 350 oC, respectively. We suggest

that VP pairs and VO pairs may decrease the as-grown lifetime of n-type wafers. These

defects may be incorporated in the ingot during the cooling stage in an ingot grown

under vacancy rich mode, which most of the commercial c-Si ingots are. This thesis

shows the importance of intrinsic-related defects in limiting the lifetime of very pure c-

Si material and is important for achieving high efficiencies for solar cells based on n-

type c-Si.

4.3 High efficiency UMG solar cell

In addition to the fundamental studies on the material properties of n-type c-Si, in this

thesis, we also show the potential of n-type UMG silicon as a substrate for high

efficiency solar cells. In chapter 3, n-type Cz UMG-Si wafers are used to fabricate solar

cells. The UMG wafers used for the cell fabrication are based on 100% non-blended

UMG feedstock. Lifetime studies on the UMG material show that the as-cut UMG

material has the potential to achieve lifetime in the millisecond range. However, the

degradation of bulk lifetime after boron diffusion is severe. An etch-back approach is

adopted to benefit from the gettering of the heavy phosphorus diffusion to maintain a

high lifetime in the bulk of the material. With this approach, a PERL cell design is

selected. An independently confirmed result of 20.96% for a UMG cell is achieved

compared to a 21.91% EG FZ control cell. The initial results were limited by a low FF

for the UMG cell shown to be caused by series resistance and edge recombination. Thus

a second batch of cells was fabricated with improved process control to avoid edge

recombination and series resistance. With this modified process we demonstrate an

unconfirmed 21.6% UMG-Si solar cell with a high FF of 82.7%, which is the highest

efficiency UMG-Si solar cell reported to date.

Simulations show that the UMG cell can potentially achieve efficiencies of 22%.

Chapter 3 presents the breakdown of materials related loss in a high efficiency UMG

solar cell. Specifically, the reduced mobility (due to material compensation of UMG


149

feedstock) is shown to lead to a negligible resistive loss (<0.1%). Furthermore,

simulations show that UMG-Si solar cell have the potential to achieve above

efficiencies above 22% close to efficiencies on electronic grade material.

This thesis also presents the impact of BO defects on the performance of n-type UMG

solar cells. We show that the Voc of UMG cells degrades by about 15mV under 1 sun

illumination after 100 hours. A regeneration process with simultaneous heating and

illumination is performed to permanently deactivate the BO defects. The results

demonstrate a partial recovery of the Voc, which is stable under illumination for at least

100 hours. The only partial recovery may be caused by the non-optimal curing

condition.

4.4 Further work

We have developed a new mobility model valid under a wide range of dopant densities,

injection and temperatures. However, the data available is only for non-compensated

silicon. Therefore further studies and measurements in compensated silicon are needed

to extend the applicability of this empirical expression.

It is clear from our work that intrinsic related defects may limit the lifetime of high

quality monocrystalline silicon. Further studies need to be performed to verify how

widespread this problem is and to relate it to growth parameters such as growth rate and

gas flow.

Our simulations show the potential for 22% UMG solar cells with our standard PERL

structure, therefore, further studies are needed with a more robust process control to

achieve higher efficiency UMG solar cells.

Our experimental results demonstrate that permanent deactivation of the BO defect in

compensated n-type silicon is achievable at least partially. Further experiments with

optimal curing conditions are needed to illustrate the possibility of full permanent

deactivation of LID in n-type compensated silicon solar cells.


150

151

List of symbols

Symbols

Symbol Description Unit

A Area cm2

CA Auger coefficient s-1.cm6

Cio Initial self-interstitials concentration at crystal front cm-3

CIs Incorporated self-interstitial concentration cm-3

Cvo Initial self-interstitials concentration at crystal front cm-3

Cv Incorporated vacancy concentration cm-3

d Thickness of middle region μm

Dmin Minority carrier diffusivity cm2.s-1

Dn Electron diffusivity cm2.s-1

Dp Hole diffusivity cm2.s-1

Eann Annihilation activation energy eV

Ec Conduction band energy eV

EFC Quasi-Fermi level of electron eV

EFV Quasi-Fermi level of hole eV

ET Defect energy level eV

FF Fill factor -

fs Solidification fraction -

G Interface axial temperature gradient K.cm-1

GQSSPC Generation rate in the sample cm-3.s-1

iF Forward current A

iR Reverse current A

J Total current density A.cm-2

J0 Recombination current fA.cm-2

J0e Emitter recombination current fA.cm-2

List of symbols

152

JL Light generated current density A.cm-2

Jmpp Current density at maximum power point A.cm-2

Jn Electron current density A.cm-2

Jp Hole current density A.cm-2

Jsc Short circuit current density A.cm-2

k0 Equilibrium segregation coefficient -

kB Boltzmann constant J.K-1

Kc Divergent compensation ratio -

LB Distribution coefficient of slag treatment -

Lmin Minority carrier diffusion length μm

mn Effective mass of electron kg

m* Effective mass of particles kg

n Electron concentration cm-3

n0 Equilibrium electron concentration cm-3

ni Intrinsic carrier concentration cm-3

nmaj Majority carrier concentration cm-3

nmin Minority carrier concentration cm-3

N Collision center concentration cm-3

N* Normalized effective density s-1

NA Acceptor concentration cm-3

NA- Ionized acceptor concentration cm-3

Ndop Net doping cm-3

ND Donor concentration cm-3

ND+ Ionized donor concentration cm-3

NI Total ionized impurities concentration cm-3

N*t.anneal Annealed normalized effective density after time t s-1

N*t.0 Maximum normalized effective density s-1

p Hole concentration cm-3

p0 Equilibrium hole concentration cm-3

PFF Pseudo fill factor -

q Electronic charge C

Q Stored charge C

r Radius m

Rann Annihilation rate s-1

List of symbols

153

Rs Series resistance Ω.cm2

Rsh Shunt resistance Ω.cm2

t Time s

T Absolute temperature K

Tb Binding temperature K

Tn Nucleation temperature K

UmOHM Ohmic voltage drop V

v Crystal growth rate cm.s-1

v Carrier velocity cm.s-1

Vmpp Voltage at maximum power point V

vn Electron velocity cm.s-1

Voc Open circuit voltage V

vth Thermal velocity cm.s-1

W Thickness cm

Xl Equilibrium impurities concentration in the liquid cm-3

Xs Equilibrium impurities concentration in the solid cm-3

Δn Excess carrier concentration cm-3

Δnav Average excess carrier concentration cm-3

Δnback Excess carrier concentration at the edge of space charge region cm-3

Δnfront Excess carrier concentration at the edge of space charge region cm-3

Δnmpp Excess carrier concentration at maximum power point cm-3

Δnoc Excess carrier concentration at open circuit cm-3

Δnscr Excess carrier concentration at the edge of space charge region cm-3

ΔU Change of voltage V

Δσ Excess conductance Ω-1

ε Electric field strength V.cm-1

µccs Carrier-carrier scattering term cm2.V-1.s-1

µI Ionized impurity scattering term cm2.V-1.s-1

µL Lattice scattering term cm2.V-1.s-1

µmaj Majority carrier mobility cm2.V-1.s-1

µmin Minority carrier mobility cm2.V-1.s-1

µn Electron mobility cm2.V-1.s-1

µp Hole mobility cm2.V-1.s-1

List of symbols

154

µsum Sum of electron and hole mobility cm2.V-1.s-1

µtotal Total mobility of different scattering terms cm2.V-1.s-1

ρc Contact resistivity Ω.cm2

σ Collision cross section cm2

τbulk Bulk lifetime s

τc Mean free time s

τeff Effective minority carrier lifetime s

τeff0 Initial minority carrier lifetime in the wafer s

τeff∞ Maximum minority carrier lifetime in the wafer s

τeff-anneal Annealed minority carrier lifetime in the wafer s

τPCD Lifetime measured by photoConductance decay s

τQSSPC Lifetime measured by quasi-steady state photoConductance s

φ Electrical potential V

ϑ Chemical potential eV

ξt v/G ratio cm2.s-1.K-1

η Efficiency of solar cell -

155

List of Publications

This thesis is based on the following publications:

Journal Papers

1. P. Zheng, F. E. Rougieux, D. Macdonald, and A. Cuevas, "Measurement and

Parameterization of Carrier Mobility Sum in Silicon as a Function of Doping,

Temperature and Injection Level," IEEE Journal of Photovoltaics, vol. 4, pp.

560-565, 2014.

2. P. Zheng, F. E. Rougieux, N. E. Grant, and D. Macdonald, "Evidence for

Vacancy-Related Recombination Active Defects in as-Grown n-Type

Czochralski Silicon," IEEE Journal of Photovoltaics, vol. 5, pp. 183-188, 2015.

3. P. Zheng, F. E. Rougieux, C. Samundsett, X. Yang, Y. Wan, J. Degoulange, et

al., "Upgraded metallurgical-grade silicon solar cells with efficiency above

20%," Applied Physics Letters, vol. 108, 122103, 2016.

4. P. Zheng, F. E. Rougieux, X. Zhang, J. Degoulange, et al., "21.1% UMG silicon

solar cell," IEEE Journal of Photovoltaics, 2016.

Conference Papers

5. P. Zheng, F. E. Rougieux, D. Macdonald, and A. Cuevas, "Parameterization of

carrier mobility sum in silicon as a function of doping, temperature and injection

level: Extension to p-type silicon," in Photovoltaic Specialist Conference

(PVSC), 2014 IEEE 40th, 2014, pp. 0129-0134.


156

6. P. Zheng, F. E. Rougieux, C. Samundsett, X. Yang, Y. Wan, J. Degoulange, et

al., "Simulation of 20.96% efficiency n-type Czochralski UMG silicon solar

cell," in 6th International Conference on Silicon Photovoltaics, SiliconPV 2016,

Chambery, France, 2016

Other publications by the author:

1. P.zheng, J.Bullock, Q.Jeangros, M.Tosun, M. Hettick, C. Sutter-Fella, et al.,

"Lithium fluoride based electron contats for high efficiency n-type crystalline

silicon solar cells," submitted to Advanced Energy Material.

2. F. E. Rougieux, P. Zheng, M. Thiboust, J. Tan, N. E. Grant, D. H. Macdonald, et

al., "A Contactless Method for Determining the Carrier Mobility Sum in Silicon

Wafers," IEEE Journal of Photovoltaics, vol. 2, pp. 41-46, 2012.

3. F. Rougieux, C. Samundsett, K. C. Fong, A. Fell, P. Zheng, D. Macdonald, et al.,

"High efficiency UMG silicon solar cells: impact of compensation on cell

parameters," Progress in Photovoltaics: Research and Applications, 2015.

4. X. Yang, P. Zheng, Q. Bi, and K. Weber, "Silicon heterojunction solar cells with

electron selective TiOx contact," Solar Energy Materials and Solar Cells, vol.

150, pp. 32-38, 2016

5. H. T. Nguyen, D. Yan, F. Wang, P. Zheng, Y. Han, and D. Macdonald, "Micro-

photoluminescence spectroscopy on heavily-doped layers of silicon solar cells,"

physica status solidi (RRL) – Rapid Research Letters, vol. 9, pp. 230-235, 2015.

6. T. Duong, N. Lal, D. Grant, D. Jacobs, P. Zheng, S. Rahman, et al.,

"Semitransparent Perovskite Solar Cell With Sputtered Front and Rear

Electrodes for a Four-Terminal Tandem," IEEE Journal of Photovoltaics, vol.

PP, pp. 1-9, 2016.


157

7. Y.Wan, C.Samundsett, J.Bullock, T.Allen, M.Hettick, P.Zheng, et al.

"Nanoscale magnesium fluoride electron-selective contacts for crystalline silicon

solar cells," submitted to Nano Letters.


158

159

Bibliography

[1] B. Burger, K. Kiefer, C. Kost, S. Nold, S. Philipps, and R. Preu, "Photovoltaics

report," Fraunhofer Institute for Solar Energy Systems, www. ise. fraunhofer.

de/mwginternal/de5fs23hu73ds/progress, 2013.

[2] C. Philibert, P. Frankl, and T. Cecilia, Technology roadmap: solar photovoltaic

energy. (OECD/IEA, 2014).

[3] U.S. Energy Information Administration (EIA), Levelized Avoided Cost of New

Generation Resources in the Annual Energy Outlook 2015.

[4] A. Hazlehurst, "Economic Analysis of Solar Power: Achieving Grid Parity," ed:

Stanford Graduate School of Business, 2010.

[5] Value Chain Activity: Producing Polysilicon.Available:

http://www.greenrhinoenergy.com/solar/industry/ind_01_silicon.php, (accessed

09.03.2016).

[6] Energy Trend.Available: http://pv.energytrend.com/pricequotes.html, (accessed

09.03.2016).

[7] M. Sontakkle. (2015) China: The new silicon valley. Available:

http://marketrealist.com/2015/02/china-new-silicon-valley/, (accessed

09.03.2016).

[8] K. Smith, H. Gummel, J. Bode, D. Cuttriss, R. Nielsen, and W. Rosenzweig,

"The solar cells and their mounting," Bell System Technical Journal, vol. 42, pp.

1765-1816, 1963.

[9] D. Macdonald, "The emergence of n-type silicon for solar cell manufacture," in

50th Annual AuSES Conference (Solar 2012), Melbourne, Australia, 2012.

[10] K. Bothe and J. Schmidt, "Electronically activated boron-oxygen-related

recombination centers in crystalline silicon," Journal of Applied Physics, vol. 99,

013701, 2006.

[11] J. Schmidt, K. Bothe, and R. Hezel, "Formation and annihilation of the

metastable defect in boron-doped Czochralski silicon," in Photovoltaic

Bibliography

160

Specialists Conference, 2002. Conference Record of the Twenty-Ninth IEEE,

2002, pp. 178-181.

[12] J. Schmidt and K. Bothe, "Structure and transformation of the metastable boron-

and oxygen-related defect center in crystalline silicon," Physical review B, vol.

69, 024107, 2004.

[13] J. E. Cotter, J. H. Guo, P. J. Cousins, M. D. Abbott, F. W. Chen, and K. C.

Fisher, "P-Type Versus n-Type Silicon Wafers: Prospects for High-Efficiency

Commercial Silicon Solar Cells," Electron Devices, IEEE Transactions on, vol.

53, pp. 1893-1901, 2006.

[14] D. Macdonald and L. J. Geerligs, "Recombination activity of interstitial iron and

other transition metal point defects in p- and n-type crystalline silicon," Applied

Physics Letters, vol. 85, pp. 4061-4063, 2004.

[15] S. Martinuzzi, O. Palais, M. Pasquinelli, D. Barakel, and F. Ferrazza, "N-type

multicrystalline silicon wafers for solar cells," in Photovoltaic Specialists

Conference, 2005. Conference Record of the Thirty-first IEEE, 2005, pp. 919-

922.

[16] A. Cuevas, S. Riepe, M. Kerr, D. Macdonald, G. Coletti, and F. Ferrazza, "N-

type multicrystalline silicon: a stable, high lifetime material," in Photovoltaic

Energy Conversion, 2003. Proceedings of 3rd World Conference on, 2003, pp.

1312-1315.

[17] C. Schmiga, J. Schmidt, M. Ghosh, A. Metz, and R. Hezel, "Gettering and

passivation of recombination centres in n-type multicrystalline silicon," in Proc.

19th European Photovoltaic Solar Energy Conf, 2004.

[18] J.-H. Guo and J. E. Cotter, "Laser-grooved backside contact solar cells with 680-

mV open-circuit voltage," Electron Devices, IEEE Transactions on, vol. 51, pp.

2186-2192, 2004.

[19] K. Masuko, M. Shigematsu, T. Hashiguchi, D. Fujishima, M. Kai, N. Yoshimura,

et al., "Achievement of more than 25% conversion efficiency with crystalline

silicon heterojunction solar cell," Photovoltaics, IEEE Journal of, vol. 4, pp.

1433-1435, 2014.

[20] M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, "Solar cell

efficiency tables (version 47)," Progress in Photovoltaics: Research and

Applications, vol. 24, pp. 3-11, 2016.

Bibliography

161

[21] H. Sakata, T. Nakai, T. Baba, M. Taguchi, S. Tsuge, K. Uchihashi, et al., "20.7%

highest efficiency large area (100.5 cm2) HIT TM cell," in Photovoltaic

Specialists Conference, 2000. Conference Record of the Twenty-Eighth IEEE,

2000, pp. 7-12.

[22] A. Burgers, L. Geerligs, A. Carr, A. Gutjahr, D. Saynova, X. Jingfeng, et al.,

"19.5% efficient n-type Si solar cells made in production," in 26th European

Photovoltaic Solar Energy Conference, 2011, pp. 1144-1147.

[23] A. Richter, M. Hermle, and S. W. Glunz, "Reassessment of the limiting

efficiency for crystalline silicon solar cells," Photovoltaics, IEEE Journal of, vol.

3, pp. 1184-1191, 2013.

[24] A. Fell, K. R. McIntosh, P. P. Altermatt, G. J. M. Janssen, R. Stangl, A. Ho-

Baillie, et al., "Input Parameters for the Simulation of Silicon Solar Cells in

2014," IEEE Journal of Photovoltaics, vol. 5, pp. 1250-1263, 2015.

[25] A. Richter, S. W. Glunz, F. Werner, J. Schmidt, and A. Cuevas, "Improved

quantitative description of Auger recombination in crystalline silicon," Physical

Review B, vol. 86, 165202, 2012.

[26] F. E. Rougieux, N. E. Grant, D. Macdonald, and J. D. Murphy, "Can vacancies

and their complexes with nonmetals prevent the lifetime reaching its intrinsic

limit in silicon?," in Photovoltaic Specialist Conference (PVSC), 2015 IEEE

42nd, 2015, pp. 1-4.

[27] E. Øvrelid, B. Geerligs, A. Wærnes, O. Raaness, I. Solheim, R. Jensen, et al.,

"Solar grade silicon by a direct metallurgical process," Silicon for the Chemical

Industry VIII, Trondheim, Norway, 2006.

[28] ITRPV working Group, International Technology Roadmap for Photovoltaic

(ITRPV) 2014 Results, 2015.

[29] Y. Delannoy, C. Alemany, K.-I. Li, P. Proulx, and C. Trassy, "Plasma-refining

process to provide solar-grade silicon," Solar Energy Materials and Solar Cells,

vol. 72, pp. 69-75, 2002.

[30] K. Hanazawa, N. Yuge, and Y. Kato, "Evaporation of phosphorus in molten

silicon by an electron beam irradiation method," Materials Transactions, vol. 45,

pp. 844-849, 2004.

[31] D. Lynch, "Winning the global race for solar silicon," The Journal of The

Minerals, Metals & Materials Society (TMS), vol. 61, pp. 41-48, 2009.

Bibliography

162

[32] S. Pizzini, "Solar grade silicon as a potential candidate material for low-cost

terrestrial solar cells," Solar energy materials, vol. 6, pp. 253-297, 1982.

[33] A. F. B. Braga, S. P. Moreira, P. R. Zampieri, J. M. G. Bacchin, and P. R. Mei,

"New processes for the production of solar-grade polycrystalline silicon: A

review," Solar energy materials and solar cells, vol. 92, pp. 418-424, 2008.

[34] R. Einhaus, J. Kraiem, F. Cocco, Y. Caratini, D. Bernou, D. Sarti, et al.,

"PHOTOSIL-Simplified production of solar silicon from metallurgical silicon,"

Proc. of the 21st European PVSEC, pp. 6-9, 2006.

[35] J. Broisch, J. Schmidt, J. Haunschild, and S. Rein, "UMG n-type Cz-silicon:

Influencing Factors of the Light-induced Degradation and its Suitability for PV

Production," Energy Procedia, vol. 55, pp. 526-532, 2014.

[36] B. Lim, F. Rougieux, D. Macdonald, K. Bothe, and J. Schmidt, "Generation and

annihilation of boron–oxygen-related recombination centers in compensated p-

and n-type silicon," Journal of Applied Physics, vol. 108, 103722, 2010.

[37] F. E. Rougieux, M. Forster, D. Macdonald, A. Cuevas, B. Lim, and J. Schmidt,

"Recombination Activity and Impact of the Boron-Oxygen-Related Defect in

Compensated N-Type Silicon," Photovoltaics, IEEE Journal of, vol. 1, pp. 54-

58, 2011.

[38] F. E. Rougieux, B. Lim, J. Schmidt, M. Forster, D. Macdonald, and A. Cuevas,

"Influence of net doping, excess carrier density and annealing on the boron

oxygen related defect density in compensated n-type silicon," Journal of Applied

Physics, vol. 110, 063708, 2011.

[39] F. Rougieux, C. Samundsett, K. C. Fong, A. Fell, P. Zheng, D. Macdonald, et al.,

"High efficiency UMG silicon solar cells: impact of compensation on cell

parameters," Progress in Photovoltaics: Research and Applications, vol. 24, pp.

725-734, 2016.

[40] Irvin and J. C, "Resistivity of Bulk Silicon and of Diffused Layers in Silicon,"

The Bell System Technical Journal vol. 41, pp. 387-410, 1962.

[41] P. W. Chapman, O. N. Tufte, J. D. Zook, and D. Long, "Electrical Properties of

Heavily Doped Silicon," Journal of Applied Physics, vol. 34, pp. 3291-3295,

1963.

[42] M. Finetti and A. M. Mazzone, "Impurity effects on conduction in heavily doped

n-type silicon," Journal of Applied Physics, vol. 48, pp. 4597-4600, 1977.

Bibliography

163

[43] W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, "The Relationship

between resistivity and dopant density for phosphorus- and boron-doped silicon

" National Bureau of Standards Special Publication 400-64, 1981.

[44] E. Fourmond, M. Forster, R. Einhaus, H. Lauvray, J. Kraiem, and M. Lemiti,

"Electrical properties of boron, phosphorus and gallium co-doped silicon,"

Energy Procedia, vol. 8, pp. 349-354, 2011.

[45] F. Schindler, M. C. Schubert, A. Kimmerle, J. Broisch, S. Rein, W. Kwapil, et

al., "Modeling majority carrier mobility in compensated crystalline silicon for

solar cells," Solar Energy Materials and Solar Cells, vol. 106, pp. 31-36, 2012.

[46] F. Dannhäuser, "Die abhängigkeit der trägerbeweglichkeit in silizium von der

konzentration der freien ladungsträger—I," Solid-State Electronics, vol. 15, pp.

1371-1375, 1972.

[47] J. Krausse, "Die abhängigkeit der trägerbeweglichkeit in silizium von der

konzentration der freien ladungsträger—II," Solid-State Electronics, vol. 15, pp.

1377-1381, 1972.

[48] D. H. Neuhaus, P. P. Altermatt, R. A. B. Sproul, A. Sinton, A. Schenk, A. Wang,

et al., "Method for measuring majority and minority carrier mobility in solar

cells," in Proceedings of the 17th European Photovoltaic Solar Energy

Conference, 2001, pp. 242-245.

[49] Z. Hameiri, T. Trupke, and R. Sinton, "Determination of Carrier Mobility Sum

in Silicon Wafers by Combined Photoluminescence and Photoconductance

Measurements," in 27th European Photovoltaic Solar Energy Conference and

Exhibition, 2012, pp. 1477 - 1481.

[50] S.M.Sze, Semiconductor Devices Physics and Technology 2nd Edition. (John

Wiley&Sons, United States of America, 2001), pp.48-50.

[51] D. K. Schroder, Semiconductor material and device characterisation. (Wiley

Inter-Science, 2006).

[52] A. K. Singh, Elecronic Devices and Integrated Circuits. (PHI Learning, 2011),

pp.79-80.

[53] B. V. Suresh, Solid State Devices and Technology. (Pearson Education India,

2010), pp.58-60.

[54] M. Lundstrom, Fundamentals of Carrier Transport. (Cambridge University

Press, 2009), pp.88-90.

Bibliography

164

[55] T. P. McLean and E. G. S. Paige, "A theory of the effects of carrier-carrier

scattering on mobility in semiconductors," Journal of Physics and Chemistry of

Solids, vol. 16, pp. 220-236, 1960.

[56] Y. Takeda and T. Pearsall, "Failure of Matthiessen's rule in the calculation of

carrier mobility and alloy scattering effects in Ga0. 47In0. 53As," Electronics

Letters, vol. 17, pp. 573-574, 1981.

[57] H. Benda and E. Spenke, "Reverse recovery processes in silicon power

rectifiers," Proceedings of the IEEE, vol. 55, pp. 1331-1354, 1967.

[58] A. Hoffmann and K. Schuster, "An experimental determination of the carrier

lifetime in p-i-n diodes from the stored carrier charge," Solid-State Electronics,

vol. 7, pp. 717-724, 1964.

[59] F. E. Rougieux, Z. Peiting, M. Thiboust, J. Tan, N. E. Grant, D. H. Macdonald,

et al., "A Contactless Method for Determining the Carrier Mobility Sum in

Silicon Wafers," Photovoltaics, IEEE Journal of, vol. 2, pp. 41-46, 2012.

[60] R. K. Ahrenkiel, B. M. Keyes, and D. L. Levi, "Recombination Processes in

Polycrystalline Photovoltaic Materials," in 13th European Photovoltaic Solar

Energy Conference:Proceedings of the International Conference, Bedford, UK,

1995, pp. 914-917.

[61] H. Nagel, C. Berge, and A. G. Aberle, "Generalized analysis of quasi-steady-

state and quasi-transient measurements of carrier lifetimes in semiconductors,"

Journal of Applied Physics, vol. 86, pp. 6218-6221, 1999.

[62] A. Cuevas and R. A. Sinton, "Prediction of the open-circuit voltage of solar cells

from the steady-state photoconductance," Progress in Photovoltaics: Research

and Applications, vol. 5, pp. 79-90, 1997.

[63] R. A. Sinton and T. Trupke, "Limitations on dynamic excess carrier lifetime

calibration methods," Progress in Photovoltaics: Research and Applications, vol.

20, pp. 246-249, 2012.

[64] S. S. Li and W. R. Thurber, "The dopant density and temperature dependence of

electron mobility and resistivity in n-type silicon," Solid-State Electronics, vol.

20, pp. 609-616, 1977.

[65] N. D. Arora, J. R. Hauser, and D. J. Roulston, "Electron and hole mobilities in

silicon as a function of concentration and temperature," Electron Devices, IEEE

Transactions on, vol. 29, pp. 292-295, 1982.

Bibliography

165

[66] D. Long, "Scattering of Conduction Electrons by Lattice Vibrations in Silicon,"

Physical Review, vol. 120, pp. 2024-2032, 1960.

[67] P. Norton, T. Braggins, and H. Levinstein, "Impurity and Lattice Scattering

Parameters as Determined from Hall and Mobility Analysis in $n$-Type

Silicon," Physical Review B, vol. 8, pp. 5632-5653, 1973.

[68] S. S. Li, "The dopant density and temperature dependence of hole mobility and

resistivity in boron doped silicon," Solid-State Electronics, vol. 21, pp. 1109-

1117, 1978.

[69] P. P. Debye and E. M. Conwell, "Electrical Properties of N-Type Germanium,"


[70] J. M. Dorkel and P. Leturcq, "Carrier mobilities in silicon semi-empirically

related to temperature, doping and injection level," Solid-State Electronics, vol.

24, pp. 821-825, 1981.

[71] M. Luong and A. W. Shaw, "Quantum Transport Theory of Impurity-Scattering-

Limited Mobility in $n$-Type Semiconductors Including Electron-Electron

Scattering," Physical Review B, vol. 4, pp. 2436-2441, 1971.

[72] C. Seok Cheow, "Theory of a forward-biased diffused-junction P-L-N

rectifier—Part I: Exact numerical solutions," Electron Devices, IEEE


[73] D. B. M. Klaassen, "A unified mobility model for device simulation—I. Model

equations and concentration dependence," Solid-State Electronics, vol. 35, pp.

953-959, 1992.

[74] D. B. M. Klaassen, "A unified mobility model for device simulation—II.

Temperature dependence of carrier mobility and lifetime," Solid-State

Electronics, vol. 35, pp. 961-967, 1992.

[75] D. B. M. Klaassen, "A unified mobility model for device simulation," in

Electron Devices Meeting, 1990. IEDM '90. Technical Digest., International,

1990, pp. 357-360.

[76] G. Masetti, M. Severi, and S. Solmi, "Modeling of carrier mobility against

carrier concentration in arsenic-, phosphorus-, and boron-doped silicon,"

Electron Devices, IEEE Transactions on, vol. 30, pp. 764-769, 1983.

[77] D. M. Caughey and R. E. Thomas, "Carrier mobilities in silicon empirically

related to doping and field," Proceedings of the IEEE, vol. 55, pp. 2192-2193,

1967.

Bibliography

166

[78] K. R. McIntosh and R. A. Sinton, "Uncertainty in photoconductance lifetime

measurements that use an inductive-coil detector," in 23rd European

Photovoltaic Solar Energy Conference, Valencia, Spain, 2008, pp. 77-82.

[79] S. Reggiani, M. Valdinoci, L. Colalongo, M. Rudan, G. Baccarani, A. D.

Stricker, et al., "Electron and hole mobility in silicon at large operating

temperatures. I. Bulk mobility," Electron Devices, IEEE Transactions on, vol.

49, pp. 490-499, 2002.

[80] S. Reggiani, M. Valdinoci, L. Colalongo, M. Rudan, G. Baccarani, A. Stricker,

et al., "Surface mobility in silicon at large operating temperature," in Simulation

of Semiconductor Processes and Devices, 2002. SISPAD 2002. International

Conference on, 2002, pp. 15-20.

[81] S. Reggiani, M. Valdinoci, L. Colalongo, and G. Baccarani, "A Unified

Analytical Model for Bulk and Surface Mobility in Si n- and p-Channel

MOSFET's," in Solid-State Device Research Conference, 1999. Proceeding of

the 29th European, 1999, pp. 240-243.

[82] W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, "Resistivity‐Dopant

Density Relationship for Boron‐Doped Silicon," Journal of The Electrochemical

Society, vol. 127, pp. 2291-2294, 1980.

[83] W. R. Thurber, R. L. Mattis, Y. M. Liu, and J. J. Filliben, "Resistivity‐Dopant

Density Relationship for Phosphorus‐Doped Silicon," Journal of The

Electrochemical Society, vol. 127, pp. 1807-1812, 1980.

[84] M. Fischetti, "Effect of the electron-plasmon interaction on the electron mobility

in silicon," Physical Review B, vol. 44, 5527, 1991.

[85] B. B. Paudyal, K. R. McIntosh, D. H. Macdonald, B. S. Richards, and R. A.

Sinton, "The implementation of temperature control to an inductive-coil

photoconductance instrument for the range of 0–230°C," Progress in

Photovoltaics: Research and Applications, vol. 16, pp. 609-613, 2008.

[86] A. Cuevas, "Modelling silicon characterisation," Energy Procedia, vol. 8, pp.

94-99, 2011.

[87] J. Tan, D. Macdonald, F. Rougieux, and A. Cuevas, "Accurate measurement of

the formation rate of iron–boron pairs in silicon," Semiconductor Science and

Technology, vol. 26, 055019, 2011.

Bibliography

167

[88] P. P. Altermatt, A. Schenk, and G. Heiser, "A simulation model for the density

of states and for incomplete ionization in crystalline silicon. I. Establishing the

model in Si:P," Journal of Applied Physics, vol. 100, 113714, 2006.

[89] P. P. Altermatt, A. Schenk, B. Schmithüsen, and G. Heiser, "A simulation model

for the density of states and for incomplete ionization in crystalline silicon. II.

Investigation of Si:As and Si:B and usage in device simulation," Journal of

Applied Physics, vol. 100, 113715, 2006.

[90] F. J. Blatt, "Scattering of carriers by ionized impurities in semiconductors,"

Journal of Physics and Chemistry of Solids, vol. 1, pp. 262-269, 1957.

[91] G. W. Ludwig and R. L. Watters, "Drift and Conductivity Mobility in Silicon,"


[92] P. J. Cousins, D. D. Smith, L. Hsin-Chiao, J. Manning, T. D. Dennis, A.

Waldhauer, et al., "Generation 3: Improved performance at lower cost," in

Photovoltaic Specialists Conference (PVSC), 2010 35th IEEE, 2010, pp.

000275-000278.

[93] K. Bothe, J. Schmidt, and R. Hezel, "Effective reduction of the metastable defect

concentration in boron-doped Czochralski silicon for solar cells," in

Photovoltaic Specialists Conference, 2002. Conference Record of the Twenty-

Ninth IEEE, 2002, pp. 194-197.

[94] J. Schmidt and K. Bothe, "Structure and transformation of the metastable boron-

and oxygen-related defect center in crystalline silicon," Physical Review B, vol.

69, 024107, 2004.

[95] V. V. Voronkov, "Grown-in defects in silicon produced by agglomeration of

vacancies and self-interstitials," Journal of Crystal Growth, vol. 310, pp. 1307-

1314, 2008.

[96] R. Falster and V. V. Voronkov, "The engineering of intrinsic point defects in

silicon wafers and crystals," Materials Science and Engineering: B, vol. 73, pp.

87-94, 2000.

[97] V. V. Voronkov and R. Falster, "Vacancy-type microdefect formation in

Czochralski silicon," Journal of Crystal Growth, vol. 194, pp. 76-88, 1998.

[98] R. Falster, "Defect control in silicon crystal growth and wafer processing," Rare

Metals, vol. 22, pp. 53-60, 2003.

Bibliography

168

[99] R. Falster and V. V. Voronkov, "Intrinsic Point Defects and Their Control in

Silicon Crystal Growth and Wafer Processing," MRS bulletin, vol. 25, pp. 28-32,

2000.

[100] J. H. Evans-Freeman, A. R. Peaker, I. D. Hawkins, P. Y. Y. Kan, J. Terry, L.

Rubaldo, et al., "High-resolution DLTS studies of vacancy-related defects in

irradiated and in ion-implanted n-type silicon," Materials Science in

Semiconductor Processing, vol. 3, pp. 237-241, 2000.

[101] F. D. Auret and P. N. K. Deenapanray, "Deep Level Transient Spectroscopy of

Defects in High-Energy Light-Particle Irradiated Si," Critical Reviews in Solid

State and Materials Sciences, vol. 29, pp. 1-44, 2004.

[102] A. Chantre and L. C. Kimerling, "Configurationally multistable defect in

silicon," Applied Physics Letters, vol. 48, pp. 1000-1002, 1986.

[103] G. D. Watkins, "Intrinsic defects in silicon," Materials Science in Semiconductor

Processing, vol. 3, pp. 227-235, 2000.

[104] S. Dannefaer, G. Suppes, and V. Avalos, "Evidence for a vacancy–phosphorus–

oxygen complex in silicon," Journal of Physics: Condensed Matter, vol. 21,

015802, 2009.

[105] J. Makinen, P. Hautojarvi, and C. Corbel, "Positron annihilation and the charge

states of the phosphorus-vacancy pair in silicon," Journal of Physics: Condensed

Matter, vol. 4, pp. 5137-5154, 1992.

[106] W. D. J. Callister, Material Science and Engineering: An introduction, 7th

Edition. (Wiley, 2006).

[107] P. Pichler, Intrinsic Point Defects, Impurities, and Their diffusion in Silicon.

(Springer-Verlag Wien, 2004).

[108] I. Addison Engineering. (2013). Interesting facts about silicon.Available:

http://www.addisonengineering.com/about-silicon.html, (accessed 09.03.2016).

[109] R. Chen, B. Trzynadlowski, and S. T. Dunham, "Phosphorus vacancy cluster

model for phosphorus diffusion gettering of metals in Si," Journal of Applied

Physics, vol. 115, 054906, 2014.

[110] G. D. Watkins and J. W. Corbett, "Defects in Irradiated Silicon. I. Electron Spin

Resonance of the Si-A Center," Physical Review, vol. 121, pp. 1001-1014, 1961.

[111] J. W. Corbett, G. D. Watkins, R. M. Chrenko, and R. S. McDonald, "Defects in

Irradiated Silicon. II. Infrared Absorption of the Si-$A$ Center," Physical

Review, vol. 121, pp. 1015-1022, 1961.

Bibliography

169

[112] W. C. O'Mara, R. B. Haber, and L. P. Hunt, Oxygen, Carbon and Nitrogen in

Silicon, In Handbook of Silicon Technology. (Noyes Publications, Park Ridge,

NJ, USA, 1990).

[113] K. Ravi and C. Varker, "Oxidation‐induced stacking faults in silicon. I.

Nucleation phenomenon," Journal of Applied Physics, vol. 45, pp. 263-271,

1974.

[114] M. Hasebe, Y. Takeoka, S. Shinoyama, and S. Naito, "Formation process of

stacking faults with ringlike distribution in CZ-Si wafers," Japanese journal of

applied physics, vol. 28, L1999, 1989.

[115] J. Haunschild, I. E. Reis, J. Geilker, and S. Rein, "Detecting efficiency‐limiting

defects in Czochralski‐grown silicon wafers in solar cell production using

photoluminescence imaging," physica status solidi (RRL)-Rapid Research

Letters, vol. 5, pp. 199-201, 2011.

[116] H. Angelskår, R. Søndenå, M. Wiig, and E. Marstein, "Characterization of

oxidation-induced stacking fault rings in Cz silicon: Photoluminescence imaging

and visual inspection after Wright etch," Energy Procedia, vol. 27, pp. 160-166,

2012.

[117] J. Š. Lukáš Válek, Defect Engineering During Czochralski Crystal Growth and

Silicon Wafer Manufacturing. (INTECH Open Access Publisher, 2012).

[118] J. Jupille and G. Thornton, Defects at Oxide Surfaces. (Springer, 2015), pp.82.

[119] M. Itsumi, "Octahedral void defects in Czochralski silicon," Journal of Crystal

Growth, vol. 237–239, Part 3, pp. 1773-1778, 2002.

[120] J. Ryuta, E. Morita, T. Tanaka, and Y. Shimanuki, "Crystal-originated

singularities on Si wafer surface after SC1 cleaning," Japanese journal of

applied physics, vol. 29, L1947, 1990.

[121] H. Föll and B. Kolbesen, "Formation and nature of swirl defects in silicon,"

Applied physics, vol. 8, pp. 319-331, 1975.

[122] L. Bernewitz and K. Mayer, "Recent observations on swirl defects in

dislocation‐free silicon," physica status solidi (a), vol. 16, pp. 579-583, 1973.

[123] J.Grabmaier, Silicon chemical etching. (Springer Berlin Heidelberg, 1982).

[124] F. Shimura, Oxygen in Silicon. (Academic Press, London, UK, 1994).

[125] A. Borghesi, B. Pivac, A. Sassella, and A. Stella, "Oxygen precipitation in

silicon," Journal of Applied Physics, vol. 77, pp. 4169-4244, 1995.

Bibliography

170

[126] W. C. Dash, "Improvements on the Pedestal Method of Growing Silicon and

Germanium Crystals," Journal of Applied Physics, vol. 31, pp. 736-737, 1960.

[127] W. C. Dash, "Growth of Silicon Crystals Free from Dislocations," Journal of

Applied Physics, vol. 30, pp. 459-474, 1959.

[128] T. Abe, "The formation mechanism of grown-in defects in CZ silicon crystals

based on thermal gradients measured by thermocouples near growth interfaces,"

Materials Science and Engineering: B, vol. 73, pp. 16-29, 2000.

[129] V. V. Voronkov, "The mechanism of swirl defects formation in silicon," Journal

of Crystal Growth, vol. 59, pp. 625-643, 1982.

[130] R. Brown, D. Maroudas, and T. Sinno, "Modelling point defect dynamics in the

crystal growth of silicon," Journal of crystal growth, vol. 137, pp. 12-25, 1994.

[131] J. A. Van Vechten, "Formation of interstitial-type dislocation loops in

tetrahedral semiconductors by precipitation of vacancies," Physical Review B,

vol. 17, pp. 3197-3206, 1978.

[132] R. Falster, V. V. Voronkov, and F. Quast, "On the Properties of the Intrinsic

Point Defects in Silicon: A Perspective from Crystal Growth and Wafer

Processing," physica status solidi (b), vol. 222, pp. 219-244, 2000.

[133] V. V. Voronkov and R. Falster, "Intrinsic point defects in silicon crystal

growth," in Solid State Phenomena, 2011, pp. 3-14.

[134] N. I. Puzanov and A. M. Eidenzon, "The effect of thermal history during crystal

growth on oxygen precipitation in Czochralski-grown silicon," Semiconductor

Science and Technology, vol. 7, pp. 406-413, 1992.

[135] T. Ueki, M. Itsumi, and T. Takeda, "Octahedral void defects observed in the

bulk of Czochralski silicon," Applied Physics Letters, vol. 70, pp. 1248-1250,

1997.

[136] K. Moriya, "Observation of micro-defects in as-grown and heat treated Si

crystals by infrared laser scattering tomography," Journal of crystal growth, vol.

94, pp. 182-196, 1989.

[137] H. Yamagishi, I. Fusegawa, N. Fujimaki, and M. Katayama, "Recognition of D

defects in silicon single crystals by preferential etching and effect on gate oxide

integrity," Semiconductor Science and Technology, vol. 7, A135, 1992.

[138] S. Sadamitsu, S. Umeno, Y. Koike, M. Hourai, S. Sumita, and T. Shigematsu,

"Dependence of the grown-in defect distribution on growth rates in Czochralski

silicon," Japanese journal of applied physics, vol. 32, 3675, 1993.

Bibliography

171

[139] V. V. Voronkov and R. Falster, "Grown-in microdefects, residual vacancies and

oxygen precipitation bands in Czochralski silicon," Journal of Crystal Growth,

vol. 204, pp. 462-474, 1999.

[140] V. V. Voronkov and R. Falster, "Intrinsic point defects and impurities in silicon

crystal growth," Journal of The Electrochemical Society, vol. 149, pp. G167-

G174, 2002.

[141] P. Petroff and A. De Kock, "The formation of interstitial swirl defects in

dislocation-free floating-zone silicon crystals," Journal of Crystal Growth, vol.

36, pp. 4-10, 1976.

[142] Y. H. Lee and J. W. Corbett, "EPR study of defects in neutron-irradiated silicon:

Quenched-in alignment under< 110>-uniaxial stress," Physical Review B, vol. 9,

pp. 4351-4361, 1974.

[143] Y. H. Lee and J. W. Corbett, "EPR Studies in Neutron-Irradiated Silicon: A

Negative Charge State of a Nonplanar Five-Vacancy Cluster (V 5-)," Physical

Review B, vol. 8, pp. 2810-2826, 1973.

[144] G. Watkins and J. Corbett, "Defects in irradiated silicon: Electron paramagnetic

resonance of the divacancy," Physical Review, vol. 138, pp. A543-A555, 1965.

[145] L. C. Kimerling, H. M. DeAngelis, and J. W. Diebold, "Silicon, ionization

energies and structural information on impurities: O – Pd-H," Solid State

Communications, vol. 16, pp. 171-177, 1975.

[146] G. Watkins and J. Corbett, "Defects in irradiated silicon: electron paramagnetic

resonance and electron-nuclear double resonance of the Si-E center," Physical

Review, vol. 134, pp. A1359-A1377, 1964.

[147] C. Londos, E. Sgourou, D. Hall, and A. Chroneos, "Vacancy-oxygen defects in

silicon: the impact of isovalent doping," Journal of Materials Science: Materials

in Electronics, vol. 25, pp. 2395-2410, 2014.

[148] F. D. Auret and P. N. Deenapanray, "Deep level transient spectroscopy of

defects in high-energy light-particle irradiated Si," Critical reviews in solid state

and materials sciences, vol. 29, pp. 1-44, 2004.

[149] F. Rougieux, N. Grant, and D. Macdonald, "Thermal deactivation of lifetime‐

limiting grown‐in point defects in n‐type Czochralski silicon wafers," physica

status solidi (RRL)-Rapid Research Letters, vol. 7, pp. 616-618, 2013.

Bibliography

172

[150] F. E. Rougieux, N. E. Grant, C. Barugkin, D. Macdonald, and J. D. Murphy,

"Influence of Annealing and Bulk Hydrogenation on Lifetime-Limiting Defects

in Nitrogen-Doped Floating Zone Silicon," Photovoltaics, IEEE Journal of, vol.

5, pp. 495-498, 2015.

[151] N. E. Grant, F. E. Rougieux, and D. Macdonald, "Low temperature activation of

grown-in defects limiting the lifetime of high purity n-type float-zone silicon

wafers," Solid State Phenomena, vol. 242, 2016.

[152] N. Grant, F. Rougieux, D. Macdonald, J. Bullock, and Y. Wan, "Grown-in

defects limiting the bulk lifetime of p-type float-zone silicon wafers," Journal of

Applied Physics, vol. 117, 055711, 2015.

[153] N. E. Grant, K. R. McIntosh, and J. T. Tan, "Evaluation of the bulk lifetime of

silicon wafers by immersion in hydrofluoric acid and illumination," ECS Journal

of Solid State Science and Technology, vol. 1, pp. P55-P61, 2012.

[154] T. Schutz-Kuchly, J. Veirman, S. Dubois, and D. R. Heslinga, "Light-Induced-

Degradation effects in boron–phosphorus compensated n-type Czochralski

silicon," Applied Physics Letters, vol. 96, 093505, 2010.

[155] M. Hirata, M. Hirata, and H. Saito, "The Interactions of Point Defects with

Impurities in Silicon," Journal of the Physical Society of Japan, vol. 27, pp. 405-

414, 1969.

[156] L. C. Kimerling, H. M. DeAngelis, and J. W. Diebold, "On the role of defect

charge state in the stability of point defects in silicon," Solid State

Communications, vol. 16, pp. 171-174, 1975.

[157] H. Saito and M. Hirata, "Nature of Radiation Defects in Silicon Single Crystals,"

Japanese Journal of Applied Physics, vol. 2, pp. 678-687, 1963.

[158] M. Hirata, M. Hirata, H. Saito, and J. H. Crawford, "Effect of Impurities on the

Annealing Behavior of Irradiated Silicon," Journal of Applied Physics, vol. 38,

pp. 2433-2438, 1967.

[159] N. Yuge, H. Baba, Y. Sakaguchi, K. Nishikawa, H. Terashima, and F. Aratani,

"Purification of metallurgical silicon up to solar grade," Solar Energy Materials

and Solar Cells, vol. 34, pp. 243-250, 1994.

[160] K.Ounadjela and A. Bloss, New Metallization technique for 6 MW pilot

production of multicrystalline solar cells using upgraded metallurgical grade

silicon, Sunnyvale2010.

Bibliography

173

[161] D. Kohle, B. Raabe, S. Braun, S. Seren, and G. Hahn, "Upgraded Metallurgical

Grade Silicon Solar Cells: A Detailed Material Analysis," in 24th European

Photovoltaic Solar Energy Conference, Hamburg, Germany, 2009, pp. 1758 -

1761.

[162] J. Kraiem, B. Drevet, F. Cocco, N. Enjalbert, S. Dubois, D. Camel, et al., "High

performance solar cells made from 100% UMG silicon obtained via the

PHOTOSIL process," in Photovoltaic Specialists Conference (PVSC), 2010 35th

IEEE, 2010, pp. 001427-001431.

[163] P. Engelhart, J. Wendt, A. Schulze, C. Klenke, A. Mohr, K. Petter, et al., "R and

D pilot line production of multi-crystalline Si solar cells exceeding cell

efficiencies of 18%," Energy Procedia, vol. 8, pp. 313-317, 2011.

[164] R. Einhaus, J. Kraiem, J. Degoulange, O. Nichiporuk, M. Forster, P. Papet, et al.,

"19% efficiency heterojunction solar cells on Cz wafers from non-blended

Upgraded Metallurgical Silicon," in Photovoltaic Specialists Conference (PVSC),

2012 38th IEEE, 2012, pp. 003234-003237.

[165] Y. Schiele, S. Wilking, F. Book, T. Wiedenmann, and G. Hahn, "Record

Efficiency of PhosTop Solar Cells from n-type Cz UMG Silicon Wafers,"


[166] G. Flamant, V. Kurtcuoglu, J. Murray, and A. Steinfeld, "Purification of

metallurgical grade silicon by a solar process," Solar Energy Materials and

Solar Cells, vol. 90, pp. 2099-2106, 2006.

[167] P. Woditsch and W. Koch, "Solar grade silicon feedstock supply for PV

industry," Solar energy materials and solar cells, vol. 72, pp. 11-26, 2002.

[168] B. Ceccaroli and O. Lohne, "Solar grade silicon feedstock," Handbook of

Photovoltaic Science and Engineering, Wiley pp. 153-204, 2003.

[169] S. Rein, T. Rehrl, W. Warta, and S. W. Glunz, "Lifetime spectroscopy for defect

characterization: Systematic analysis of the possibilities and restrictions,"

Journal of Applied Physics, vol. 91, pp. 2059-2070, 2002.

[170] W. Shockley and W. Read Jr, "Statistics of the recombinations of holes and

electrons," Physical review, vol. 87, pp. 835-842, 1952.

[171] R. N. Hall, "Electron-hole recombination in germanium," Physical Review, vol.

87, 387, 1952.

[172] J. Safarian, G. Tranell, and M. Tangstad, "Processes for upgrading metallurgical

grade silicon to solar grade silicon," Energy Procedia, vol. 20, pp. 88-97, 2012.

Bibliography

174

[173] A. Luque and S. Hegedus, Handbook of photovoltaic science and engineering.

(John Wiley & Sons, 2011), pp.184-187.

[174] V. Zadde, A. Pinov, D. Strebkov, E. Belov, N. Efimov, E. Lebedev, et al., "New

method of solar grade silicon production," in 12th Workshop on Crystalline

Silicon Solar Cell Materials and Processes, Breckenridge, 11–14 August, 2002,

pp. 179-189.

[175] G. F. Wakefield, T. Chu, G. Brown, and V. Harrap, Solar silicon definition.

Final report, 15 Oct 1974-15 Sep 1975, Texas Instruments, Inc., Dallas

(USA)1975.

[176] G. Wakefield, P. Maycock, and T. Chu, "11th IEEE Photovoltaic Specialists

Conference," ed: IEEE, New York, 1975.

[177] J. R. Davis Jr, A. Rohatgi, R. H. Hopkins, P. D. Blais, P. Rai-Choudhury, J. R.

Mccormick, et al., "Impurities in silicon solar cells," Electron Devices, IEEE


[178] E. Dornberger, "Tiny spheres with a big effect," Innovations, Wacker Co.

internal newsletter, 2005.

[179] H. Block and G. Wagner, "The bayer route to low cost solar grade silicon," in

Proc. 16th Eur. Photovoltaic Solar Energy Conf.“Crystalline Silicon Solar Cells

and Technologies, 2000, pp. 1-6.

[180] A. Tilg and L. Mleczko, "Predictive Model of Silane Pyrolysis in a fluid-bed

reactor," presented at the Silicon for the chemical Industry V, Norway, 2000.

[181] Tokuyama Corp., Responsible Care & Eco Management Department Tokuyama

Corporation-Responsible Care Report, 2005.

[182] Chisso Corporation, Production technology co-development of Chisso solar-

grade silicon, 2006.

[183] B. Sørensen, "Life-cycle analysis of present and future Si-based solar cells," in

Proc. 2nd World Conf. Pv Solae Energy Conversion, Vienna, 1998.

[184] B. Kindembe, Thematic Research Report on Environmental Issues, 2004.

Available:http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.531.8594&r

ep=rep1&type=pdf, (accessed 09.03.2016).

[185] F. A. Trumbore, "Solid solubilities of impurity elements in germanium and

silicon*," Bell System Technical Journal, vol. 39, pp. 205-233, 1960.

Bibliography

175

[186] R. Hopkins, R. Seidensticker, J. Davis, P. Rai-Choudhury, P. Blais, and J.

McCormick, "Crystal growth considerations in the use of “solar grade” silicon,"

Journal of Crystal Growth, vol. 42, pp. 493-498, 1977.

[187] R. Hull, Properties of crystalline silicon. (IET, 1999), pp.16-22.

[188] J. Dietl, "Hydrometallurgical purification of metallurgical-grade silicon," Solar

Cells, vol. 10, pp. 145-154, 1983.

[189] I. Santos, A. Goncalves, C. S. Santos, M. Almeida, M. Afonso, and M. J. Cruz,

"Purification of metallurgical grade silicon by acid leaching," Hydrometallurgy,

vol. 23, pp. 237-246, 1990.

[190] S.-S. Lian, R. Kammel, and M. Kheiri, "Preliminary study of hydrometallurgical

refining of MG-silicon with attrition grinding," Solar energy materials and solar

cells, vol. 26, pp. 269-276, 1992.

[191] Voos W., 1961. Patent U.S. Patent 2, 972, 521.

[192] L. Hunt, V. Dosaj, J. McCormick, and L. Crossman, "Purification of

metallurgical-grade silicon to solar-grade quality," in International Symposium

on Solar Energy, 1976, pp. 200-215.

[193] T. Chu and S. S. Chu, "Partial purification of metallurgical silicon by acid

extraction," Journal of The Electrochemical Society, vol. 130, pp. 455-457, 1983.

[194] C. E. Norman, E. M. Absi, and R. E. Thomas, "Solar-grade silicon substrates by

a powder-to-ribbon process," Canadian journal of Physics, vol. 63, pp. 859-862,

1985.

[195] J. Juneja and T. Mukherjee, "A study of the purification of metallurgical grade

silicon," Hydrometallurgy, vol. 16, pp. 69-75, 1986.

[196] J.-j. WU, Y. Bin, Y.-n. DAI, and K. Morita, "Boron removal from metallurgical

grade silicon by oxidizing refining," Transactions of Nonferrous Metals Society

of China, vol. 19, pp. 463-467, 2009.

[197] K. Suzuki, T. Kumagai, and N. Sano, "Removal of Boron from Metallurgical-

grade Silicon by Applying the Plasma Treatment," ISIJ international, vol. 32, pp.

630-634, 1992.

[198] A. Yvon, E. Fourmond, C. Ndzogha, Y. Delannoy, and C. Trassy, "Inductive

Plasma Process For Refining Of Solar Grade Silicon," in EPM 2003 4th

International Conference on Electromagnetic Processing of Materials, 2003, pp.

125-130.

Bibliography

176

[199] C. Alemany, C. Trassy, B. Pateyron, K.-I. Li, and Y. Delannoy, "Refining of

metallurgical-grade silicon by inductive plasma," Solar energy materials and

solar cells, vol. 72, pp. 41-48, 2002.

[200] K. Suzuki, K. Sakaguchi, T. Nakagiri, and N. Sano, "Gaseous Removal of

Phosphorus and Boron from Molten Silicon " Journal of Japan Institute of

Metals and Materials, vol. 54, pp. 161-167, 1990.

[201] B. Gribov and K. Zinov'ev, "Preparation of high-purity silicon for solar cells,"

Inorganic materials, vol. 39, pp. 653-662, 2003.

[202] J.-j. Wu, Y.-l. Li, K.-x. WEI, Y. Bin, and Y.-n. DAI, "Boron removal in

purifying metallurgical grade silicon by CaO–SiO 2 slag refining," Transactions

of Nonferrous Metals Society of China, vol. 24, pp. 1231-1236, 2014.

[203] T. Weiss and K. Schwerdtfeger, "Chemical equilibria between silicon and slag

melts," Metallurgical and Materials Transactions B, vol. 25, pp. 497-504, 1994.

[204] L. A. V. Teixeira, Y. Tokuda, T. Yoko, and K. Morita, "Behavior and state of

boron in CaO-SiO2 slags during refining of solar grade silicon," ISIJ

international, vol. 49, pp. 777-782, 2009.

[205] D.-w. Luo, L. Ning, Y.-p. Lu, G.-l. Zhang, and T.-j. Li, "Removal of boron from

metallurgical grade silicon by electromagnetic induction slag melting,"

Transactions of Nonferrous Metals Society of China, vol. 21, pp. 1178-1184,

2011.

[206] M. Johnston and M. Barati, "Distribution of impurity elements in slag–silicon

equilibria for oxidative refining of metallurgical silicon for solar cell

applications," Solar energy materials and solar cells, vol. 94, pp. 2085-2090,

2010.

[207] C. P. Khattak and F. Schmid, "Growth of the world's largest sapphire crystals,"

Journal of crystal growth, vol. 225, pp. 572-579, 2001.

[208] K. Suzuki and N. Sano, "Thermodynamics for removal of boron from

metallurgical silicon by flux treatment," in Tenth EC Photovoltaic Solar Energy

Conference, 1991, pp. 273-275.

[209] T. Ikeda and M. Maeda, "Purification of metallurgical silicon for solar-grade

silicon by electron beam button melting," ISIJ international, vol. 32, pp. 635-

642, 1992.

Bibliography

177

[210] J. Pires, J. Otubo, A. Braga, and P. Mei, "The purification of metallurgical grade

silicon by electron beam melting," Journal of Materials Processing Technology,

vol. 169, pp. 16-20, 2005.

[211] T. Yoshikawa and K. Morita, "Removal of phosphorus by the solidification

refining with Si–Al melts," Science and Technology of Advanced Materials, vol.

4, pp. 531-537, 2003.

[212] T. Yoshikawa, K. Arimura, and K. Morita, "Boron removal by titanium addition

in solidification refining of silicon with Si-Al melt," Metallurgical and

Materials Transactions B, vol. 36, pp. 837-842, 2005.

[213] N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, et al.,

"Purification of metallurgical-grade silicon up to solar grade," Progress in

Photovoltaics: Research and Applications, vol. 9, pp. 203-209, 2001.

[214] T. Margaria, F. Cocco, J. Kraiem, J. Degoulange, D. Pelletier, D. Sarti, et al.,

"Status of the Photosil project for the production of solar grade silicon from

metallurgical silicon," Proc. of 25th European PVSC, pp. 1506-1509, 2010.

[215] T. Margaria, F. Cocco, L. Neulat, J. Kraiem, R. Einhaus, J. Degoulange, et al.,

"UMG Silicon from the PHOTOSIL project–a status overview in 2011 on the

way towards industrial production," Proceedings of the 26th PVSEC, Hamburg,

2011.

[216] R. Einhaus, D. Grosset-Bourbange, B. Drevet, D. Camel, D. Pelletier, F. Coco,

et al., "Puryfing UMG silicon at the French PHOTOSIL project," in

Photovoltaics International, 2010, pp. 60-65.

[217] Elkem Solar-investment decision-Skøyen Internal Report, 27 October 2006.

[218] L. Geerligs, G. Wyers, R. Jensen, O. Raaness, A. Waernes, S. Santén, et al.,

Solar-grade silicon by a direct route based on carbothermic reduction of silica:

requirements and production technology. (Energy research Centre of the

Netherlands ECN, 2002).

[219] M. Levy, P. Yu, Y. Zhang, and M. Sarachik, "Photoluminescence of heavily

doped, compensated Si: P, B," Physical Review B, vol. 49, pp. 1677-1684, 1994.

[220] J. Libal, S. Novaglia, M. Acciarri, S. Binetti, R. Petres, J. Arumughan, et al.,

"Effect of compensation and of metallic impurities on the electrical properties of

Cz-grown solar grade silicon," Journal of Applied Physics, vol. 104, 104507,

2008.

Bibliography

178

[221] S. Dubois, N. Enjalbert, and J. Garandet, "Effects of the compensation level on

the carrier lifetime of crystalline silicon," Applied Physics Letters, vol. 93,

032114, 2008.

[222] B. Lim, M. Wolf, and J. Schmidt, "Carrier mobilities in multicrystalline silicon

wafers made from UMG‐Si," physica status solidi (c), vol. 8, pp. 835-838, 2011.

[223] A. Cuevas, "The paradox of compensated silicon," in Optoelectronic and

Microelectronic Materials and Devices, 2008. COMMAD 2008. Conference on,

2008, pp. 238-241.

[224] H. Schlangenotto, H. Maeder, and W. Gerlach, "Temperature dependence of the

radiative recombination coefficient in silicon," physica status solidi (a), vol. 21,

pp. 357-367, 1974.

[225] M. Tyagi and R. Van Overstraeten, "Minority carrier recombination in heavily-

doped silicon," Solid-State Electronics, vol. 26, pp. 577-597, 1983.

[226] J. Kraiem, R. Einhaus, and H. Lauvray, "Doping engineering as a method to

increase the performance of purified MG silicon during ingot crystallisation," in

Photovoltaic Specialists Conference (PVSC), 2009 34th IEEE, 2009, pp.

001327-001330.

[227] J. Veirman, S. Dubois, N. Enjalbert, J.-P. Garandet, and M. Lemiti, "Electronic

properties of highly-doped and compensated solar-grade silicon wafers and solar

cells," Journal of Applied Physics, vol. 109, 103711, 2011.

[228] J. Veirman, S. Dubois, N. Enjalbert, J. Garandet, B. Martel, D. Heslinga, et al.,

"BP COMPENSATION IN SOG SILICON: CURE OR CURSE?," Proceedings

of the 24th EU-PVSEC, Hamburg, Germany, 2009.

[229] D. Macdonald and A. Cuevas, "Recombination in compensated crystalline

silicon for solar cells," Journal of Applied Physics, vol. 109, 043704, 2011.

[230] C. Xiao, D. Yang, X. Yu, X. Gu, and D. Que, "Influence of the compensation

level on the performance of p-type crystalline silicon solar cells: Theoretical

calculations and experimental study," Solar Energy Materials and Solar Cells,

vol. 107, pp. 263-271, 2012.

[231] S. Pizzini and C. Calligarich, "On the Effect of Impurities on the Photovoltaic

Behavior of Solar‐Grade Silicon I. The Role of Boron and Phosphorous Primary

Impurities in p‐type Single‐Crystal Silicon," Journal of the Electrochemical

Society, vol. 131, pp. 2128-2132, 1984.

Bibliography

179

[232] J. Veirman, S. Dubois, J. Stendera, B. Martel, N. Enjalbert, and T. Desrues,

"Mapping of the dopant compensation effects on the reverse and forward

characteristics of solar cells," in Photovoltaic Specialists Conference (PVSC),

2012 38th IEEE, 2012, pp. 000302-000306.

[233] C. Xiao, D. Yang, X. Yu, P. Wang, P. Chen, and D. Que, "Effect of dopant

compensation on the performance of Czochralski silicon solar cells," Solar

Energy Materials and Solar Cells, vol. 101, pp. 102-106, 2012.

[234] M. Green, Solar Cells Operating Principles, Technology and System

Applications. (Prentice Hall, 1982), pp.96-98.

[235] S. De Wolf, J. Szlufcik, Y. Delannoy, I. Perichaud, C. Häßler, and R. Einhaus,

"Solar cells from upgraded metallurgical grade (UMG) and plasma-purified

UMG multi-crystalline silicon substrates," Solar energy materials and solar

cells, vol. 72, pp. 49-58, 2002.

[236] D. Kohler, B. Raabe, S. Braun, S. Seren, and G. Hahn, "Upgraded metallurgical

grade silicon solar cells: a detailed material analysis," in 24th European

Photovoltaic Solar Energy Conference, 2009, pp. 1758-1761.

[237] T. Schutz‐Kuchly, V. Sanzone, and Y. Veschetti, "N‐type solar‐grade silicon

purified via the metallurgical route: characterisation and fabrication of solar

cells," Progress in Photovoltaics: Research and Applications, vol. 21, pp. 1214-

1221, 2013.

[238] T. Chen, Y. Zhao, Z. Dong, T. Liu, J. Wang, and H. Xie, "Analysis of solar cells

fabricated from UMG-Si purified by a novel metallurgical method,"

Semiconductor Science and Technology, vol. 28, 015024, 2013.

[239] D. Macdonald, F. Rougieux, A. Cuevas, B. Lim, J. Schmidt, M. Di Sabatino, et

al., "Light-induced boron-oxygen defect generation in compensated p-type

Czochralski silicon," Journal of Applied Physics, vol. 105, 093704, 2009.

[240] K. A. Münzer, "Hydrogenated Silicon Nitride for Regeneration of Light Induced

Degradation," in 24th European Photovoltaic Solar Energy Conference

Hamburg, Germany, 2009, pp. 1558 - 1561.

[241] A. Herguth, G. Schubert, M. Kaes, and G. Hahn, "A New Approach to Prevent

the Negative Impact of the Metastable Defect in Boron Doped CZ Silicon Solar

Cells," in Photovoltaic Energy Conversion, Conference Record of the 2006

IEEE 4th World Conference on, 2006, pp. 940-943.

Bibliography

180

[242] T. Niewelt, J. Broisch, J. Schön, J. Haunschild, S. Rein, W. Warta, et al., "Light-

induced Degradation and Regeneration in n-type Silicon," Energy Procedia, vol.

77, pp. 626-632, 2015.

[243] S. Wilking, M. Forster, A. Herguth, and G. Hahn, "From simulation to

experiment: Understanding BO-regeneration kinetics," Solar Energy Materials

and Solar Cells, vol. 142, pp. 87-91, 2015.

[244] B. J. Hallam, S. R. Wenham, P. G. Hamer, M. D. Abbott, A. Sugianto, C. E.

Chan, et al., "Hydrogen Passivation of B-O Defects in Czochralski Silicon,"


[245] R. Søndenå, A. Holt, and A.-K. Soiland, "Electrical Properties of Compensated

n- and p-Type Monocrystalline Silicon," in 26th European Photovoltaic Solar

Energy Conference and Exhibition, Hamburg, Germany, 2011, pp. 1824 - 1828.

[246] B. Lim, K. Bothe, and J. Schmidt, "Deactivation of the boron–oxygen

recombination center in silicon by illumination at elevated temperature," physica

status solidi (RRL) – Rapid Research Letters, vol. 2, pp. 93-95, 2008.

[247] R. A. Sinton and A. Cuevas, "Contactless determination of current–voltage

characteristics and minority‐carrier lifetimes in semiconductors from quasi‐

steady‐state photoconductance data," Applied Physics Letters, vol. 69, pp. 2510-

2512, 1996.

[248] E. Basaran, C. P. Parry, R. A. Kubiak, T. E. Whall, and E. H. C. Parker,

"Electrochemical capacitance-voltage depth profiling of heavily boron-doped

silicon," Journal of Crystal Growth, vol. 157, pp. 109-112, 1995.

[249] R. R. King, R. A. Sinton, and R. M. Swanson, "Studies of diffused phosphorus

emitters: saturation current, surface recombination velocity, and quantum

efficiency," IEEE Transactions on Electron Devices, vol. 37, pp. 365-371, 1990.

[250] R. A. Sinton and R. M. Swanson, "Recombination in highly injected silicon,"

Electron Devices, IEEE Transactions on, vol. 34, pp. 1380-1389, 1987.

[251] D. Kane and R. Swanson, "Measurement of the emitter saturation current by a

contactless photoconductivity decay method," in IEEE photovoltaic specialists

conference. 18, 1985, pp. 578-583.

[252] D. K. Schroder and D. L. Meier, "Solar cell contact resistance;A review," IEEE

Transactions on Electron Devices, vol. 31, pp. 637-647, 1984.

[253] M. J. Turner and E. H. Rhoderick, "Metal-silicon Schottky barriers," Solid-State

Electronics, vol. 11, pp. 291-300, 1968.

Bibliography

181

[254] H. Berger, "Contact resistance and contact resistivity," Journal of the

Electrochemical Society, vol. 119, pp. 507-514, 1972.

[255] K. R. McIntosh, "Lumps, humps and bumps: Three detrimental effects in the

current-voltage curve of silicon solar cells," University of New South Wales,

2001.

[256] C.-T. Sah, R. Noyce, and W. Shockley, "Carrier generation and recombination

in pn junctions and pn junction characteristics," Proceedings of the IRE, vol. 45,

pp. 1228-1243, 1957.

[257] R. A. Sinton and A. Cuevas, "A Quasi-Steady-State Open-Circuit Voltage

Method for Solar Cell Characterization," in 16th European Photovoltaic Solar

Energy Conference, Hamburg, Germany, 2000, pp. 1152–1155.

[258] D. Pysch, A. Mette, and S. W. Glunz, "A review and comparison of different

methods to determine the series resistance of solar cells," Solar Energy

Materials and Solar Cells, vol. 91, pp. 1698-1706, 2007.

[259] V. V. Voronkov, R. Falster, B. Lim, and J. Schmidt, "Permanent recovery of

electron lifetime in pre-annealed silicon samples: A model based on Ostwald

ripening," Journal of Applied Physics, vol. 112, 113717, 2012.

[260] C. Sun, F. E. Rougieux, and D. Macdonald, "A unified approach to modelling

the charge state of monatomic hydrogen and other defects in crystalline silicon,"

Journal of Applied Physics, vol. 117, 045702, 2015.

[261] A. Fell, "A free and fast three-dimensional/two-dimensional solar cell simulator

featuring conductive boundary and quasi-neutrality approximations," Electron

Devices, IEEE Transactions on, vol. 60, pp. 733-738, 2013.

[262] A. Cuevas, P. A. Basore, G. Giroult‐Matlakowski, and C. Dubois, "Surface

recombination velocity of highly doped n‐type silicon," Journal of Applied

Physics, vol. 80, pp. 3370-3375, 1996.

[263] J. Benick, B. Hoex, M. Van de Sanden, W. Kessels, O. Schultz, and S. W. Glunz,

"High efficiency n-type Si solar cells on Al2O3-passivated boron emitters," Appl.

Phys. Lett, vol. 92, 253504, 2008.

[264] PVLighthouse.Available: https://www.pvlighthouse.com.au/, (accessed

21.03.2016).

[265] R. Brendel, S. Dreissigacker, N.-P. Harder, and P. Altermatt, "Theory of

analyzing free energy losses in solar cells," Applied Physics Letters, vol. 93,

173503, 2008.

Bibliography

182

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