Interpretation of Admittance, Voltage, And Current-Voltage Signatures in Cu(in,Ga)Se2 Thin Film...

8/3/2019 Interpretation of Admittance, Voltage, And Current-Voltage Signatures in Cu(in,Ga)Se2 Thin Film Solar Cells

1/13

Interpretation of admittance, capacitance-voltage, and current-voltagesignatures in Cu(In,Ga)Se2 thin film solar cellsTobias Eisenbarth, Thomas Unold, Raquel Caballero, Christian A. Kaufmann, and Hans-Werner Schock

Citation: J. Appl. Phys. 107, 034509 (2010); doi: 10.1063/1.3277043

View online: http://dx.doi.org/10.1063/1.3277043

View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v107/i3

Published by the American Institute of Physics.

Additional information on J. Appl. Phys.

Journal Homepage: http://jap.aip.org/

Journal Information: http://jap.aip.org/about/about_the_journal

Top downloads: http://jap.aip.org/features/most_downloadedInformation for Authors: http://jap.aip.org/authors

Downloaded 25 Nov 2011 to 160.78.60.200. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
http://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Tobias%20Eisenbarth&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Thomas%20Unold&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Raquel%20Caballero&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Christian%20A.%20Kaufmann&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Hans-Werner%20Schock&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/?ver=pdfcovhttp://link.aip.org/link/doi/10.1063/1.3277043?ver=pdfcovhttp://jap.aip.org/resource/1/JAPIAU/v107/i3?ver=pdfcovhttp://www.aip.org/?ver=pdfcovhttp://jap.aip.org/?ver=pdfcovhttp://jap.aip.org/about/about_the_journal?ver=pdfcovhttp://jap.aip.org/features/most_downloaded?ver=pdfcovhttp://jap.aip.org/authors?ver=pdfcovhttp://jap.aip.org/authors?ver=pdfcovhttp://jap.aip.org/features/most_downloaded?ver=pdfcovhttp://jap.aip.org/about/about_the_journal?ver=pdfcovhttp://jap.aip.org/?ver=pdfcovhttp://www.aip.org/?ver=pdfcovhttp://jap.aip.org/resource/1/JAPIAU/v107/i3?ver=pdfcovhttp://link.aip.org/link/doi/10.1063/1.3277043?ver=pdfcovhttp://jap.aip.org/?ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Hans-Werner%20Schock&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Christian%20A.%20Kaufmann&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Raquel%20Caballero&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Thomas%20Unold&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://jap.aip.org/search?sortby=newestdate&q=&searchzone=2&searchtype=searchin&faceted=faceted&key=AIP_ALL&possible1=Tobias%20Eisenbarth&possible1zone=author&alias=&displayid=AIP&ver=pdfcovhttp://aipadvances.aip.org/?ver=pdfcovhttp://jap.aip.org/?ver=pdfcov


2/13

Interpretation of admittance, capacitance-voltage, and current-voltagesignatures in CuIn,GaSe2 thin film solar cells

Tobias Eisenbarth, Thomas Unold,a Raquel Caballero, Christian A. Kaufmann, andHans-Werner Schock

Helmholtz-Zentrum Berlin fr Materialien und Energie, Glienicker Strasse 100, 14109 Berlin, Germany

Received 3 August 2009; accepted 26 November 2009; published online 12 February 2010

A series of CuIn,GaSe2 CIGS thin film solar cells with differently prepared heterojunctions hasbeen investigated by admittance spectroscopy, capacitance-voltage CV profiling, and temperaturedependent current-voltage IVT measurements. The devices with different CdS buffer layerthicknesses, with an In2S3 buffer or with a Schottky barrier junction, all show the characteristic

admittance step at shallow energies between 40 and 160 meV, which has often been referred to as

the N1 defect. No correlation between the buffer layer thickness and the capacitance step is found.

IVT measurements show that the dielectric relaxation frequency of charge carriers in the CdS layers

is smaller than the N1-resonance frequency at low temperatures where the N1 step in admittance is

observed. These results strongly contradict the common assignment of the N1 response to a donor

defect at or close to the heterointerface. In contrast, an explanation for the N1 response is proposed,

which relates the admittance step to a non-Ohmic back-contact acting as a second junction in the

device. The model, which is substantiated with numerical device simulations, allows a unified

explanation of characteristic admittance, CV, and IVT features commonly observed in CIGS solar

cells. 2010 American Institute of Physics. doi:10.1063/1.3277043

I. INTRODUCTION

During the past decades, thin film solar cells employing

the quaternary semiconductor CuIn,GaSe2 CIGS as aphotoactive layer have made significant progress with the

demonstration of conversion efficiencies close to 20%.1

However, knowledge about defects in CIGS and their influ-

ence on the device performance is still incomplete. Phenom-

ena such as the rollover, crossover, and a red kink in the IV

characteristics are often observed for CIGS solar cells and

have been subject to controversial debate for many years.Capacitance profiling is a standard technique widely used for

deriving material quantities essential to the understanding of

solar cell device operation, such as the carrier concentration

and the distribution of defects in the absorber layer. For

CIGS capacitance profiling yields charge carrier profiles,

which are very difficult to interpret.

Controversy has also surrounded the interpretation of ad-

mittance measurements on CIGS solar cells. In many such

studies, CIGS solar cells have been found to exhibit a shal-

low defect contribution with an activation energy EA100 meV, which has been denoted as the N1 defect bymany authors, in order to distinguish it from another com-

monly observed deeper defect state contribution, N2, with an

activation energy EA250 300 meV.2

The identification of

the spatial location of the N1 defect has been a subject of

discussion for the past 20 years. Air annealing experiments3

revealed an energetic shift of the N1 defect to deeper ener-

gies, whereas the energetic position of the N2 defect was

unaffected. This observation suggested the identification of

the N1 as an interface defect. Also, deep level transient spec-

troscopy DLTS investigations4 associated this defect with a

minority carrier trap thus supporting the interface defect

theory. On the other hand, admittance measurements with

applied reverse bias2

indicated no change in the energetic

position of the N1. Such a behavior is a general characteristic

of a bulk defect, but may also be consistent with an interface

contribution, if the Fermi level is pinned at the interface.

Thus, in accordance with this result, doping-type inversion

and Fermi level pinning at the interface were deduced.4

Such

a Fermi level pinning at the interface was also used to ex-plain the minor role of recombination at the heterointerface.

5

The interface inversion was assumed3

to be caused by the

VSe donor vacancy providing the necessary charge at the in-

terface. This picture also seemed to be in agreement with the

N1 shift during annealing experiments, by assuming a passi-

vation of selenium vacancies by oxygen impurities.

These interpretations of the N1-admittance response rely

on an interaction of electrons in the conduction band with the

N1-interface states in order to explain the admittance mea-

surements. Consequently, the N1 contribution to capacitance

measurements should be affected by changes in the charge

distribution on the n-side of the heterojunction. In particular,one expects a dependence of the defect step height in admit-

tance on the extension of the space charge region SCR at

the n-side of the junction and therefore also on the thickness

of the CdS buffer layer. Indeed, a reduction in the step height

with decreased CdS buffer layer thickness was found in one

study.6

However, in several other studies,7,8,2

the change in

the admittance step could not be quantitatively correlated

with changes in the n-side of the heterojunction. To under-

stand this discrepancy, it was proposed that the N1 relatedaElectronic mail: [email protected].

JOURNAL OF APPLIED PHYSICS 107, 034509 2010

0021-8979/2010/1073 /034509/12/$30.00 2010 American Institute of Physics107, 034509-1

http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://-/?-http://-/?-http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043http://-/?-http://dx.doi.org/10.1063/1.3277043http://dx.doi.org/10.1063/1.3277043


3/13

defect states are not located at the interface but within an

n-type inverted region in the absorber close to the

heterointerface.9

Other characteristics and unusual features in CIGS solar

cells are the observed crossing of the dark and illuminated IV

curves crossover,10 the distortion of the red illuminated IVcurve in the fourth quadrant and fill factor losses red kink,11

and the partial saturation of the forward current rollover.12

The IV rollover was initially explained by a double-diode

effect13

caused by a Schottky diode at the back-contact with

opposite polarity compared to the heterojunction. However,

subsequent detailed investigations of the CIGS/Mo interface

indicated an Ohmic back-contact and revealed good collec-

tion efficiencies for electrons generated at the

back-contact.1416

Further studies17

showed the crossover ef-

fect only for blue light but not for red illumination, indicat-

ing that the crossover was caused by photon absorption andcharge carrier generation in the CdS buffer layer. Based on

the assumption of an Ohmic back-contact and a significant

influence of the CdS buffer layer on the device characteris-

tics, a model was introduced assuming deep acceptor states

in the CdS buffer layer, which compensate donors and result

in a low net CdS charge density in equilibrium.18

Such an

insulating characteristic causes a substantial fraction of the

built-in voltage to drop across the CdS resulting in a barrier

for both injected and photogenerated carriers as shown in

Fig. 1a, thus explaining the red kink in the IV characteristicdescribed above.

10However, since such a barrier is inconsis-

tent with Fermi level pinning at the buffer/absorber interface

Fig. 1b a revised model was put forward to explain thetemperature dependent current-voltage IVT crossover ef-fects and the N1-admittance characteristics.

6For this model

the presence of a so-called p+ layer with deep acceptors in

an ordered defect compound ODC layer close to the het-erointerface was assumed. The IV crossover was explained

by an illumination-induced change in the potential barrier

associated with the p+ layer: Photogenerated holes in the

CdS and the ODC neutralize ionized deep acceptors in the

ODC leading to a reduction in the voltage drop in the ODC.

The resulting increase in the electron density leads to an

increased recombination under illumination. This concept of

a p+ layer has been generally adopted for the explanation of

the crossover behavior. We note that all of the above men-

tioned models for explaining the IVT characteristics in CIGS

solar cells are very sensitive to specific assumptions about

material properties such as band offsets, interface defect, and

charge density, and the values of the capture cross sections of

defects.

Another controversial issue in CIGS is the interpretation

of capacitance-voltage CV profiling measurements. The de-

termination of the built-in voltage and doping concentrationfrom a standard interpretation of a MottSchottky plot

breaks down when the location of charge response is signifi-

cantly shifted away from the edge of the depletion region

due to the presence of deeper states within the band gap.

Polycrystalline materials, such as CIGS thin films and de-

vices, are very likely to contain a significant number of deep

defects. The measurement of defect profiles Ntx by meansof CV profiling has often led to U-shaped profiles with an

apparent increase in the defect density toward the bulk and

an increase toward the heterointerface.8

Recent

publications19,20

explained the increase in defect profiles at

large distances from the heterointerface by an accumulation

of static charge in deep acceptor states caused by the dc biassweep.

21The increase in the defect profiles toward the h et-

erointerface has often been interpreted as a real effect.22

Here, a systematic analysis of capacitance and IVT measure-

ments on standard CIGS solar cells is provided. The results

are discussed in the context of existing models leading to a

contradiction with a number of assumptions that have been

essential to these models. In turn, an alternative comprehen-

sive model is outlined, which can consistently explain most

phenomena observed in capacitance and IVT measurements.

The outline of this article is as follows. Section II sum-

marizes the possible admittance contributions. Section III

gives a brief outline of the experimental procedures used in

this study. In Sec. IV admittance and capacitance profiling

data, as well the IVT results, are presented. In Sec. V the

results are discussed in the light of the existing models and

an alternative, much simpler explanation for the main mea-

surement characteristics is presented. In Sec. VI the model is

substantiated by device simulations and final conclusions are

drawn in Sec. VII.

II. ADMITTANCE SPECTROSCOPY

Admittance spectroscopy involves the measurement of

the complex admittance

Y,T = iC,T + G,T , 1

consisting of the capacitance C and the conductance G, as a

function of frequency and temperature T. In the case of a

p-n junction containing only shallow donors and acceptors,

the capacitance is determined by the width of the SCR, pro-

vided the majority carriers can respond at the ac frequency

= 2f and temperature T of the measurement. The charac-

teristic frequency of carrier response is related to the dielec-

tric relaxation time D by

FIG. 1. Band diagrams show possible barriers for the diode current. aIllumination dependent net carrier concentration in the CdS modulates the

barrier height for the current transport at the CdS/CIGS interface. b Lightmodulated charge occupation of deep acceptor states in the OVC changes

the barrier height in the OVC layer whereas the position of the Fermi level

at the CdS/CIGS interface stays constant.

034509-2 Eisenbarth et al. J. Appl. Phys. 107, 034509 2010



4/13

D =2

D

=

, 2

with the dielectric constant and conductivity . For mea-

surement frequencies D, the carriers are frozen out

Fig. 2, the whole semiconductor behaves as a dielectric,and the capacitance approaches its geometrical value Cgeo

=A /d, where d is the sample thickness.At higher temperatures additional steps in the admittance

spectra may occur due to the charging and discharging of

defects at a location where the energy level Et of electron

hole traps crosses the quasi Fermi level EFn EFp. This isillustrated in Fig. 2 left as a step between the capacitance athigher frequencies, CHf, and the capacitance at lower fre-

quencies, CLf step 1. The same step is also visible if thecapacitance is plotted versus the temperature as shown in

Fig. 2 right. For consistency with the notation commonlyused in literature, the lower capacitance plateau will be

called CHf and the higher capacitance plateau will be called

CLf for both cases. The characteristic frequency for this ca-

pacitance response is related to the thermal emission depthEA of the defect and can be expressed by the following equa-

tion:

0 = 2f0 = NC,Vvthn,peEA/kT = 20T

2eEA/kT, 3

where NC,V is the effective density of states in the conduction

or valence band, vth is the thermal velocity, and n,p is the

electron/hole capture cross section. On the right hand side of

Eq. 3, a thermal emission prefactor 0 is introduced, whichcomprises all temperature independent terms of the thermal

velocity vth and the effective density of states NC,V. As shown

in earlier investigations,23

an increase in 0 with increasing

activation energy EA

is commonly found, in accordance with

the generally observed MeyerNeldel rule.24

The junction capacitance response may be obtained from

an integration of the Poisson equation and can be written as

C=A

x x =

xxdx

0

xdx

, 4

where x describes the distance to the interface and is the

variation of charge density caused by the oscillating bias. In

the general case the integral extends over both sides of the

homojunction or heterojunction device. In Sec. II A and II B

the capacitance response expected for different defects and

junction geometries proposed for CIGS devices in literature

is briefly outlined.

A. Bulk defect response

Figure 3a shows a p-type absorber with a shallow dop-ing density NA and a defect level EtA above the valence band,

crossing the Fermi level within the p-side of the SCR. The

applied alternating voltage induces a change in the charge

density at the edges of the SCR and at the position xtA where

the defect crosses the Fermi level. For smaller than the

thermal emission frequency of the defect, 0, the first mo-

ment of charge response x decreases to a value xp=NtAxtA +NAxp / NtA +NA. For frequencies larger than 0,the defect does not follow the alternating voltage. Thus, the

two values of the capacitances CHf and CLf are

CLf = A1

xp + xn CHf = A1

xp + xn . 5

B. Interface defect response

In the case of a defect crossing the Fermi level at or

close to the interface Fig. 3b, an interaction of the defectlevel EtD with electrons from the conduction band takes

place, if the energetic distance from the Fermi level at the

interface to the conduction band minimum is sufficiently

small. At frequencies, larger than the thermal emission rate

0 of the defects at the interface, the capacitance is deter-

mined by the extension of the space charge regions xn and xp

FIG. 2. Admittance spectra for a standard CIGS solar cell reveal the freeze-

out of the majority carriers of the absorber layer. With increasing tempera-

tures an admittance step occurs between CHf high frequency and CLf lowfrequency.

FIG. 3. Possible defect responses of the device with a single discrete defect

illustrated for a pn-junction. a An acceptor level EtA crosses the Fermilevel in the SCR of the bulk and affects the charge response xp of thep-side. b A donor level EtD crossing the Fermi level at or close to theheterointerface and shifts the charge response xn of the n-side of the

junction.




5/13

as described in Sec. II A. For 0 the space charge of the

p-type region is essentially counterbalanced by the charge

response at the interface, reducing xn to zero.

The two values of the capacitance are

CLf = A 1xp

CHf = A 1xp + xn

. 6This capture and emission of electrons by defect states at the

interface depends on the supply of electrons from the n-side.This means that both processes, electron supply through the

buffer and capture/emission of electrons by the interface

states, are connected in series.

III. EXPERIMENT

CuIn1xGaxSe2 thin films were grown on Mo coated float

glass substrates using a multistage coevaporation physical

vapour deposition PVD process.25,26 Solar cells with a totalarea of 0.5 cm2 were prepared from the absorber layers by

chemical bath deposition of a CdS buffer layer, rf sputtering

of a transparent ZnO/ZnO:Al bilayer front contact, and

evaporation of a Ni/Al contact grid. All devices investigated

were produced using absorber layers from a single deposi-

tion process. The CdS series thickness of the CdS buffer

layer was varied by changing the dipping time in the chemi-

cal bath. Schottky-contact devices were produced by evapo-

rating Al contacts immediately after etching the absorber sur-

face with a 1% solution of bromine in methanol. For one

device an In2S3 buffer layer evaporated by PVD technique27

was employed.

Solar cell characterization was performed under standard

conditions: AM1.5 illumination, 100 mW/cm2 intensity, and

at 25 C. Temperature dependent electrical measurements

were carried out using a closed-cycle helium cryostat with a

measurement range 40310 K. The sample temperature was

determined by a calibrated Si diode mounted on a glass sub-

strate identical to the glass substrates used for the CIGS

deposition. Admittance spectroscopy was performed with an

HP4284 LCR meter and four-point probes. To ensure a re-

laxed state of the investigated devices, the samples were kept

at 300 K for 1 h in darkness prior to cooling down. Drive-

level capacitance profiling DLCP was measured using thesame setup. IVT measurements were performed with a Kei-

thley 238 source-measure unit using the same cryostat and

the same electrical contacts utilized for the capacitance mea-

surements. The thickness of the deposited CdS buffer layerwas determined in a scanning electron microscope SEM oncomplete solar cell device cross sections.

IV. RESULTS

The solar cell parameters of the different devices with

varying CdS thickness are shown in Table I. The thickness of

the buffer layers was determined from SEM cross sections. A

best efficiency of 15% is reached for devices with CdS-layer

thicknesses of 25 and 60 nm, whereas the lowest efficiency is

found for the device without a CdS buffer layer.

A. Admittance

The admittance spectra for the samples with different

CdS thicknesses, In2S3 buffer layers, and Schottky contacts

measured at zero bias are shown in Fig. 4. All spectra show

two distinct plateaus CHf and CLf, respectively, and a transi-

tion region in between. The plateau of almost constant CHfcorresponds to the sum of the SCRs of the devices. For all

samples the capacitance decreases toward the geometric ca-

pacitance value at low temperatures indicating the freeze-out

of the majority carriers. The value of the geometric capaci-

tance is estimated at Cgeo =5.2 nF cm2 for a total devicethickness of 2 m and a dielectric constant CIGS =11.70.

28

The activation energy of the capacitance step between

the CHf and CLf plateaus can be evaluated from the inflection

points of the C-f-T spectra. An Arrhenius plot for the differ-

ent samples is shown in Fig. 5a with the calculated activa-tion energies, and the corresponding thermal prefactors 0are shown in Fig. 5b as a function of the activation energy.The values for the N1 step from literature

29,8,4,3have also

been added. A MeyerNeldel type relationship24

between the

prefactor and the activation energy is found, which agrees

very well with the results from literature. Note that this re-

lationship between prefactor and activation energy is found

TABLE I. Device parameters of the samples from the CdS thickness varia-

tion with composition ratios of Ga / III0.27 and Cu/ III0.88.

CdS-SEM

nmVOCmV

JSCmA cm2

FF

%

%

0 413 31.2 56.8 7.3

25 652 32.1 72.9 15.2

60 654 30.4 76 15.1

160 652 29.8 74.3 14.4

FIG. 4. Admittance spectra for solar cells with different CdS thicknesses,

In2S3 buffer layers, and Schottky contacts in dependence of the temperature

T. For all heterostructures an evident admittance step is visible between CLfand CHf.




6/13

for all structures, regardless of the presence, type, or thick-

ness of the buffer layer. From the good agreement of the

activation energies and prefactors we conclude that the ca-

pacitance step observed in our measurements corresponds to

the N1 step reported in literature for all samples measured.

As mentioned above, this N1-admittance response was

previously interpreted as a defect contribution at or close to

the absorber/buffer interface. In this model,6

CHf reflects the

contribution of the n- and p-side SCR widths xn and xp

whereas CLf is determined only by the SCR width xp of theabsorber Eq. 6. Thus the measured difference in spacecharge width x = /CHf /CLf should directly yield the

thickness of the presumably depleted buffer layer. The val-ues of /CLf, /CHf, and x are shown in Table II for all

measured devices. It can be seen that the total SCR width

xtotal = /CHf and the activation energy of N1 increases with

increasing thickness of CdS, whereas x shows no clear cor-

relation with the CdS-layer thickness. In particular, it can be

seen that even devices with a highly doped n-side such as the

Schottky contact also show a significant difference between

CHf and CLf. Admittance measurements performed with ap-

plied reverse bias of 1 V do not lead to a shift of the

activation energy, in agreement with previous results re-

ported in literature.2

Also shown in Table II are values for the

net doping density NA deduced from the capacitance values

of the high frequency plateaus in Fig. 4. It can be seen that

these values are around 2 31015 cm3 for all sampleswith a somewhat higher value for the device with the In2S3buffer layer.

B. Capacitance profiling

Capacitance profiles were measured by means of the

DLCP and the CV-profiling technique. Both methods showed

good agreement, with the DLCP measurement featuring an

improved signal-to-noise ratio. For this reason, in Sec. IV,

only the DLCP profiles will be reported. In the following the

concentration Nx extracted from the CV techniques iscalled the defect concentration, comprising both the carrier

and the defect concentration. In order to avoid metastability

effects arising from voltage bias perturbation, the CIGS solar

cells were cooled down in the relaxed state. The measure-ment temperature was selected such that the low frequencies

1 kHz were just below the N1-turn-on frequency whereasfor high frequencies 1 MHz only the free carrier concen-tration should contribute to the profile.

In Fig. 6a, the DLCP profiles for 25 nm CdS are shownfor low and high frequencies. The defect profiles show the

typical U-shaped form commonly reported in literature,8,19

with a minimum at a profiling distance of 400800 nm. Both

profiles exhibit a significant increase in the defect profile

toward the junction and toward the bulk of the sample.

Trying to discern differences between the low frequency

and high frequency profiles, it can be seen that the curves

have an almost identical shape, but seem to be shifted by adistance xCV. If the apparent x-shift of the curves is taken

into account, there is no actual difference in the magnitude of

the profiling density visible, indicating that the magnitude of

the defect concentration is not affected by the N1-signal re-

sponse. Note also that exactly the same behavior is observed

for the DLCP profiles of the Schottky contacts as shown in

Fig. 6b.The CV profiles of all samples investigated show a simi-

lar behavior with respect to low frequency and high fre-

quency measurements. Also, as is shown in Fig. 7, the shift

in profiling distance xCV and the shift xC-f-T computed

FIG. 5. a Arrhenius diagram derived from the admittance results in Fig. 4.

b The change in the thermal emission prefactor with increasing activationenergy reflects the MeyerNeldel rule and is compared to the values from

literature Refs. 29, 8, 4, and 3.

TABLE II. Comparison of the spatial extensions derived from CHf and CLf in admittance for the different CdS

thicknesses, InS buffers, and the Schottky contacts. The carrier concentration NA is extracted from CHf with an

assumed built-in voltage of 0.9 V.

CdS-SEM

nmx

nm /CLfnm

/CHfnm

EAmeV

0s1 K2

NAcm3

0 99 592 691 63 6 700 2.41015

25 156 616 772 85 8 200 2.11015

60 235 681 916 160 270 000 1.61015

160 214 821 1035 161 240 000 1.51015

50 In2S3 144 288 432 106 37 000 8.01015

0 Schottky 98 531 629 40 1 000 3.01015




7/13

from the admittance measurements closely agree with each

other whereas again no direct correlation of xCV with the

CdS thickness is found.

It has previously been argued that the increase in thedefect concentration toward the heterojunction, as found in

our measurement, represents a real increase in defect

concentration.19

However, we note that the increase toward

the heterojunction is only observed for very large positive

voltages, corresponding to forward biasing the main junc-

tion. In Fig. 8, this is illustrated for the 60 nm CdS sample

measured at 130 K where the different applied biases are

indicated for the 10 kHz profile. To observe the minimum in

the defect profile, a modest forward bias 0.3 V is necessary,and for the strong apparent increase in defect concentration

at x = 200 nm a very large forward bias of 0.9 V is necessary.

Since this large forward bias even exceeds the built-in volt-

age of the junction, the interpretation of an apparent increase

in defect concentration at such a large bias is questionable aswill be discussed in Sec. V below.

C. IVT

IVT measurements have been performed for the same

devices and are discussed in this section. To ensure a relaxed

state, the samples were kept in darkness at 300 K for 1 h and

then cooled down in darkness. The measurements were then

performed starting at low temperatures and proceeding up to

room temperature. The recording of the IV curves started

from low intensities 0% up to full intensity 100%.Dark IV curves for different devices are shown in Fig. 9

for a measurement performed at 100 K. It can be seen Fig.

FIG. 6. a DLCP profiles for 25 nm CdS are shown for high 1 MHz andlow 1 kHz frequencies. The profiles are measured at temperatures wherethe N1 has a strong impact on the admittance in this frequency range. Hence

the DLCP profiles at 1 kHz should be affected by the N1 but not the curves

at 1 MHz. However, the shape of the profiles does not change and only a

shift by xCV occurs. b The same effect occurs for the Schottky-contactdevice.

FIG. 7. Admittance step xC-f-T plotted against the shift xCV derived from

the difference of high and low frequency DLCP profiles. Expect the sample

without CdS 0 nm CdS, both are in good agreement.

FIG. 8. DLCP profile for the device with a 60 nm CdS layer measured at 10

kHz and 130 K. For dc values +0.3 V an increase toward the bulk mate-

rial is observable. Between +0.3 and +0.9 V a minimum and an increase in

NDLCP toward the heterointerface is observable. For voltages +0.9 V a

steep increase in NDLCP and an increase in the profile distance x can beobserved. We note that the measured VOC of the device is close to 0.9 V at

this temperature.

FIG. 9. a Dark IV curves of the devices with different CdS thicknessesmeasured at 100 K in the relaxed condition. b Layer resistance plottedagainst the buffer thickness extracted from a. The displayed series resis-tances are calculated in the forward bias range around 1.2 V. The specific

resistance is calculated from the slope.




8/13

9a that the current through the devices is limited by asignificant series resistance RS, which increases with increas-

ing CdS thickness. When the observed series resistance is

plotted versus the CdS thickness as shown in Fig. 9b, alinear behavior is found. This indicates that the series resis-

tance is caused by the bulk resistivity of the CdS, with a

value ofCdS=1.6107 m at 100 K.

The generally accepted interpretation of the N1-

admittance response assumes a defect contribution at or close

to the heterointerface, which implies a supply of electrons

from the ZnO through the CdS. To estimate whether current

transport through the CdS may be limiting the N1-

admittance response, the dielectric turn-on frequency corre-

sponding to the observed resistivity of the CdS at different

temperatures can be computed using the dielectric relaxation

time30

D = 1 /D Eq. 2 as follows:

D = 1CdS

. 7

The CdS turn-on frequency D is shown together with the

inflection frequency 0 of the N1 response for the device

with 25 nm CdS in Fig. 10. The values have been calculated

assuming a dielectric constant of CdS = 100 for the CdS

buffer layer. It can be seen that the N1-inflection frequency

0 is larger than D for the whole temperature range. This

result indicates that a heterointerface defect causing the N1

response is highly unlikely as will be discussed below.

Illuminated and dark IV curves are shown together for

different temperatures in Fig. 11a for temperatures between100 and 300 K. It can be seen that the superposition of dark

and illuminated IV curves is violated and that a crossover of

the dark and illuminated curves is observed, in agreement

with the literature data mentioned above. It can be seen that

the effect is much more pronounced at lower temperatures

than at room temperature. In Fig. 11b illuminated IV curvesare shown for different illumination intensities at a measure-

ment temperature of 100 K. The curves show a significant

rollover effect in the forward bias range, which becomes

more pronounced for lower illumination intensities. A more

detailed investigation of these effects will be presented in a

separate forthcoming publication.

V. DISCUSSION

A. Evaluation of existing models

In this section the experimental results presented in Sec.

IV will be discussed with regard to the different models pro-

posed earlier to explain the N1-admittance response. We start

with summarizing the main experimental results obtained in

Sec. IV.

1 An admittance response corresponding to the N1-admittance signal reported in literature has been found

for all CIGS devices investigated. However, the capaci-

tance step x = /CHf /CLf does not agree with the

different CdS buffer layer thicknesses present in the de-

vices. A CIGS Schottky barrier device with neither CdS

nor ZnO layers present and a device with an In2S3 buffer

show N1 steps with x =100 nm. These last two de-

vices have not received any CdS treatment and thus

should have strongly modified interface properties com-

pared to the other samples.

2 Dark IV measurements at low temperatures 100150 K

show that the resistivity of CdS limits the current flowthrough the device, with a dielectric relaxation fre-

quency smaller than the measured inflection frequency

of the N1-admittance response.

3 DLCP measurements at frequencies lower and higherthan the N1-resonance frequency show identical profile

shapes, shifted by a distance xCV, which closely corre-

sponds to the admittance step xC-f-T.

The first two findings are in strong contradiction to the

commonly accepted model, which explains the N1 response

with the presence of a CdS/CIGS interface defect that is

being charged and discharged through conduction band elec-

FIG. 10. Reciprocal value D of the calculated dielectric relaxation time

Eq. 7 is plotted together with the inflection point 0 from admittanceagainst the temperature. D is higher than 0 by one order of magnitude in

the shown temperature range.

FIG. 11. a The dark and illuminated 100% IV curves are displayed

between 100 and 300 K. The crossover occurs in the whole temperaturerange and increases for decreasing temperatures. b IV curves for differentillumination intensities at 100 K. The rollover effect and its dependence on

illumination intensity can be observed.




9/13

trons from the CdS side. The presence of a capacitance step

ofx = 100 nm for the sample with 0 nm CdS cannot also be

explained with a freeze-out of the i-ZnO for high measure-

ment frequencies since the doping concentration31

of this

layer is larger than 1017 cm3. In addition, for the Schottky

barrier device, no CdS and no ZnO is present, but still a

capacitance step of about 100 nm is observed. Because of the

large resistivity of the CdS layer also the charging and dis-

charging of a donor defect either directly at the interface or

at a buried junction interface about 100 nm away from the

main junction are unlikely.

The third result indicates that the N1-admittance re-

sponse does not arise from a bulk defect contribution be-

cause in this case the profiling density would be expected to

change for low and high measurement frequencies. Appar-

ently this is not the case neither for solar cells with or with-

out CdS nor for Schottky contacts.

Therefore it is concluded that none of the hitherto pro-

posed models, intended to explain the N1-admittance signa-ture, is compatible with the experimental results presented in

this paper.

In Sec. V B an alternative model will be proposed that,

in our opinion, provides a natural explanation for the N1-

admittance signature. The main ingredient of this model is

the assumption of a non-Ohmic back-contact at the

CIGS/Mo interface, a concept that has been discussed earlier

for CdTe and also CIGS solar cells and appears physically

very reasonable. By discussing the effects of a back-contact

barrier on the ac and dc responses of CIGS devices, it will be

shown that the experimental results presented in this paper

can be explained consistently.

B. Alternative model: Admittance response in thepresence of back-contact barrier

In Fig. 12 the band diagram of a CdS/CIGS junction is

shown with a non-Ohmic Schottky barrier at the CIGS/Mo

back-contact. The difference between the Fermi level in

equilibrium and the valence band maximum at the Mo metal

surface defines the barrier height B of the back-contact. In

addition to the main junction depletion region wj, a second

depletion region with a width of wC is present at the

CIGS/Mo back junction resulting from the non-Ohmic back-

contact. It is assumed that the main junction and the back-

contact can be treated as independent circuit elements with

no interaction between the two diodes. This is a reasonable

assumption for the relaxed state with a doping density NA1015 cm3 and a device thickness d2 m, where wj600 nm and wC200 nm for a typical back barrier heightofB =0.2 eV.

The equivalent circuit model shown in Fig. 13 consists

of a series connection of two diodes with opposite polarity.The resulting complex admittance is derived from the

equivalent circuit model in Fig. 13 as follows:

1

Ytotal=

1

Gj + iCj+

1

GC + iCC. 8

The total capacitance Ctotal of the solar cell is defined by the

measured admittance in the parallel equivalent circuit Ytotal= Gtotal + iCtotal and thus Ctotal results from the imaginary

part ImY as follows:

Ctotal =CCGj

2 + CjGC2 + 2CcCjCc + Cj

GC + Gj2 + 2Cc + Cj

2. 9

It is useful to analyze Eq. 9 using the characteristic fre-quency C defined as follows:

32

C =1

C

=GC + Gj

CC + Cj. 10

Two limiting cases can be distinguished.

1 For high frequencies C of the applied alternatingvoltage, the capacitance is reduced to a series connection

of CC and Cj.

CHf =CCCj

CC + Cj. 11

2 For low frequencies C and for V=0 where theback-contact does not limit the current GCGj, thetotal capacitance equals the junction capacitance

CLf = Cj . 12

Therefore the applied alternating voltage does not drop

across the back-contact for low frequencies C and

GCGj case 2. The characteristic frequency C hasthe same activation energy as GC and this activation

energy corresponds to the barrier height B of the

back-contact.33

For frequencies C the barrier at the

FIG. 12. The band diagram shows a CdS/CIGS/Mo structure with a

Schottky contact with the height B at the CIGS/Mo interface. The addi-

tional junction at the back-contact causes a depletion width wC in addition to

the main junction depletion region wj. The index c denotes the back-contact

parameters whereas the junction parameters are labeled with j.

FIG. 13. Equivalent circuit describing the double-diode behavior caused by

the Schottky barrier at the back-contact.




10/13

back-contact impedes the electron transport over the bar-

rier and the applied alternating voltage drops also across

the back-contact case 1.

The current across a semiconductor-metal Schottky bar-

rier can be described by34

J J0eqV/kT 1 = qNVhEe

qB/kTeqV/kT 1, 13

where the saturation current density J0

is given by the effec-

tive density of states NV of the valence band, the mobility hof holes, electric field E, and the barrier height B of the

metal-semiconductor junction.

In this model the activation energies derived from the

Arrhenius diagram Fig. 5 have to be recalculated, as theseenergies were obtained using Eq. 3, which assumes a T2

dependency of the thermal emission prefactor 0. For a ca-

pacitance step caused by a Schottky contact, it is expected

that the thermal emission prefactor 0 depends on qNVh /SEq. 13, where S denotes the dielectric constant of thesemiconductor. If one assumes a temperature independent

mobility h in the measured temperature range 100200

K35

and a T1.5

temperature dependence of the effective den-sity of states NV, the Arrhenius diagram should be plotted as

ln0 /T1.5 versus T1 to obtain the correct temperature in-

dependent prefactor.

Considering the distribution of the current and bias

within the equivalent circuit model Fig. 13 of the double-diode model, it was previously shown that a Schottky contact

at the back-contact may be responsible for the crossover and

rollover in the IV characteristic of CdTe solar cell

devices.36,37

For the purpose of this paper, we will restrict

ourselves mainly to the discussion of the effect of a back-

contact barrier on capacitance measurements. However, it

should be mentioned that a non-Ohmic back-contact can give

a natural explanation for the anomalous IV features com-monly observed in CIGS.

C. Analysis of experimental data with the double-diode model

If the N1-admittance step is caused by a back-contact

barrier as proposed in Sec. V B, then the N1-activation en-

ergy EA should reflect the barrier height B and the observed

step x between CLf and CHf should reflect the back barrier

depletion width. This depletion width can be related to the

barrier height by

wC =2SB

e2NA, 14

where NA is the carrier concentration of the CIGS absorber at

the back-contact. Thus it is possible to obtain NA from plot-

ting x vs EA. Such a plot is shown in Fig. 14 from whicha value ofNA = 2.80.410

15 cm3 can be extracted. This

value is in good agreement with the carrier concentration of

the CIGS absorber in the relaxed state obtained from CHf in

Sec. III Table II.The double-diode model can also provide a natural ex-

planation for the behavior of defect concentration profiles

observed in CV measurements. In Fig. 15 the reciprocal val-

ues of the CV raw data from the carrier profile of Fig. 8 are

shown. The profiling distance x=A /C0 is determined bythe small signal capacitance C0. In the double-diode model,

the profiling distance xHf for high frequencies arises from aseries connection of the main and the back-contact junction

whereas for low frequencies only the main junction contrib-

utes. This is expected to cause a shift xCV in the profilingdistance in agreement with the experimental finding. As can

be seen in Fig. 15 this difference between /CLf and /CHfstays constant at around 200 nm for Vdc+0.9 V, a value

which corresponds to the open circuit voltage value VOC at

150 K derived from IVT measurements and represents a

good estimate for the built-in potential Vbi in the device. If

the device is forward biased the situation becomes more

complicated. For applied voltages larger than the built-in

voltage VVbi of the main junction, the back diode startsto block also at low frequency and this is why the capaci-

tance step or profiling distance step xCV is no longer ob-

served as is shown in Fig. 15. Also, as the depletion width of

the back diode widens for VVbi, the total capacitance of

the device actually starts to decrease again, which causes the

profiling distance to apparently roll over, as shown in Fig. 8.

For Vdc+0.9 V the x value stays constant for the highfrequency range whereas x starts to increase for the lowfrequency range and approaches also the x values200 nm of the high frequencies. At the same time, sincein the CV-profiling measurement, and essentially also in the

DLCP method, the defect concentration is computed from

NCVC03/ dC/dV,38 the contribution of the back diode for

FIG. 14. The admittance step x of the samples with varied CdS thickness,

In2S3 buffer, and Schottky contact is plotted vs the root of the corresponding

activation energy calculated from the N1 contribution in admittance. From

the slope a carrier concentration can be determined.

FIG. 15. The result from Fig. 8 is displayed for x in dependence of theapplied dc bias for high and low frequencies. For the low frequency mea-

surement, the profiling distance x starts to increase with increasing dc biasfor bias voltages +0.9 V.




11/13

a large forward bias appears as a large virtual increase inthe defect profile, which seems to occur close to the hetero-

junction. We note again that admittance measurements under

such large forward bias conditions VVbi should lead to avery large dc junction current making the measurement of

the capacitance contribution impossible39

if no back diode

is present. The fact that the measurement of a meaningful

forward bias capacitance signal is possible at low T is an-

other strong piece of evidence that a barrier at the back-

contact influences the ac and dc measurements.

Although the majority of the experimental data can be

well explained by the model assuming a barrier at the back-

contact, there are a number of results that appear more diffi-

cult to be reconciled within this model. These are 1 theobserved change in activation energy of the N1 defect upon

annealing,3 2 a weak dependence of the activation energy

on the CdS thickness Table II, and 3 a typically observedminority carrier signature of the N1 response in DLTS

measurements.4

To explain the observations 1 and 2 within the backdiode model, a change in the back barrier height with anneal-

ing has to be assumed. Since the CdS treatment is applied at

elevated temperatures between 60 and 80 C and because

the thicknesses of the buffer layers are a function of the

dipping time in the chemical bath, a progressive annealing of

the back junction with increasing deposition time may also

occur. Previous investigations of CIGS heterostructures have

shown a shift in the N1-activation energy upon annealing the

device independent of whether CdS buffer layers were

present in the devices.40

This strongly indicates that the an-

nealing induces changes in the device that are not related to

the CdS/CIGS interface. Concerning point 3, the observa-

tion of a minority trap signature in DLTS appears to be incontradiction to our assignment of the N1 response to a back

barrier in the device. However, as was shown in Ref. 33, a

minority or majority carrier signal may be obtained when the

voltage pulse in the DLTS experiment drops across twoback-to-back connected junctions, depending on the specifics

of the two junctions involved.

D. Simulation of admittance and CV using a double-diode model

Different models for the ac and dc responses of CIGS

heterojunctions can be evaluated using numerical device

simulation in which the Poisson equation and the continuity

equations are solved in one dimension for the full device

configuration. It will be shown in this section that numerical

simulation can reproduce the experimental results by inclu-

sion of a back-contact barrier. In Refs. 36 and 37 it was

already shown for CdTe-solar cells that a barrier at the back-

contact can explain the rollover and crossover effects in the

IVT characteristics. A detailed analysis of the IVT character-

istics in CIGS solar cells will be published elsewhere. The

simulations were performed using the SCAPS1D program de-

veloped at the University of Gent.41

A barrier height ofB = 0.23 eV is assumed, defined by

the distance between the Fermi level and the valence band at

the CIGS/Mo interface. The parameters used for the CdS

buffer, and i-ZnO and n-ZnO window layers are stated in

Table III. In the double-diode model, both the depletion

width of the main junction and the back-contact are affected

by the carrier concentration within the absorber layer. To

keep the model simple, one homogeneous absorber layer is

defined. We note that in order to get good agreement betweenthe simulated and the experimental curves e.g., the admit-tance step height, an inhomogeneous carrier concentrationin the CIGS absorber could be assumed. Such a modification

would require only small changes in the doping concentra-

tion, which is reasonable to expect from the generally inho-

mogeneous composition of the multinary semiconductor ab-

sorber layer.

Using the parameters stated in Table III, the simulated

admittance spectra Fig. 16 show a step corresponding tothe experimental result found for the devices. As described

above, for C, GC is not activated, causing the applied

TABLE III. Simulation parameters of the device layers. The letter A/D denotes the type of doping, e.g.,

acceptors/donors. The thermal velocity for holes and electrons equals 107 cm/s for all layers.

Parameter CIGS CdS i-ZnO n-ZnO

d m 1.8 0.06 0.12 0.2

eV 4.5 4.45 4.55 4.55

EG eV 1.15 2.45 3.4 3.4

11.7 10 10 10

NC cm3 21018 21018 11019 11019

NV cm3 21018 1.51019 11019 11019

n cm2/V s 50 50 50 50

p cm2/V s 20 20 20 20

NA/D cm3 2.31015 A 1.01015 D 5.01017 D 1.01018 D

FIG. 16. Simulated C-f curves for different temperatures. An assumed back-

contact barrier explains the capacitance step in the C-f spectra.




12/13

alternating voltage to drop also across the back-contact case1, that is, series connection of CC and Cj. For C thecapacitance signal is given by the junction capacitance Cjcase 2. The resulting capacitance step corresponds to theN1 step typically observed in CIGS as shown in Sec. IV.

There is disagreement in the frequency axis between the ex-

perimental and simulated curves concerning the temperature

dependence. This is due to a discrepancy between the emis-

sion prefactor derived from the experiment data and the

emission prefactor contained in the numerical simulation.

This discrepancy can be attributed to the assumption of a

pure thermionic emission model for the majority carrier

transport at the back-contact implemented in the SCAPS simu-

lation code. Measured and simulated prefactors and activa-

tion energies depend strongly on the specifics of the current

transport through the back junction, including tunneling con-

tributions and the effect of an inhomogeneous distribution of

barrier heights.Using the same parameters as used for the C-f-T simu-

lation Table III, CV profiles for 150 K can be calculatedFig. 17 with and without the presence of a barrier B at theback-contact. If a barrier at the back-contact is included, the

profiles triangles and squares show an increase toward theheterointerface caused by an increase in the back barrier

depletion region for large forward bias voltages. This in-

crease disappears if the barrier B at the back-contact is

eliminated in the simulation line. The shape of the simu-lated profiles does not change for low and high measurement

frequencies with respect to the N1-resonance frequency in

close agreement with the experimental data shown in Fig. 6.

The simulation also confirms that the shift in capacitanceprofiles corresponds to the depletion width of the back-

contact, which in turn depends on barrier height and net dop-

ing density of the CIGS layer within the back diode deple-

tion region.

However, the simulated profiles shown in Fig. 17 do not

exhibit an increase in the defect concentration toward the

bulk of the sample. To reproduce such an increase in the

defect concentration toward the bulk, as is often observed

experimentally, a deep acceptor state Nt is introduced in the

absorber layer energetically located at 0.55 eV above the

valence band. For simplicity the defect is assumed to be

uniformly distributed throughout the absorber layer with a

defect concentration of 2.01016 cm3 and a capture cross

section of 1.01015 cm2 for holes and electrons.

In Fig. 18 the simulated profiles for a CIGS device with

a back barrier are shown with and without the presence of

the deep defects described above. It can be seen that the main

effect of the deep defects is an apparent increase in defect

concentration toward the bulk of the sample, although in the

simulation this defect was assumed to be distributed homo-

geneously throughout the sample. This apparent increase in

the defect profile is caused by a quasistatic charge in the

deep defect Nt close to the heterointerface, which cannotfollow the alternating voltage Vac dynamically but can re-

spond to the much slower dc bias sweep, Vdc. As stated

above we have kept the simulation parameters as simple as

possible to show the possible effects of a back barrier and of

deep defects on experimental capacitance profiling curves.

However, it is well known that large compositional gradients

are typically present in CIGS samples, such that a spatial

variation of certain material properties such as doping level

and deep defect density has to be expected. It was the inten-

tion in this section to show that significant spatial variations

in the measured defect profiles may already arise from as-

suming completely uniform material properties.

VI. CONCLUSIONS

A systematic investigation of different CIGS thin film

device structures was presented. The experimental results for

devices with CdS buffer layers of different thicknesses,

Schottky contacts, and alternative buffer layers cannot be

reconciled with the previously discussed interpretation of the

N1 response as a defect at or close to the heterointerface.It has been shown that a non-Ohmic back-contact can

explain the N1 response in admittance and CV measure-

ments. Such a barrier at the back-contact is consistent with

the apparent increase in the defect concentration toward the

heterointerface as observed in CV profiles. As known for

CdTe based solar cells, a back barrier may also be respon-

sible for the occurrence of the crossover and rollover effects

in IV measurements.

The alternative interpretation of the N1-admittance re-

sponse in CIGS opens up new paths to explain the metasta-

bility phenomena in these devices, because the model does

not require Fermi level pinning at the heterointerface.

FIG. 17. Capacitance profiles simulated with parameters from Table III. The

profiles with a back barrier B are shown for 10 kHz squares and 1 MHztriangles. A shift between Hf and Lf is discernable without a qualitativechange in the curves. NCV profiles without a barrier B line show no shiftand no change in shape for low 10 kHz and high 1 MHz frequencies. Theincrease toward the interface disappears.

FIG. 18. NCV profiles at Hf 1 MHz simulated with a back-contact barrierwith diamonds and without triangles an additional deep defect state Nt.




13/13

ACKNOWLEDGMENTS

This work was funded by the European Commission,

Athlet-project under Contract No. 019680. The authors

would like to thank P. Krber, T. Mnchenberg, M. Kirsch,

C. Kelch, and P. Pistor for technical support.

1R. N. Bhattacharya, M. C. Contreras, B. Egaas, R. Noufi, A. Kanevce, and

J. R. Sites, Appl. Phys. Lett. 89, 253503 2006.2

T. Walter, R. Herberholz, C. Mller, and H. W. Schock, J. Appl. Phys.80

,4411 1996.3U. Rau, D. Braunger, R. Herberholz, J.-F. Guillemoles, L. Kronik, D.

Cahen, and H. W. Schock, J. Appl. Phys. 86, 497 1999.4R. Herberholz, M. Igalson, and H. W. Schock, J. Appl. Phys. 83, 318

1998.5R. Scheer, J. Appl. Phys. 105, 104505 2009.

6A. Niemegeers, M. Burgelman, R. Herberholz, U. Rau, D. Hariskos, and

H. W. Schock, Prog. Photovoltaics 6, 407 1998.7M. Igalson, M. Bodegard, L. Stolt, and A. Jasenk, Thin Solid Films 431

432, 153 2003.8J. T. Heath, J. D. Cohen, and W. N. Shafarman, J. Appl. Phys. 95, 1000

2004.9M. Igalson and M. Edoff, Thin Solid Films 480481, 322 2005.

10M. Gloeckler, C. R. Jenkins, and J. R. Sites, Mater. Res. Soc. Symp. Proc.

763, 231 2003.11

I. L. Eisgruber, J. E. Granata, J. R. Sites, J. Hou, and J. Kessler, Sol.

Energy Mater. Sol. Cells 53, 367 1998.12

M. Topic, F. Smole, and J. Furlan, Sol. Energy Mater. Sol. Cells 49, 311

1997.13

W. Miller and L. C. Olsen, IEEE Trans. Electron Devices 31, 654 1984.14

W. N. Shafarman and J. E. Phillips, Proceedings of the 25th IEEE Photo-

voltaic Specialist Conference IEEE, Washington, DC, 1996, p. 841.15

P. E. Russell, O. Jamjoum, R. K. Ahrenkiel, L. L. Kazmerski, R. A. Mick-

elsen, and W. S. Chen, Appl. Phys. Lett. 40, 995 1982.16

R. Scheer, C. Knieper, and L. Stolt, Appl. Phys. Lett. 67, 3007 1995.17

M. Burgelman, F. Engelhardt, J. F. Guillemoles, R. Herberholz, M. Igal-

son, R. Klenk, M. Lampert, T. Meyer, V. Nadenau, A. Niemegeers, J.

Parisi, U. Rau, H. W. Schock, M. Schmitt, O. Seifert, T. Walter, and S.

Zott, Prog. Photovoltaics 5, 121 1997.18

G. Agostinelli, E. D. Dunlop, D. L. Btzner, A. N. Tiwari, P. Nollet, M.

Burgelman, and M. Kntges, Proceedings of the Third WCPEC, 2003

unpublished.19M. Igalson, A. Urbaniak, and M. Edoff, Thin Solid Films 517, 2153

2009.20

M. Cwil, M. Igalson, P. Zabierowski, and S. Siebentritt, J. Appl. Phys.

103, 063701 2008.21

L. C. Kimerling, J. Appl. Phys. 45, 1839 1974.22

M. Cwil, M. Igalson, P. Zabierowski, C. A. Kaufmann, and A. Neisser,

Thin Solid Films 515, 6229 2007.23

R. Herberholz, T. Walter, C. Mller, T. Friedlmeier, H. W. Schock, M.

Saad, M. C. Lux-Steiner, and V. Alberts, Appl. Phys. Lett. 69, 2888

1996.24

A. Yelon, B. Movaghar, and R. S. Crandall, Rep. Prog. Phys. 69, 1145

2006.25A. M. Gabor, J. R. Tuttle, M. H. Bode, A. Franz, A. L. Tennant, M. A.

Contrereas, R. Noufi, D. Garth Jensen, and A. M. Hermann, Sol. Energy

Mater. Sol. Cells 4142, 247 1996.26

C. A. Kaufmann, A. Neisser, R. Klenk, and R. Scheer, Thin Solid Films

480481, 515 2005.27

P. Pistor, R. Caballero, D. Hariskos, V. Izquierdo-Roca, R. Wchter, S.

Schorr, and R. Klenk, Sol. Energy Mater. Sol. Cells 93, 148 2009.28

C. Rincn, M. A. Arsene, S. M. Wasim, F. Voillot, J. P. Peyrade, P. Bocar-

anda, and A. Albacete, Mater. Lett. 29, 87 1996.29

T. Eisenbarth, T. Unold, R. Caballero, C. A. Kaufmann, D. Abou-Ras, and

H.-W. Schock, Thin Solid Films 517, 2244 2009.30

K. W. Ber, Survey of Semiconductor Physics Van Nostrand Reinhold,New York, 1990, Vol. I, p. 1135.

31R. Klenk in Transparent Conductive Zinc Oxide, edited by R. Ellmer, A.

Klein, and B. Rech, Vol. 104, pp. 415437 Springer Series in Materials

Science, 2008.32

A. Niemegeers, S. Gillis, and M. Burgelman, in Proceedings of the Second

World Conference on Photovoltaic Solar Energy Conversion, Wien, Aus-

tria, July 1998 unpublished, p. 1071.33

M. Burgelman and P. Nollet, Solid State Ionics 176, 2171 2005.34

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. Wiley, New York,1981, p. 245.

35J.-W. Lee, J. D. Cohen, and W. N. Shafarman, Thin Solid Films 480481,

336 2005.36

A. Niemegeers and M. Burgelman, J. Appl. Phys. 81, 2881 1997.37

S. H. Demtsu and J. R. Sites, Thin Solid Films 510, 320 2006.38

NDLCPC03/C1, where C1 is the first order term in a Taylor series of C

=dQ /dV= C0 + C1xdV.39

S. S. Hegedus and W. N. Shafarman, Prog. Photovoltaics 12, 155 2004.40

C. Deibel, V. Dyakonov, and J. Parisi, Appl. Phys. Lett. 82, 3559 2003.41

M. Burgelman, P. Nollet, and S. Degrave, Thin Solid Films 361362, 527

2000.

http://dx.doi.org/10.1063/1.2410230http://dx.doi.org/10.1063/1.363401http://dx.doi.org/10.1063/1.370758http://dx.doi.org/10.1063/1.366686http://dx.doi.org/10.1063/1.3126523http://dx.doi.org/10.1002/(SICI)1099-159X(199811/12)6:6%3C407::AID-PIP230%3E3.0.CO;2-Uhttp://dx.doi.org/10.1016/S0040-6090(03)00221-9http://dx.doi.org/10.1063/1.1633982http://dx.doi.org/10.1016/j.tsf.2004.11.205http://dx.doi.org/10.1016/S0927-0248(98)00035-Xhttp://dx.doi.org/10.1016/S0927-0248(98)00035-Xhttp://dx.doi.org/10.1016/S0927-0248(97)00058-5http://dx.doi.org/10.1109/T-ED.1984.21585http://dx.doi.org/10.1063/1.92955http://dx.doi.org/10.1063/1.114934http://dx.doi.org/10.1002/(SICI)1099-159X(199703/04)5:2%3C121::AID-PIP159%3E3.0.CO;2-4http://dx.doi.org/10.1016/j.tsf.2008.10.092http://dx.doi.org/10.1063/1.2884708http://dx.doi.org/10.1063/1.1663500http://dx.doi.org/10.1016/j.tsf.2006.12.102http://dx.doi.org/10.1063/1.117352http://dx.doi.org/10.1088/0034-4885/69/4/R04http://dx.doi.org/10.1016/0927-0248(95)00122-0http://dx.doi.org/10.1016/0927-0248(95)00122-0http://dx.doi.org/10.1016/j.tsf.2004.11.067http://dx.doi.org/10.1016/j.solmat.2008.09.015http://dx.doi.org/10.1016/S0167-577X(96)00133-4http://dx.doi.org/10.1016/j.tsf.2008.10.142http://dx.doi.org/10.1016/j.ssi.2004.08.048http://dx.doi.org/10.1016/j.tsf.2004.11.087http://dx.doi.org/10.1063/1.363946http://dx.doi.org/10.1016/j.tsf.2006.01.004http://dx.doi.org/10.1002/pip.518http://dx.doi.org/10.1063/1.1576500http://dx.doi.org/10.1016/S0040-6090(99)00825-1http://dx.doi.org/10.1016/S0040-6090(99)00825-1http://dx.doi.org/10.1063/1.1576500http://dx.doi.org/10.1002/pip.518http://dx.doi.org/10.1016/j.tsf.2006.01.004http://dx.doi.org/10.1063/1.363946http://dx.doi.org/10.1016/j.tsf.2004.11.087http://dx.doi.org/10.1016/j.ssi.2004.08.048http://dx.doi.org/10.1016/j.tsf.2008.10.142http://dx.doi.org/10.1016/S0167-577X(96)00133-4http://dx.doi.org/10.1016/j.solmat.2008.09.015http://dx.doi.org/10.1016/j.tsf.2004.11.067http://dx.doi.org/10.1016/0927-0248(95)00122-0http://dx.doi.org/10.1016/0927-0248(95)00122-0http://dx.doi.org/10.1088/0034-4885/69/4/R04http://dx.doi.org/10.1063/1.117352http://dx.doi.org/10.1016/j.tsf.2006.12.102http://dx.doi.org/10.1063/1.1663500http://dx.doi.org/10.1063/1.2884708http://dx.doi.org/10.1016/j.tsf.2008.10.092http://dx.doi.org/10.1002/(SICI)1099-159X(199703/04)5:2%3C121::AID-PIP159%3E3.0.CO;2-4http://dx.doi.org/10.1063/1.114934http://dx.doi.org/10.1063/1.92955http://dx.doi.org/10.1109/T-ED.1984.21585http://dx.doi.org/10.1016/S0927-0248(97)00058-5http://dx.doi.org/10.1016/S0927-0248(98)00035-Xhttp://dx.doi.org/10.1016/S0927-0248(98)00035-Xhttp://dx.doi.org/10.1016/j.tsf.2004.11.205http://dx.doi.org/10.1063/1.1633982http://dx.doi.org/10.1016/S0040-6090(03)00221-9http://dx.doi.org/10.1002/(SICI)1099-159X(199811/12)6:6%3C407::AID-PIP230%3E3.0.CO;2-Uhttp://dx.doi.org/10.1063/1.3126523http://dx.doi.org/10.1063/1.366686http://dx.doi.org/10.1063/1.370758http://dx.doi.org/10.1063/1.363401http://dx.doi.org/10.1063/1.2410230

Interpretation of Admittance, Voltage, And Current-Voltage Signatures in Cu(in,Ga)Se2 Thin Film...

Documents

Transcript of Interpretation of Admittance, Voltage, And Current-Voltage Signatures in Cu(in,Ga)Se2 Thin Film...