Normal and anti Meyer-Neldel rule in conductivity of highly crystallized

undoped microcrystalline silicon films

Sanjay K. Ram, Satyendra Kumar

Samtel Centre for Display Technologies & Dept. of Physics, I.I.T.Kanpur, India

&P. Roca i Cabarrocas,

LPICM (UMR 7647 du CNRS), Ecole Polytechnique, France

ICANS-22, Colorado, U.S.A

IntroductionExperimental and characterization detailsElectrical transport behavior : classification of materialObservation of Meyer Neldel rule (MNR) & Anti MNR in single phase undoped μc-Si:HMNR & Anti MNR in μc-Si:H in literatureConclusions

Outline

Meyer Neldel Rule (MNR)Observed in:

Materials:

Ionic Materials Chalcogenide glassesOrganic thin filmsAmorphous Silicondoped μc-Si:H

Processes:

Annealing Phenomena Trapping in crystalline SemiconductorsAging of insulating polymersBiological death ratesChemical reactionsElectrical conductionmicroscopic origin of MNR

& physical meaning of G ??

electrical transport in a-Si:H/disordered semiconductor: MNR σ0=σ00 eGEa ,

where G or EMN (=1/G)

and σ00 are MNR parameters

σd=σ0.exp(-Ea/kT)

Statistical shift of Fermi level

Activated process: Y=A.exp (-B/X)

MNR A=A’.exp(GB)where G and A’ are MNR parameters

Anti Meyer Neldel RuleCorrelation between σ0 and Ea appears to change sign

– a negative value of MN energy (EMN) is seen

Experimentally observed in:– Heavily doped μc-Si:H

– Heterogeneous Si (het-Si) thin film transistor

– Organic semiconductors

Theoretically explained:

In doped μc-Si:H

Lucovsky and Overhof (LO): considering a degenerate case Ef moving

deep into the band tail

In a-Si:H (experimentally NOT observed)

Statistical shift model

According to Mott: σd(T) =σM exp(-(EC - EF)/kT))

EC(T ) = EC0 - γCT ; EF(T ) = EF

0 - γFT

Ea= EC0 - EF

0,

σd=σo exp (–Ea / kT )

σo=σM exp [(γC - γF) / k]

σ0=σ00 exp (GEa) --- MNR

Statistical Shift Model

According to LO model in a degenerate case Ef

moves above Ec in the crystalline phase

consequently Ef can move deeply into the tail states in the disordered region, giving rise to anti MNR behavior.

Energy band diagram as proposed by Lucovsky et al, J.N.C.S. 164-166, 973 (1993)

The reason for observed anti MNR

Many complex issues/phenomena related to

electrical transport properties were explained

while searching for the origin of MNR in a-Si:H

MNR has also been reported in doped μc-Si:H

o with MNR parameters similar to those obtained in a

Si:H

o Explained in terms of statistical shift model

analogous to a-Si:H

Motivation

Issues:

• μc-Si:H has complex and heterogeneous microstructure

• Electronic transport in single phase μc-Si:H films???

– Non-varying high crystallinity and non-existent amorphous phase

– Is it dominated by crystalline phase ???or

By interfacial regions between crystallites or grains???

General observations:

• Optical properties of μc-Si:H are governed by crystalline

component

• Electrical transport is still dominated by a-Si:H phase

Our Results

We prepared large numbers of single phase μc-Si:H filmshaving varying degree of microstructure and morphology

Both MNR and anti-MNR can be observed in single phase

μc-Si:H films, depending on film microstructure

Objectives

Search for both the origin and significance of these

relationships as observed in single phase μc-Si:H material

Experimental layout

High purity SiF4, Ar and H2 as feed gases

μc-Si:Hfilm

Substrate: Corning 1773 +

Parallel-plate glow discharge plasma deposition system

Thermal evaporation of Al

Opto-electronic transport

measurement

Ts=100-300 oC Rf frequency 13.56 MHzAFM+

X-ray Diffraction

+Raman

+Spectroscopy Ellipsometry

Results: Microstructural Characterization

• Total crystallinity >90% from beginning– No amorphous phase– Rest density deficit

• Two sizes of crystallites, large and small: LG & SG• LG fraction (Fcl) increases with film growth• Conglomeration ↑ with film growth• Variable effect of H2 dilution at different growth

stages

Classification of filmsType-A material• Small grains (SG)

• Low amount of conglomeration (without column formation)

• High density of intergrain boundary regions containing disordered phase.

Type-C material• Highest fraction of LG.

• Well formed large columns

• Least amount of disordered phase in the columnar boundaries.

Type-B material• Rising fraction of

LG.

• Marked morphological variation: column formation

• Moderate amount of disordered phase in the columnar boundaries.

0 20 40 60 80 100

10-2

10-1

1

101

102

103

104

type-Ctype-Btype-A

σ0Ea

0.1

0.2

0.3

0.4

0.5

Fcl (%)

E a (eV

)

σ 0 (Ω c

m)-1

Classification of films: electrical transport behavior and Fcl

0.0 0.2 0.4 0.6 0.8

10-2

100

102

104

anti MNR parametersG = -44.6 eV-1

or EMN=-22.5 meVσ00= 87 (Ωcm)-1

MNR parametersG=25.3 eV-1 (EMN=39.5 meV)σ00=7.2x10-4 (Ωcm)-1

γf ~ 0

γf ~ γc

σ 0 (Ω c

m)-1

Ea (eV)

type-A type-B type-C

σ0 vs. Eaσo and Ea is found to

follow a linear relationship for the Type-A and Type-B samples.

Type-A samples are having high values of Eaand σ0

This shows γF is extremely small in Type-A samples due to its pinning

The values of MNR parameters nearly the same as found in a-Si:H.

Correlation between σoand Ea appears to change sign for type-C samples: anti-MNR

Findings

MNR & anti MNR in single phase μc-Si:H

MNR: type-A μc-Si:H

• Consists mainly of SG with an increased number of SG boundaries.

– No question of formation of potential barrier (i.e., transport through crystallites)

– transport will be governed by the band tail transport.

• Ea saturates (≈ 0.55 eV) and σo ≈ 103 (Ωcm)-1.

– EF is lying in the gap where the DOS does not vary much and there is a minimal movement of EF, or γF ≈ 0

• The initial data points for type-A have higher σo [≈ 104 (Ωcm)-1] and Ea

(≈ 0.66 eV)

– because of a shift in EC and/or a negative value of γF, as happens in a-Si:H for Ea towards the higher side.

MNR: type-B μc-Si:H

The improvement in film microstructure delocalization of the tail states– EF moves towards the band edges, closer to the current path at EC.

– The statistical shift γF, depends on the temperature and the initial position of EF, and when the EF is closer to any of the tail states and the tail states are steep, γF is rapid and marked.

Transition between Type-A and Type-B materials– Nearly constant σo [70-90 (Ωcm)-1] with the fall in Ea (0.54-0.40 eV),– Indicating that the temperature shift of EF and that of the CB have

become equal, canceling each other out (i.e., γF ≈ γC )– In this case, the EF is pinned near the minimum of the DOS between the

exponential CBT and the tail of the defect states (DB–)

– With increasing crystallinity and/or improvement in the microstructure, the minimum shifts towards EC leading to a decrease of Ea.

Anti MNR: type-C μc-Si:H

• The value of EMN = -22.5 meV is close to the value reported in heavily doped µc-Si:H (-20meV)

• EB diagram as suggested by LO model seems inapplicable to

our undoped µc-Si:H case

– Calculated free electron concentrations do not suggest

degenerate condition.

– Consideration of equal band edge discontinuities at both ends of

c-Si and a-Si:H interface Doubtful

– Also, in a degenerate case, the conductivity behavior of

polycrystalline material is found to exhibit a T 2 dependence of σd

• Applying Statistical shift model

– Considering transport through the encapsulating disordered tissue, a band tail transport is mandatory.

– The large columnar microstructure in a long range orderingdelocalizes an appreciable range of states in the tail state distribution.

– In addition, higher density of available free carriers and low value of defect density can cause a large increase in DB– density together with a decrease in DB+ states in the gap a lower DOS near the CB edge possibility of a steeper CB tail.

– In this situation, if EF is lying in the plateau region of the DOS, it may create an anti MNR situation.

Anti MNR: type-C μc-Si:H

Evidence of Anti MNR in μc-Si:H in

Literature

#1undoped µc-Si:H#2p-doped µc-Si:H

0.0 0.2 0.4 0.6 0.810-3

10-1

101

103

105

Ea(eV)

anti-MNR line of type-C μc-Si:H

MNR line of types: A & B μc-Si:HMNR line of a-Si:H

#1 (rH=21) #1 (rH=32) #2 #3 (a-Si:H) this work

σ 0 (Ω

.cm

)-1

Undoped µc-Si:H

0.0 0.2 0.4 0.6 0.810-3

10-1

101

103

MNR line (#7) [a-Si,C:H+μc-Si,C alloy]

anti MNR line (#7) [heavily doped μc-Si:H]

#4 (thickness series) #4 (doped series) #5 dope series, p-nc-Si-SiC:H alloy#5 dilution series, p-nc-Si-SiC:H alloy #6 (Boron doped μc-Si:H) #7

σ 0 (Ω.c

m)-1

Ea (eV)

Doped µc-Si:H

MNR parameters Anti MNR parameters

Samples σ00

(Ω.cm)-1 G

(eV-1) EMN

(meV)σ00

(Ω.cm)-1 G

(eV-1) EMN

(meV) This work Type-A&B

Type-C Published

Data Case#1 (rH=21) Case#1 (rH=32) Case#2 Case#3 Case#4 Case#5 Case#6 Case#7 Case#8 Case#9

7.2×10-4

--

4×10-3

3.2×10-6

1.7×10-4 7.7×10-3

0.32 4.2×10-3 3.2×10-6

2.3 0.5

7.2×10-3

25.3

--

20.7

36.6

23.4 24

15.4 15.3 31.3 8.5

11.8 20

39.5

--

48.4

27.3

42.7 41.6 65.1 65.4 31.9

118.384.5 50

-- 87

1.26×1010

--

6 -- 59 21 2.4 309 -- --

--

-44.6

-97.7

--

-32.5 --

-66.1 -64.9 -39.9 -49.5

-- --

--

-22.5

-10.2

--

-30.8 --

-15.1 -15.4 -25.1 -20.2

-- --

5 10 15 20 25 30 35 4010-6

10-4

10-2

100a-Si,C:H alloy (#7)

a-Si:H (#3)

p-nc-Si-SiC:H alloy (#5)

Porous Si (#9)

#1 (rH=21) #1 (rH=32) #2 #3 #4 #5 #6 #7 #8 #9 this work FitσM=100 (Ωcm)-1 (at γf=γc)

Emin=0.61 eVσ0=1.2x103 (Ωcm)-1 (at γf=0)

σ 00 (Ω

.cm

)-1

G (eV-1)

If one has a collection of G and σ00 then:

σ00=σM exp [(γC- γF)/k –GEa]

σ00=σM exp [(γC- γF)/k –G(EC0 –EF

0)]

At a position of EF in DOS where

γF(EC0-Emin)=0

σ00=σM exp [(γC/k) –GEmin]

The quantity Emin is a measure for the

position of the DOS minimum within

the mobility gap.

If γC is known then for such a value of

σ00 where G=0, one can obtain σM

Conclusions•Both MNR and anti MNR can be seen in the dark conductivity behavior of highly crystalline single phase undoped µc-Si:H material, depending on the microstructure and the correlative DOS features.•A shift in the Fermi level of µc-Si:H material induced by any means (doping or any change in microstructure and the consequent DOS features) can give rise to an appearance of MNR behavior in the dc conductivity.•The statistical shift model can successfully explain both the MNR and anti MNR behavior in our material.•Corroborative evidence of similar electrical transport behavior of µc-Si:H in literature is present-------------------------------------------------------------------------------“Influence of the statistical shift of Fermi level on the conductivity behavior in microcrystalline silicon” by Sanjay K. Ram, Satyendra Kumar, P. Roca i Cabarrocas; Physical Review B 77, 045212 (2008).

Appendix

MNR parameters

• The value of MNR parameter G for a particular µc Si:H material is related to the microstructure and DOS characteristic of that material, although different sets of MNR parameters G and σ00 values can exist for the materials of the same µc Si:H system.

• If the shift in band edges γc is known, then for such a value of σ00 where G=0 (derived by extrapolation), one can obtain the value of σM. This information can further provide those values of σ0 (from Eq. 6), where γf =0, and where γc = γf, both very important positions for providing simplified information about the nature of carrier transport in the material. The quantity Emin is a measure for the position of the DOS minimum within the mobility gap.

0 20 40 60 800

200

400

600

800

1000

1200

Fi

lm T

hick

ness

(nm

)

Fcl (%)0

200

400

600

800

1000

1200

10-7 10-6 10-5 10-4 10-3 10-2

Film

Thi

ckne

ss (n

m)

σd (Ω cm)-1

0.1 0.2 0.3 0.4 0.5 0.6Ea (eV)

0 100 200 300 400

Freq

uenc

y (a

rb. u

nit)

Conglomerate surface grain size (nm)

d = 55 nm

d = 180 nm

d = 390 nm

d = 590 nm

d = 950 nm

Electrical transport behavior, Size distribution of surface grains and Fcl with film growth

200 400 600 800 1000 12000

20

40

60

80

100 (a)

Film Thickness (nm)

F cf ,

F cl ,

F v (%)

by S

E

Fcf Fcl F

v

200 400 600 800 10000

20

40

60

80

100(b)

X

a, Xc1

, Xc2

(%) b

y R

S

Film Thickness (nm)

Xc1 (%) Xc2 (%) Xa (%)

~50 nm ~400 nm ~900 nm

Summary of RS and SE studies on the fractional composition of films