This document summarizes research on the electrical transport behavior of undoped microcrystalline silicon (μc-Si:H) films. The key points are: 1) Both Meyer-Neldel rule (MNR) and anti-MNR behavior were observed in single-phase μc-Si:H films, depending on microstructure. 2) Films were classified into three types based on microstructure and electrical properties. Type A showed MNR, Type B transitioned between MNR and anti-MNR, and Type C showed clear anti-MNR. 3) The statistical shift model can explain MNR in Type A-B, while anti-MNR in Type

1. ICANS-22, Colorado, U.S.A
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

2. Outline
Introduction
Experimental and characterization details
Electrical transport behavior : classification of
material
Observation of Meyer Neldel rule (MNR) & Anti
MNR in single phase undoped μc-Si:H
MNR & Anti MNR in μc-Si:H in literature
Conclusions

3. Meyer Neldel Rule (MNR)
Observed in:
Materials: Processes:
Activated process:
Annealing Phenomena
Ionic Materials Y=A.exp (-B/X)
Trapping in crystalline
Chalcogenide glasses MNR A=A’.exp(GB)
Semiconductors
Organic thin films where G and A’ are
Aging of insulating polymers
Amorphous Silicon MNR parameters
Biological death rates
doped μc-Si:H
Chemical reactions
Electrical conduction
microscopic origin of MNR
& physical meaning of G ??
Statistical shift of Fermi level
electrical transport in a-Si:H/
σ0=σ00 eGEa ,
σd=σ0.exp(-Ea/kT) MNR
disordered semiconductor:
where G or EMN (=1/G)
and σ00 are MNR parameters

4. Anti Meyer Neldel Rule
Correlation 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

5. Statistical Shift Model
According to Mott: σd(T) =σM exp(-(EC - EF)/kT))
EC(T ) = EC0 - γCT ; EF(T ) = EF0 - γFT
Ea= EC0 - EF0,
σd=σo exp (–Ea / kT )
σo=σM exp [(γC - γF) / k]
σ0=σ00 exp (GEa) --- MNR

6. The reason for observed anti MNR
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)

7. Motivation
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

8. General observations:
• Optical properties of μc-Si:H are governed by crystalline
component
• Electrical transport is still dominated by a-Si:H phase
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???

9. Our Results
We prepared large numbers of single phase μc-Si:H films
having 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

10. Experimental layout
Parallel-plate glow discharge plasma deposition system
Substrate: High purity SiF4, Ar
+
Corning 1773 and H2 as feed gases
AFM Rf frequency 13.56 MHz
Ts=100-300 oC
+
X-ray
μc-Si:H Opto-electronic
Diffraction
film transport
+
Raman measurement
+
Thermal evaporation of Al
Spectroscopy
Ellipsometry

11. 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

12. Classification of films
Type-C material
Type-B material
Type-A material
• Highest fraction of LG.
• Rising fraction of
• Small grains (SG)
LG. • Well formed large
• Low amount of
columns
• Marked
conglomeration
morphological
(without column • Least amount of
variation: column
formation) disordered phase in the
formation columnar boundaries.
• High density of
• Moderate amount
intergrain boundary
of disordered phase
regions containing
in the columnar
disordered phase.
boundaries.

13. Classification of films: electrical transport behavior and Fcl
σ0
4
10
Ea 0.5
3
10
2
-1
10 0.4
σ0 (Ω cm)
Ea (eV)
1
10
0.3
1
0.2
-1
10
-2
10 0.1
type-B
type-A type-C
0 20 40 60 80 100
Fcl (%)

14. σ0 vs. Ea Findings
σo and Ea is found to
follow a linear relationship
MNR parameters
type-A
for the Type-A and Type-B
type-B -1
G=25.3 eV (EMN=39.5 meV)
4
10 type-C
σ00=7.2x10 (Ωcm)
-4 -1
samples.
γf ~ 0
anti MNR parameters
Type-A samples are
-1
2 -1
G = -44.6 eV
γf ~ γc
10
σ0 (Ω cm)
having high values of Ea
or EMN=-22.5 meV
σ00= 87 (Ωcm)
-1
and σ0
0
10 γF
This shows is
extremely small in Type-A
samples due to its pinning
-2
10
The values of MNR
0.8 parameters nearly the same
0.0 0.2 0.4 0.6
as found in a-Si:H.
Ea (eV)
Correlation between σo
MNR & anti MNR in single phase μc-Si:H and Ea appears to change
sign for type-C samples:
anti-MNR

15. 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.

16. 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.

17. 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

18. Anti MNR: type-C μc-Si:H
• 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 ordering
delocalizes 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.

19. Evidence of Anti MNR in μc-Si:H
in
Literature

20. Undoped µc-Si:H
5
10
#1 (rH=21) MNR line of types: A & B μc-Si:H
#1 (rH=32) MNR line of a-Si:H
#2
3
10 #3 (a-Si:H)
-1
this work
σ0 (Ω.cm)
1
10
-1
10
anti-MNR line of type-C μc-Si:H
-3
10
0.0 0.2 0.4 0.6 0.8
#1undoped µc-Si:H
Ea(eV) #2p-doped µc-Si:H

21. Doped µc-Si:H
anti MNR line (#7)
[heavily doped μc-Si:H]
3
10
-1
σ0 (Ω.cm)
MNR line (#7)
1
10 [a-Si,C:H+μc-Si,C alloy]
-1
10 #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
-3
10
0.0 0.2 0.4 0.6 0.8
Ea (eV)

22. MNR parameters Anti MNR parameters
σ00 σ00
EMN EMN
G G
-1 -1
-1
(eV-1)
Samples (Ω.cm) (Ω.cm)
(eV ) (meV) (meV)
This work
7.2×10-4
Type-A&B 25.3 --
39.5 --
--
Type-C -- -- -44.6
-- -22.5
87
Published
Data
4×10-3 1.26×1010
Case#1 20.7 -97.7
48.4 -10.2
(rH=21)
3.2×10-6
Case#1 --
36.6 --
27.3 --
(rH=32)
1.7×10-4
Case#2 6
23.4 -32.5
42.7 -30.8
7.7×10-3
Case#3 --
24 --
41.6 --
Case#4 0.32 59
15.4 -66.1
65.1 -15.1
4.2×10-3
Case#5 21
15.3 -64.9
65.4 -15.4
3.2×10-6
Case#6 2.4
31.3 -39.9
31.9 -25.1
2.3
Case#7 309
8.5 -49.5
118.3 -20.2
0.5
Case#8 --
11.8 --
84.5 --
7.2×10-3
Case#9 --
20 --
50 --

23. If one has a collection of G and σ00 then:
a-Si,C:H alloy (#7) #1 (rH=21)
σ00=σM exp [(γC- γF)/k –GEa]
0 #1 (rH=32)
10 Porous Si (#9)
#2
#3
σ00=σM exp [(γC- γF)/k –G(EC0 –EF0)]
a-Si:H (#3) #4
-1
σ00 (Ω.cm)
#5
-2
10
At a position of EF in DOS where
#6
#7
#8
p-nc-Si-SiC:H alloy (#5)
γF(EC0-Emin)=0
#9
-4
10 this work
-1
σM=100 (Ωcm) (at γf=γc) Fit
σ00=σM exp [(γC/k) –GEmin]
Emin=0.61 eV
3 -1
σ0=1.2x10 (Ωcm) (at γf=0)
The quantity Emin is a measure for the
-6
10
5 10 15 20 25 30 35 40
-1
G (eV ) 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

24. 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).

25. Appendix

26. 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.

27. Electrical transport behavior, Size distribution of surface
grains and Fcl with film growth
Ea (eV)
0.1 0.2 0.3 0.4 0.5 0.6
1200 1200
d = 950 nm
1000 1000
Film Thickness (nm)
Film Thickness (nm)
d = 590 nm
Frequency (arb. unit)
800 800
600 d = 390 nm 600
400 400
d = 180 nm
200 200
d = 55 nm
0
0
0 100 200 300 400 0
-7 -6 -5 -4 -3 -2 20 40 60 80
10 10 10 10 10 10 Fcl (%)
Conglomerate surface grain size (nm)
σd (Ω cm)
-1

28. Summary of RS and SE studies on the fractional
composition of films
100 Xc1 (%) 100
Fcf (b)
(a)
Fcl
Fcf , Fcl , Fv (%) by SE
Xc2 (%)
Xa, Xc1, Xc2 (%) by RS
80 Xa (%) 80
Fv
60 60
40 40
20 20
0 0
200 400 600 800 1000 1200 200 400 600 800 1000
Film Thickness (nm)
Film Thickness (nm)
~50 nm ~400 nm ~900 nm