It is known that there is a bimodal size distribution in microcrystalline silicon. How can the deconvolution of the Raman spectra be done with incorporation of a bimodal CSD to obtain more accurate and physical picture of the microstructure in this material?

1. Evidence of Bimodal Crystallite Size
Distribution in µc-Si:H Films
Sanjay K. Ram1,2, Md. Nazrul Islam3, Satyendra Kumar2
and P. Roca i Cabarrocas1
LPICM (UMR 7647 du CNRS ), Ecole Polytechnique, France
1
Dept. of Physics, I.I.T. Kanpur, India
2
QAED-SRG, Space Application Centre (ISRO), Ahmedabad – 380015, India
3

2. Outline
• Introduction: motivation
• Experimental Details
• Microstructural Characterization
– Spectroscopic ellipsometry
– Atomic force microscopy
– X-ray diffraction
– Bifacial Raman spectroscopy
• Conclusions

3. Complex microstructure of μc-Si:H
columnar boundaries
grains grain boundaries
conglomerate crystallites
surface
roughness
voids
Film
growth
substrate
Three main length scales for disorder:
Local disorder: µc-Si:H contains a disordered amorphous phase
Nanometrical disorder: nanocrystals consist of small crystalline (c-Si) grains of
random orientation and a few tens of nanometres size.
Micrometrical disorder: conglomerates are formed by a multitude of nanocrystals and
generally acquire a pencil-like shape or inverted pyramid type shape.

4. Motivation
• Need for proper microstructural characterization
• Different microstructural tools: different length
scales
• Influence on carrier transport
– Film morphology
– compositional variation in constituent crystallites
– crystallite size distribution (CSD)
• Elucidation of CSD in single phase µc-Si:H as
studied by different microstructural tools

5. Sample preparation
PECVD
RF
Parallel-plate glow discharge HH
H Si H H
N H H
plasma deposition system
H H
H
Si N Si N Si N
μc-Si:H
Substrate: Corning 1773
film
Flow ratio
High purity feed gases:
(R)= SiF4/H2
SiF4 , Ar & H2
R=1/1 R=1/5 R=1/10
Rf frequency 13.56 MHz
Ts=200 oC
Thickness series

6. Film characterization
Electrical Properties
Structural Properties
σd(T) measurement
15K≤T ≤ 450K
Xray Diffraction
σPh(T,∅) measurement
15K≤T ≤ 325K
Raman Scattering
CPM measurement
Spectroscopy Ellipsometry
Hall effect
TRMC
Atomic Force Microscopy

7. Spectroscopic Ellipsometry : measured imaginary part
of the pseudo-dielectric function <ε2> spectra
30 * Reference c-Si in BEMA model :
E2 (4.2 eV)
E1 (3.4 eV) LPCVD polysilicon with large
25 d=390 nm
(pc-Si-l) and fine (pc-Si-f) grains
d=170 nm
d=590 nm
20 d=950 nm
d=55 nm E2 (4.2 eV)
50
E1 (3.4 eV)
< ε2 >
15 40 c-Si
pc-Si-l
30
< ε2 >
pc-Si-f
10 a-Si
20
μ c-Si:H
5 10 (d = 950 nm)
0
0 (a)
-10
2 3 4 5
-5 Energy (eV)
2 3 4 5
Energy (eV)
thickness series of R=1/10

8. Analyses of SE data: schematic view for two films
(initial and final growth stages)
TSL (8.3 nm)
Fcf = 73.6 %, Fcl = 0 %,
Fv = 26.4 %, Fa =0 %
TSL (7.9 nm)
MBL (918.9 nm)
d = 950 nm
Fcf = 32.3 %, Fcl = 0.6 %,
Fcf = 50.4%, Fcl = 40.8%,
Fv = 67.1%, Fa =0 %
Fv=8.8 %, Fa=0%
d = 55 nm
BL (48.2 nm)
BIL (27.7 nm)
Fcf = 88.4 %, Fcl = 0 %,
Fcf = 0 %, Fcl = 0 %,
Fv = 10.1 %, Fa = 1.5 %
Fv = 35.6 %, Fa =64.4 %

9. X-ray diffraction analysis
Exp. XRD peak (400)
Exp. XRD peak (111)
Total Fit
Total Fit
Peak 1 (22.4 nm)
Intensity (arb. unit)
Peak 1 (14.8 nm)
Intensity (arb. unit)
Peak 2 (9 nm)
Peak 2 (4.8 nm)
26 27 28 29 30 31 32 33 68.0 68.5 69.0 69.5 70.0
2θ (degree) 2θ (degree)
Intensity (arb.unit)
(400)
(111)
thickness ~ 1 µm
(220)
(311)
20 30 40 50 60 70
Cu Kα 2θ (degrees) Exp. XRD peak (311)
Exp. XRD peak (220)
Total Fit
Total Fit (11.4 nm)
Peak 1 (48 nm)
Intensity (arb. unit)
Intensity (arb. unit)
Peak 2 (11.4 nm)
45 46 47 48 49 50 55 56 57 58
2θ (degree)
2θ (degree)

10. Surface morphology by AFM
σrms= 4 nm + 0.3 nm
d = 950 nm
10
Roughness by SE, σSE(nm)
8
σrms= 3.3 nm + 0.1 nm
Frequency (arb. unit)
d = 590 nm
6
σrms= 4.3 nm + 0.4 nm
4
d = 390 nm
2
σSE= 0.85 σrms + 0.3nm
σrms= 7 nm + 0.1 nm
0
0 2 4 6 8 10
d = 180 nm
Roughness by AFM, σrms(nm)
σrms= 2.1 nm + 0.2 nm
d = 55 nm
0 100 200 300 400
Conglomerate surface grain size (nm)
thickness series of R=1/10

11. Presence of Size Distribution
Surface Morphology X-ray diffraction
by AFM
Exp. XRD peak (220)
Total Fit
Intensity (arb. unit)
Peak 1
Peak 2
46 47 48 49 50
Frequency (arb. unit)
2θ (degree)
0.2 Intensity (arb. unit)
(111)
(d)
0.1
(220)
(311) (400)
0.0
0 100 200 300 400 20 30 40 50 60 70
Surface grain size (nm) Cu Kα 2θ (degrees)

12. Bifacial Raman Study
1.2 1.2 glass side exp. data of F0E31
film side exp. data of F0E31
cd1
cd1
cd2
cd2
Intensity (arb. unit)
a
Intensity (arb. unit)
fit with - cd1cd2 fit with - cd1cd2a
0.9 0.9
0.6 0.6
0.3 0.3
0.0
0.0
400 425 450 475 500 525 550
450 475 500 525 550
-1
Raman Shift (cm ) -1
Raman Shift (cm )
collection collection
excitation
excitation
Small grain (cd1) Large grain (cd2) a-Si:H
Sample #E31
Fitting
film (1200 nm, Size (nm) XC1 Size (nm) XC2
Model Xa (%)
R=1/1) [σ (nm)] [σ (nm)] glass
(%) (%)
glass
film
Film side cd1+cd2 6.1, [1.68] 20 72.7, [0] 80 0
Glass side cd1+cd2+a 6.6, [1.13] 8.4 97.7, [4.7] 52.4 39.2

13. Deconvolution of Raman Spectroscopy Data
• Conventionally: RS profiles are deconvoluted
assuming:
– a single mean crystallite size
– a peak assigned to grain boundary material
– an amorphous phase is included to account for the
asymmetric tail
• Samples in our study:
– No a-Si:H phase
– Presence of two (mean) sizes of crystallites
• Previous efforts to include CSD in fitting of Raman
Data
– To achieve a more accurate mathematical fitting of the
asymmetry observed in the RS profile as a result of CSD

14. Incorporation of CSD in Raman Analysis
According to our model, Φ(L) representing the CSD of an
ensemble of spherical crystallites, total Raman intensity profile
for the whole ensemble of nanocrystallites becomes:
(1)
I (ω , L0 , σ ) = ∫ Φ (L )I (ω , L )dL
'
For a normal CSD, Φ(L) is given as:
⎡ (L − L 0 )2 ⎤
Φ (L ) =
1 (2)
exp ⎢− ⎥
2σ
2πσ 2
2
⎢ ⎥
⎣ ⎦
where the mean crystallite size L0 and the standard deviation σ are
the characteristics of the CSD.
•Islam & Kumar, Appl. Phys. Lett.
78 (2001) 715.
•Ram et al Thin Solid Films 515
(2007) 7619

15. By putting Eq.(1) into Eq.(2) and then integrating the results over
the crystallite sizes L, and by restricting the dispersion parameter σ
to be less than L0/3 one gets the modified Raman intensity profile
as:
(3)
⎧ q 2 L2 f 2 (q )⎫
f (q )q 2 exp⎨− 0
⎬
2α ⎭
⎩
I (ω , L0 , σ ) ∝
{ω − ω (q )}2 + (Γ0 2)2
where the parameter ⎛ q 2σ 2 ⎞
f (q ) = 1 ⎜1 + ⎟ ,
⎜ ⎟
α
⎝ ⎠
which incorporates the distribution broadening parameter σ into
the Raman intensity profile. •Islam & Kumar, Appl. Phys. Lett.
78 (2001) 715.
•Ram et al Thin Solid Films 515
(2007) 7619

16. RS Data Deconvolution : Our Model
inclusion of crystallite size distribution
• In the absence of an explicit amorphous hump, the
asymmetry in the Raman lineshape of RS profiles, seen as
a low energy tail, is attributed to the distribution of
smaller sized crystallites
• Incorporation of a bimodal CSD in the deconvolution of
RS profiles:
– avoids the overestimation of amorphous content while
fitting the low frequency tail
– Avoids the inaccuracies in the estimation of the total
crystalline volume fraction in the fully crystalline µc-Si:H
material.
• RS(F) data bimodal CSD
• RS(G) data bimodal CSD + an amorphous phase

17. RS analysis
fit model quot;cd1+cd2quot;
cd1
cd2
* deconvolution of
d = 950 nm, RS(F)
RS profiles using a
Intensity (arb. unit)
bimodal size
cd1
fit model quot;cd1+cd2+aquot;
distribution of
cd2
d = 950 nm, RS(G)
large crystallite
a
grains (LG ~70–
80nm) and small
fit model quot;cd+aquot; cd
crystallite grains
d = 55 nm, RS(F) a
(SG ~6–8nm)
fit model quot;cd+aquot;
cd
a
d = 55 nm, RS(G)
400 450 500 550
-1
Raman shift (cm )

18. Fractional composition of films: Qualitative
agreement between RS and SE studies
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)
Samples belong to thickness series of R=1/10

19. Summary of variation in fractional compositions and roughness with film growth
Roughness by SE, σSE (nm)
Top surface layer (c)
6
thickness series of R=1/1
5
4
3
100 RS(F) (a)
2
80
1
60 Xc1
100
Fractional compositions by RS (%)
(b)
Bulk Layer Xc2
40
Xa
80
20
Fcf
60
Fractional compositions by SE (%)
0
Fcl
40 100 RS(G) (b)
Fv
Xc1
Fa
80
20 Xc2
Xa
60
0
100
40
Interface Layer (a)
80 20
60 0
0 200 400 600 800 1000 1200
40 Film Thickness (nm)
20
Fa
Samples belong to thickness series of R=1/1
0 Fv
200 400 600 800 1000 1200
Film thickness (nm)

20. Conclusions
• Microstructural characterization studies on plasma
deposited highly crystalline µc-Si:H films to explore the
distribution in the crystallite sizes
• SE two types of crystallites having two distinct sizes
• XRD two mean sizes of crystallites
• Surface morphological images size distribution
• Deconvolution of experimentally observed RS profiles
using a bimodal size distribution of crystallites
• In Raman spectra of single-phase µc-Si:H material:
appearance of a strong and longer low-frequency tail,
without any distinguishable amorphous hump, can be due
to the presence of size distribution in nanocrystallites,
instead of a contribution from disordered or amorphous
phase.

21. Thanks