Low Temperature Growth of Hydrogenated Silicon Prepared by PECVD from Argon Diluted Silane Plasma

doi:10.4236/csta.2012.13012

Paper Menu >>

Journal Menu >>

Crystal Structure Theory and Applications, 2012, 1, 62-67

http://dx.doi.org/10.4236/csta.2012.13012 Published Online December 2012 (http://www.SciRP.org/journal/csta)

Low Temperature Growth of Hydrogenated Silicon

Prepared by PECVD from Argon Diluted Silane Plasma

Rachid Amrani1,2*, Pascale Abboud1, Larbi Chahed2, Yvan Cuminal1

1IES, UMR, Université Montpellier II, Place Eugène Bataillon, Montpellier, France

2LPCMME, Département de Physique, Université d’Oran ES-Sénia, Oran, Algérie

Email: *[email protected], [email protected]

Received October 7, 2012; revised November 14, 2012; accepted November 23, 2012

ABSTRACT

In order to contribute to the understanding of the optoelectronics properties of hydrogenated nanocrystalline silicon thin

films, a detailed study has been conducted. The samples were deposited by 13.56 MHz PECVD (Plasma-Enhanced

Chemical Vapor Deposition) of silane argon mixture. The argon dilution of silane for all samples studied was 96% by

volume. The substrate temperature was fixed at 200˚C. The influence of depositions parameters on optical proprieties of

samples was studied by UV-Vis-NIR spectroscopy. The structural evolution was studied by Raman spectroscopy and

X-ray diffraction (XRD). Intrinsic-layer samples depositions were made in this experiment in order to obtain the transi-

tion from the amorphous to crystalline phase materials. The deposition pressure varied from 400 mTorr to 1400 mTorr

and the rf power from 50 to 250 W. The structural evolution studies show that beyond 200 W, we observed an amor-

phous-nanocrystalline transition, with an increase in crystalline fraction by increasing rf power and working pressure.

Films near the amorphous to nanocrystalline transition region are grown at reasonably high deposition rates (~10 Å/s),

which are highly desirable for the fabrication of cost effective devices. The deposition rate increases with increasing rf

power and process pressure. Different crystalline fractions (21% to 95%) and crystallite size (6 - 16 nm) can be

achieved by controlling the process pressure and rf power. These structural changes are well correlated to the variation

of optical proprieties of the thin films.

Keywords: Silicon; PECVD; Deposition Rate; Amorphous Nanocrystalline Transition; Argon; Low Temperature

1. Introduction

For high quality solar cell applications, materials with

high optical absorption, high carrier mobility and low

fabrication cost are demanded. Crystalline silicon (C-Si),

the most popular electronic material, has an indirect

bandgap and, hence, poor optical absorption. On the

other hand, hydrogenated amorphous silicon (a-Si:H) has

high optical absorption, but it suffers from low carrier

mobility, photo-induced degradation also named Stabler-

Wronski effect [1,2] and, hence, poor optoelectronic

properties. Recently, thin film hydrogenated nanocry-

stalline silicon (nc-Si:H) deposited by Plasma Enhanced

Chemical Vapor Deposition (PECVD) emerged as a ma-

terial for large-area electronics applications [3-6]. The

fabrication cost for nc-Si:H optoelectronic applications is

expected to be low, since thin films of nc-Si:H can be

deposited directly over large-area substrates using the

same fabrication facilities well established for a-Si:H

devices. Plasma deposited hydrogenated nanocrystalline

silicon (nc-Si:H) offers the possibilities of high carrier

mobility and stability against Staebler-Wronski effects

[6-9].

An enhanced optical absorption has been observed in

nanocrystalline silicon films [10,11]. The nanocrystalline

can absorb the photons of weak energies whereas amor-

phous silicon effectively absorbs the photons of high

energies. The optical absorption of nc-Si:H is evidently

highly dependent on the crystalline fraction. In contrast

to the a-Si:H film, the nc-Si:H film shows an increased

absorption below 1.8 eV and a reduced absorption above

2.0 eV. With decreasing crystallinity, the absorption co-

efficient decreases at lower photon energies nearly up to

1.4 eV, and increases beyond 2.0 eV [12].

The absorption coefficient of nc-Si:H is almost an or-

der of magnitude higher than that of c-Si. Thus, only ~2

μm thick layer is necessary for the nanocrystalline cell

compared to the >100 μm thick wafer used for a c-Si cell.

The plasma-enhanced chemical vapor deposition

(PECVD) method from silane plasma is widely used to

deposit the amorphous and nanocrystalline hydrogenated

silicon Si:H [13,14]. The importance of the effects of the

gas dilution on the kinetics of powder formation is im-

*Corresponding author.

R. AMRANI ET AL. 63

portant when one wants to transfer one process from one

dilution to another. This is particularly important for

example when we want to increase the deposition rate.

When silane (SiH4) is diluted with hydrogen, the device

quality nc-Si:H films prepared by PECVD method at

optimized deposition parameters show lower deposition

rate. In the present paper, the Si:H samples were pre-

pared from (SiH4 + Ar) plasma in a conventional capaci-

tive coupled rf (13.56 MHZ) PECVD system. The struc-

tural evolution of the samples was investigated by means

of X-ray diffraction and Raman scattering measurements.

The optical characterization of these thin films was also

appraised by UV-Vis-NIR spectroscopy in order to study

the influence of deposition parameters on the optical pro-

perties of thin films. The purpose of this work is to in-

vestigate the optical and structural properties of the thin

Si:H films to be able to apply them for the photovoltaic

applications with high deposition rate.

2. Experimental Procedure

The argon diluted hydrogenated silicon Si:H thin films

were deposited in a conventional rf (13.56 MHz) PECVD

chamber at substrate temperature of 200˚C. The deposi-

tion pressure varied from 400 mTorr to 1000 mTorr, at

various rf power (50, 100, 200 and 250 W). Samples

were grown on glass substrates. The magnitude of the

residual stress depends on the thin film and the substrate

properties. The residual stress was qualitatively estimated.

A big residual stress results usually in fracturing and

emitting layer from the substrate. In order to avoid this

complexity, a SiO2 underlayer was deposited. As conse-

quence, no layer delamination was observed.

The structural properties of the samples were investi-

gated by means of X-ray diffraction in standard (θ - 2θ

scans) configuration. The XRD studies are performed at

grazing angle of incidence using CuKα X-ray radiation (λ =

1.54056 Å). The crystallinity was also characterized by

Raman scattering measurements. All Raman spectra were

measured with an Ar-Ion laser at a wavelength of 473.5

nm. The power of the Raman laser was kept about 2 mW

to avoid laser induced crystallization on the films. The

Raman spectra of nc-Si:H consisted of a narrow line at

520 cm–1 due to a crystalline phase and a broad line

around 480 cm–1 due to an amorphous phase. The third

component between 500 and 510 cm–1 is due to the band

dilation at grain boundaries. The optical constants of

these films are estimated with the help of UV–Vis-NIR

transmission measurements in the range of 300 - 2700

nm. The samples images were taken by Scanning elec-

tron Microscope (SEM).

3. Results and discussion

The variation of deposition rate plotted as a function of

argon dilution in silane as shown in Figure 1, with 1000

mTorr working pressure, 100 W rf power, 50 sccm silane

flow and with different argon flow of 6, 50 and 1200

sccm. It is well known that the gas phase particles ap-

pearance time in silane argon plasma decreases when the

gas ration argon to silane increases [15-19]. This is par-

ticularly important to increase the deposition rate. It is

seen from Figure 1, for 1 minute deposition time, the

deposition rate increases from ~2 Å/s to ~16 Å/s, when

the argon dilution in silane increases from 10% to 96%.

But with increase in the deposition time to 10 minutes,

the growth rate decreases to 8 Å/s. Indeed, due to the

presence of powder trapped in the plasma, film growth is

prevented.

In order to obtain high deposition rate and without dust

trapped in the plasma, the silane flow was decreased to

10 sccm and the argon flow was fixed at 250 sccm. The

deposition time was fixed at 15 minutes.

As shown in Figure 2(a), the deposition rate increases

from ~6 Å/s to ~7.5 Å/s when the process pressure in-

creases from 400 mTorr to 1000 mTorr. With further

increase in process pressure to 1400 mTorr, the deposi-

tion rate decreases.

The impingement rate of gas molecules is given by;

2πB

mk T

with P is the process pressure, m is the molecular mass,

kB is Boltzmann’s constant and T is the gas temperature

[20]. Thus, with increase in process pressure the im-

pingement rate of silane increases. As a result, the num-

ber of film-forming radicals and hence the deposition

rate increases.

However, the powders electrostatically trapped in the

plasma prevent the films growth. So, for deposition

without dust trapped in the reactor, the working pressure

must be below the critical value of 1000 mTorr. As

Figure 1. Variation of deposition rate plotted as a function

of argon dilution in silane.

R. AMRANI ET AL.

(a)

(b)

Figure 2. Variation of deposition rate plotted as a function

of process pressure (a) and rf power (b).

shown in Figure 2(b), at certain working pressure, it is

observed that with increase in rf power, the deposition

rate increases. To achieve a better understanding of the

optical proprieties of Si:H, the optical transmission of

films was measured by UV-Vis-NIR spectrophotometer.

The films thickness t and the refraction index n were

determined using the method proposed by Swanepoel

[21].

Detailed analysis of the refractive index spectra was

performed using the model suggested by Wemple and

Didomenico [11,22,23]. At energies below than of the

optical bandgap, the refractive index is related to the

square of the photon energy (ħω)2 by:

 









The plot of 1/[n2(ħω) − 1] versus (ħω)2 allows the de-

termination of the average gap EM, the energy of disper-

sion ED, and static refractive index n0. The results of this

analysis are reported in Table 1.

The dispersion energy ED, characteristic of the mate-

rial, represents the oscillator force of the inter-band opti-

cal transition and depends on the average number of co-

ordination. The greater value of ED obtained for the sam-

ples, indicates a greater coordinance average number,

which is associated with a reduction of porosity in these

films and consequently a reduction in the disordered

fields in the vicinity of structural heterogeneities (micro-

cavities). This result is in accord with the values of the

refraction index. The static index n0, index of refraction

corresponding to zero energy, represents the compactness

of material. The static refractive index increases with

increase in process pressure indicating increase in the

material density in the film.

Micro-Raman spectroscopy has been widely used as a

powerful technique to characterize deposited thin layers.

Figure 3 shows Raman spectra of Si:H films deposited at

various process pressure and rf power. For samples de-

posited below 200 W, a broad peak located around 480

cm–1, characteristic of a completely amorphous structure.

Beyond 200 W rf power and beyond 800 mTorr pressure

deposition, the (TO) band can be correctly fitted using

three Gaussian components centered around 480, 510

and 520 cm–1, suggesting the presence in these films a

mixture of amorphous as well as crystalline structure

with different grain size [23-26]. The mean grain size

may be calculated from the formula;



Raman 2πd





where β = 2 nm²/cm and



 is the peak shift for

nanocrystalline as compared to that of c-Si [27].

The crystalline fraction Fc can be estimated from the

deconvoluted peaks of Raman spectra, as shown in Fig-

ure 4. The first scattering Ia in the region of 460 - 490

cm–1 comes from the TO vibration modes of amorphous

silicon, the intermediate component Ib arises near 500 -

510 cm–1 due to the band dilation at grain boundaries and

the third component Ic at 514 - 520 cm–1 is attributed to

the crystalline phase. Considering the intermediate

Table 1. Values of the films thickness t, the static refractive

index n0, the dispersion energy ED and the average gap EM,

obtained for the films grown at 100 and 200 W and with

different process pressures.

RF power (W)Pressure (mTorr) t (nm) n0 ED (eV) EM (eV)

100 400 551.7 3.6 17.681.8

100 600 569.7 3.64 18.081.78

100 800 603 3.71 19.921.76

100 1000 680.4 3.73 20.261.8

200 400 612 3.5 17.441.78

200 600 648 3.53 17.471.63

200 800 697.5 3.56 17.521.56

200 1000 747 3.58 17.651.45

R. AMRANI ET AL. 65

Figure 3. Typical Raman spectra obtained in the TO-like

mode, for films deposited (a): with deposition pressure of

1000 mTorr and varying rf power (50, 100 and 200 W) and

(b): rf power 200 W and varying pressure (600, 800 and

1000 mTorr).

Figure 4. The deconvoluted peaks of Raman spectra for the

film deposited at 1200 mTorr and 200 W.

component as a portion of the crystal, the ratio of the

volume fraction of crystalline is defined by Fc = (Ic +

Ib)/(Ic + Ib + μIa), where μ is a scattering factor.

As the grain size is about a few nanometers, we can

take μ ≈ 1 [28,29].

The results for the crystalline fraction and Raman

Crystallite size dRaman are summarized in Table 2.

Additional information about the structural changes of

the films is gained from the XRD results. XRD patterns

of two typical samples at the same pressure (1400 mTorr)

with different rf power, as indicated, are shown in Figure

5. For the sample deposited at 100 W, no crystal grains

are detected, indicating that there is no apparent stru-

ctural evolution in the thin films. When rf power reaches

200 W, diffraction peaks arise. With the increase of rf

power, there appear three peaks symbolizing three dif-

ferent silicon crystalline orientations. The peaks observed

at angles of 28˚, 47˚ and 56˚ are assigned to Si(111),

Si(220) and Si(311) reflection planes of faced-centred

cubic silicon, respectively, demonstrating a proper grow-

th of nc-Si:H. Also, the growth of grains in the thin films

is multi-oriented. The mean grain size dXRD estimated

using the classical Scherrer’s formula [30] is also indi-

cated in Table 2.

The average crystallite size increases with increasing

working pressure, these results are consistent with Ra-

man scattering results and give further strong support to

the formation of nc-Si:H films by PECVD with argon to

silane mixture. Crystallite sizes measured by XRD me-

thod turned out difference with those measured by Ra-

man method. The difference can be due to the different

detection sensitivity of characterization techniques.

Table 2. Raman crystallites size dRaman, XRD average grain

size dXRD and crystalline fraction obtained for samples de-

posited at 200 W rf power and various working pressure.

RF power (W)Pressure (mTorr)dRaman (nm) dXRD (nm)Fc (%)

200 600 -- -- --

200 800 6.4 7.1 21

200 1000 9.8 9.5 42

200 1200 11.5 12.2 61

200 1400 16.2 15.1 95

Figure 5. Low angle X-ray diffraction pattern of two typical

samples deposited at the same pressure (1400 mTorr) with

different rf power (100 and 200 W). The spectra are shifted

vertically for better clarity.

R. AMRANI ET AL.

SEM images revel significant difference between amor-

phous and nanocrystalline samples. As shown in Figure

6(a), SEM studies of samples deposited at 400 mTorr

and 200 W show smooth conchoidal surface morphol-

ogy.

From the cross-sectional SEM on the fractured sur-

faces of the films also no columnar structure is observed.

Figure 6(b) shows SEM image of sample deposited at

1000 mTorr and 200 W. The film has uniformly distri-

buted grains.

The application of Tauc approximation [31] to calcu-

late the optical gap for nanocrystalline silicon is still a

subject of debate. Thus, there are several ambiguities

about the band gap of nc-Si:H films because the material

contains both amorphous and crystalline phases. In the

nanocrystalline areas, the indirect band-gap should be

around 1.1 eV (close to the crystalline silicon value),

while in the amorphous areas, it is around 2 eV (similar

to the a-Si:H value, depending on the process parame-

ters).

The average gap EM seems quite suitable to describe

the variation of the optical properties of the amorphous

and nanocrystalline silicon thin films [11,22,23]. As

show in Table 1, for the samples deposited at 100 W, the

average gap EM, is around 1.8 eV. But for films grown at

200 W and beyond process pressure of 800 mTorr, EM

decreases considerably. This confirms once again, that

beyond these deposition parameters, an amorphous to

nanocrystalline transition is observed.

As seen from Table 1, the average gap of nc-Si:H

films (deposited at 200 W) decreases to 1.45 as deposi-

tion pressure increases to 1000 mTorr. We believe that

the low average gap of nc-Si:H films may be due to the

increase in crystalline volume fraction in the film, as

revealed by Raman spectroscopic analysis. This infer-

ence is further strengthened by the observed variation in

static refractive index with process pressure.

4. Conclusion

We have shown that hydrogenated nanocrystalline silicon

Figure 6. Scanning electron Microscope (SEM) images of

(a): Amorphous sample with SiO2 under-layer; and (b):

nanocrystalline sample.

con (nc-Si:H) films can be prepared with highly argon

silane dilution PECVD at high deposition rates and at

low substrate temperature (200˚C). Samples obtained

have a great compactness. Optical and structural thin

films properties of Si:H can be tuned by adjusting the

deposition conditions. Films with different crystalline

fractions and crystallite size are achieved by controlling

the process pressure. The ease of depositing films with

tunable average band gap and at high deposition rate is

useful for photovoltaic applications. Low-temperature

processes particularly adequate for large-area devices

open up not only very important cost-reduction potential,

but also new possibilities such as making semi-trans-

parent or flexible modules.

5. Acknowledgements

This work was supported by the grant Averroes Program

funded by the European commission.

REFERENCES

[1] W. E. Spear and P. G. LeComber, “Substitutional Doping

of Amorphous Silicon,” Solid State Communications, Vol.

17, No. 9, 1975, pp. 1193-1196.

doi:10.1016/0038-1098(75)90284-7

[2] D. L. Staebler and C. R. Wronki, “Reversible Conducti-

vity Changes in Discharge—Produced Amorphous Si,”

Applied Physics Letters, Vol. 31, No. 4, 1977, 3 p.

doi:10.1063/1.89674

[3] M. Ito, C. Koch, V. Svrcek, M. B. Schubert and J. H.

Werner, “Silicon Thin Film Solar Cells Deposited under

80˚C,” Thin Solid Films, Vol. 383, No. 1-2, 2001, pp.

129-131. doi:10.1016/S0040-6090(00)01590-X

[4] A. V. Shah, J. Meier, E. Vallat-Sauvan, N. Wyrsch, U.

Kroll, C. Droz and U. Graf, “Material and Solar Cell Re-

search in Microcrystalline Silicon,” Solar Energy Mate-

rials & Solar Cells, Vol. 78, No. 1-4, 2003, pp. 469-491.

[5] J. Meier, R. Fluckiger, H. Keppner and A. V. Shah,

“Complete Microcrystalline p-i-n Solar Cell—Crystalline

or Amorphous Cell Behavior?” Applied Physics Letters,

Vol. 65, No. 7, 1994, p. 860. doi:10.1063/1.112183

[6] C. H. Lee, A. Sazonov and A. Nathan, “High-Mobility

Nanocrystalline Silicon Thin-Film Transistors Fabricated

by Plasma-Enhanced Chemical Vapor Deposition,” Appli-

ed Physics Letters, Vol. 86, No. 22, 2005, Article ID:

222106. doi:10.1063/1.1942641

[7] I. C. Cheng, S. Allen and S. Wagner, “Evolution of Nano-

crystalline Silicon Thin Film Transistor Channel Layers,”

Journal of Non-Crystalline Solids, Vol. 720, No. 1, 2004,

pp. 338-340.

[8] P. R. i Cabarrocas, R. Brenot, P. Bulkin, R. Vanderha-

ghen, B. Drevillon and I. French, “Stable Microcrystalline

Silicon Thin-Film Transistors Produced by the Layer-by-

Layer Technique,” Journal of Applied Physics, Vol. 86,

No. 12, 1999, p. 7079.

doi:10.1063/1.371795

R. AMRANI ET AL.

[9] A. Shah, E. Vallat-Sauvain, P. Torres, J. Meier, U. Kroll,

C. Hof, C. Droz, M. Goerlitzer, N. Wyrsch and M. Vane-

cek, “Intrinsic Microcrystalline Silicon (μc-Si:H) Depos-

ited by VHF-GD (Very High Frequency-Glow Discharge):

A New Material for Photovoltaics and Optoelectronics,”

Materials Science and Engineering: B, Vol. 69-70, 2000,

pp. 219-226. doi:10.1016/S0921-5107(99)00299-8

[10] Z. Remes, “Study of Defects and Microstructure of Amor-

phous and Microcrystalline Silicon Thin Films and Poly-

crystalline Diamond Using Optical Methods,” Ph.D. The-

sis, Charles University, Prague, 1999.

[11] R. Amrani, D. Benlekehal, R. Baghdad, D. Senouci, A.

Zeinert, K. Zellama, L. Chahed, J. D. Sib and Y. Bouizem,

“Low-Temperature Growth of Nanocrystalline Silicon

Films Prepared by RF Magnetron Sputtering: Structural

and Optical Studies,” Journal of Non-Crystalline Solids,

Vol. 354, No. 19-25, 2008, pp. 2291-2295.

doi:10.1016/j.jnoncrysol.2007.10.044

[12] F. Siebke, S. Yata, Y. Hishikawa and M. Tanaka, “Cor-

relation between Structure and Optoelectronic Properties

of Undoped Microcrystalline Silicon,” Journal of Non-

Crystalline Solids, Vol. 227-230, No. 2, 1998, pp. 977-

981. doi:10.1016/S0022-3093(98)00261-0

[13] A. Matsuda, “Thin-Film Silicon—Growth Process and

Solar Cell Application,” Japanese Journal of Applied

Physics, Vol. 43, 2004, pp. 7909-7920.

doi:10.1143/JJAP.43.7909

[14] R. A. Street, “Large Area Electronics, Applications and

Requirements,” Physica Status Solidi A, Vol. 166, No. 2,

1998, pp. 695-705.

doi:10.1002/(SICI)1521-396X(199804)166:2<695::AID-

PSSA695>3.0.CO;2-U

[15] J. L. Dorier, C. Hollenstein and A. A. Howling, “Powder

Dynamics in Very High Frequency Silane Plasmas,”

Journal of Vacuum Science & Technology A, Vol. A10,

No. 4, 1992, pp. 1048-1052. doi:10.1116/1.578200

[16] J. L. Dorier, C. Hollenstein and A. A. Howling, “Spatio-

temporal Powder Formation and Trapping in Radio Fre-

quency Silane Plasmas Using Two-Dimensional Polariza-

tion—Sensitive Laser Scattering,” Journal of Vacuum

Science & Technology A, Vol. 13, No. 3, 1995, pp.

918-928. doi:10.1116/1.579852

[17] A. A. Howling, J. L. Dorier, C. Hollenstein, U. Kroll and

F. Finger, “Frequency Effects in Silane Plasmas for

Plasma Enhanced Chemical Vapor Deposition,” Journal

of Vacuum Science & Technology A, Vol. 10, No. 4, 1992,

pp. 1080-1085. doi:10.1116/1.578205

[18] J. L. Dorier, “Genèse, Croissance et Conséquences de

Particules Dans les Plasmas en Silane à Basse Pression et

Basse Température,” Ph.D. Thesis, 1996.

[19] A. Bouchoule, “Dusty Plasma: Physics, Chemistry and

Technological Impacts in Plasma Processing,” Wiley,

New York, 1999.

[20] S. Kasap and P. Capper, “Springer Handbook of Elec-

tronic and Photonic Materials,” Springer Publication,

2006.

[21] R. Swanpoel, “Determination of the Thickness and Op-

tical Constants of Amorphous Silicon,” Journal of Phy-

sics E: Scientific Instruments, Vol. 16, No. 12, 1983, pp.

1214-1222. doi:10.1088/0022-3735/16/12/023

[22] S. H. Wemple and M. Didomenico, “Behavior of the

Electronic Dielectric Constant in Covalent and Ionic Ma-

terials,” Physical Review B, Vol. 3, No. 4, 1971, pp. 1338-

1351. doi:10.1103/PhysRevB.3.1338

[23] R. Amrani, F. Pichot, J. Podlecki, A. Foucaran, L. Chah-

ed and Y. Cuminal, “Optical and Structural Proprieties of

nc-Si:H Prepared by Argon Diluted Silane PECVD,”

Journal of Non-Crystalline Solids, Vol. 358, No. 17, 2012,

pp. 1978-1982. doi:10.1016/j.jnoncrysol.2012.01.022

[24] S. Veprek, F. A Sarott and Z. Iqbal, “Effect of Grain Boun-

daries on the Raman Spectra, Optical Absorption, and

Elastic Light Scattering in Nanometer-Sized Crystalline

Silicon,” Physical Review B, Vol. 36, No. 6, 1987, p.

3444.

[25] H. S. Mavi, A. K. Shukla, S. C. Abbi and K. P. Jain,

“Raman Study of Amorphous to Microcrystalline Phase

Transition in cw Laser Annealed a-Si:H Films,” Journal

of Physic Science, Vol. 66, No. 11, 1989, p. 5322.

doi:10.1063/1.343723

[26] Y. He, Y. Wei, G. Zheng, M. Yu and M. Liu, “An Ex-

ploratory Study of the Conduction Mechanism of Hydro-

genated Nanocrystalline Silicon Films,” Journal of Ap-

plied Physics, Vol. 82, No. 7, 1997, p. 3408.

doi:10.1063/1.365656

[27] Y. He, C. Yin, G. Cheng, L. Wang, X. Liu and G. H. Hu,

“The Structure and Properties of Nanosize Crystalline

Silicon Films,” Journal of Applied Physics, Vol. 75, No.

2, 1994, pp. 797-803. doi:10.1063/1.356432

[28] G. Yue, J. D. Lorentzien, J. Lin, D. Han and Q. Wang,

“Photoluminescence and Raman Studies in Thin-Film

Materials: Transition from Amorphous to Microcrystal-

line Silicon,” Applied Physics Letters, Vol. 75, No. 4,

1988, pp. 492-494. doi:10.1063/1.124426

[29] D. Beeman, R. Tsu and M. F. Tporpe, “Structural Infor-

mation from the Raman Spectrum of Amorphous Sili-

con,” Physical Review B, Vol. 32, No. 2, 1985, pp. 874-

878. doi:10.1103/PhysRevB.32.874

[30] P. Scherrer, “Bestimmung der Grösse und Derinneren

Struktur von Kolloidteilchen Mittels Röntgenstrahlen,”

Nachrichten von der Gesellschaft der Wissenschaften zu

Göttingen, Mathematisch-Physikalische Klasse, Vol. 26,

No. 1, 1918, pp. 98-100.

[31] J. Tauc, “Optical Properties of Solids,” Abeles, North

Holland, Amsterdam, 1972.