JOURNAL OF APPLIED PHYSICS 108, 063512 共2010兲

Nonlinear optical properties of silicon nanoclusters/nanocrystals doped
SiO2 films: Annealing temperature dependence
Masahiko Ito, Kenji Imakita, Minoru Fujii,a兲 and Shinji Hayashi
Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University,
Rokkodai, Nada, Kobe 657-8501, Japan

共Received 20 May 2010; accepted 16 July 2010; published online 20 September 2010兲
Comprehensive studies on nonlinear refractive indices 共n2兲 of SiO2 films containing Si nanocrystals
and/or nanoclusters 共SiO2 : Si-ncs兲 are performed. The comparison of the nonlinear refractive indiceswith the electron spin resonance signals reveals that defect states play a major role in the large n2
when the annealing temperature is low, i.e., when Si nanoclusters exist in films. On the other hand,when Si nanocrystals are grown by high-temperature annealing, the contribution of defect states
becomes small and that of the quantized electronic states of Si nanocrystals becomes large. The
present results demonstrate that both the defect states and the quantized electronic states should betaken into account to explain the origin of large n2 of SiO2 : Si-ncs and to optimize the structure to
maximize n2. © 2010 American Institute of Physics. 关doi:10.1063/1.3480821兴
I. INTRODUCTION

Silicon dioxide 共SiO2兲 films containing silicon 共Si兲 nanocrystals have been attracting great attention as Si-based optoelectronic materials because of the high luminescence efficiency in the visible and near infrared regions and the large
nonlinear optical responses.1–6 Since they can be prepared bya conventional semiconductor technology such as
sputtering,6–8 chemical vapor deposition,3–5,9 and ion
implantation,1,2,10 they are considered to be one of the key
materials for future silicon-based nonlinear optical devices
such as all optical switches and modulators.11
In this material, Si nanocrystals are considered to be
responsible for the large nonlinear optical responses. In fact,large nonlinear refractive indices 共n2兲 have been reported invarious forms of Si nanocrystal samples.1–6,12–23 An example
is porous Si prepared by electrochemical etching of Si
wafers.12–14 Another one is laser ablated Si nanocrystals deposited on a quartz substrate15–17 and dispersed in organic
solvents.18,19 In the case of SiO2 films containing Si nanocrystals, large n2 has been observed irrespective of the preparation procedures, i.e., plasma enhanced chemical vapor
deposition,3–5 sputtering,6 and ion implantation.1,2 The reported values of n2 are much larger than those of bulk Si
crystal 共⬃10−14 cm2 / W兲 共Refs. 24–26兲 and SiO2共⬃10−16 cm2 / W兲,27,28 although they are distributed in a very
wide range 共共⬃−10−7兲 – ⬃ 10−13 cm2 / W兲.1–6
Because of the large variation in the reported values ofn2, comparison of experimental data with calculation is notstraightforward and thus the origin of large n2 is not fully
elucidated. The most widely believed origin is the quantizedelectronic states in nanocrystals.3–5 The enhancement of n2
by the quantum size effects has been discussed experimentally and theoretically for a variety of semiconductor
nanocrystals.29–34 In the case of Si nanocrystals in silica matrices, strong enhancement of n2 with decreasing the size ispredicted theoretically.35,36 This has been proved, althougha兲Electronic mail: fujii@eedept.kobe-u.ac.jp.

0021-8979/2010/108共6兲/063512/5/$30.00

quantitatively, by some experimental studies.3,4 Another possible origin of large n2 is defects in or on the surface ofsilicon nanocrystals. Vijayalakshmi et al.2proposed that surface states contribute to large n2 of Si nanocrystals. Takagahara and Hanamura37 reported that localization of excitons at
disorders or impurities enhances its oscillator strength, andhence the nonlinear optical responses.
One of the purposes of this work is to distinguish thecontributions of quantized electronic states and defect states
to n2 of SiO2 films containing Si nanocrystals and/or nanoclusters. To achieve this purpose, we prepare a large numberof samples in wide ranges of preparation parameters andclarify the relation between the preparation parameters andn2. For the characterization of samples, we perform electron
spin resonance 共ESR兲 and Raman scattering spectroscopy.
We show that both defect states and quantized electronic
states contribute to n2 and the relative contributions dependon preparation parameters.

II. EXPERIMENTAL PROCEDURE

In this work, we prepare SiO2 films containing Si nanocrystals and/or Si nanoclusters by a cosputtering method inwide ranges of preparation parameters. As we discuss later,
depending on the preparation parameters, Si nanocrystals or
nanoclusters are formed in the films.7,8 Hereafter, we denote
both types of the samples as SiO2 : Si-ncs.
Si and SiO2 were simultaneously sputter-deposited in Ar
gas on a quartz substrate, and the deposited film 共about
12 ␮m in thickness兲 was annealed in a N2 gas atmospherefor 30 min at temperatures from 600 to 1250 ° C. The excess
Si concentration was changed from 6 to 22 vol %. The annealing temperature strongly affects the sample
morphology.38 In as-deposited samples, very small amorphous Si nanoclusters are dispersed in a film. The number
and size of Si nanoclusters increase with increasing the annealing temperature. When the annealing temperature

108, 063512-1© 2010 American Institute of Physics

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J. Appl. Phys. 108, 063512 共2010兲

Ito et al.

1.00(a) Open Aperture : Top-1110n2 (cm /W)

063512-222(vol.%)20.99(a) Excess Si conc.

0.97
1.1 (b) Close Aperture : T-1216(vol.%)10

6(vol.%)

-13

10 -7
10

cl

(b)
1.0

 (cm/W)

Normalized transmittance

0.98

0.9

Excess Si conc.
22(vol.%)

-8

10

-9

10

16(vol.%)1.1 (c) Ratio : Tcl/Top

6(vol.%)

0.9
-20

-10

0

10

20

z (mm)
FIG. 1. 共Color online兲 Typical z-scan traces, 共a兲 an open aperture, 共b兲 a close
aperture, 共c兲 the ratio, for the sample with the excess Si concentration of 22
vol % and the annealing temperature of 1150 ° C. The peak intensity of theincident light is 2.9 GW/ cm2. Solid curves are the results of the fitting by
the z-scan model 共Ref. 39兲.

reaches ⬃1000 ° C, Si nanocrystals start to emerge. The ratioof nanocrystals to nanoclusters increases at higher annealing
temperatures.
X-band ESR was measured by a conventional ESR spectrometer 共JES-TE300, JEOL兲 at room temperature. The
modulation frequency and amplitude for ESR measurements
were 100 kHz and 320 G, respectively. The g value wasdetermined by using the signal from Mn2+ / MgO powder as acalibration reference. Raman measurements were carried out
in a conventional 90° scattering configuration by using a
triple monochromator equipped with a charge-coupled device detector. The excitation source was the 488 nm line of
an Ar-ion laser.
The nonlinear optical responses 关n2 and two photon absorption coefficient 共␤兲兴 of SiO2 : Si-ncs were measured by az-scan method.6,39 The excitation source was the modelocked Ti:sapphire femtosecond laser with the pulse width of
70 fs and the repetition frequency of 82 MHz. The photon
energy was varied from 1.52 to 1.66 eV. The incident beam
was focused on a sample by a lens with the focal length of 50
mm. The beam waist and diffraction length determined by aknife edge method were 15 ␮m and 1 mm, respectively. The
peak intensity was lower than 12 GW/ cm2 to avoid thermal
effects.
III. RESULTS AND DISCUSSION
A. Annealing temperature dependence of n2 and ␤

Figure 1 shows a typical result of a z-scan measurement;
共a兲 an open aperture 共Top兲, 共b兲 a close aperture 共Tcl兲, and 共c兲
the ratio 共Tcl / Top兲. Open squares and solid curves represent

3

10

Excess Si conc.
22(vol.%)16(vol.%)2

10

6(vol.%)

2.007 (d)g value

1.0

ESR signal intensity

-10

10 4
10 (c)

Excess Si conc.
22(vol.%)2.006

16(vol.%)2.005
6(vol.%)

2.004
as-depo.
0
400

800

1200
o

Annealing temperature ( C)
FIG. 2. 共Color online兲 Annealing temperature dependence of 共a兲 n2, 共b兲 ␤,
共c兲 ESR signal intensity, and 共d兲 g value for series of samples with different
excess Si concentrations 共䊐: 6, 䊊: 16, 䉭: 22 vol %兲. In 共b兲, ␤ for the
samples with the excess Si concentration of 6 vol % and the annealing
temperatures of 600 and 700 ° C are not shown because they are below thedetection limit.

experimental data and results of fitting by the model commonly used for the analysis of the z-scan measurement,
respectively.39 Details of the analysis procedure are shown in
our previous papers.6,40 The results are well-fitted by themodel and thus the n2 and the ␤ are obtained with highaccuracy.
Figures 2共a兲 and 2共b兲 show annealing temperature dependence of n2 and ␤, respectively, for the samples withthree different excess Si concentrations. At almost all annealing temperatures studied, n2 and ␤ are larger for the samples
with larger amount of excess Si. For a fixed excess Si concentration, n2 exhibits complicated annealing temperaturedependence. The dependence is similar for all series ofsamples with different excess Si concentrations. When theannealing temperature is low 共ⱗ700 ° C兲, n2 is smaller thanthat of as-deposited samples. At higher annealing temperatures, it increases and reaches the maximum at around
800– 900 ° C, and then decreases. ␤ shows similar annealing
temperature dependence. This complicated annealing tem-

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ESR Signal Intensity (arb. units)(a)J. Appl. Phys. 108, 063512 共2010兲

Ito et al.

10-11

(b)

Ta
1250oCTa
1250oC

1150oC
1150oC

900oC
800oC
700oC

Intensity (arb.units)

1000oC

1000oC
900oC
800oC

n2 (cm2/W)

063512-3

22

10-12

16
6

10-13
100

Excess Si
conc. (vol.%)

1000
ESR signal intensity

700oC

600oC

600oC

as-depo

FIG. 4. 共Color online兲 n2 as a function of ESR signal intensity. The data ofall samples, i.e., different excess Si concentrations 共䊐: 6, 䊊: 16, 䉭: 22
vol %兲 and different annealing temperatures, are plotted.

as-depo
Excess Si
22 (vol.%)

332

334 336 338 340
Magnetic Field (mT)

Excess Si
22 (vol.%)

300

400

500

600

700

Raman shift (cm-1)

FIG. 3. 共Color online兲 Annealing temperature dependence of 共a兲 ESR spectra and 共b兲 Raman spectra for the samples with the excess Si of 22 vol %.

perature dependence of n2 strongly suggests that the origin of
the large n2 cannot be explained by a simple quantum confinement model. If only the quantized electronic states are
the origin of the large n2, n2 should monotonously decrease
with increasing the annealing temperature because of the size
increase in Si nanoclusters or nanocrystals.35
As the origin of the large n2 of SiO2 : Si-ncs, defect states
are also considered.2,37 To study the correlation between thedefect density and n2, we performed ESR measurements.
Figure 3共a兲 shows ESR spectra for the samples with 22
vol % excess Si. We can see that the signal intensity depends
strongly on the annealing temperature. Figures 2共c兲 and 2共d兲show annealing temperature dependence of the ESR signal
intensity and the g value, respectively. Before discussing theorigin of the ESR signals in detail, we roughly compare theannealing temperature dependence of the intensity with thatof n2. At the first glance, the annealing temperature dependence of the ESR intensity is similar to that of n2. Thissuggests that defects contribute at least partly to the n2 and␤. However, if we closely compare Figs. 2共a兲 and 2共c兲, we
notice some differences. For example, above 900 ° C, thespin density, i.e., ESR signal intensity, decreases much fasterthan n2 and ␤. Furthermore, compared to n2 and ␤, spin
density does not depend strongly on the excess Si concentration. In Fig. 4, n2 is plotted as a function of the ESR signal
intensity. Although there exists a correlation between thesetwo values, the data are scattered more than one order ofmagnitude. The large scattering of the data suggests that defects are not an only origin of the large n2. We believe thatthe contribution of the quantized electronic states of Si nanocrystals or nanoclusters in addition to the defect states resultsin the large scattering of the data.
B. Origin of large n2 at different annealing
temperatures

From the above discussion, it is clear that defects play asignificant role in the large n2 of SiO2 : Si-ncs. Here, we iden-

tify the defects from ESR and Raman data. As shown in Fig.
2共d兲, the g value gradually increases up to 800 ° C and,above this temperature, it increases rapidly. The behavior of
the g value suggests the existence of different kinds ofdefects.41 The signal with the g value of ⬃2.004 is usuallyassigned to the defects in SiOx 共EX center兲,42 while that withthe g value of ⬃2.006 to dangling-bonds at Si– SiO2 interfaces 共Pb center兲.43
A comparison of Figs. 2共c兲 and 2共d兲 leads us to the following model. As-deposited samples have a large number of
EX centers and they contribute to the large n2. The EX center
density decreases by annealing. This results in the decreasein n2 when the annealing temperature is relatively low
共600– 700 ° C兲. At around 800 ° C, the signal from the Pb
center appears and the density increases till ⬃900 ° C. The
large n2 in this range is thus considered to arise mainly fromPb centers. Above this temperature, the defect density decreases rapidly. Around the temperature where the defectdensity decreases, Si nanocrystals start to grow. Probably thedecrease in the surface-to-volume ratio by the formation andgrowth of nanocrystals results in the decrease in the defectdensity. The evidence of Si nanocrystals formation is obtained in Raman spectra. Figure 3共b兲 shows Raman spectra
for the samples with 22 vol % excess Si. Below 900 ° C, thespectra are amorphous-like, suggesting the existence ofamorphous clusters.44 A crystalline peak 共520 cm−1兲 starts toappear at 1000 ° C and it becomes sharper at higher annealing temperatures. This evidences the growth of Si nanocrystals and is consistent with the decrease in the ESR signal
intensity at the high annealing temperature range.
In the annealing temperature range where the growth of
Si nanocrystals is confirmed, the annealing temperature dependence of the ESR signal intensity is different from that ofn2 关Figs. 2共a兲 and 2共c兲兴. For example, at 1250 ° C, despite avery small defect density, the n2 is relatively large. Moreover, despite almost the same defect density at 1250 ° C for
the samples with different excess Si concentrations, n2 islarger for those with larger excess Si. These discrepancies
suggest the existence of other origins for the large n2. We
believe that in this annealing temperature range, quantizedelectronic states brought by quantum size effects are the major origin of large n2 as have been predicted by some previous studies.3–6 In fact, in our previous work, we observed
size-dependence of n2 for the samples annealed at highAuthor complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

063512-4

J. Appl. Phys. 108, 063512 共2010兲

Ito et al.

2n2 (cm /W)(a)

Excess Si conc. 22 (vol.%)

-12

10

16 (vol.%)
6 (vol.%)

-13

10

(b)

Excess Si conc. 22 (vol.%) (cm/W)-8

1x10

16 (vol.%)

-9

1x10

6 (vol.%)-10

Figure of merit (n2/)

1x10

(c)
10

Excess Si conc.
6 (vol.%)16 (vol.%)

22 (vol.%)

1
1.5

1.6

1.7

Photon energy (eV)FIG. 5. 共Color online兲 Photon energy dependence of 共a兲 n2, 共b兲 ␤, and 共c兲
NFOM 共n2 / ␤␭兲 for the samples with different excess Si concentrations 共䊐:6, 䊊: 16, 䉭: 22 vol %兲. The data of samples annealed at 1150 ° C areshown.

temperatures.6 The experimental results agreed fairly wellwith a calculation which took into account quantized electronic states of Si nanocrystals.35,36

C. Photon energy dependence of the nonlinear
optical properties of SiO2 : Si-ncs

For optical switching and modulation applications oflarge n2, nonlinear figure of merit 共NFOM兲, n2 / ␤␭, where ␭
is a wavelength, is proposed as one of the important parameters to deduce the device performance. Figures 5共a兲–5共c兲
show the photon energy dependence of n2, ␤, and NFOM,
respectively, for the samples annealed at 1150 ° C. Althoughn2 gradually decreases with decreasing the photon energy,
NFOM increases because of the rapid decrease in ␤. Similar
photon energy dependence is observed for the samples annealed at other temperatures.
Yıldırım and Bulutay35,36 calculated the real part of thirdorder nonlinear susceptibility 共Re ␹共3兲兲, which is proportional
to n2, of Si nanocrystals doped SiO2 by an atomic pseudopotential approach. According to them, Re ␹共3兲 slightly decreases from 800 to 1550 nm. They also show that the
NFOM drastically increases below the band gap energy ofSi-ncs. Although our measurements are limited to the range
from 1.52 to 1.66 eV, considering these reports and Fig. 5共c兲,SiO2 : Si-ncs are expected to show large NFOM at the com-munication wavelength. In fact, Spano et al..5 reported that
Si-ncs doped SiOxNy thin films have a large n2 at 1550 nm
共⬃5 ⫻ 10−13 cm2 / W兲.
IV. CONCLUSION

We performed comprehensive studies on third order nonlinear optical properties of SiO2 films containing Si nanocrystals and/or nanoclusters by changing the annealing temperature and the excess Si concentration in wide ranges toreveal the origin of large n2 and ␤. We demonstrated that n2and ␤ exhibit complicated annealing temperature dependence. The detailed comparison of n2 and ESR data revealed
that defect states play a major role in the large n2 when theannealing temperature is low, while their contributions become small when Si nanocrystals are grown in the films byhigh-temperature annealing. In the high-temperature annealing range, quantized electronic states of Si nanocrystals are
considered to be the major origin of the large n2. Therefore,in SiO2 : Si-ncs systems, to maximize n2, the structure and the
preparation parameters should be optimized by taking into
account both the quantized electronic states and the defectstates.
ACKNOWLEDGMENTS

This work was partly supported by the Research Grant in
the Natural Science from Mitsubishi Foundation and by the
Research Grant in Kawanishi-Shinmeiwa-Kinen Foundation.
1

S. Vijayalakshmi, H. Grebel, Z. Iqbal, and C. W. White, J. Appl. Phys. 84,
6502 共1998兲.
2
S. Vijayalakshmi, H. Grebel, G. Yaglioglu, R. Pino, R. Dorsinville, and C.
W. White, J. Appl. Phys. 88, 6418 共2000兲.
3G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G.
Franzò, and F. Priolo, J. Appl. Phys. 91, 4607 共2002兲.
4
S. Hernández, P. Pellegrino, A. Martínez, Y. Lebour, B. Garrido, R. Spano,
M. Cazzanelli, N. Daldosso, L. Pavesi, E. Jordana, and J. M. Fedeli, J.
Appl. Phys. 103, 064309 共2008兲.
5
R. Spano, N. Daldosso, M. Cazzanelli, L. Ferraioli, L. Tartara, J. Yu, V.
Degiorgio, E. Jordana, J. M. Fedeli, and L. Pavesi, Opt. Express 17, 3941
共2009兲.
6
K. Imakita, M. Ito, M. Fujii, and S. Hayashi, J. Appl. Phys. 105, 093531
共2009兲.
7
Y. Kanzawa, T. Kageyama, S. Takeoka, M. Fujii, S. Hayashi, and K.
Yamamoto, Solid State Commun. 102, 533 共1997兲.
8
S. Takeoka, M. Fujii, and S. Hayashi, Phys. Rev. B 62, 16820 共2000兲.
9F. Iacona, G. Franzo, and C. Spinella, J. Appl. Phys. 87, 1295 共2000兲.
10
S. Guha, B. Qadri, R. G. Musket, M. A. Wall, and T. Shimizu-Iwayama, J.
Appl. Phys. 88, 3954 共2000兲.
11
B. Jalali, Phys. Status Solidi A 205, 213 共2008兲.
12
Y. Kanemitsu, S. Okamoto, and A. Mito, Phys. Rev. B 52, 10752 共1995兲.
13
F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii, and V. S.
Dneprovskii, Appl. Phys. Lett. 67, 323 共1995兲.
14
S. Lettieri, O. Fiore, P. Maddalena, D. Ninno, G. D. Francia, and V. L.
Ferrara, Opt. Commun. 168, 383 共1999兲.
15
S. Vijayalakshmi, M. A. George, and H. Grebel, Appl. Phys. Lett. 70, 708
共1997兲.
16
S. Vijayalakshmi, F. Shen, and H. Grebel, Appl. Phys. Lett. 71, 3332
共1997兲.
17
S. Vijayalakshmi, A. Lan, Z. Iqbal, and H. Grebel, J. Appl. Phys. 92, 2490
共2002兲.
18
E. Koudoumas, O. Kokkinaki, M. Konstantaki, N. Kornilios, S. Couris, S.
Korovin, V. Pustovoi, and V. E. Ogluzdin, Opt. Mater. 30, 260 共2007兲.
19
P. Cheng, H. Zhu, Y. Bai, Y. Zhang, T. He, and Y. Mo, Opt. Commun. 270,
391 共2007兲.
20
S. Moon, A. Lin, B. H. Kim, P. R. Watekar, and W. T. Han, J. Non-Cryst.
Solids 354, 602 共2008兲.

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

063512-5
21

J. Appl. Phys. 108, 063512 共2010兲

Ito et al.

E. Borcella, M. Falconieri, S. Botti, S. Martelli, F. Bignoli, L. Costa, S.
Grandi, L. Sangaletti, B. Allieri, and L. Depero, Mater. Sci. Eng., B 79, 55
共2001兲.
22
C. Torres-Torres, A. López-Suárez, L. Tamayo-Rivera, R. Rangel-Rojo, A.
Crespo-Sosa, J. C. Alonso, and A. Oliver, Opt. Express 16, 18390 共2008兲.
23
A. López-Suárez, C. Torres-Torres, R. Rangel-Rojo, J. A. Royes-Esqueda,
G. Santana, J. C. Alonso, A. Ortiz, and A. Oliver, Opt. Express 17, 10056
共2009兲.
24
Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P.
Agrawal, Appl. Phys. Lett. 91, 021111 共2007兲.
25
A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90,
191104 共2007兲.
26
M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 共2003兲.
27
R. W. Boyd, Nonlinear Optics 共Academic, San Diego, 2008兲, p. 212.
28
A. Maeda, M. Ono, H. Kishida, T. Manako, A. Sawa, M. Kawasaki, Y.
Tokura, and H. Okamoto, Phys. Rev. B 70, 125117 共2004兲.
29
A. Dowd, R. G. Elliman, M. Samoc, and B. Luther-Davies, Appl. Phys.
Lett. 74, 239 共1999兲.
30
L. Razzari, A. Gnoli, M. Righini, A. Dâna, and A. Aydinli, Appl. Phys.
Lett. 88, 181901 共2006兲.
31
T. D. Krauss and F. W. Wise, Appl. Phys. Lett. 65, 1739 共1994兲.
32
H. P. Li, B. Liu, C. H. Kam, Y. L. Lam, W. X. Que, L. M. Gan, C. H.
Chew, and G. Q. Xu, Opt. Mater. 14, 321 共2000兲.

33

S. Schmitt-Rink, D. A. B. Miller, and D. S. Chemla, Phys. Rev. B 35, 8113
共1987兲.
34
L. Banyai, Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B 38, 8142
共1988兲.
35
H. Yıldırım and C. Bulutay, Phys. Rev. B 78, 115307 共2008兲.
36
H. Yıldırım and C. Bulutay, Opt. Commun. 281, 4118 共2008兲.
37
T. Takagahara and E. Hanamura, Phys. Rev. Lett. 56, 2533 共1986兲.
38
F. Iacona, C. Bongiorno, C. Spinella, S. Boninelli, and F. Priolo, J. Appl.
Phys. 95, 3723 共2004兲.
39
M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland,IEEE J. Quantum Electron. 26, 760 共1990兲.
40
K. Imakita, M. Ito, M. Fujii, and S. Hayashi, Opt. Express 17, 7368
共2009兲.
41
S. M. Prokes, W. E. Carlos, S. Veprek, and C. Ossadnik, Phys. Rev. B 58,
15632 共1998兲.
42
A. Stesmans and F. Scheerlinck, Phys. Rev. B 51, 4987 共1995兲.
43
M. Fujii, A. Mimura, S. Hayashi, K. Yamamoto, C. Urakawa, and H. Ohta,
J. Appl. Phys. 87, 1855 共2000兲.
44N. Daldosso, G. Das, G. Dalba, S. Larcheri, R. Grisenti, G. Mariotto, L.
Pavesi, F. Rocca, F. Priolo, G. Franzo, A. Irrera, M. Miritello, D. Pacifici,and F. Iacona, Silicon Nanocrystal Nucleation as a Function of the Annealing Temperature in SiOx Films, MRS Symposia Proceedings No. 770
共Materials Research Society, Pittsburgh, 2003兲, p. I1.3.1.

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp