JOURNAL OF APPLIED PHYSICS 105, 093531 共2009兲

Nonlinear optical properties of Si nanocrystals embedded in SiO2 preparedby a cosputtering method
Kenji Imakita, Masahiko Ito, 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 15 January 2009; accepted 30 March 2009; published online 12 May 2009兲
Nonlinear optical properties of Si nanocrystals 共Si-ncs兲 doped SiO2 prepared by a cosputtering
method were studied by z-scan technique in a femtosecond regime at around 1.6 eV. The nonlinear
refractive index 共n2兲 and nonlinear absorption coefficient 共␤兲 were strongly enhanced compared tothose of bulk Si and found to be about ⬃2 ⫻ 10−13 cm2 / W and ⬃0.8 cm/ GW, respectively. In thephoton energy region from 1.48 to 1.65 eV, the n2 and ␤ spectra followed the absorption spectra andno enhancement was observed in the band-edge photoluminescence region. In the diameter range of
2.7–5.4 nm, the size dependence of n2 coincided well with that calculated by a pseudopotential
approach, suggesting that the discrete energy states of Si-ncs are responsible for the observed
enhanced optical nonlinearity. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3125446兴
I. INTRODUCTION

Silicon nanocrystal 共Si-nc兲 is a topic of great interest inview of potential application in the field of optoelectronics.1,2
The most interesting feature of this material is the strong
photoluminescence 共PL兲. Motivated by the potential for Si
based light emitting devices, the origin of the PL has extensively been studied and often assigned to spatially confinedcarriers within Si-ncs.3–5 To clarify the energy band structure
and optical responses of Si-ncs, detailed theoretical calculations have been performed;5–8 it has been shown that, in
addition to the size, the surface passivation8 and the shape
distortion7 significantly affect the band-gap energy of Si-ncs.
Si-nc is also a promising material toward the application of
optical switching devices. Nonlinear optical refractive index
共n2兲 of Si-ncs has been reported to be enhanced more than
two orders of magnitudes than that of bulk Si in a relativelytransparent energy range.9–12 The elucidation of the origin of
the large nonlinear optical response of Si-ncs has been attracting a great interest today.
There have been many reports on nonlinear optical response of various forms of Si-ncs. For example, a strong
enhancement of the nonlinear optical response has been observed in chemically etched porous Si,13,14 Si-ncs doped
SiOxNy deposited by plasma enhanced chemical vapor deposition 共PECVD兲,15,16 Si-ncs doped SiO2 prepared by ion
implantation,17 laser ablated Si-ncs deposited on quarts
substrate,18,19 Si-ncs doped SiO2 prepared by a sol-gel
method,20 and so on. The nonlinear optical properties of Sincs depend strongly on the preparation method. The reported
values of n2 varied from ⬃10−7 to ⬃10−13 cm2 / W, and both
positive and negative n2 were reported for various forms of
Si-ncs.13–20 This implies that the origin of the enhancement
may differ depending on the preparation methods and condia兲

Author to whom correspondence should be addressed. Electronic mail:fujii@eedept.kobe-u.ac.jp.

0021-8979/2009/105共9兲/093531/5/$25.00

tions. Therefore, further systematic studies for well-definedSi-nc samples are needed to elucidate the mechanism oflarge optical nonlinearity.
In this work, the nonlinear optical response of Si-ncs
doped SiO2 is studied for samples prepared by a conventional cosputtering method. Our samples are well-defined Sincs-doped SiO2, where the simple quantum size effect can
explain its linear optical properties. For example, they show
strong PL above the bandgap of bulk Si 共at around 1.4 eV兲.
The origin of the PL is the band edge luminescence due tothe recombination of quantum confined electron-hole pairs
within Si-ncs, evidenced by the resonantly excited PL
spectra,21 the temperature dependence of the PL lifetime,4and resonant quenching of PL bands by energy transfer tonearby materials.22 Since the quantum efficiency of the PL israther high,23 the PL peak energy well coincides with thetheoretically predicated bandgap energy of Si-ncs.4 The Si-nc
samples are thus considered to be suitable for the systematic
study to elucidate the mechanism of the nonlinear opticalresponse of Si-ncs. In this paper, the size and photon-energy
dependence of the nonlinear optical response of Si-ncs doped
SiO2 are discussed. These studies lead us to better understanding of the origin of the enhanced optical nonlinearity of
Si-ncs.
II. EXPERIMENTAL PROCEDURE

Si-ncs doped SiO2 was prepared by a cosputtering
method. Si and SiO2 were simultaneously sputter depositedin Ar gas on a quartz substrate and then the deposited SiOx
films were annealed in a N2 gas 共99.999%兲 atmosphere for
30 min above 1100 ° C to grow nanocrystals in the films. In
this method, the size of Si-ncs can be controlled by changing
the concentration of Si in the films or changing the annealing
temperature 共Ta兲. The size of Si-ncs was estimated by crosssectional transmission electron microscopic observations.
The average diameter 共D兲 was from 2.7 to 5.5 nm. The concentration of excess Si共Cex Si兲 ranges from 3 to 11 vol %,estimated by electron probe microscope analysis. The thick-

105, 093531-1© 2009 American Institute of Physics

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J. Appl. Phys. 105, 093531 共2009兲

Imakita et al.

共1兲

where I0, L, and z0 are the peak intensity of the beam, sample
thickness, and the diffraction length of the beam, respectively. Note that Top does not depend on the nonlinear refractive index 共n2兲 but does only on ␤, thus open aperture measurement provides the information on ␤.
When a small aperture is placed in front of the detector
to cut peripheral region of the transmitted light 共closed aperture兲, the transmittance 共Tcl兲 depends both on n2 and ␤. The
information on n2 is extracted by the division of Tcl by Top,4⌬␾,关共z/z0兲2 + 9兴关共z/z0兲2 + 1兴

共2兲

where ⌬␾ is the nonlinear phase change. n2 is obtained from⌬␾ as,n2 =␭␣⌬␾,2␲I0共1 − e−␣L兲20.2
fitted curve1

1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3 3.6

Absorbance / 8 µm

30Photon energy (eV)FIG. 1. PL 共left axis兲 and absorption 共right axis兲 spectra of a typical sample
共Cex Si = 3.3 vol %, Ta = 1100 ° C, D = 2.7 nm兲. The dashed line is a resultof fitting by assuming an indirect bandgap semiconductor 关冑␣h␯ ⬀ 共h␯− Eg兲兴. The optical bandgap is estimated to be 2.4 eV.

within Si-ncs. The optical bandgap 共Eg兲 estimated from theabsorption spectrum by using the 冑␣h␯ ⬀ 共h␯ − Eg兲 relation isaround 2.4 eV. Therefore, in the energy range investigated inthis paper 共at around 1.6 eV兲, the samples are highly transparent.
Figure 2 shows typical results of z-scan measurements
for 共a兲 a closed aperture 共Tcl兲, 共b兲 an open aperture 共Top兲, and共c兲 the ratio 共Tcl / Top兲. Open squares and solid curves represent experimental data and fitted results, respectively. In
Figs. 2共b兲 and 2共c兲, Eqs. 共1兲 and 共2兲, respectively, are used
for the fittings. The solid curve in Fig. 2共a兲 is generated byusing the parameters obtained by the fittings of Figs. 2共b兲and 2共c兲. The agreement between the experimental data andthe fitted curves is very good and the diffraction length estimated from the fitting well coincides with those measured bya knife edge method. The clear symmetrical valley to peak
1.02 (a) Closed

共3兲

where ␣ and ␭ are the linear absorption coefficient and thewavelength of the beam, respectively.
For the Gaussian beam, we used the mode-locked Ti:sapphire femtosecond laser with the pulse width of 70 fs andthe repetition frequency of 82 MHz. The photon energy waschanged from 1.48 to 1.65 eV, which overlaps PL emission
energy bands of Si-ncs. The incident beam was focused on asample by a lens with the focus length of 100 mm, and thebeam waist and diffraction length determined by a knife edge
method were 18 ␮m and 1.1 mm, respectively. The peakintensity of the beam was typically 10 GW/ cm2. No notablechange of nonlinear optical properties was observed in theintensity range of 0.5– 20 GW/ cm2, suggesting that thermal
effect is negligible in this measurement condition.15,16 The
validity of the obtained data was checked by measuring a
fused quarts plate as a reference.

Tcl

Tcl/Top共z兲 = 1 +CexSi 3.3 vol%o
Ta 1100 C

0.0

1.00

0.98
1.002 (b) Open
1.000
Top

␤ I 0LTop共z兲 = 1 +,
1 + 共z/z0兲20.4
PL Intensity (arb.units)

ness of the samples was estimated by a physical-contact-typesurface roughness measurement and to be about 8 ␮m. PL
spectra were measured by using a single grating monochromator and an InGaAs near-infrared diode array. The spectral
response of the detection system was calibrated with the aidof a reference spectrum of a standard tungsten lamp.
For the measurement of the nonlinear optical propertiesof Si-ncs, a z-scan method was used. Details of the z-scanmethod is found elsewhere.24 Briefly, in the z-scan method,
the tight focusing Gaussian beam is vertically irradiated ontoa sample and the sample is moved along the direction of thebeam propagation 共z-axis兲. The transmitted light intensity isrecorded as a function of the distance from the focal point
共z兲. When whole transmitted light is detected 共open aperture兲, the transmittance 关Top共z兲兴 is determined by the nonlinear absorption coefficient 共␤兲, and its dependence on z is

0.998
0.996
0.994
1.02 (c) Ratio

Tcl / T op

093531-2

1.00
oIII. RESULTS AND DISCUSSION

Figure 1 shows PL 共left-hand axis兲 and absorption spectra 共right-hand axis兲 of a typical sample 共Cex Si = 3.3 vol %,Ta = 1100 ° C, D = 2.7 nm兲. A broad PL peak at around 1.4
eV is assigned to the recombination of electron-hole pairs

Ta 1100 C
C exSi 3.3 vol%

0.98
-8

-4

0
Z (mm)

4

8

FIG. 2. Results of z-scan measurements for 共a兲 a closed aperture 共Tcl兲, 共b兲 anopen aperture 共Top兲, and 共c兲 the ratio of the two results 共Tcl / Top兲. The
squares are experimental results and the solid curves are results of fittings.

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J. Appl. Phys. 105, 093531 共2009兲

Imakita et al.

PL spectra(arb. units)2

1.5
Absorption
spectra(arb. units)

0

1.4

1.6

o

Ta ( C)
5

1.0

0.5

1

6

0.0
1.8

n2 (10 -13cm 2/W)

n2 (10 -13 cm 2/W)

3

β (cm/GW)

093531-3

1100
1150
1200
1250

CexSi
(vol%)

4

11.1

3
6.7
2

Photon Energy (eV)FIG. 3. n2 共left axis兲 and ␤ 共right axis兲 spectra of a typical sample 共Cex Si= 3.3 vol %, Ta = 1100 ° C, D = 2.7 nm兲. The dashed and dotted curves are
PL and absorption spectra, respectively.

trace in Fig. 2共a兲 suggests that the sign of n2 is positive andthat the nonlinearity is mainly refractive. The analysis of thez-scan traces by Eqs. 共1兲–共3兲 reveals that n2 is ⬃1.4
⫻ 10−13 cm2 / W and ␤ is ⬃0.5 cm/ GW, being similar values to previous reports.9,15
The observed n2 is one order of magnitude larger thanthe bulk-Si value and three orders of magnitude than theamorphous SiO2 value. In other words, addition of
3.3 vol % Si-ncs into SiO2 results in as much as three ordersof magnitudes enhancement of n2 compared to SiO2. It is
worth noting that the linear refractive index of Si-ncs doped
SiO2 is explained simply by the volume ratio of Si and SiO2
and is less than 1.6 in the present case, being very close tothat of amorphous SiO2. The small linear refractive index
allows us to minimize the optical coupling loss with a conventional SiO2 fiber. Therefore, both the linear and nonlinear
refractive indices of Si-nc’s doped SiO2 are suitable for optical switching devices.
In order to elucidate the origin of the enhancement of n2,
the photon-energy dependence of n2 and ␤ is investigated. In
Fig. 3, n2 共left-hand axis兲 and ␤ 共right-hand axis兲 are plotted
as a function of photon energy. n2 increases from 0.98
⫻ 10−13 to 1.4⫻ 10−13 cm2 / W with increasing the photon
energy from 1.48 to 1.65 eV. Similarly, ␤ increases from 0.3
to 0.5 cm/GW in the same range. The dashed and dotted lines
are the PL and absorption spectra, respectively. A larger nonlinear optical response is obtained in a larger absorbanceregion, but not in a larger PL region. In the case of directbandgap semiconductors such as CuCl and CuBr, the nonlinear refractive index is the highest at the energy of the lowest
level exciton absorption peak.25 On the other hand, in absorption spectra of Si-ncs, clear features due to exciton absorption are not observed and the spectra are almostfeatureless.26 The energy dependence of n2 in Fig. 3 seems tofollow the broad absorption spectra. Similar results were reported by Kanemitsu et al.14 for porous Si. They found by
third harmonic generation measurements that third ordernonlinear susceptibility 共␹共3兲兲 shows no enhancement in the
PL spectrum region, and pointed out two possible mechanisms. First, phonon-assisted optical transitions and resultant
small oscillator strength due to indirect bandgap nature ofporous Si result in the small enhancement in the PL spectrum
region. Second, the PL from porous Si may come not from

3.3
1
1.50

1.55

1.60

1.65

Photon energy (eV)FIG. 4. 共Color online兲 n2 spectra of samples with different excess Si concentrations 共Cex Si兲 and different annealing temperatures 共Ta兲. The samecolored 共or shaped兲 symbols are used for the same Cex Si 共or Ta兲 samples.

the band edge but from surface or defect levels with small
density of states. If the actual band-edge energy region is far
from the PL spectrum region, the enhancement is not expected in the PL spectrum region.
Basically, the same discussion can be applied to understand the data in Fig. 3. However, in the present samples, asmentioned in the introduction, PL from Si-ncs can be assigned to the band-edge luminescence due to the recombination of confined electron-hole pairs as evidenced by somekinds of experiments.4,21,22 Thus the second hypothesis canbe excluded. Probably, small oscillator strength due to theindirect bandgap nature causes the small enhancement at the
PL energy.
The systematic control of the size and the concentrationof Si-ncs provide further information to understand themechanism of the large nonlinear response. In Fig. 4, thephoton-energy dependence of n2 for samples with different
Cex Si and different Ta are shown. The same colored 共or
shaped兲 symbols are used for the samples with the sameCex Si 共or Ta兲. For all the samples, n2 is larger in higher
photon energy. It is also interesting to note that n2 strongly
depends on Cex Si, while hardly does on Ta. In Fig. 5, Cex Si
dependence of n2 is shown. n2 is nearly proportional to
Cex Si, suggesting that Cex Si is a dominant factor to determine the nonlinear optical response of the samples.
From the experimentally obtained macroscopic nonlinear refractive index of the Si and SiO2 composites, the microscopic nonlinear refractive index of Si-ncs 共n̄2兲 is estimated by the relation n2 = pf 4n̄2, where p is the Si volume
fraction 共Cex Si / 100兲 and f is the local field correction
factor27 given by 3⑀SiO2 / 共⑀SiO2 + 2⑀Si兲, where ⑀SiO2 and ⑀Si are
the real part of the dielectric constant of SiO2 and Si. The
estimated values of n̄2 are 2 – 3 ⫻ 10−10 cm2 / W for all thesamples and to be four orders of magnitudes larger than thebulk-Si value. In the inset of Fig. 5, the obtained n̄2 is plotted
as a function of the diameter of Si-ncs. n̄2 increases slightly
with decreasing the size of Si-ncs. This result is qualitatively
consistent with other reports, where the modification of theband structure by the quantum confinement effect is sug-

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093531-4

J. Appl. Phys. 105, 093531 共2009兲

Imakita et al.

852n2 (10 cm /W)7

n2 (10 -13cm 2/W)

-10

6
5

4
3
2
0
2

4
3

~1/D

1

3

3
4
5
6
Diameter (nm)210

at 1.6eV
0

4

8

12

CexSi (vol%)FIG. 5. Si concentration dependence of n2. The inset shows the size dependence of the microscopic nonlinear refractive index of Si-ncs. The dottedline is a 1 / D3 dependence predicted by a simple quantum confinement
model.

gested to be the origin of the enhancement of optical nonlinear response of Si-ncs.15,16 On the other hands, the result
cannot quantitatively be explained by a simple quantum confinement model, which predicts the enhancement with the
1 / D3 dependence 共D is the diameter of Si-ncs兲29 as shown by
a dotted line in the inset of Fig. 5. While the model predicts
as much as eight times enhancement by the size reduction
from 5.4 to 2.7 nm, the data show the enhancement of only
about 30% in the size range.
To our knowledge, quantitative discussion on the size
dependence of nonlinear optical response of Si-ncs has been
made only in limited number of papers.15,16 Vijaya Prakash etal.16 reported nonlinear optical response of Si-ncs doped
SiOxNy prepared by PECVD and demonstrated a strong enhancement of ␹共3兲 when the size of Si-ncs was very small
共less than 1 nm兲. However, as they mentioned in the paper,the data were strongly scattered and thus the size dependence
in the range of the present work was not very clear. Furthermore, the effect of Si concentration was not taken into account in the analysis. On the other hand, Hemandez et al.15
discussed size dependence of ␹共3兲 by taking into account the
Si concentration for similar Si-nc samples. They observed⬃1 / D3 dependence of ␹共3兲 and suggested that the modification of the band structure by the quantum confinement effectis responsible for the enhanced nonlinear optical response of
Si-ncs. However, the discussion, i.e., the fitting of data points
by the ⬃1 / D3 dependence, was based only on three experimental points, and thus the dependency is not very convincing.
The results of Fig. 5 show for the first time detailed size
dependence of the nonlinear optical response of Si-ncs. The
observed deviation from ⬃1 / D3 dependence indicates thatthe nonlinear optical response of Si-ncs cannot be fully explained by the simple quantum confinement model. Recently,
some investigations have revealed that the size dependenceof the nonlinear optical response of semiconductor nanocrystals differs depending on the size range.28,29 In a strong confinement regime where the size is much smaller than that of

the exciton Bohr radius 共aB兲, i.e., D Ⰶ 2aB, the nonlinear optical response increases with decreasing the size, while in a
weak confinement regime 共D Ⰷ 2aB兲, it increases with increasing the size.28–32 The above mentioned simple quantum
confinement model is the case of the strong confinement regime. Since the size range of Si-ncs studied in this work is
comparable to the exciton Bohr radius of bulk Si, the competition of the two different size dependences may result inthe observed small size dependence.
Very recently, Yildirim and Bulutay33 calculated the nonlinear optical properties of Si-ncs and Ge nanocrystals 共Gencs兲 in SiO2 by an atomistic pseudopotential approach. Theircalculations focused on the third-order nonlinearities of Sincs by assuming no interface defects, no strain and thermal
effects, and no compounding contribution of the excited carriers. They showed that ␹共3兲 of Si-ncs and Ge-ncs hardly
depend on the size in the size range above 2.5 nm, while theysignificantly increase with decreasing the size in the size
range below 2.5 nm. Since the size range of this work is
2.7–5.4 nm, the predicted small size dependence above 2.5
nm agree qualitatively with the present results. Furthermore,they predicted that ␹共3兲 of Si-ncs is about 4–5 orders of magnitudes enhanced compared to that of bulk Si when the size
is around 3.0 nm. This enhancement factor also coincides
well with experimentally obtained ones 共four orders of magnitudes兲. These agreement may allow us to conclude that thediscrete energy states of Si-ncs is responsible for the observed enhanced optical nonlinearity.
It should be mentioned here that defects within nanocrystals or at the surface can also cause the enhancement of
the optical nonlinear response.34 Takagahara and Hanamura34
reported that localization of excitons at disorders or impurities enhances its oscillator strength, and hence the nonlinear
optical properties. They pointed out that sometimes this effect is more important than the dimensional confinement effect. In the model, the size dependence of the nonlinear optical response is expected to be very small. However, thismodel is considered to be not suitable to explain the observed enhanced nonlinear optical response of Si-ncs. As
mentioned above, the nonlinear optical response of thepresent samples is hardly modified by annealing conditions.
On the other hand, the quality, i.e., the defect density, of
Si-ncs depends strongly on the annealing condition.23 This
inconsistency rules out the possibility of defect-related enhancement of the nonlinear response.
As mentioned in the introduction, the shape distortion of
Si-ncs significantly modifies the electronic band structure
and may also modify the nonlinear optical response. However, the present results give no information on the effect of
shape distortion.
IV. CONCLUSION

Nonlinear optical response of Si-ncs doped SiO2 prepared by a cosputtering method is studied by z-scan technique in a femtosecond regime at around 1.6 eV. An additionof a very small amount of Si-ncs into SiO2 results in as muchas three orders of magnitudes enhancement of n2 comparedto SiO2 and one order of magnitude to bulk Si, while theAuthor complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

093531-5

linear refractive index is kept low 共less than 1.6兲. The small
index mismatch with a conventional SiO2 fiber and the large
nonlinear response make Si-ncs doped SiO2 an ideal candidate for realizing Si-based optical switching devices. In order
to elucidate the origin of the enhanced optical response, thesize dependence of n2 is studied in detail in the diameter
range of 2.7–5.4 nm. We show that the size dependence isvery small in the range, although small increase in n2 withdecreasing the size is observed. The observed size dependence agrees very well with that calculated by pseudopotential approach, suggesting that the discrete energy states of
Si-ncs is responsible for the observed enhanced optical nonlinearity.
ACKNOWLEDGMENTS

This work is supported by Asahi Glass Co. Ltd. and a
Grant-in-Aid for Scientific Research from the Ministry of
Education, Culture, Sports, Science and Technology, Japan.
We would like to thank Dr. Tomoharu Hasegawa and Dr.
Madoka Ono of Asahi Glass Co. Ltd. for their experimental
supports and excellent discussions for this work.
1

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