JOURNAL OF APPLIED PHYSICS 106, 013517 共2009兲

Enhancement of photoluminescence from silicon nanocrystals by metalnanostructures made by nanosphere lithography
Yugo Mochizuki,1 Minoru Fujii,1,a兲 Shinji Hayashi,1 Takaaki Tsuruoka,2 andKensuke Akamatsu2
1

Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University,
Rokkodai, Nada, Kobe 657-8501, Japan
2
Frontiers of Innovative Research in Science and Technology, Konan University, Minatojima-minamimachi,
Chuo-ku, Kobe 650-0047, Japan

共Received 26 March 2009; accepted 1 June 2009; published online 9 July 2009兲
The effect of metal nanostructures prepared by nanosphere lithography on photoluminescence 共PL兲properties of silicon nanocrystals 共Si-ncs兲 is studied. By placing Ag nanotriangles or Au nanovoidson SiO2 films containing Si-ncs, the PL intensity is enhanced. For the sample having Ag
nanotriangles, the largest PL enhancement is obtained when the excitation wavelength coincides
with the absorption band of Ag nanotriangles. This suggests that the enhancement of the incident
field by surface plasmon polariton 共SPP兲 excitation is responsible for the PL enhancement. On theother hand, for the sample having Au nanovoids, the PL enhancement is mainly made by theenhancement of effective radiative decay rate of Si-ncs by efficient excitation and scattering of
SPPs. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3159030兴
I. INTRODUCTION

A Si-based light emitting device is one of the most important optical elements in realizing Si-based optoelectronic
circuits that integrate electronic and photonic elements on a
Si wafer. Silicon nanocrystals 共Si-ncs兲 have been attracting
great interests as a key material of Si-based light emitting
devices. Si-ncs exhibit visible and near infrared luminescence at room temperature due to the recombination of quantum confined excitons.1–4 Confinement of excitons in a space
smaller than the exciton Bohr radius of bulk Si crystals increases the overlap of electron and hole wave functions inboth real and momentum spaces, resulting in the enhancement of the radiative recombination rate.2,3 However, evenfor Si-ncs as small as a few nanometers in diameter, indirect
band gap nature of bulk Si crystals is strongly inherited,5 andthus the spontaneous emission rate is still not large enoughcompared to that of direct band gap semiconductor and theluminescence quantum efficiency is rather low.2,3 Therefore,
the improvement of the luminescence property is very important for their application to light emitting devices.
One of the approaches to enhance luminescence of Sincs is to utilize the coupling of electronic excitation of Si-ncs
to surface plasmon polaritons 共SPPs兲 supported by metalnanostructures. For example, by placing a nanoporous gold
共Au兲 layer near Si-ncs, enhancement of the photoluminescence 共PL兲 intensity was demonstrated.6–10 The SPP resonance energy can be controlled in a wide wavelength range
by the size and the shape of metal nanostructures. By placing
a silver 共Ag兲 island array with different sizes and pitches
near Si-ncs, PL enhancement at specific wavelength ranges
was achieved.6 The PL enhancement was also observed for a
simple system consisting of a flat metal film and an organic
grating.7,8 Metal films with rough surface are also reported toa兲Electronic mail: fujii@eedept.kobe-u.ac.jp.

0021-8979/2009/106共1兲/013517/5/$25.00

exhibit strong PL enhancement.10 The enhancement is usually explained by electromagnetic coupling of excitons in
Si-ncs with dipolar plasmon modes of metalnanostructures.9,11
From previous studies on SPP mediated PL enhancementof Si-ncs, it has been recognized that the precise control ofthe shape and arrangement of metal nanostructures is essential in obtaining desirable PL properties. In previous studies,
the metal structures were mainly produced by electron-beamlithography.12 Although high-resolution precise patterns canbe achieved by the electron-beam lithography, the technique
is time consuming and not cost effective. Nanosphere lithography 共NSL兲 is a simple and low cost process to fabricate
various kinds of periodic nanostructures. In this technique,the submicron latex spheres self-assembled into a hexagonal
pattern are used as a template to create various kinds ofordered two-dimensional 共2D兲 array of desired materials. Its
effectiveness for the formation of metal nanostructures has
been demonstrated.13 For example, Ag nanotriangles and Au
nanovoids have possibility of stronger PL enhancement thansimple structures made by conventional lithography technique due to their abrasive shapes.
The purpose of this work is to demonstrate the effectiveness of the NSL technique for the PL enhancement of Si
nanocrystals. We study PL properties of Si-ncs having metalnanostructures made by NSL. We prepare two types of metalnanostructures, i.e., a Ag nanotriangle array and a Au nanovoid array, and study how PL properties of Si-ncs are modified by the metal nanostructures. We also discuss the mechanism of PL enhancement from PL excitation spectra, angle,
and polarization resolved PL spectra and PL time transients.
II. SAMPLE PREPARATION

SiO2 films containing Si-ncs 共Si-nc: SiO2兲 were preparedby a cosputtering method.14,15 Si and SiO2 were simulta106, 013517-1© 2009 American Institute of Physics

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J. Appl. Phys. 106, 013517 共2009兲

Mochizuki et al.

(a) nanotriangle

40(b) nanovoid

1 Pm

PL Intensity (arb. units)

013517-2

5 Pm

FIG. 1. SEM images of a Ag nanotriangle array and a Au nanovoid array.

w/o metal
with metal

Ag height 40nm
30

ex=630 nm
20
10

(a)

0
650

700

750

800

850

900

950

Wavelength (nm)III. RESULTS AND DISCUSSION
A. Ag nanotriangle array

Absorptance (%)

Reflectance (%) Transmittance (%)

Figures 2共a兲 and 2共b兲 show transmittance 共T兲 and reflectance 共R兲 spectra, respectively, for the samples with different
90
80
70
60

(a)

50

Ag height
17 nm
40 nm
85 nm
100 nm

(b)
20
10
0
30

(c)

20
10
0
300 400 500 600 700 800 900 1000

Wavelength (nm)FIG. 2. 共Color online兲 共a兲 Transmittance, 共b兲 reflectance, and 共c兲 absorptance spectra of the samples with Ag nanotriangle arrays. The height of Ag
nanotriangles is changed from 17 to 100 nm.

0.15

1.0
0.5
0.0
3.0

0.10
0.05

(b)

2.5

0.00
0.5

Ag height 85 nm

2.0

0.4
0.3

1.5
0.2

1.0
0.5

0.1

(d)

0.0
400

450

500 550 600
Wavelength (nm)

0.0
650

3

Ag height 40 nm

2

0.2

1
0

0.1

(c)

2.5 Ag height 100 nm

0.3

1.5

0.2

1.0

0.0
400

0.0
0.5
0.4

2.0

0.5

0.3

0.1

(e)
450

500 550 600
Wavelength (nm)Absorptance

1.5

0.20

AbsorptanceAg height 17 nm

Absorptance
Enhancement factor

2.0

Absorptance
Enhancement factor

Enhancement factor

0.4

Enhancement factor

neously sputter deposited on a SiO2 substrate and the deposited films 共150 nm in thickness兲 were annealed in a nitrogengas atmosphere for 30 min at 1150 ° C. To prepare a Ag
nanotriangle array, Ag was deposited by vacuum evaporation
through a 2D crystal of polystyrene 共PS兲 nanospheres placedon the Si-nc: SiO2 films.13 The diameter of PS nanospheres
was 500 nm. The height of Ag nanotriangles was controlled
by the thickness of Ag. After the Ag deposition, the PS nanosphere templates were removed by immersing the samples intoluene for several hours. For the preparation of a Au nanovoid array, a Ti film 共5 nm in thickness兲 and a Au film 共20
nm in thickness兲 were deposited on Si-nc: SiO2 films prior to
the formation of 2D crystal of PS nanospheres 共750 nm indiameter兲. Through the PS nanosphere crystal Au was grownby an electrochemical plating. The thickness of Au was controlled by monitoring the current during the plating. PS
nanospheres were removed by toluene after the Au growth.
Figures 1共a兲 and 1共b兲 show scanning electron microscope
共SEM兲 images of the surface of the sample with a Ag nanotriangle array and a Au nanovoid array, respectively.

0.0
650

FIG. 3. 共Color online兲 共a兲 PL spectra of the sample with and without a Ag
nanotriangle array. The height of Ag nanotriangles is 40 nm. Excitation
wavelength is 630 nm. 关共b兲–共e兲兴 Absorptance spectra 共solid curves兲 共rightaxis兲 and excitation wavelength dependence of PL enhancement factors
共filled squares兲 共left axis兲. The error bars represent maximum and minimum
values. Ag nanotriangle heights are 共b兲 17, 共c兲 40, 共d兲 85, and 共e兲 100 nm,
respectively.

height Ag nanotriangles. The incident angle of the reflectance measurement is 5°. Figure 2共c兲 shows the absorptance
共A兲 defined by 1-T-R. The absorptance corresponds to thenumber of photons absorbed by the sample. In Fig. 2共c兲, twobands are seen around 350 and 500–700 nm. The 350 nm
band is assigned to the interband transition of Ag, while the
500–700 nm band is due to the excitation of localized SPPs.
The SPP band shifts toward shorter wavelength with increasing the Ag nanotriangle height. The shift is mainly due to thechange in the aspect ratio with increasing the height.16,17
Figure 3共a兲 compares PL spectra of Si-ncs with andwithout Ag nanotriangles. The excitation source for the PL
measurements is the optical parametric oscillator pumped by
the third harmonic of a Nd:YAG laser 共pulse width of 5 nm,
repetition of 20 Hz兲. The excitation wavelength is 630 nm.
The samples are excited from the substrate side with theincident angle of 45° and detected from the same side byusing a single grating monochromator with a liquid nitrogencooled charge coupled device. The solid angle of the PL
detection is about 18°. The spectral response of the detection
system is corrected with the aid of a reference spectrum of astandard tungsten lamp. In Fig. 3共a兲, a broad PL band due tothe recombination of excitons in Si-ncs is seen around 800
nm in both samples. PL intensity is enhanced by a factor of 3
by the Ag nanotriangles. In Figs. 3共b兲–3共e兲, the PL enhancement factors are plotted as a function of the excitation wavelength for the samples with the Ag heights of 17, 40, 85, and
100 nm, respectively. The PL enhancement factors are obtained by dividing PL spectra of the sample with metal bythat without metal. The excitation wavelength is changed
from 430 to 630 nm. The absorptance spectra are also shown

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J. Appl. Phys. 106, 013517 共2009兲

Mochizuki et al.

(a)

Au thin film
(region 2) w/o metal(region 3)
SiSi-nc:SiO2
Substrate

Intensity (arb.unit)

1200

Au nanovoids(region 1)

900

G1

300 (b)0
650 700 750 800 850 900 950

30
20 exc = 488 nm

o
o

30

o

21

TM
o
o
21 -3015

Intensity (arb.unit)

Intensity (arb.unit)o21 -3020

 exc = 488 nm
o

30

o

21

10

z

1.6
1.4
-G1

5

0.000

1.8 (c)Wavelength (nm)FIG. 4. 共Color online兲 共a兲 Schematic illustration of sample structure, 共b兲 PL
spectra of regions 1, 2, and 3. Excitation wavelength is 488 nm. 关共c兲 and 共d兲兴Angle and polarization dependence of PL spectra of region 1. The detection
angle is changed from 21° to 30°. 共c兲 TE polarization and 共d兲 TMpolarization.

in the same figures. The excitation wavelength dependenceof the PL enhancement factors coincides very well with thatof the absorptance spectra. This is a clear evidence that PL isenhanced by strong fields accompanies by the excitation of
localized SPPs of Ag nanotriangles. Figure 3 also demonstrates that the wavelength of the largest PL enhancement
can be controlled simply by changing the height of Ag nanotriangles.
B. Au nanovoid array

Figure 4共a兲 shows a schematic illustration of the sample
with a Au nanovoid array. We prepare three regions in eachsample to make exact comparison of the PL intensity possible. Region 1 has Au nanovoids, while region 2 has a Au
thin flat film. Region 3 is a bear sample without metal. Figure 4共b兲 shows the PL spectra for regions 1, 2, and 3. The
excitation source is a 488 nm line of an Ar ion laser. The
excitation light is incident from the substrate side with theangle of 45° and the PL is detected from the same side of thesample. The solid angle of the PL detection is about 18°. The
PL intensity of region 2 is enhanced by a factor of 1.5 compared to that of region 3. This is simply due to the reflectionof incident and emitted light by the Au thin film. In region 1,
the PL intensity is enhanced by a factor of 2.7 compared tothat of region 3 and by a factor of 2.0 compared to that ofregion 2.
The PL from region 1 has strong angle dependence. For
the measurement of the angle dependence of PL spectra, theexcitation light is illuminated normal to the surface throughthe transparent fused quartz substrate and the PL is detectedfrom the sample surface, i.e., from the side of Au nanovoids,
by changing the angle ␪ from 0° 共normal to the surface兲 to50° 关Fig. 4共a兲兴. PL was detected through an aperture approximately 1 mm in diameter, which limits the angular acceptance to about 1°. Figures 4共c兲 and 4共d兲 show the angle de-Energy (eV)00
650 700 750 800 850 900 950 650 700 750 800 850 900 950

Wavelength (nm)x

1.8 (b)10 (d)

(c)



G2

600

Wavelength (nm)
40 TE

y

(a)

region 1  = 488 nm
exc
region 2
region 3

Energy (eV)013517-3

0.002

0.004

-1

0.006

Wavenumber (nm )

1.6

1.4
0.000

S2
2G1
(n,m)=(2,0)

0.002

0.004

-1

0.006

Wavenumber (nm )FIG. 5. 共Color online兲 共a兲 Definition of grating vectors and coordinates. 关共b兲
and 共c兲兴 Dispersion relations. Circles correspond to experimentally obtained
data. The color map is obtained by calculation. The region in red color
represents larger power dissipation. The scattering orders 共m , n兲 are 共b兲
共⫺1,0兲 and 共c兲 共2,0兲. The insets are corresponding grating vectors.

pendent PL spectra for TE and TM polarizations,
respectively. TE and TM polarizations are defined as theirelectric fields being perpendicular and parallel to the incident
plane, respectively. The PL peak wavelength shifts depending on the detection angle in both the TE and TM polarizations. From the angle dependence of PL peak wavelengths,
the dispersion relations are obtained. The experimentally obtained dispersion relations are shown in Fig. 5 by open
circles. To facilitate the comparison with calculation, thesame experimental data are displayed in both Figs. 5共b兲 and5共c兲.
In order to assign the modes, we calculate the dispersion
relations by the formula developed by Chance et al.,18 byassumingafour-layer
systemconsistingofair/ Au/ Si-nc: SiO2 / SiO2. In the calculation, an emitter is regarded as an oscillating electric dipole and the power dissipated from an isotropic dipole positioned at the center of a
Si-nc: SiO2 layer is calculated as a function of a wavenumber. For the calculation, the refractive indices of Au, Si, andSiO2 are taken from literature19–22 and that of the Si-nc: SiO2
layer is estimated from the Bruggeman effective medium
theory.23 In the presence of a grating, the wave vector of SPP
is augmented or reduced. Figure 5共a兲 shows the definition ofជ 2兲 and coordinates. For a 2D
ជ 1 and G
the grating vectors 共G
grating, the coupling condition between radiative modes
propagating in the x-z plane and nonradiative modes, such as
SPPs, propagating in the x-y plane is expressed as

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k0共␻兲sin ␪
0

,

1
0

+ nG

1/2

3/2

=

k储共␻兲
0

共1兲

where km共␻兲 and k储共␻兲 denote the in-plane wave vector of
the mode and the emitted light, respectively, k0共␻兲 represents
the absolute value of the wave vector of the emitted light, ␻is the angular frequency, ␾ is the azimuthal angle of the
propagation of nonradiative modes, ␪ is the polar angle ofជ 1兩 = 兩Gជ 2兩 = 2␲ / ⌳ isthe propagation of radiative modes, G = 兩Gthe grating vector with the grating period ⌳, and m and n are
the orders of the scattering process arising from the gratingជ 1 and G
ជ 2, respectively. In order to reproduce exvectors G
perimentally obtained dispersion relations, we adjusted thevalues of the grating period. The best result is obtained when
the grating period is 800 nm. This value is slightly different
from the actual diameter of PS nanospheres. Similar deviation of the effective grating period from the actual PS nanosphere diameter has been reported by some groups13,24 and isconsidered to arise from the deviation of the metal nanostructure shape from the sine wave. At the wavelength rangeof Si-ncs emission, SPPs experience two scattering processes, i.e., 共m , n兲 = 共−1 , 0兲 , 共2 , 0兲.
The calculated dispersion relations are shown in Figs.
5共b兲 and 5共c兲 by color gradients. The insets are the corresponding grating vectors. The red region and the blue one
represent larger and smaller power dissipations, respectively.
The strong power dissipation corresponds to the SPP modes
propagating at the interface between Au and the active layer
共Au/ Si-nc: SiO2 SPP兲. In Figs. 5共b兲 and 5共c兲, the overall
agreement between calculated and experimentally obtained
dispersion relation is good. The agreement indicates that theemission from region 1 mainly arises from the coupling of
excitons in Si-ncs to SPPs. In Figs. 5共b兲 and 5共c兲, small
difference is seen between the calculated and experimentallyobtained dispersion relations. This probably arises fromsmall deviation of actual refractive index of the active layerfrom that estimated from the Bruggeman effective medium
theory and from too simplified assumption in the calculationthat the metal film is flat. Furthermore, in Fig. 5, modes thatare not identified by calculation exist. They may arise fromthe scattering by defects in the periodic structure.
The inset of Fig. 6共a兲 shows the PL decay curves forregions 1, 2, and 3 detected at 830 nm. For time-resolved PL
measurements, the samples were excited by a 405 nm laser
diode. The signals were detected by a near infrared photomultiplier tube 共R5509-72, Hamamatsu Photonics兲. The time
resolution of the system was about 3 ␮s. The decay rates ofthe samples with a Au nanovoid array 共region 1兲 and a Au
thin film 共region 2兲 are larger than that of the region without
Au 共region 3兲. The larger decay rates in regions 1 and 2 aredue to dissipation of the excitation energy to Au nanovoids
and Au thin films, respectively. No significant difference ofthe decay rates can be seen in regions 1 and 2, indicating thatthe existence of nanovoids structure does not influence thedecay rate. In order to investigate the wavelength dependence of the decay rates, we measure PL decay curves in the

(a)

20
15

10

 =830nm

0

10

-1

10

-2

-3

10
0.0

10
region 1
region 2
region 3

50

0.2

0.4 0.6 0.8
Time (ms)exc = 405 nm

(b)

2.8

2.8
PL intensity enhancement(region 1 / region 3)(exc = 488 nm)
decay rate
(region 1 / region 3)( exc = 405 nm)

2.4
2.0
1.6
0.0

1.0

2.4
2.0
1.6

750

800

850

900

0.0
950

PL enhancement factor

sin ␾

+ mG

Nomalized PL intensity (a.u.)cos ␾Dcay rate (kHz)冉 冊 冉 冊 冉冑 冊 冉 冊
冉冊

k m共 ␻ 兲=

J. Appl. Phys. 106, 013517 共2009兲

Mochizuki et al.

Decay rate enhancement013517-4

Wavelength (nm)FIG. 6. 共Color online兲 共a兲 Wavelength dependence of PL decay rates forregions 1 共filled square兲, 2 共filled circle兲, and 3 共filled triangle兲. Inset: PL
decay curves of regions 1, 2, and 3 detected at 830 nm. Decay curves ofregions 1 and 2 are very similar. 共b兲 The wavelength dependence of PL
intensity enhancement factor 共right axis兲 and decay rate enhancement factor
共left axis兲.

750–930 nm region and estimated the decay rates by fitting
the decay curves by a stretched exponential function.25 The
results are shown in Fig. 6共a兲. Closed squares, circles, andtriangles represent PL decay rates obtained from regions 1, 2,
and 3, respectively. In all cases, the decay rate increases at
shorter wavelengths, i.e., when PL from smaller Si-ncs is
detected. This is due to the increase in the radiative decayrate by the quantum size effect.26 The decay rate of regions 1
and 2 are always larger than that of region 3 in the wholeemission wavelength range.
Figure 6共b兲 shows the enhancement factors of the decayrate obtained by dividing the decay rate of region 1 by that ofregion 3 共left axis兲. On the right axis, the enhancement factors of the PL intensity are also shown. The enhancement
factors of the decay rate and the intensity show very similar
wavelength dependence. This indicates that the PL enhancement is mainly due to the enhancement of the effective radiative decay rate by efficient excitation and scattering of
SPPs supported by Au nanovoids. Note that, in the case of
Au nanovoids, PL enhancement due to the enhanced incident
field is not expected because the excitation wavelengths 共488
or 405 nm兲 are far from the SPP resonance wavelength.
IV. CONCLUSION

We demonstrated the effectiveness of metal nanostructures made by NSL for the improvement of PL properties of
Si-ncs. By placing Ag nanotriangles and Au nanovoids on
top of SiO2 films containing Si-ncs, enhancements of the PL
intensity by factors of 3 and 2.7 were achieved. For the
sample having Ag nanotriangles, the largest PL enhancement
was obtained when the excitation wavelength coincides withthe absorption band of Ag nanotriangles. This suggests thatthe enhancement of the incident field by SPP excitation is
responsible for the PL enhancement. On the other hand, for

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013517-5

the sample having Au nanovoids, the enhancement was
mainly made by the enhancement of the effective radiative
decay rate of Si-ncs by efficient excitation and scattering of
SPPs. Within the present work, either the excitation efficiency or the radiative decay rate was enhanced dependingon the shape and the kinds of metal. By refining the design ofthe metal structure, e.g., by combining the two structures inthis work, simultaneous enhancement of the both processes
may be possible.
ACKNOWLEDGMENTS

This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture,
Sports, Science and Technology, Japan.
L. T. Canham, Appl. Phys. Lett. 57, 1046 共1990兲.
C. Delerue, M. Lannoo, G. Allan, and E. Martin, Thin Solid Films 255, 27
共1995兲.
3
D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B
215, 871 共1999兲.
4
S. Takeoka, M. Fujii, and S. Hayashi, Phys. Rev. B 62, 16820 共2000兲.
5I. Sychugov, R. Juhasz, J. Valenta, and J. Linnros, Phys. Rev. Lett. 94,
087405 共2005兲.
6
J. S. Biteen, N. Lewis, H. A. Atwater, H. Mertens, and A. Polman, Appl.
Phys. Lett. 88, 131109 共2006兲.
7
E. Takeda, T. Nakamura, M. Fujii, S. Miura, and S. Hayashi, Appl. Phys.
Lett. 89, 101907 共2006兲.
8
E. Takeda, M. Fujii, T. Nakamura, Y. Mochizuki, and S. Hayashi, J. Appl.
Phys. 102, 023506 共2007兲.
9
H. Mertens, J. S. Biteen, H. A. Atwater, and A. Polman, Nano Lett. 6,
1
2

J. Appl. Phys. 106, 013517 共2009兲

Mochizuki et al.

2622 共2006兲.
K. Okamoto, A. Scherer, and Y. Kawakami, Phys. Status Solidi 5, 2822
共2008兲 共c兲.
11
H. Mertens and A. Polman, J. Appl. Phys. 105, 044302 共2009兲.
12
J. S. Biteen, D. Pacifici, N. S. Lewis, and H. A. Atwater, Nano Lett. 5,1768 共2005兲.
13
R. M. Cole, Y. Sugawara, J. J. Baumberg, S. Mahajan, M. Abdelsalam,and P. N. Bartlett, Phys. Rev. Lett. 97, 137401 共2006兲.
14
Y. Kanzawa, T. Kageyama, S. Takeoka, M. Fujii, S. Hayashi, and K.
Yamamoto, Solid State Commun. 102, 533 共1997兲.
15
M. Fujii, A. Mimura, S. Hayashi, and K. Yamamoto, Appl. Phys. Lett. 75,
184 共1999兲.
16
K. L. Shuford, M. A. Ratner, and G. C. Schatz, J. Chem. Phys. 123,
114713 共2005兲.
17
W. Huang, W. Qian, and M. A. El-Sayed, J. Phys. Chem. B 109, 18881
共2005兲.
18
R. R. Chance, A. Prock, and R. Silbey, Adv. Chem. Phys. 37, 1 共1978兲.
19
W. L. Barnes, J. Mod. Opt. 45, 661 共1998兲.
20
D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids,
edited by E. D. Palik 共Academic, Orlando, FL, 1985兲.
21
D. F. Edwards, Handbook of Optical Constants of Solids, edited by E. D.
Palik 共Academic, Orlando, FL, 1985兲.
22
H. R. Philipp, Handbook of Optical Constants of Solids, edited by E. D.
Palik 共Academic, Orlando, FL, 1985兲.
23
P. A. Snow, E. K. Squire, P. S. J. Russell, and L. T. Canham, J. Appl. Phys.
86, 1781 共1999兲.
24
T. A. Kelf, Y. Sugawara, R. M. Cole, J. J. Baumberg, M. E. Abdelsalam,
S. Cintra, S. Mahajan, A. E. Russell, and P. N. Bartlett, Phys. Rev. B 74,
245415 共2006兲.
25
G. Mauckner, K. Thonke, T. Baier, T. Walter, and R. Sauer, J. Appl. Phys.
75, 4167 共1994兲.
26
S. Miura, T. Nakamura, M. Fujii, M. Inui, and S. Hayashi, Phys. Rev. B
73, 245333 共2006兲.
10

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