JOURNAL OF APPLIED PHYSICS 102, 023506 共2007兲

Enhancement of photoluminescence from excitons in silicon nanocrystals
via coupling to surface plasmon polaritons
Eiji Takeda, Minoru Fujii,a兲 Toshihiro Nakamura, Yugo Mochizuki, and Shinji Hayashi
Department of Electrical and Electronic Engineering, Faculty of Engineering, Kobe University, Rokkodai,
Nada, Kobe 657-8501, Japan

共Received 27 March 2007; accepted 29 May 2007; published online 17 July 2007兲
The enhancement of photoluminescence 共PL兲 is demonstrated from silicon nanocrystals 共Si-ncs兲 bystrong coupling of excitons to surface plasmon polaritons 共SPPs兲 supported by a Au thin film. SPPs
excited via excitons in Si-ncs were Bragg scattered to photons by one- or two-dimensional gratings,
and strong and directional PL was obtained. From the angular dependence of PL spectra, dispersion
relations of electromagnetic modes involved in the light emission process were obtained. The
overall agreement between experimentally obtained and theoretically calculated dispersion relations
confirmed that the strong and directional PL is mediated by SPPs. The PL decay rate of Si-ncs
increased by placing a Au thin film on top and the wavelength dependence of the rate enhancementagreed well with that of the calculated SPP excitation rate. This suggests that the observed PL
enhancement is due to efficient energy transfer from excitons to SPPs followed by efficientscattering of SPPs to photons, resulting in the enhancement of luminescence quantum efficiency.
© 2007 American Institute of Physics. 关DOI: 10.1063/1.2753571兴
I. INTRODUCTION

Silicon nanocrystals 共Si-ncs兲 show photoluminescence
共PL兲 at room temperature due to the recombination of excitons confined in a zero-dimensional quantum confinedsystem.1–4 As excitons are confined in a space smaller thanthe exciton Bohr radius of bulk Si crystals, the overlap ofelectron and hole wave functions becomes larger in both real
and momentum spaces, resulting in the enhancement of theradiative recombination rate.2,3 However, even for Si-ncs as
small as a few nanometers in diameter, the indirect band gap
nature of bulk Si crystals is strongly inherited,5 and thus the
spontaneous emission rate is still not large enough comparedto that of the direct band gap semiconductor and the luminescence quantum efficiency is rather low.2,3 Therefore, theenhancement of luminescence efficiency of Si-ncs is in highdemand for its application to optoelectric devices.
One of the approaches to enhance luminescence efficiency of Si-ncs is to realize the coupling of electronic excitation of Si-ncs to surface plasmon polaritons 共SPPs兲 supported by metal nanostructures. For example, by placing ananoporous Au layer near Si-ncs, enhancement of PL from
Si-ncs was demonstrated.6 The SPP resonance energy ofmetal nanostructures can be tuned in a wide wavelength
range by controlling the size and shape. In fact, the enhancement of PL from Si-ncs at specific wavelength ranges has
been shown by placing an Ag island array with different
sizes and pitches.7 Further, polarization-selective enhancement of PL is realized by using an anisotropic metal
structure.8
PL enhancement is also possible by using a flat thinmetal film if SPPs are scattered properly and converted tophotons efficiently. In previous work, it was demonstrated
that strong directional PL from Si-ncs caused by the couplinga兲Electronic mail: fujii@eedept.kobe-u.ac.jp

0021-8979/2007/102共2兲/023506/6/$23.00

of electronic excitation of Si-ncs and SPPs supported by ametal thin film and the scattering of the SPPs by a onedimensional 共1D兲 organic grating. One advantage of using aflat metal film and a grating to convert electronic excitation
to photons via SPPs is that dispersion relations are obtained
from angle-resolved PL spectra and by analyzing the relation, the origin 共mode兲 of PL peaks can be identified
unambiguously.9 However, in the previous work using a 1D
grating, the degree of the enhancement was limited. This isbecause only SPPs having the momentum to the direction
parallel to the grating vector can be Bragg scattered and converted to photons and others are lost to heat.10 This problem
is overcome by using a two-dimensional 共2D兲 grating, which
has two orthogonal grating vectors and can scatter SPPs
propagating in all in-plane directions to photons.11
In this work, we study PL from Si-ncs for the samples
consisting of SiO2 films containing Si-ncs, a flat thin Au film,
and a 1D or 2D organic grating. Dispersion relations fromangle-resolved PL spectra are obtained, and from the dispersion relations, the modes contributing to the PL enhancement
are discussed. The coupling of electronic excitation of Si-ncs
to SPPs results in the enhancement of the PL decay rate.
From the comparison between experimentally obtained
wavelength dependence of the PL decay rate enhancement
and calculated power dissipation to SPPs and other modes,
the mechanisms of the rate enhancement and also the intensity enhancement are discussed.
II. EXPERIMENTAL PROCEDURE

SiO2 films containing Si-ncs 共Si-nc: SiO2 films兲 wereprepared by a cosputtering method.12–14 Si and SiO2 were
simultaneously sputter deposited on a SiO2 substrate, and thedeposited films 共150 nm in thickness兲 were annealed in anitrogen gas atmosphere for 30 min at 1250 ° C. Si-ncs weregrown in the films during the annealing. After the annealing,

102, 023506-1© 2007 American Institute of Physics

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J. Appl. Phys. 102, 023506 共2007兲

FIG. 2. 共Color online兲 共a兲 PL spectra collected at ␪ = 23° for the sample witha flat photoresist layer 共sample IA兲 共dotted line兲, that with flat photoresist
and Au layers 共sample IB兲 共dashed line兲, and that with 1D grating on top ofa Au layer 共sample IC兲 共solid line兲. 共b兲 Angle-integrated PL spectra forsamples IA 共dotted line兲, IB 共dashed line兲, and IC 共solid line兲.

FIG. 1. 共Color online兲 共a兲 Schematic illustration of sample structure, 共b兲
definition of grating vectors and coordinates, and 共c兲 AFM image of thesurface of the sample with a 2D grating.

a Au film 50 nm in thickness was deposited. The corrugatedsurface was obtained by exposing a photoresist 共TDMRAR80 HP, Tokyo Ohka Kogyo兲 film spin coated on a Au film
to an interference pattern produced with a 325 nm line of a
He-Cd laser. Subsequent exposure after the rotation of thesample by 60° about the surface normal resulted in a hexagonal 2D corrugation. The schematic illustration of thesample structure, the definition of the grating vectors 共G1 andG2兲 and coordinates, and an atomic force microscope 共AFM兲
image of the surface of the sample with a 2D grating areshown in Figs. 1共a兲–1共c兲, respectively. As shown in Fig. 1共a兲,
we refer the sample with a flat photoresist layer to sample
IIA, that with flat photoresist and Au layers to sample IIB,
and that with 2D grating on top of the Au layer to sample
IIC. We also prepared similar series of samples with a 1D
grating. These samples are referred to samples IA, IB, andIC.
In order to measure angular dependence of PL spectrafrom the corrugated surface, samples were mounted on arotating stage with the grating vector G1 parallel to the incident plane, and illuminated through the transparent fusedquartz substrate. The excitation source was a 488 nm line of
an Ar ion laser. The excitation light was incident normal to
the surface, whereas the collection angle ␪ was changed from0° 共normal to the surface兲 to 60°. PL was collected from thecorrugated side through an aperture approximately 1 mm indiameter, which limits the angular acceptance to about 1°.
PL spectra were measured by using a single grating monochromator with a liquid nitrogen cooled Si charge coupleddevice. The spectral response of the detection system wascalibrated with the aid of a reference spectrum of a standard
tungsten lamp.
For time-resolved PL measurements, the samples were
excited by a 488 nm line of an optical parametric oscillator
pumped by the third harmonic of a neodium:yttrium–
aluminum–garnet laser 共pulse energy 0.5 mJ/ cm2, pulse
width 5 ns and repetition frequency 20 Hz兲 through a transparent fused-quartz substrate. The signals were detected either from the grating side or from the substrate side by a nearinfrared photomultiplier tube 共R5509-72, Hamamatsu Photonics兲 and a multichannel scaler 共SR430, Stanford Research
Systems兲. The time resolution of the system was 5.12 ␮s.
The detection wavelengths were changed from 800 to 1000
nm.
III. RESULTS AND DISCUSSION
A. PL spectra and dispersion relations

Figure 2共a兲 shows the PL spectra for samples IA, IB, andIC collected at ␪ = 23°. The PL band covering the 700–1000

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023506-3

Takeda et al.

FIG. 3. 共Color online兲 共a兲 PL spectra collected at ␪ = 23° for the sample witha flat photoresist layer 共sample IIA兲 共dotted line兲, that with flat photoresist
and Au layers 共sample IIB兲 共dashed line兲, and that with 2D grating on top ofa Au layer 共sample IIC兲 共solid line兲. 共b兲 Angle-integrated PL spectra forsamples IIA 共dotted line兲, IIB 共dashed line兲, and IIC 共solid line兲. 共c兲
Polarization-resolved PL spectra of sample IIC at ␪ = 23°. Solid, dashed, anddotted lines represent unpolarized, TM polarized and TE polarized emission,respectively. 共d兲 Angular dependence of PL spectra of sample IIC. The detection angle ␪ is changed from 21° to 25°. The numbers 共m , n兲 represent theorders of the scattering processes of SPP modes associated with the interface
between Au and Si-nc: SiO2 layers.

nm range arises from Si-ncs, whereas that below 700 nm
from the photoresist. In the following, we will pay attention
only to the PL from Si-ncs. In Fig. 2共a兲, in the presence ofthe grating, the shape of the PL spectrum is strongly modified and several peaks are observed. At the wavelength of thehighest PL intensity of sample IC, the intensity is enhanced
by a factor of 2 compared to that of sample IA and by aJ. Appl. Phys. 102, 023506 共2007兲

factor of 30 compared to that of sample IB. To compare theintegrated PL intensities among the samples, the spectra aremeasured in the polar angle range from 10° to 60° in 1°
intervals and are summed together. The results are shown in
Fig. 2共b兲. For a 1D grating, the integrated PL intensity ofsample IC is larger than that of sample IB but is smaller thanthat of sample IA.
Figure 3共a兲 shows the PL spectra for samples IIA, IIB,
and IIC collected at ␪ = 23°. Compared to the sample with the
1D grating 共sample IC兲, the peaks are sharper and the number of the peaks increases. Further, the enhancement of theintensity is more pronounced, i.e., the enhancement factors
are 5.2 compared to that of sample IIA and 57 compared tothat of sample IIB. As can be seen in Fig. 3共b兲, the integrated
PL intensity for sample IIC is slightly larger than that for
sample IIA. This is due to the scattering of SPPs propagating
in all in-plane direction by the 2D grating.15
Figure 3共c兲 shows polarization-resolved PL spectra forsample IIC at ␪ = 23°. Solid, dashed and dotted lines represent unpolarized, transverse magnetic 共TM兲 polarized, andtransverse electric 共TE兲 polarized emissions, respectively. TE
and TM polarization are defined as their electric field being
perpendicular and parallel to the x − z plane, respectively. The
peaks at 740 and 850 nm are TM polarized, whereas those at
810 and 930 nm have both the TM and TE polarization components. Figure 3共d兲 shows angular dependence of PL spectra for sample IIC. We can see the shift of the peaks byincreasing the collection angle. The shift is due to Bragg
scattering of SPP or waveguide modes. From the angulardependence of PL peak wavelengths, the dispersion relations
are obtained. The experimentally obtained dispersion relations are shown in Fig. 4 by open and closed circles, andsquares. To facilitate the assignment of the data, the same
experimental data are displayed in Figs. 4共a兲–4共d兲.
In order to assign the modes, we calculate the dispersion
relations by the formalism developed by Chance et al.16 byassumingafive-layer
systemconsistingofair/ photoresist/ Au/ Si-nc: SiO2 / SiO2.9,17,18 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 an optically active Si-nc: SiO2 layer is calculated as a function of an in-plane wave vector. For the calculation, the refractive indices of Au, Si, and SiO2 are takenfrom the literature19–21 and that of the Si-nc: SiO2 layer isestimated from the Bruggeman effective medium theory.22
The refractive index of the photoresist layer is obtained by anoncontact thin film metrology system 共FilmTek 1000, Scientific Computing International兲. The wavelength dispersionof the refractive indices of Au, Si, SiO2 and the photoresist
are taken into account. In the presence of a grating the wave
vector of SPP or waveguide modes is augmented or reduced,
and the modes can couple to photons. For a 2D grating, thecoupling condition between radiative modes propagating in
the x − z plane and nonradiative modes, such as SPP or waveguide modes, propagating in the x − y plane is expressed as

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FIG. 4. 共Color online兲 Dispersion relations for sample IIC. Circles andsquares correspond to experimentally obtained data, whereas the color maps
are obtained from calculation. The region deeper in color represents larger
dissipated power. The scattering orders 共m , n兲 are 共a兲 共−1 , 0兲, 共b兲 共2 , 0兲, 共c兲
共0 , −1兲, and 共d兲 共1 , 1兲. The insets are corresponding grating vectors.

冉 冊 冉 冊 冉冑 冊
冉 冊
冉冊

k m共 ␻ 兲
=
=

cos ␸
sin ␸

+ mG

1
0

+ nG

1/2

3/2

k储共␻兲
0

k0共␻兲sin ␪
0

,

共1兲

where km共␻兲 and k储共␻兲 denote the in-plane wave vector of aguided 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 ofthe propagation of nonradiative modes, ␪ is the polar angleof the propagation of radiative modes, G = 兩G1兩 = 兩G2兩
= 2␲ / ⌳ is the grating vector with the grating period ⌳, andm and n are the orders of the scattering process arising fromthe grating vectors G1 and G2, respectively. In order to reproduce experimentally obtained dispersion relations, we adjusted the values of the grating period and the thickness ofthe photoresist layer. The best result is obtained when thegrating period and photoresist layer thickness are 737 and361 nm, respectively. These values are close to measured
ones. At the range of the wavelength of Si-ncs emission,
SPPs experience four scattering processes, i.e., 共m , n兲 = 共−1 , 0兲 , 共2 , 0兲 , 共0 , −1兲 , 共1 , 1兲.
The calculated dispersion relations are shown in Figs.
4共a兲–4共d兲 by color gradients. The insets are the corresponding grating vectors. The region deeper in color represents
larger power dissipation. 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,whereas the weak one to the SPP modes propagating at theinterface between Au and the photoresist layer 共Au/PR SPP兲.
In Fig. 4, we can see a good agreement between the calculated dispersion relations of the SPP modes and the dispersion relations obtained experimentally. The agreement allows
us to assign the origin of the observed peaks. Closed circles
and squares are assigned to Au/ Si-nc: SiO2 SPP and Au/PR
SPP, respectively. This analysis reveals that the four strong
peaks in Fig. 3 are mediated by Au/ Si-nc: SiO2 SPP. The
corresponding scattering orders are indicated in Fig. 3共d兲.
The overall agreement implies that the strong PL peaks in
Fig. 3 arise from the coupling of excitons in Si-ncs to SPPs.
In Fig. 4, modes that are not identified by calculation exist.
They may arise from the extraharmonic components of thegrating profile.23
As shown in Fig. 3共c兲, the peaks at 740, 810, 850, and930 nm correspond to the scattering orders 共2 , 0兲, 共1 , 1兲,
共−1 , 0兲, and 共0 , −1兲, respectively. The intensity ratio of TM
polarized emission to TE polarized one is large if the propagation direction of SPPs is close to the x direction. Therefore, the peaks at 740 and 850 nm are only TM polarized,
whereas those at 810 and 930 nm have both the TM and TE
polarized emission.
B. PL decay rates

The inset of Fig. 5 shows the PL decay curves forsamples IIA and IIC detected at 850 nm. For sample IIC, thePL was detected from the grating side 共solid curve兲 and thesubstrate side 共dashed curve兲, whereas for sample IIA, it was
detected from the substrate side 共dotted curve兲. In order toinvestigate the wavelength dependence of the decay rates wemeasured PL decay curves in a whole emission wavelength
range and estimated the decay rates by fitting the decay
curves by a stretched exponential function.24 The results areshown in Fig. 5. Closed and open circles represent PL decay
rates for sample IIC detected from the grating side and fromthe substrate side, respectively, whereas triangles denote
those obtained for sample IIA. In all cases, the decay rateincreases as the emission wavelength is shortened due to thequantum size effect.25 By placing a Au film, the decay rate isenhanced in the whole wavelength range, whereas it does notdepend on whether PL comes from the grating side or theother side.

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FIG. 5. 共Color online兲 Wavelength dependence of PL decay rates forsamples IIA and IIC. Closed and open circles represent PL for sample IIC
detected from the grating side and from substrate side, respectively, whereas
triangles denote PL obtained for sample IIA. The inset shows the decay
curves detected at 850 nm. Solid and dashed lines represent PL for sample
IIC detected from the grating side and from the substrate side, respectively,
whereas the dotted line represents PL obtained for sample IIA.

In Fig. 6, the decay rates of sample IIC detected from thegrating side normalized to those of sample IIA are plotted asa function of wavelength. We can see the increase of thenormalized rate as the emission wavelength shortens. In order to analyze the wavelength dependence of the rate enhancement, we calculate power dissipation, which corresponds to the normalized decay rate, by using the sameformalism to calculate the dispersion relation in theprevious.16,17 Details of the calculation procedure are foundin Ref. 26. In the calculation, the contributions of dipoles
positioned in the 150 nm thick active layer are averaged overthe layer thickness. First, we performed calculation under theassumption that the internal quantum efficiency is 100%.
However, the result did not agree with the experimental result in Fig. 6. We therefore regarded the internal quantum
efficiency of Si-ncs as a fitting parameter, and the parameter
was chosen so that the calculated total decay rate agreed withthe experimentally obtained normalized decay rate. The best
agreement was obtained when the internal quantum efficiency is 45%. The solid curve in Fig. 6 is the calculated
total decay rate. We can see a good agreement between experimental and calculated results.

FIG. 6. 共Color online兲 PL decay rates of sample IIC detected from thegrating side normalized to those of sample IIA as a function of wavelength.
Squares correspond to experimentally obtained data, whereas the solid line
denote a calculated normalized decay rate. Relative contributions of radiative decay rates 共dashed line兲, SPP excitation rates 共dotted line兲, and LSW
excitation rates 共dotted-dashed line兲 to the total normalized decay rates arealso shown.

In this calculation, we can also analyze relative contributions of different modes to which power of a dipole
dissipates.26 The contributions of the radiative decay rate, therate of energy transfer to SPPs, and that to lossy surface
waves 共LSWs兲 to the total normalized decay rate are shownin Fig. 6 as dashed, dotted, and dotted-dashed curves, respectively. In Fig. 6, the contribution of the LSW excitation rate
to the total decay rate is very small and it does not depend
strongly on the wavelength. Spontaneous emission and SPP
excitation rates contribute to the total power dissipation
nearly equally. The spontaneous emission rate increases
slightly as the wavelength shortens because of the increased
photonic mode density, whereas the SPP excitation rate increases much faster. The increase of the SPP excitation rate
is mainly due to larger density of state of SPPs at shorter
wavelength. In Fig. 6, we can see that the wavelength dependence of the SPP excitation rate is very similar to that ofexperimentally obtained normalized decay rate. This meansthat the observed enhancement of the decay rate is mainly
due to the excitation of SPPs.
Because of the energy transfer to SPPs, the recombination rate of excitons confined in Si-ncs near a Au film can be
expressed as Wtotal = Wr + Wnr + WSPP, where Wr and Wnr represent the radiative and nonradiative decay rates of Si-ncs,
respectively, and WSPP denotes the rate of energy transferfrom excitons to SPPs. If excited SPPs are scattered with theefficiency of ␩SPP, the PL quantum efficiency is expressed as␩ = 共Wr + ␩SPPWSPP兲 / Wtotal.27 In the present work, the PL
quantum efficiency is enhanced by a Au thin film and a 2D
organic grating. This implies that excited SPPs are efficiently
scattered by the 2D organic grating and ␩SPP is rather large.

IV. CONCLUSION

We demonstrated that the coupling of electronic excitation of Si-ncs and SPPs supported by a Au thin film followedby scattering of the SPPs by a 2D organic grating results instrong directional PL. From the angular dependence of PL
spectra, the dispersion relations were obtained and from theanalysis of the dispersion relation, the excitation of SPPs wasunambiguously demonstrated. The excitation of SPPs was
accompanied by the enhancement of the decay rate. The
wavelength dependence of the decay rate enhancement confirmed that the observed PL enhancement is due to the excitation of SPPs and efficient scattering of SPPs to photons.
Although the enhancement of PL was realized becauseof the coupling of electronic excitation of Si-ncs to SPPs, theenhancement was rather limited. This was because coupling
between Si-ncs and SPPs and that between SPPs and photons
were not optimized. In fact, the rate of SPP excitation 共WSPP兲was not very large, i.e., comparable to the spontaneous emission rate. Further enhancement of WSPP may be possible bytuning Au/ Si-nc: SiO2 SPP, which was excited more efficiently than Au/PR SPP, can be enhanced by using a metal
grating instead of the combination of flat metal and an organic grating. However, although these improvements probably enhance the PL efficiency more, it is not clear whether
the degree of the enhancement is enough to make Si-ncs

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023506-6

practical materials for light emitting devices or not. This
point will be discussed after applying all possible improvements to sample structures.
ACKNOWLEDGMENT

This work is supported by a Grant-in-Aid for Scientific
Research from the Ministry of Education, Culture, Sports,
Science, and Technology of Japan.
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