JOURNAL OF APPLIED PHYSICSVOLUME 93, NUMBER 4

15 FEBRUARY 2003

Enhanced optical properties of Si1À x Gex alloy nanocrystals in a planar
microcavity
Kimiaki Toshikiyo
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan

Minoru Fujiia) and Shinji Hayashi
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai,Nada, Kobe 657-8501, Japan

共Received 3 September 2002; accepted 22 November 2002兲
The emission properties of Si1⫺x Gex alloy nanocrystals (nc-Si1⫺x Gex ) in an optical microcavity
were studied, and the results were compared with those of nc-Si in the same structure. The cavity
consists of two distributed Si/SiO2 Bragg reflectors 共DBRs兲 sandwiching a thin SiO2 film containing
nc-Si1⫺x Gex . The commonly observed cavity effects, that is, spectral narrowing, highdirectionality, and photoluminescence 共PL兲 enhancement in the normal direction, were observed. In
nc-Si1⫺x Gex , PL lifetime was lengthened by cavity formation, while that of nc-Si was shortened.
This difference is due to the different dielectric contrast between active layers and DBRs. © 2003
American Institute of Physics. 关DOI: 10.1063/1.1539289兴

I. INTRODUCTION

II. EXPERIMENT

During the past decade, nanometer-sized Si and Ge crystals (nc-Si and nc-Ge) have been extensively studied because they offer new possibilities for indirect band-gap semiconductors as new materials in photoelectronic applications.
It has been demonstrated that the photoluminescence 共PL兲energy of nc-Si is tunable from the bulk band gap to thevisible region by simply controlling its size.1– 6 The tuning
range can be expanded by Si1⫺x Gex alloy formation, because
the band gap 共luminescence兲 energy of nanometer-sized
Si1⫺x Gex alloy crystals (nc-Si1⫺x Gex ) changes from thewidened bandgap of nc-Si to that of nc-Ge depending on
x.7–10 The wide tunability of PL peak energy prompts greatinterest in the development of Si-based light-emitting devices.
The emission properties of such materials can be further
improved by constructing a microcavity structure; that is,putting an active layer into two distributed Bragg reflectors
共DBRs兲. When a phonon is confined in a microcavity in resonance with the emission of the active medium, the lightemission becomes spectrally sharp and is strongly enhancedin the direction of confinement.11–17The emission energy canbe tuned by properly choosing the parameters of Bragg reflectors and the thickness of the active region.
In this article, we report our study of the PL properties ofnc-Si1⫺x Gex in a microcavity, and compare those properties
with those of nc-Si in the same structure. We will show that,
although the PL properties of nc-Si1⫺x Gex and nc-Si
samples are modified in a very similar way by microcavity
formation, different effects appear for PL decay dynamics.
We will discuss how the dielectric contrast between an activelayer and the surrounding DBRs affects PL decay dynamics.

The active layer of our microcavity is a SiO2 thin film
containing either nc-Si or nc-Si1⫺x Gex . The Bragg reflectors on top and bottom of the active layers are pairs of Si and
SiO2 layers, repeated three times. The thicknesses of theBragg reflectors and the active layer were chosen to be ␭ c /4nand ␭ c /n, respectively, where ␭ c is the wavelength of theresonance and n is the reflective index of the medium. The
thicknesses and refractive indexes of the layers are summarized in Table I. The refractive index values of the activelayers (n c ) were estimated by spectroscopic ellipsometry.
A multitarget sputtering apparatus was used to deposit
multilayer films.6 –10 The layers of Bragg reflectors were deposited by alternately operating Si or SiO2 sputtering guns,
while active layers were deposited by operating Si, Ge, andSiO2 guns simultaneously 共in the case of nc-Si, Si, and SiO2guns兲. The sputtering rate of each gun was independently
controlled by adjusting the sputtering power and the distance
between sputtering targets and substrates. After the deposition of a microcavity structure on a fused quartz substrate,
the film was annealed in an N2 gas atmosphere for 30 min at1100°C. During the annealing, either nc-Si or nc-Si1⫺x Gex
was grown in a SiO2 matrix. The cross section of the cavity
structure was examined by using a high-resolution transmission electron microscope 共HRTEM兲. In Fig. 1共a兲, the crosssection of a sample is shown. We can see that the Si/SiO2
interfaces are rather smooth, with less than 10 nm of roughness. Figure 1共b兲 shows a HRTEM image of an active layer
containing nc-Si1⫺x Gex . Spherical nanocrystals as small as
4 –5 nm in diameter were grown in amorphous SiO2 matrices. The formation of Si1⫺x Gex alloy was confirmed by electron diffraction and Raman spectroscopy.7
PL spectra were measured with a single monochromatorequipped with a liquid-N2 -cooled Ge detector. The excitation source was the 488.0-nm line of an Ar-ion laser. The
angle of incident beam was about 45° from the surface of thea兲Author to whom correspondence should be addressed; electronic mail:fujii@eedept.kobe-u.ac.jp

0021-8979/2003/93(4)/2178/4/$20.00

2178© 2003 American Institute of Physics

Downloaded 18 Nov 2004 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

J. Appl. Phys., Vol. 93, No. 4, 15 February 2003

Toshikiyo, Fujii, and Hayashi

2179

TABLE I. Growth parameters and refractive index data of two microvcavities. l H and l L are the thicknesses of the various layers of the DBR. Here,n H , n L , and n c refer to the refractive index values for the high- and lowrefractive index layers, 共Si and SiO2 兲 共Ref. 17兲, and the central layer, respectively, and ␭ c is the PL peak wavelength.

nc-Si
nc-Si0.9Ge0.1

l H (nm)l L (nm)nHnLnc␭ c (nm)

61
66

149
162

3.56
3.56

1.45
1.45

1.70
2.18

867
940

sample, and PL emitted perpendicular to the surface was detected. The solid angle for the collection of emitted light wasless than 1⫻10⫺3 ␲ sr. For time-response measurements, anear-infrared photomultiplier with an InP/Inx Ga1⫺x As photocathode was used with a photon-counting mode. The overall time resolution of the system was about 40 ns.

III. RESULTS AND DISCUSSIONFigure 2共a兲 shows a reflectivity spectrum of a DBR atroom temperature. A high reflectivity region 共stop band兲 appears between 1.1 and 1.7 eV. Putting SiO2 layers containing
nc-Si 关Fig. 2共b兲兴 and nc-Si1⫺x Gex 关Fig. 2共c兲兴 into twoDBRs causes dips 共resonant peaks兲 to appear in the highreflectance stop band. The energy and the linewidth of theresonant peaks are 1.43 eV and 17 meV, respectively, fornc-Si, and 1.32 eV and 16 meV, respectively, fornc-Si0.9Ge0.1 .
Figures 3共a兲 and 3共b兲 show PL spectra of nc-Si andnc-Si0.9Ge0.1 , respectively, obtained in the direction normal
to the sample surfaces. Dashed curves represent the spectra
without DBRs. The PL bandwidths 共full widths at half maximum兲 are 315 meV for nc-Si, and 345 meV fornc-Si0.9Ge0.1 . The PL spectra are narrowed down to 17 meVfor nc-Si, and 16 meV for nc-Si0.9Ge0.1 , by microcavity
structure formation. The quality factors 共Q兲 are 87 and 85,
respectively. Furthermore, PL intensity is enhanced by a fac-FIG. 1. Cross-sectional HRTEM image of a microcavity, which consists of共a兲 two distributed Si/SiO2 Bragg reflectors and 共b兲 a central active layer
with nc-Si1⫺x Gex .

FIG. 2. Reflectivity spectra of 共a兲 DBR, 共b兲 nc-Si, and 共c兲 nc-Si0.9Ge0.1 inmicrocavities at room temperature. For the sample having cavity structure,
the sharp dips 共arrows兲 appear in the high reflectance stop band.

tor of about 20. The net enhancement is about 122 for both
samples because a part of the excitation light is lost by thetop DBR.
The enhancement of the luminescence intensity at theresonance wavelength is observed only in the normal direction, while the intensity is suppressed in other direction. ThisFIG. 3. PL from 共a兲 nc-Si and 共b兲 nc-Si0.9Ge0.1 in microcavities at roomtemperature. PL spectra without DBRs are broad 共dashed curve兲. By microcavity structure formation, PL spectra are narrowed drastically 共solid curve兲.

Downloaded 18 Nov 2004 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

2180

J. Appl. Phys., Vol. 93, No. 4, 15 February 2003

Toshikiyo, Fujii, and Hayashi

FIG. 5. Room-temperature time decay of the PL for the microcavities 共solidcurve兲 and the non-cavities 共dashed curve兲.

FIG. 4. 共a兲 Integrated PL intensity, and 共b兲 and 共c兲 wavelength peak position
as a function of detection angle with respect to the normal direction.

redistribution of the emission is a well-known cavity
effect.11–16 The enhancement value in the normal direction
can be calculated from the finesse of the cavity, if reflectivityof top and bottom DBRs are high enough.18 For ␦-functionlike emission spectra occurring at the resonance wavelengthof the cavity, the peak intensity enhancement factor G compared to an emitter without mirrors isG⫽␨ 共 1⫹ 冑R bottom兲 2 共 1⫺R top兲 ␶ cav,2␶ act共 1⫺ 冑R topR bottom兲 2

共1兲

where ␨ is an antinode enhancement factor depending on theposition of an active region in an electric field antinode of
the cavity standing wave. This value is nearly 1 due to a
thick active region. The R top and R bottom are the calculated
reflectivities of the top and bottom DBRs; the R top andR bottom are 98.1% and 98.5% for nc-Si, respectively, and97.3% and 98.4%, respectively, for nc-Si0.9Ge0.1 . The ␶ cavand ␶ act are the respective PL lifetimes with and without thecavity. The calculated G is 120.5 for nc-Si, and 122.4 fornc-Si0.9Ge0.1 . These values are very close to those observed.
Figure 4共a兲 shows the angle dependence of PL intensities
for our microcavity structures and bare films. In microcavity
structures, PL is strongly directed along the optical axis of
the cavity. The PL intensities are the maximum at normal to

the surface ( ␪ ⫽0°) and then decrease rapidly with increases
in the detection angle. On the other hand, for noncavity
structures, the intensities are almost constant over the entire
detection angle range. Figures 4共b兲 and 4共c兲 show the angle
dependences of the PL peak wavelengths for nc-Si andnc-Si0.9Ge0.1 , respectively. For off-normal angles, the emission wavelength shifts toward a shorter wavelength. The degree of the wavelength shift obeys a cosine of the internal
cavity angle, which is approximated by the detection angle
共␪兲 divided by the average cavity refraction index (n eff). The
PL peak wavelength can thus be expressed approximately as␭⫽␭ c cos(␪/ne f f). 12 By fitting the experimental results tothis formula, n eff can roughly be estimated. The estimatedvalues are 1.9 for nc-Si and 2.1 for nc-Si0.9Ge0.1 .
Figure 5 shows PL decay curves detected at the PLmaximum. The decay curves are nonexponential. Nonexponential decay curves are commonly observed for similarsystems.7 The PL decay of nc-Si0.9Ge0.1 is faster than that ofnc-Si. This is consistent with our previous results.7,8 The
decay curve is changed slightly by microcavity formation.
The lifetime of nc-Si PL is shortened, while the lifetime ofnc-Si0.9Ge0.1 is made longer. The time in which the PL intensity becomes 1/e of maximum intensity is 189.5 ␮s fornc-Si, and 90.5 ␮s for nc-Si0.9Ge0.1 .
In a simple model, the spontaneous emission rate of asemiconductor R sp (ប ␻ ) is divided into an electric partM (ប ␻ ) and a photonic part G(ប ␻ ). 19 In principle, M (ប ␻ )is not changed by cavity formation. In the present samples,
this is confirmed by measuring the PL spectrum from thecavity edge ( ␪ ⫽90°). The spectrum from the cavity edge
was almost the same as that of samples without the cavitystructures.
In a microcavity, the electronic transition occurs only inthe active layer. However, the optical mode, to which theexcitonic transition couples, is extending into the DBR. As aresult, the refractive index which affects G(ប ␻ ) is not thatof the active layer but an average of the refractive indexes ofthe layers in which the optical mode extends. Under the assumption that energy distribution of the optical mode falls
monotonically, the penetration length (l p ) of the opticalmode into a DBR is given by20

Downloaded 18 Nov 2004 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

J. Appl. Phys., Vol. 93, No. 4, 15 February 2003

Toshikiyo, Fujii, and Hayashi

TABLE II. Optical mode extension into the distributed Bragg reflectors andeffective refractive index (n eff) for the various microcavities. Here, l top
p and
are the penetration lengths on the surface side and on the substratel bottompside, respectively, and ␶ cav and ␶ act are the PL lifetimes of the cavity andnoncavity, respectively.

nc-Si
nc-Si0.9Ge0.1

l p⫽

l topp (nm)l bottom(nm)pn eff(n c /n eff) 3

␶ cav / ␶ act

255
276

269
291

1.93
2.09

0.68
1.13

0.93
1.25

␭ c q 共 1⫹a 2 p m⫺1 兲共 1⫺ p m 兲,
4n c 1⫺p1⫹q 2 a 2 p 2m⫺2共2兲

where q⫽n c /n L , p⫽n L /n H , a⫽n H /n sur or a⫽n H /n sub ;whether the top DBR or the bottom DBR is considered, n surand n sub are the refractive indexes of air and silicon dioxide,respectively, and m is the number of stacks in the DBR. Thebottom) are summacalculated penetration lengths (l topp and l p
rized in Table II. The table shows that the optical mode isextended deeply into the DBRs.
The effective refractive index of the DBR (n DBR) can beapproximated by the spatial average between the high andthe low refractive indexes, that is, n DBR⫽(n H l H ⫹n L l L )/(l H⫹l L ). The effective refractive index (n eff) can be approximated by the average over the spatial extent of the opticalmode:16
ne f f⫽bottomn DBRl top⫹␭ cp ⫹n DBR l pbottoml top⫹␭ c /n cp ⫹l p.

共3兲

The n eff calculated by this formula agrees very well withthose estimated from Fig. 4. The important fact is that n eff islarger than n c for nc-Si, while n eff is smaller than n c for
nc-Si0.9Ge0.1 . The photonic part of the spontaneous recombination rate is proportional to the cube of the refractive
index of the material (n 3 ). 19 If M (ប ␻ ) is not changed bymicrocavity formation, the spontaneous recombination ratechanges in proportion to n 3 . In Table II, the values of(n c /n eff) 3 and ␶ cav / ␶ act are compared. We can see that theincrease and decrease of ␶ cav by microcavity formation for
nc-Si1⫺x Gex and nc-Si can be qualitatively explained by thedifferent dielectric contrast between the active layer and theDBRs. The quantitative disagreement may arise from oversimplification of the model and the fact that the PL lifetime
reflects not only the radiative recombination process but also
the nonradiative recombination processes. Nonradiative recombination processes are considered to be unaffected bymicrocavity formation.
IV. CONCLUSION

We studied the emission properties of nc-Si1⫺x Gex in
Si/SiO2 planar microcavity by measuring PL and time-2181

resolved PL and comparing the results with those for nc-Si.
We observed the commonly observed microcavity effects,
that is, spectral narrowing, high directionality and enhancement of PL lines. In contrast to nc-Si, where the PL lifetime
was shortened by microcavity formation, the PL lifetime ofnc-Si1⫺x Gex became longer compared to the PL from a barefilm. This result can be well explained by considering thedifference in the dielectric contrast of active layer and that ofDBRs into which an optical mode extends.

ACKNOWLEDGMENTS

This work was supported by a Grant-in-Aid for Science
Research from the Ministry of Education, Science and Culture, Japan, and a Grant for Research for the Future Programfrom the Japan Society for the Promotion of Science 共JSPSRFTF-98P-01203兲. One of the authors 共K.T.兲 would like tothank the Japan Society for the Promotion of Science.

1

H. Takagi, H. Ogawa, Y. Yamazaki, A. Ishizaki, and T. Nakagiri, Appl.
Phys. Lett. 56, 2379 共1990兲.
2
S. Schuppler, S. L. Friedman, M. A. Marcus, D. L. Adler, Y. -H. Xie, F. M.
Ross, Y. J. Chabal, T. D. Harris, L. E. Brus, W. L. Brown, E. E. Chanban,
P. F. Szajowski, S. B. Christman, and P. H. Citrin, Phys. Rev. B 52, 4910
共1995兲.
3
D. Kovalev, H. Heckler, G. Polisski, and F. Koch, Phys. Status Solidi B215, 871 共1999兲.
4
Y. Kanzawa, T. Kageyama, S. Takeoka, M. Fujii, S. Hayashi, and K.
Yamamoto, Solid State Commun. 102, 533 共1997兲.
5
M. Fujii, S. Hayashi, and K. Yamamoto, in Recent Research Developmentin Applied Physics, edited by S. G. Pandalai 共Transworld Research Network, Trivandrum, 1998兲, Vol. 1, p. 193.
6
S. Takeoka, M. Fujii, and S. Hayashi, Phys. Rev. B 62, 16820 共2000兲.
7
S. Takeoka, K. Toshikiyo, M. Fujii, S. Hayashi, and K. Yamamoto, Phys.
Rev. B 61, 15988 共2000兲.
8
M. Fujii, D. Kovalev, J. Diener, F. Koch, S. Takeoka, and S. Hayashi, J.
Appl. Phys. 88, 5772 共2000兲.
9K. Toshikiyo, M. Tokunaga, S. Takeoka, M. Fujii, and S. Hayashi, J. Appl.
Phys. 89, 4917 共2001兲.
10K. Toshikiyo, M. Tokunaga, S. Takeoka, M. Fujii, S. Hayashi, and K.
Moriwaki, J. Appl. Phys. 90, 5147 共2001兲.
11S. Chan and P. M. Fauchet, Appl. Phys. Lett. 75, 274 共1999兲.
12
H. A. Lopez and P. M. Fauchet, Appl. Phys. Lett. 77, 3704 共2000兲.
13F. Iacona, G. Franzo, E. C. Moreira, and F. Priolo, J. Appl. Phys. 89, 8354
共2001兲.
14
A. Serpenguzel and S. Tanriseven, Appl. Phys. Lett. 78, 1388 共2001兲.
15
A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M.
Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 共1993兲.
16
M. Cazzanelli and L. Pavesi, Phys. Rev. B 56, 15264 共1997兲.
17
H. R. Philipp, Handbook of Optical Constants of Solids, edited by E. D.
Palik 共Academic, New York, 1985兲, p. 765.
18
N. E. J. Hunt and E. F. Schubert, Microcavities and Photonic Bandgaps:
Physics and Applications, edited by J. Rarity and C. Weisbuch 共Kluwer
Academic, Dordrecht, 1995兲, p. 343.
19H. B. Bebb and E. W. Williams, Semiconductors and Semimetals, editedby R. K. Willardson and A. C. Beer 共Academic, New York, 1972兲, Vol. 8,
p. 181.
20
D. I. Babic and S. W. Corzine, IEEE J. Quantum Electron. 28, 514 共1992兲.

Downloaded 18 Nov 2004 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp