*Corresponding author. Fax: #1-787-764-9006.E-mail address: rksoni@rrpac.upr.clu.edu (R.K. Soni)

Journal of Luminescence 83}84 (1999) 187}191

Size-dependent optical properties of silicon nanocrystals

R.K. Soni*, L.F. Fonseca, O. Resto, M. Buzaianu, S.Z. Weisz

Department of Physics, University of Puerto Rico, P.O. Box 23343, Rio Piedras, PR 00931, USA

Abstract

We have synthesized green and red luminescent silicon nanocrystals in a SiO2

matrix by RF co-sputtering on a quartzsubstrate. The transmission coe$cient measurements were used to estimate the nanocrystal size distribution. The sizedistribution reveals peaks in the range 1.1}2.6 nm with a long tail towards the larger size. As the nanocrystal size reducesphotoluminescence spectrum shifts from red to green wavelengths. The measured PL emission energy is in agreementwith the corrected LDA calculations. With decreasing nanocrystal size, the phonon Raman spectra exhibit softeningaccompanied with increasing asymmetrical broadening. The observed line shape is explained by considering phononcon"nement in a spherical nanocrystal. The major contribution to the phonon line shape comes from those nanocrystalsthat favor resonance interaction with either incoming or outgoing photon. ( 1999 Elsevier Science B.V. All rightsreserved.

Keywords: Silicon nanocrystals; Si}SiO2"lm; Photoluminescence; Raman scattering; Quantum con"nement

1. Introduction

Nanometer size silicon crystals show marked im-provement in photoluminescence (PL) quantum ef-"ciency compared to bulk silicon and are, therefore,attractive for silicon based optoelectronic applica-tions [1]. The PL observed from Si nanocrystals isattributed to quantum size e!ects. The e!ect ofcarrier con"nement and band gap upshift in siliconnanocrystals has been discussed intensively in theliterature [1]. The photoluminescence energy forsilicon nanocrystals have been calculated by usingthe empirical pseudopotentials (EPS) [2], thethird-nearest-neighbor tight binding [3] and time-dependent tight binding techniques [4]. Despite the

apparent disagreement in predicting the PL emis-sion energies, these calculations demonstrate thatthe PL energy increases as the nanocrystal sizedecreases and the dominant contribution to thevisible light emission comes from nanocrystalssmaller than 2 nm. The resonantly excite PL spec-trum has shown long radiative lifetime in the Sinanocrystals and provides an important evidencethat the phonons are directly involved in theradiative recombination process [5]. Clearly, thissuggests that the Si nanocrystal electronic bandstructure remains indirect type. Theoretical calcu-lations, however, indicate that quasi-direct gap innanocrystal silicon is possible for sizes 1.0}1.5 nmin diameter [3].

Raman scattering technique is commonly usedfor semiquantitative determination of size e!ects onvibrational modes, such as con"ned opticalphonon, surface phonon and con"ned acoustic

0022-2313/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 0 9 6 - 4

Fig. 1. Transmission spectra from di!erent positions of aSi}SiO

2"lm annealed at 11003C. The "lm is divided in 50 equal

segments; the number on each spectrum designates the segmentnumber. The number 1 and 50 are assigned to the SiO

2rich and

Si rich end of the "lm, respectively. The absorption edge shifts tolower wavelengths with decreasing silicon nanocrystal size anddensity.

phonon, in nanocrystals [6}9]. An adequate know-ledge of the bulk phonon dispersion is a prerequi-site for understanding lattice dynamical propertiesand electron}phonon interactions in nanocrystals.The e!ect of carrier con"nement on opticalphonons in silicon nanoparticles has been widelystudied by Raman scattering [6}8]. The size e!ectis re#ected in a "nite wave vector of nanocrystaland corresponding lowering of phonon frequencyfrom those of the bulk. A quantum con"nementmodel that takes into account the "nite phononwave vector and Gaussian size distribution forspherical nanocrystals is generally invoked to ex-plain the observed Raman line shape. Here, weinvestigate the size-dependent photoluminescenceand Raman scattering from silicon nanocrystalsdispersed in a SiO

2matrix grown on a quartz

substrate. We emphasize the role of nanocrystalsthat favor the resonant interaction with incomingor outgoing photon.

2. Experiment

The Si}SiO2"lm was synthesized on the quartz

substrate by RF co-sputtering. The substrate wasa 6-in long quartz strip. The chamber was "rstevacuated down to 1.0]10~7 Torr and the depos-ition was performed under an argon pressure of2.0]10~2 Torr at deposition temperature of1153C. On a SiO

2target (6 in in diameter) small

pieces of Si tips (area &0.1 in2) were placed andthey were co-sputtered for 3 h. The number of Sitips and their position on the SiO

2were used to

control the size of silicon nanoparticles. The "lmwas subsequently annealed in nitrogen ambient at11003C for 30 min. The deposited "lm has an areaof 5]0.2 in and thickness of the order of 1.7 lm.Both the size and density of silicon nanocrystalsvary continuously along the length of the "lm. Thetransmission measurements were made in the range190}820 nm using a HP-8452A spectrophotometer.The photoluminescence and Raman measurementswere performed in a quasi back-scattering geo-metry at room temperature using the 514.5 nm lineof an Ar` laser. The spectra were dispersed bya TRIAX 320 spectrometer and detected bya cooled photomultiplier with GaAs photocathode.

3. Results

Fig. 1 shows typical transmission spectra takenfrom di!erent positions on the Si}SiO

2"lm. The

deposited "lm is divided in 50 equal segments anddesignated a number, number 1 is assigned to SiO

2rich end and 50 to the Si rich end of the "lm. Eachof these segments has di!erent nanocrystal densityand size. In order to study the size dependence ofoptical properties, we measured the transmissionspectrum from each one of these segments. Theoptical absorption edge shifts to higher energy asone moves from silicon rich side (position 50) toSiO

2rich side (position 1) of the sample due to

nanocrystal size reduction. The transmission coef-"cient of the "lm is related to the energy absorbedby the Si nanocrystal of size R imbedded in theSiO

2matrix. Assuming that the energy upshift is

given by A/R1.3 (A is a constant), and the absorp-tion is primarily due to interband transitionsbetween the quantum con"ned states of sphericalSi nanocrystals, the size distribution can be

188 R.K. Soni et al. / Journal of Luminescence 83}84 (1999) 187}191

Fig. 2. Calculated nanocrystal size distribution in Si}SiO2"lms

annealed at 11003C at the positions where transmission spectrawere taken. The size distribution is narrower for smaller sizes.

Fig. 3. Size-dependent PL spectra from silicon nanocrystalsembedded in SiO

2. The average size of the nanocrystal is cal-

culated from the transmission data.

approximated with the "rst derivative of the trans-mission spectrum [10]. We have used the transmis-sion measurements to estimate the nanocrystal sizedistribution in the "lm, the estimated size distribu-tion is asymmetric with a long tail towards thelarger size and centered around 1.1}2.6 nm asshown in Fig. 2.

Fig. 3 shows the PL emission spectra fromSi}SiO

2"lm excited with the green 514.5 nm

(2.412 eV) line of an argon ion laser. The PL spec-trum is broad and shifts to higher energy withdecreasing size. In addition, there is a large reduc-tion in integrated PL intensity for smaller sizes dueto lower density. The peaks are observed at 782 nm(1.59 eV) and 601 nm (2.06 eV) for dot sizes of 2.6and 1.4 nm, respectively. According to Delerueet al. [11], EPS or tight binding as well as correctedab initio local density approximation (LDA) tech-niques give reliable predictions for Si nanocrystalband gap. It has also been pointed out that thequasi particle gaps and exciton coulomb energiesof Si nanocrystals require a large correction tothe band gap which are not included in the oneelectron theory. The exciton gap is de"ned as

E%9#'

"EQP'

!E#06-

, where the quasi-particle gapEQP'

is the di!erence in energies resulting from theseparate addition of an electron and hole to thesystem while the correction E

#06-results from the

corresponding attraction between these two quasi-particles. Our PL results are in agreement withcorrected LDA calculation [11]. We attribute thefeatureless broad PL spectrum to band-to-bandrecombination in Si nanocrystal and #uctuation intheir sizes. For the 1.4 nm nanocrystal, we also seestructure towards the high energy (2.2 eV) due toresonant excitation with laser line. It should benoted that PL energy is lower than the absorptionedge at each segment of the "lm, and this di!erenceis appreciably large towards the SiO

2side of the

"lm where the nanoparticle sizes are smaller. Self-trapped exciton at the interface between Si andSiO

2or a defect state is considered to be respon-

sible for the observed Stokes shift of PL emissionenergy [11].

The Raman spectra from Si}SiO2"lm were ex-

cited with 514.5 nm (2.41 eV) laser line of an argonion laser from the region that emits green-orangeluminescence. Fig. 4 shows representative spectrafrom three di!erent positions of the sample charac-terized by the average nanocrystal diameter. The

R.K. Soni et al. / Journal of Luminescence 83}84 (1999) 187}191 189

Fig. 4. Size-dependent Raman spectra from silicon nanocrys-tals. The average size of the nanocrystal is calculated from thetransmission data.

observed spectra show phonon softening and lineshape broadening with decreasing size. As the sizedecreases from 2.2 to 1.4 nm, the Raman peak shiftsfrom 511 to 502 cm~1. The Raman lines are asym-metrically broadened with a tail towards the low-energy side. In the uncorrected data, the integratedintensity remains fairly constant. The broad lineshape arises from size distribution in an ensembleof nanocrystals, which leads to a large #uctuationin wave vectors, particularly for size smaller than2 nm.

In order to explain the observed resonance lineshape, we assume that the optical vibrations arecon"ned to the spherical nanocrystal with e!ectivewave vector,

qn"

kn

R, (1)

where knis nth node of the spherical Bessel function

j1, and R is the nanocrystal radius. A quadratic

bulk Si dispersion gives the eigen frequencies,

u2n(R)"u2

0!b2q2

n(R), (2)

where u0

is the bulk silicon optical phononfrequency (520.5 cm~1) and b is a parameter(6.977]1012 s~1) describing the dispersion of theoptical phonon in the bulk silicon. The observedRaman frequencies are in agreement with the cal-culated eigenfrequencies of optical vibrations ofzero angular momentum (l"0) mode as a functionof R in a spherical Si nanocrystal embedded inthe SiO

2. It should be pointed out that a precise

determination of nanocrystal size, particularly forR(1 nm, is necessary for the estimation of equiva-lent wave vectors and corresponding eigen-frequencies. The Raman line shape can be writtenas I(u, R) [9],

I(u4, R)"I

0

]+n

1

[(+ul!Ek1(R)) (+u4!Ek2(R))!Ck1Ck2]2#[Ck2(+ul!Ek1(R))#Ck1(+u

4!Ek2(R))]2

]C/p

[+ul!+u4!+u

n(R)]2#C2

, (3)

where I0

is the product of scattering e$ciency andeigenvalues of the appropriate scattering matrix

elements over all the intermediate states, R is themean nanocrystal radius, Ek1(R) and Ek2(R) arethe eigenenergy for R in the k

1and k

2intermediate

states, respectively, Ck(C) is the intermediate state(phonon) lifetime broadening, ul and u

4are the

excited laser energy and scattered photon energy,respectively. In the incoming resonance process,ul coincides with one of the electronic states Ek

1(R)

while outgoing resonance occurs when us ap-proaches Ek

2. The resonance conditions is de-

scribed as +ul"Ek1(R) for incoming resonance,

and +ul!+un(R)"Ek

2(R) for outgoing reso-

nance. We assume that the intermediate electronicstate is an electron}hole pair state and the elec-tron}phonon couple via deformation potential

190 R.K. Soni et al. / Journal of Luminescence 83}84 (1999) 187}191

Fig. 5. Calculated resonance contribution to the experimentallyobserved Raman line shape of 1.4 nm silicon nanocrystal.

interaction. The resonant nanocrystals at the laserphotons at 2.412 eV have diameters in the range1.3}1.4 nm. Fig. 5 shows the calculated line shapefor 1.4 nm nanocrystal. It is evident form the"gure that the main contribution to the Raman lineshape comes from the resonant radii, though non-resonant nanocrystals provide broad constantbackground to the Raman spectrum.

4. Conclusions

We have synthesized Si nanocrystals in a SiO2

matrix on quartz strip by RF co-sputtering. Thesilicon nanocrystals are dispersed in size along thelength of the strip. Optical transmission measure-ments were employed to estimate the nanocrystalsize distribution which shows peaks in the range1.1}2.6 nm with an asymmetrical tail towards thelarge particle size. The PL emission from theSi}SiO

2"lm exhibits broadband in the red and

green region, and their energies are in agreementwith corrected LDA calculation of Si nanocrystals.

Size dependence of the Raman scattering wasperformed on Si nanocrystals, the results showphonon softening and large asymmetrical broaden-ing. With decreasing nanocrystals size, broadeningincreases further due to #uctuation in e!ectivewave vector associated with size distribution. Theobserved Raman frequency and asymmetry wascalculated by considering phonon con"nement ina spherical nanocrystal. For small size, the lineshape is dominated by the resonant nanocrystalsthat favor incoming or outgoing resonance. Theelectronic state responsible for the resonant inter-action with nanocrystal has a large lifetimebroadening of the order of 25 meV. The weak res-onance enhancement seen under the resonant con-dition is indicative of band-to-band transitions inthe Raman process.

Acknowledgements

Authors acknowledge partial support from USARO grant No. DAAH04-96 and NASA grant No.NCCW-0088.

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