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Decay of nonequilibrium phonons in nanocrystalline silicon
Physica B 263—264 (1999) 473—475
Decay of nonequilibrium phonons in nanocrystalline silicon M. van der Voort *, G.D.J. Smit , A.V. Akimov , J.I. Dijkhuis , N.A. Feoktistov, A.A. Kaplyanskii, A.B. Pevtsov Department of Condensed Matter, Faculty of Physics and Astronomy, Debye Institute, Utrecht University, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands A.F. Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia
Abstract We present results of pulsed Raman experiments at 1.8 K on the lifetimes of phonons in silicon nanocrystals embedded in amorphous silicon (a-nc-Si : H). In the spectral region of the TO vibrations in the nanocrystallites, the observed dynamics is different both from that found in a-Si : H and c-Si. The TO-phonon decay appears to become slower with decreasing phonon frequency and crystallite size. That smaller nanoparticles have a slower anharmonic decay may be explained by the effect of phonon confinement. Furthermore, for TA-like vibrations in a-nc-Si : H we measured a much longer decay time (&50 ns) than for the same vibrations in a-Si : H. 1999 Elsevier Science B.V. All rights reserved. Keywords: Raman scattering; Nanocrystalline silicon; Phonon decay
Numerous studies have been carried out to investigate the effects of confinement on the properties of phonons in semiconductor nanoparticles [1]. By Raman scattering experiments, size-dependent shifts and broadening of the peaks of optical and acoustic phonons have been observed [2,3,8—11]. Yet little attention has been paid to the dynamical aspects of confined phonons. In this contribution we present results of experiments on optically created nonequilibrium THz-phonons in Si nanoparticles, studied with pulsed Raman spectroscopy. Phonon occupation numbers N(u) can be derived from Raman spectra by using the wellknown relation N(u)"I (u)/[I (u)!I (u)], 1 1 1 * Corresponding author. Fax: #31-30-2532403; e-mail: [email protected].
where I (u) and I (u) are the Stokes and anti1 1 Stokes intensities at Raman shift u, respectively. Such a technique was successfully used earlier to study the dynamics of phonons in a-Si [5,12]. Those experiments revealed that the lifetime of TO phonons in a-Si has a value of &70 ns (three orders of magnitude longer than in c-Si). In addition, a decrease of the phonon lifetime with decreasing u was observed, which is the opposite of the behavior encountered in crystals. The samples we used were thin (0.5 lm) a-Si : H films with and without crystalline nanoparticles (nc-Si), grown by PECVD, on sapphire substrates (for details see Ref. [4]). From a careful analysis of the Raman spectrum of the a-nc-Si : H sample, an average nanocrystallite size of 5 nm and a 25% volume fraction of nc-Si were estimated [4]. At 1.8 K, nonequilibrium phonons were generated
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 4 1 1 - 2
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M. van der Voort et al. / Physica B 263—264 (1999) 473—475
during the fast ((1 ps) relaxation of hot charge carriers. These were created by the 10-ns pulses of a frequency-doubled Nd : YAG laser with an average intensity at the sample of 0.5 W/cm, and a repetition rate of 30 Hz. Raman-scattered light of the same pulses was collected in a backscattering geometry, dispersed in a double monochromator (spectral slit-width &12 cm\), and detected by a photomultiplier tube followed by photon-counting electronics. To investigate the temporal evolution of the phonon populations on time scales larger than the duration of the laser pulses, a pump—probe configuration was used. For this purpose, a second (identical) Nd : YAG laser was synchronized with the first. Pulses of the second laser (probe) had been electronically delayed with respect to those of the first (pump). By measuring anti-Stokes intensities as a function of the delay, *t, between pump and probe, the dynamics of nonequilibrium phonons was examined in the range of 10 ns up to 15 ms. In part of the experiments the Raman detection scheme was by means of a triple grating monochromator equipped with a nitrogen-cooled CCD camera. In Fig. 1 we present the Stokes and anti-Stokes Raman spectra of the samples with and without nanocrystals (solid and dashed curves, respectively) as measured with the CCD. The broad lines typical for vibrations in a-Si : H can be distinguished. The
Fig. 1. Raman spectra of a-nc-Si : H (solid lines) and a-Si : H (dashed lines) as measured with the CCD (resolution &20 cm\).
Stokes TO peak of the a-nc-Si : H films is known to consist of a superposition of a broad amorphous TO peak (480 cm\) and a 15 cm\-wide line centered at 515 cm\ that corresponds to TO vibrations in nc-Si. The width of the latter line is partly due to the dispersion of the nc-Si nanocrystallite sizes. The smaller nanocrystals give a smaller TO Raman shift [2,8,9]. As the resolution of the spectrometer was not sufficient to resolve the amorphous and nanocrystallite peaks, only a shift of the total TO peak is apparent in Fig. 1. The Stokes and anti-Stokes TO peaks shown in Fig. 2 are obtained from the a-nc-Si : H film exploiting the higher resolution of the doublemonochromator detection setup. In this picture, the contributions of phonons in a-Si : H and nc-Si can be distinguished. Strikingly, the part of the anti-Stokes spectrum that corresponds to the TO phonons in the nanocrystals peaks at an approximately 10-cm\ lower energy than in the Stokes spectrum. This result leads us to the conclusion that the larger (95 nm) nanocrystals, which produce the larger (u9515cm\) Raman shifts, are less populated with phonons than small (&1 nm) nanocrystals, that give a smaller (u"505 cm\) Raman shift. We attribute this to an increase of the phonon lifetime with decreasing nanocrystallite size. To support this idea, we used the pump-probe setup to study the temporal evolution of the TO peak at selected frequencies u (indicated by the arrows in Fig. 2).
Fig. 2. Stokes and anti-Stokes TO peaks of the a-nc-Si : H film obtained with the double-monochromator detection setup.
M. van der Voort et al. / Physica B 263—264 (1999) 473—475
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50-ns decay at u&150 cm\, which is much longer than in a-Si : H without nc-Si at the same u [5,12]. This may be explained by the contribution of longliving Lamb modes [7] from the smallest nanocrystallites to the Raman spectrum in the TA region. In summary, we succeeded in studying dynamical aspects of phonons confined in silicon nanocrystals by pulsed Raman experiments. Further experimental and theoretical studies are required to come to a better understanding of the phenomena observed. Fig. 3. Time-dependent anti-Stokes intensity measured at three frequencies as a function of the delay *t.
In Fig. 3 the time-dependent anti-Stokes intensity measured at three frequencies is plotted as a function of the delay *t. It appears that the decay of phonons at the lowest frequency (495 cm\) is the slowest (q&50 ns). For higher frequencies (corresponding to larger nc-Si particles) the decay becomes faster, and at a frequency of 515 cm\, lifetimes are even shorter ((10 ns) than can be measured with the time resolution of our setup. From these results, we conclude that the smaller nanoparticles have slower anharmonic decay of TO vibrations. This slowing down of the anharmonic decay may be related to phonon confinement effects that become important as soon as the wavelength of THz phonons approaches the size of the nanocrystallites. Then, the phonon spectrum of a single nanocrystal exhibits gaps, i.e. becomes discrete, which leads to suppression of anharmonic break up [6]. We additionally note that we observed differences between the phonon decay in a-nc-Si : H and a-Si : H in the spectral region of TA phonons (u& 150 cm\) as well. In a-nc-Si : H we measured a
The authors gratefully acknowledge F.J.M. Wollenberg, P. Jurrius and C.R. de Kok for invaluable technical assistance. This work is financially supported by the Dutch “Stichting voor Fundamenteel Onderzoek der Materie” and the “Russian Foundation for Fundamental Research” (Grants 960216952 and 98-0217350).
References [1] J.P. Leburton, J. Pasqual, C. Sotomayor Torres (Eds.), Phonons in Semiconductor Nanostructures, vol. 236 of Nato Science Series E: Applied Sciences, Kluwer Academic Publishers, Dordrecht, 1993. [2] H. Richter, Z.P. Wang, L. Ley, Solid State Commun. 39 (1981) 625. [3] B. Champagnon, B. Andriasolo, E. Duval, J. Chem. Phys. 94 (1991) 5237. [4] V.G. Golubev et al., Phys. Solid State 39 (1997) 1197. [5] A.J. Scholten, A.V. Akimov, J.I. Dijkhuis, Phys. Rev. B 47 (1993) 13910. [6] R. Orbach, A. Jagannathan, J. Phys. Chem. 98 (1994) 7411. [7] S.P. Feofilov et al., J. Lumin. 66/67 (1996) 349. [8] Z. Iqbal, S. Vepr\ ek, J. Phys. C 15 (1982) 377. [9] I.H. Campbell, P.M. Fauchet, Solid State Commun. 58 (1986) 739. [10] A. Tanaka, S. Onari, T. Arai, Phys. Rev. B 47 (1993) 1237. [11] M. Fujii, Y. Kanzawa, Phys. Rev. B 54 (1996) R8373. [12] A.J. Scholten, A.V. Akimov, J.I. Dijkhuis, Phys. Rev. B 53 (1996) 3837.
Decay of nonequilibrium phonons in nanocrystalline silicon M. van der Voort *, G.D.J. Smit , A.V. Akimov , J.I. Dijkhuis , N.A. Feoktistov, A.A. Kaplyanskii, A.B. Pevtsov Department of Condensed Matter, Faculty of Physics and Astronomy, Debye Institute, Utrecht University, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands A.F. Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia
Abstract We present results of pulsed Raman experiments at 1.8 K on the lifetimes of phonons in silicon nanocrystals embedded in amorphous silicon (a-nc-Si : H). In the spectral region of the TO vibrations in the nanocrystallites, the observed dynamics is different both from that found in a-Si : H and c-Si. The TO-phonon decay appears to become slower with decreasing phonon frequency and crystallite size. That smaller nanoparticles have a slower anharmonic decay may be explained by the effect of phonon confinement. Furthermore, for TA-like vibrations in a-nc-Si : H we measured a much longer decay time (&50 ns) than for the same vibrations in a-Si : H. 1999 Elsevier Science B.V. All rights reserved. Keywords: Raman scattering; Nanocrystalline silicon; Phonon decay
Numerous studies have been carried out to investigate the effects of confinement on the properties of phonons in semiconductor nanoparticles [1]. By Raman scattering experiments, size-dependent shifts and broadening of the peaks of optical and acoustic phonons have been observed [2,3,8—11]. Yet little attention has been paid to the dynamical aspects of confined phonons. In this contribution we present results of experiments on optically created nonequilibrium THz-phonons in Si nanoparticles, studied with pulsed Raman spectroscopy. Phonon occupation numbers N(u) can be derived from Raman spectra by using the wellknown relation N(u)"I (u)/[I (u)!I (u)], 1 1 1 * Corresponding author. Fax: #31-30-2532403; e-mail: [email protected].
where I (u) and I (u) are the Stokes and anti1 1 Stokes intensities at Raman shift u, respectively. Such a technique was successfully used earlier to study the dynamics of phonons in a-Si [5,12]. Those experiments revealed that the lifetime of TO phonons in a-Si has a value of &70 ns (three orders of magnitude longer than in c-Si). In addition, a decrease of the phonon lifetime with decreasing u was observed, which is the opposite of the behavior encountered in crystals. The samples we used were thin (0.5 lm) a-Si : H films with and without crystalline nanoparticles (nc-Si), grown by PECVD, on sapphire substrates (for details see Ref. [4]). From a careful analysis of the Raman spectrum of the a-nc-Si : H sample, an average nanocrystallite size of 5 nm and a 25% volume fraction of nc-Si were estimated [4]. At 1.8 K, nonequilibrium phonons were generated
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 4 1 1 - 2
474
M. van der Voort et al. / Physica B 263—264 (1999) 473—475
during the fast ((1 ps) relaxation of hot charge carriers. These were created by the 10-ns pulses of a frequency-doubled Nd : YAG laser with an average intensity at the sample of 0.5 W/cm, and a repetition rate of 30 Hz. Raman-scattered light of the same pulses was collected in a backscattering geometry, dispersed in a double monochromator (spectral slit-width &12 cm\), and detected by a photomultiplier tube followed by photon-counting electronics. To investigate the temporal evolution of the phonon populations on time scales larger than the duration of the laser pulses, a pump—probe configuration was used. For this purpose, a second (identical) Nd : YAG laser was synchronized with the first. Pulses of the second laser (probe) had been electronically delayed with respect to those of the first (pump). By measuring anti-Stokes intensities as a function of the delay, *t, between pump and probe, the dynamics of nonequilibrium phonons was examined in the range of 10 ns up to 15 ms. In part of the experiments the Raman detection scheme was by means of a triple grating monochromator equipped with a nitrogen-cooled CCD camera. In Fig. 1 we present the Stokes and anti-Stokes Raman spectra of the samples with and without nanocrystals (solid and dashed curves, respectively) as measured with the CCD. The broad lines typical for vibrations in a-Si : H can be distinguished. The
Fig. 1. Raman spectra of a-nc-Si : H (solid lines) and a-Si : H (dashed lines) as measured with the CCD (resolution &20 cm\).
Stokes TO peak of the a-nc-Si : H films is known to consist of a superposition of a broad amorphous TO peak (480 cm\) and a 15 cm\-wide line centered at 515 cm\ that corresponds to TO vibrations in nc-Si. The width of the latter line is partly due to the dispersion of the nc-Si nanocrystallite sizes. The smaller nanocrystals give a smaller TO Raman shift [2,8,9]. As the resolution of the spectrometer was not sufficient to resolve the amorphous and nanocrystallite peaks, only a shift of the total TO peak is apparent in Fig. 1. The Stokes and anti-Stokes TO peaks shown in Fig. 2 are obtained from the a-nc-Si : H film exploiting the higher resolution of the doublemonochromator detection setup. In this picture, the contributions of phonons in a-Si : H and nc-Si can be distinguished. Strikingly, the part of the anti-Stokes spectrum that corresponds to the TO phonons in the nanocrystals peaks at an approximately 10-cm\ lower energy than in the Stokes spectrum. This result leads us to the conclusion that the larger (95 nm) nanocrystals, which produce the larger (u9515cm\) Raman shifts, are less populated with phonons than small (&1 nm) nanocrystals, that give a smaller (u"505 cm\) Raman shift. We attribute this to an increase of the phonon lifetime with decreasing nanocrystallite size. To support this idea, we used the pump-probe setup to study the temporal evolution of the TO peak at selected frequencies u (indicated by the arrows in Fig. 2).
Fig. 2. Stokes and anti-Stokes TO peaks of the a-nc-Si : H film obtained with the double-monochromator detection setup.
M. van der Voort et al. / Physica B 263—264 (1999) 473—475
475
50-ns decay at u&150 cm\, which is much longer than in a-Si : H without nc-Si at the same u [5,12]. This may be explained by the contribution of longliving Lamb modes [7] from the smallest nanocrystallites to the Raman spectrum in the TA region. In summary, we succeeded in studying dynamical aspects of phonons confined in silicon nanocrystals by pulsed Raman experiments. Further experimental and theoretical studies are required to come to a better understanding of the phenomena observed. Fig. 3. Time-dependent anti-Stokes intensity measured at three frequencies as a function of the delay *t.
In Fig. 3 the time-dependent anti-Stokes intensity measured at three frequencies is plotted as a function of the delay *t. It appears that the decay of phonons at the lowest frequency (495 cm\) is the slowest (q&50 ns). For higher frequencies (corresponding to larger nc-Si particles) the decay becomes faster, and at a frequency of 515 cm\, lifetimes are even shorter ((10 ns) than can be measured with the time resolution of our setup. From these results, we conclude that the smaller nanoparticles have slower anharmonic decay of TO vibrations. This slowing down of the anharmonic decay may be related to phonon confinement effects that become important as soon as the wavelength of THz phonons approaches the size of the nanocrystallites. Then, the phonon spectrum of a single nanocrystal exhibits gaps, i.e. becomes discrete, which leads to suppression of anharmonic break up [6]. We additionally note that we observed differences between the phonon decay in a-nc-Si : H and a-Si : H in the spectral region of TA phonons (u& 150 cm\) as well. In a-nc-Si : H we measured a
The authors gratefully acknowledge F.J.M. Wollenberg, P. Jurrius and C.R. de Kok for invaluable technical assistance. This work is financially supported by the Dutch “Stichting voor Fundamenteel Onderzoek der Materie” and the “Russian Foundation for Fundamental Research” (Grants 960216952 and 98-0217350).
References [1] J.P. Leburton, J. Pasqual, C. Sotomayor Torres (Eds.), Phonons in Semiconductor Nanostructures, vol. 236 of Nato Science Series E: Applied Sciences, Kluwer Academic Publishers, Dordrecht, 1993. [2] H. Richter, Z.P. Wang, L. Ley, Solid State Commun. 39 (1981) 625. [3] B. Champagnon, B. Andriasolo, E. Duval, J. Chem. Phys. 94 (1991) 5237. [4] V.G. Golubev et al., Phys. Solid State 39 (1997) 1197. [5] A.J. Scholten, A.V. Akimov, J.I. Dijkhuis, Phys. Rev. B 47 (1993) 13910. [6] R. Orbach, A. Jagannathan, J. Phys. Chem. 98 (1994) 7411. [7] S.P. Feofilov et al., J. Lumin. 66/67 (1996) 349. [8] Z. Iqbal, S. Vepr\ ek, J. Phys. C 15 (1982) 377. [9] I.H. Campbell, P.M. Fauchet, Solid State Commun. 58 (1986) 739. [10] A. Tanaka, S. Onari, T. Arai, Phys. Rev. B 47 (1993) 1237. [11] M. Fujii, Y. Kanzawa, Phys. Rev. B 54 (1996) R8373. [12] A.J. Scholten, A.V. Akimov, J.I. Dijkhuis, Phys. Rev. B 53 (1996) 3837.