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Quantum confinement and Anderson localization of carriers in semiconductor nanoparticles: toward design of molecular electronics materials
Thin Solid Films 393 Ž2001. 103᎐108
Quantum confinement and Anderson localization of carriers in semiconductor nanoparticles: toward design of molecular electronics materials Yoshihiko KanemitsuU , Yunosuke Fukunishi Graduate School of Materials Science, Nara Institute of Science and Technology, Ikoma, Nara 630-0101, Japan
Abstract We have studied the photoluminescence ŽPL. process in amorphous silicon Ža-Si. and crystalline silicon Žc-Si. nanoparticles in order to understand the quantum confinement and localization of electron wave functions in nanometer and molecular scale materials. The a-Si and c-Si nanoparticles were prepared by electrochemical etching of hydrogenated a-Si films and c-Si wafers. The PL spectra of a-Si and c-Si nanoparticles are blueshifted from those of bulk a-Si and c-Si. The global PL spectrum of a-Si nanoparticles is similar to that of c-Si nanoparticles. However, the characteristics of resonantly excited PL spectra and PL decay dynamics of a-Si nanoparticles are different from those of c-Si nanoparticles. Luminescence properties of a-Si and c-Si nanoparticles are discussed in terms of the quantum confinement and the Anderson localization of electron wave functions in nanoscale materials. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Nanoparticles; Molecular electronics; Quantum confinement; Anderson localization
1. Introduction Recently, considerable interest has been focused on optical and electronic properties of semiconductor nanoparticles, because they exhibit a wealth of quantum phenomena and their size-dependent optical and electrical properties open a field of applications including fluorescent biological labels, single-electron transistors, and so on w1,2x. Since electrons and excitons are strongly confined in a small volume, nanoparticles behave as molecules: nanoparticles have a discrete energy spectrum and their electronic properties are sensitive to the size of nanocrystals and the physical properties of surrounding materials. It is expected that semiconductor nanoparticles are one of the most promising U
Corresponding author. Tel.: q81-743-72-6011; fax: q81-743-726011. E-mail address: [email protected] ŽY. Kanemitsu..
materials for nanoscale and molecular electronics devices w3,4x. In nanoscale and molecular-scale materials, the coherence of electron wave functions is an essential factor for the control of the optical and electronic properties. If the wave functions of electrons and excitons are delocalized over nanoparticles or molecules, the optical and electronic properties are very sensitive to the size of nanoparticles and molecules. The quantum confinement effects determine the size-dependent electronic properties. However, the structural disorder causes the Anderson localization of electrons and excitons. If the electron wave functions are strongly localized in a small volume within nanoparticles, the optical and electronic properties are not sensitive to the size of nanoparticles. The local structure determines the optical and electronic properties of nanoparticles. Therefore, the understanding of quantum confinement and Anderson localization of electrons are very important
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for the design and development of nanoscale materials and devices. An elemental semiconductor, silicon, is a good material for the fabrication of very small structures, because there is no composition fluctuation in the nanoparticle interior w5x. In addition, we can prepare crystalline Si Žc-Si. and amorphous Si Ža-Si. nanoparticles using electrochemical etching techniques. c-Si nanoparticles fabricated by electrochemical etching of c-Si wafers, so called porous c-Si, show efficient light emission in the visible spectral region at room temperature. The typical size of c-Si nanoparticles in porous c-Si samples is in the range of 2᎐5 nm w5᎐7x. Porous a-Si also shows visible luminescence at room temperature w8᎐12x. The typical size of a-Si nanoparticles in the porous layer is in the range 3᎐5 nm w12x. The typical size of nanoparticles in the porous a-Si layer is very similar to that in the porous c-Si layer. These c-Si and a-Si nanoparticles gives a new opportunity for the study of the quantum confinement and localization of carriers in nanoscale materials. In this work, we have studied photoluminescence ŽPL. properties of a-Si and c-Si nanoparticle samples and discuss the quantum confinement and the Anderson localization of carriers in nanoparticles. 2. Experiment The a-Si and c-Si nanoparticle samples were fabricated by electrochemical etching of a-Si films and c-Si wafers. The details of sample preparation and characterization were shown in Wehrsphon et al. w10,11x for a-Si and in Kanemitsu and Okamoto w13x for c-Si. The a-Si nanoparticles samples were fabricated at EcolePolytechnique. The 1% B-doped a-Si:H films were deposited on optically polished stainless steel by rf-plasma decomposition of silane, diborate and hydrogen gases in a capacitively coupled reactor at 13.56 MHz. The electrochemical anodization of 1% B-doped a-Si:H films was carried out in HF-ethanol solution ŽHFrH 2 OrC 2 H 5 OH s 1:1:2. at a constant current density of 10 mArcm2 . For comparison, c-Si nanoparticle samples were prepared from c-Si wafers Žp-type, 3᎐5 ⍀ cm. under the same anodization conditions. Surface morphology of a-Si nanoparticle samples was studied using an atomic force microscopy ŽAFM. system ŽTopometrix, TMX-2100.. The average height change on the surface is approximately 5 nm and a homogeneous porous layer is formed on the a-Si film. Since the device-grade a-Si films were used as starting materials, luminescence of these samples is spatially homogeneous, compared with the previous samples w11x. It is considered that the spatially homogeneous and stable PL from a-Si nanoparticle samples is related to the homogenous surface morphology of the samples. For global PL measurements in the visible and nearinfrared spectral region, the PL signals under 325-nm
or 488-nm laser excitation were dispersed by a 27-cm monochromator and detected by a cooled Ge diode detector or a cooled CCD detector. For resonantly excited PL and visible PL measurements, a wavelength-tunable Ti:Al 2 O 3 laser was used, and the PL spectra were measured by a 50-cm double-grating monochromator and detected by a photomultiplier. Time-resolved PL spectra were measured using a streak camera and a single photon counting technique under frequency-doubled picosecond Ti:A 2 O 3 laser excitation. The spectral sensitivity of the measuring systems was calibrated using a tungsten standard lamp. The samples were mounted on the cold finger of a temperature-variable closed-cycle He gas cryostat during the measurements. 3. Results and discussion Fig. 1 shows global PL spectra of Ža. undoped a-Si:H, Žb. a-Si nanoparticles, Žc. bulk c-Si and Žd. c-Si nanoparticles in the visible and near-infrared spectral region under non-resonant excitation at 13 K. Undoped a-Si:H samples show a broad PL near 1.35 eV. This broad PL is due to the transition between conduction and valence band-tail states w14x. However, in our 1% B-doped a-Si:H films Žstarting materials., PL bands are not observed in the 350᎐1700-nm spectral region. By forming nanoparticles from heavily doped a-Si:H films, the a-Si nanoparticle samples show visible luminescence near 1.6 eV. The PL peak energy in the a-Si nanoparticle sample Ž; 1.6 eV. is blueshifted from that of bulk a-Si:H Ž; 1.35 eV.. In addition, the 0.8᎐0.9-eV PL related to defects in B-doped Si:H is not observed in our nanoparticle samples. The observed PL spectrum of the a-Si nanoparticle sample is similar to that of the c-Si nanoparticle sample. It is known that the luminescence efficiency of bulk
Fig. 1. Visible and near-infrared luminescence spectra of: Ža. undoped a-Si film, Žb. a-Si nanoparticles, Žc. bulk c-Si and Žd. c-Si nanoparticles at 13 K.
Y. Kanemitsu, Y. Fukunishi r Thin Solid Films 393 (2001) 103᎐108
a-Si:H depends on doping amount of acceptors or donors. Radiative recombination occurs at localized states near the band edge Žthe band-tail state. and non-radiative recombination occurs at midgap states. Heavily doped a-Si:H is a poor luminescent material even at low temperatures, because midgap states due to defects are formed by doping. However, our experiments show that a-Si nanoparticles fabricated from heavily doped a-Si films clearly show luminescence. By fabricating nanostructures, the midgap states acting as non-radiative recombination centers would decrease. This is related to the formation of porous layer. The electrochemical etching of Si skeleton occurs preferentially at defects w15x, and it is considered that a-Si nanoparticles in the porous layer Žrest material. behave as undoped a-Si:H, a good luminescent material. In fact, the 0.8᎐0.9-eV PL related to defects is not experimentally observed in a-Si nanoparticles, as shown in Fig. 1. Visible luminescence is clearly observed in a-Si nanoparticles, as a consequence of the reduction of the defect luminescence and the non-radiative recombination of carriers. The a-Si and c-Si nanoparticle samples show broad PL in the visible spectral region and their PL spectra are similar to each other. In order to clarify the origin of the broad PL spectrum, we applied resonant excitation spectroscopy to the a-Si and c-Si samples, because resonant excitation at energies within the PL band results in fine structures. Fig. 2 shows PL spectra of a-Si and c-Si nanoparticle samples at 8 K under resonant excitation at energies within the red PL band, where the zero on the abscissa scale corresponds to the excitation energy. The fine structures in the PL spectrum are observed in both a-Si and c-Si samples under resonant excitation. In the c-Si nanoparticle sample wcurve Žd. in Fig. 2x, the step-like structures appear in the spectrum. The TO Ž ⌬ . and TA Ž ⌬ . phonon energies of bulk c-Si are shown by the arrows in the figure, where TO Ž ⌬ . and TA Ž ⌬ . are the transverse optical phonon and the transverse acoustic phonon at the conduction-bandminimum ⌬ point in bulk c-Si w16᎐19x. PL fine structures in c-Si nanoparticles can be explained by the momentum-conserving phonon-assisted luminescence processes. In addition, the spectral shape of the resonantly excited PL of the c-Si sample depends on the excitation laser energy w18x. The broad PL spectrum is due to the size and shape distribution of c-Si nanoparticles in the sample w18x. Even in the a-Si nanoparticle samples, fine structures are observed under resonant laser excitation. The observed peak energy in the a-Si nanoparticle sample wcurves Ža᎐c. in Fig. 2x is equal to the TO phonon energy in bulk a-Si:H. The observed phonon-related structures in a-Si nanoparticles are very similar to the Raman spectrum in the vicinity of the TO phonon
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Fig. 2. Resonantly excited luminescence spectra of Ža᎐c. a-Si nanoparticles and Žd. c-Si nanoparticles at the low-energy side of the excitation energies at 8 K: Ža. 1.592, Žb. 1.662, Žc. 1.711 and Žd. 1.543 eV. The zero on the abscissa scale corresponds to the excitation laser energy. The TO Ž ⌬ . and TA Ž ⌬ . phonon energies correspond to the transverse optical phonon and the transverse acoustic phonon at the conduction-band-minimum ⌬ point in bulk c-Si, respectively.
modes near 480 cmy1 in a-Si:H films w20,21x. In addition, the spectral shape of the phonon-related structures in a-Si nanoparticles does not depend on the excitation laser energy wsee, curves Ža᎐c. in Fig. 2x. Therefore, it is considered that these phonon-related signals are due to the Raman process, rather than the luminescence process. Moreover, the intensity of the resonantly excited PL in a-Si nanoparticles is much weaker that that in c-Si nanoparticles. The weak intensity of the resonantly excited PL suggests that visible PL comes from localized states rather than the extended state with a large density of states. The characteristics of resonantly excited PL in a-Si nanoparticles are completely different from those of c-Si nanoparticles: The exciton recombination mechanism in a-Si nanoparticles is different from that in c-Si nanoparticles. Fig. 3 shows the temperature dependence of the PL intensity in a-Si and c-Si nanoparticles and bulk a-Si and c-Si under cw laser excitation. Bulk c-Si is an indirect gap semiconductor and its PL intensity abruptly decreases with an increase of temperature. In bulk undoped a-Si, there exit non-radiative recombination centers related to structural disorder and dangling bonds. At high temperatures, carriers trapped in the band-tail state are thermally excited to the extended state. The mobile carries in the extended state are captured at the non-radiative recombination centers. In a-Si, the thermal quenching of the PL intensity is determined by the thermally activated process of carriers from the band-tail state to the extended state
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Y. Kanemitsu, Y. Fukunishi r Thin Solid Films 393 (2001) 103᎐108
Fig. 3. Temperature dependence of the total PL intensity of a-Si nanoparticles Ž䢇., bulk a-Si Ž'., c-Si nanoparticles Ž`. and bulk c-Si Ž^..
w14,22x. Then, the PL intensity of a-Si films abruptly decreases with an increase of temperature. Therefore, both bulk c-Si and bulk a-Si do not show luminescence at room temperature. However, in c-Si and a-Si nanoparticle samples, visible PL is observed even at room temperature and the PL intensities in both a-Si and c-Si nanoparticle samples are insensitive to the measurement temperature, compared with the cases of bulk a-Si and bulk c-Si. This implies that the non-radiative recombination of carriers is drastically reduced by the confinement of carriers in a small volume, similar to the case of a-Si based quantum wells w23,24x. The size reduction to a few nanometers cause the blueshift of the PL spectrum and the reduction of the thermal quenching of the PL intensity in a-Si and c-Si materials. In order to discuss the luminescence mechanism in nanoparticles, we study PL dynamics of the fast-decay component of the a-Si and c-Si nanoparticle samples in the nanosecond time region. The study of decay dynamics of luminescence provides direct information on the radiative and non-radiative recombination processes in nanoparticles w25,26x. The PL decay profile consists of two components, the fast-decay and slow-decay components in both a-Si and c-Si nanoparticles w25᎐28x. The PL decay dynamics at the initial stage strongly reflect the difference in the carrier relaxation processes between a-Si and c-Si nanoparticle samples w27x. Fig. 4 shows PL decay profiles of the a-Si nanoparticle sample at different emission energies wŽa. 1.91, Žb. 1.80, Žc. 1.65, and Žd. 1.55 eVx under 3.10-eV and 1.1-ps laser excitation at 10 K. The PL decay curves show
Fig. 4. PL decay profiles of the a-Si nanoparticle sample at different emission energies: Ža. 1.91, Žb. 1.80, Žc. 1.65 and Žd. 1.55 eV. The decay dynamics was measured under 3.10-eV and 1.1-ps laser excitation at 10 K. The PL decay curves in the fast component are fitted by two exponential functions Žsolid lines..
non-exponential even in the nanosecond time region. The PL decay profiles of the fast component, I F Ž t ., are approximately fitted by two exponential components Žsolid curves in Fig. 4.. In the fast-decay component of the a-Si and c-Si samples, the decay profile, I F Ž t ., has essentially the same non-exponential shape at different emission energies. Therefore, in order to compare the PL decay dynamics between the a-Si and c-Si samples, the mean PL lifetime of the fast-decay component, PL , is defined by, PL s
1 IF Ž0.
HI
F
Ž t . dt
where I F Ž0. is the initial PL intensity of the fast component just after pulsed laser excitation. The mean PL decay rate y1 PL at 10 K is summarized as a function of the emission phonon energy in Fig. 5. In both a-Si and
Fig. 5. PL decay rate y1 PL of a-Si and c-Si nanoparticles as a function of the emission photon energy at 10 K.
Y. Kanemitsu, Y. Fukunishi r Thin Solid Films 393 (2001) 103᎐108
c-Si nanoparticle samples, the PL decay rate depends on the emission photon energy at low temperatures. In c-Si nanoparticles, the wave functions of electrons and holes are delocalized over the 3᎐5-nm nanoparticles, because in bulk c-Si the Bohr radius of free excitons is approximately 4.3 nm w4x. It is considered that the exciton recombination rate in c-Si nanoparticles is sensitive to the nanoparticle size. In c-Si nanoparticles, the spectral shape of the resonantly excited PL depends on the excitation laser energy, as mentioned above. Since the bulk c-Si shows a narrow PL spectrum Žsee Fig. 1., a single c-Si nanoparticle will show a narrow PL spectrum. Then, it is concluded that the broad PL spectrum is mainly due to the size fluctuation of nanoparticles in the sample. Since there is a correlation between the emission photon energy and the nanoparticle size w7x, the observed energy-dependence of the PL lifetime mainly reflects the size dependence of the PL lifetime. However, in a-Si, the localization length of carriers is estimated to be 1 nm or less w29᎐31x. This is smaller than the size of a-Si nanoparticles Ž; 3᎐5 nm. w10᎐12x. It is believed that the electron wavefunction is strongly localized within nanoparticles and the PL lifetime is not sensitive to the size of a-Si nanoparticles. Moreover, bulk a-Si shows a broad PL spectrum even at low temperatures, as shown in Fig. 1. It is considered that the broad PL spectrum of a-Si nanoparticles is due to the radiative recombination in the band-tail state of nanoparticles, rather than the size fluctuation of a-Si nanoparticles w27x. The single a-Si nanoparticle will show a broad PL spectrum, because broad luminescence in a-Si is due to the radiative transitions in the band-tail state. In addition, in the band-tail emission, the PL lifetime becomes longer with a decrease of the emission photon energy, because the average distance of electrons and holes for the radiative tunneling becomes longer at deeper localized state. In a-Si nanoparticles, visible PL is attributed to the radiative recombination of carriers localized in the band-tail state. In a-Si based materials, one usually considers the mostly delocalized state Žthe extended state. and the weakly localized state Žthe band-tail state. in the light absorption and emission processes. With a decrease of the nanoparticle size, the extended state shifts to higher energy, but the deep localized state Žthe strongly localized state. does not change. Therefore, it is expected that in a-Si nanoparticle the quantum confinement of carriers causes the spreading of the band tail. In fact, the PL bandwidth of a-Si nanoparticles is larger than that of bulk a-Si, as shown in Fig. 1. The spreading of the band tail reduces the thermal emission rate of carriers localized in the band-tail state and then sup-
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presses the thermal quenching of the PL intensity in a-Si nanoparticles, as shown in Fig. 3. Moreover, in a-Si nanoparticles, the PL lifetime is very short even at low temperatures, compared with the case of bulk a-Si w32x. At low temperatures, the dominant recombination is radiative tunneling in a-Si based materials w14x. In a-Si nanoparticles, the average tunneling distance for radiative recombination decreases and then the average PL lifetime becomes shorter. The radiative recombination rate is enhanced in a-Si nanoparticles, because the electrons and holes are confined in a small volume. The short lifetime of carriers reduces the energy relaxation of carriers into lowerenergy states and then increases the average energy of carriers for radiative recombination in the band-tail state. Because of the short lifetime of carriers confined in a small volume and the spreading of the band tail, we can observe the blueshift of the PL peak energy in a-Si nanoparticles. The formation of nanoparticles causes the strong modification of luminescence properties of both a-Si and c-Si materials. The blueshift of the PL spectrum and the remarkable reduction of the thermal quenching of the PL intensity are observed in both a-Si and c-Si nanoparticles. However, the PL mechanism is different from each other. In c-Si nanoparticles, quantum confinement effects play an essential role in the modification of band structures and optical responses. In a-Si nanoparticles, the Anderson localization determines the carrier dynamics and the luminescence is due to the radiative recombination in the band-tail states. The non-radiative recombination centers exist in a-Si nanoparticles due to the structural disorder. It is believed that the crystalline nanoparticle is a better luminescence material and the crystallinity of the interior state of nanoparticles is very important even in nanoscale and molecular scale materials. 4. Conclusion We have studied luminescence properties of a-Si and c-Si nanoparticles by means of resonantly excited PL spectra and time-resolved PL decay dynamics measurements. The formation of nanoparticles cause the blueshift of the PL spectrum and the remarkable reduction of the thermal quenching of the PL intensity in both a-Si and c-Si materials. In a-Si nanoparticles the electron wave functions do not extend over nanoparticles, but luminescence properties of nanoparticles are completely different from those of bulk a-Si. Luminescence properties of amorphous materials can be modified by changing the size of nanostructures. It is demonstrated that optical responses of nanoparticles are modified by the spatial confinement of carriers in
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amorphous materials and the quantum confinement of carriers in crystalline materials. Acknowledgements The authors would like to thank Dr J.-N. Chazalviel, Dr R.B. Wehrspohn and Dr M. Gros-Jean of CNRS´ cole-Polytechnique for providing porous a-Si samples, E Professor T. Kushida for discussion and M. Kobayashi of NAIST for technical assistance with AFM. This work was partly supported by a Grant-In-Aid for Scientific Research ŽB. from The Japan Society for the Promotion of Science Ž噛 11440095., The Yamada Science Foundation, The Kawasaki Steel 21st Century Foundation, The Kansai Research Foundation for Technology Promotion and The Yazaki Memorial Foundation for Science and Technology. References w1x L.E. Brus, A. Efros, T. Itoh ŽEds.., Spectroscopy of Isolated and Assembled Semiconductor Nanocrystals, J. Lumin 76 Ž1996.. w2x J.R. Heath ŽEd.., Nanoscale Materials, Acc. Chem. Res, 32Ž5. Ž1999. Special Issue. w3x T. Ogawa, Y. Kanemitsu ŽEds.., Optical Properties of Low-Dimensional Materials, World Scientific, Singapore, 1995. w4x Y. Kanemitsu, in: D.J. Lockwood ŽEd.., Light Emission in Silicon, Semiconductors and Semimetals, 49, Academic Press, New York, 1998, p. 157. w5x Y. Kanemitsu, Phys. Rep. 263 Ž1995. 1 and references therein. w6x A. Cullis, L.T. Canham, L. Calcott, J. Appl. Phys. 82 Ž1997. 909 and references therein. w7x Y. Kanemitsu, S. Okamoto, Mater. Sci. Eng. B 48 Ž1997. 108. w8x E. Bustarret, M. Ligeon, L. Ortega, Solid State Commun. 83 Ž1992. 461. w9x E. Bustarret, E. Sauvaian, M. Ligeon, M. Rosenbauer, Thin Solid Films 276 Ž1996. 134.
w10x R.B. Wehrspohn, J.-N. Chazalviel, F. Ozanam, I. Solomon, Phys. Rev. Lett. 77 Ž1996. 1885. w11x R.B. Wehrspohn, J.-N. Chazalviel, F. Ozanam, I. Solomon, European Phys. J. B 8 Ž1999. 179. w12x E. Bustarret, E. Sauvaian, M. Ligeon, Phil. Mag. Lett. 75 Ž1997. 35. w13x Y. Kanemitsu, S. Okamoto, Phys. Rev. B 56 Ž1997. R1696. w14x R.A. Street, Hydrogenated Amorphous Silicon, Cambridge University Press, Cambridge, 1991. w15x P. Schmuki, L.E. Erickson, D.J. Lockwood, Phys. Rev. Lett. 80 Ž1998. 4060. w16x P.D.J. Calcott, K.J. Nash, L.T. Canham, M.J. Kane, D. Brumhead, J. Phys. Condens. Matter 5 Ž1993. L91. w17x P.D.J. Calcott, K.J. Nash, L.T. Canham, M.J. Kane, D. Brumhead, J. Lumin. 57 Ž1994. 271. w18x Y. Kanemitsu, S. Okamoto, Phys. Rev. B 58 Ž1998. 9652. w19x D. Kovalev, H. Heckler, M. Ben-Chorin, G. Polisski, M. Schwartzkopff, F. Koch, Phys. Rev. Lett. 81 Ž1998. 2803. w20x M.H. Brodsky, in: M. Cardona ŽEd.., Light Scattering in Solids, Springer, Berlin, 1975, p. 208. w21x J.E. Smith Jr., M.H. Brodsky, B.L. Crowder, M.I. Nathan, A. Pinczuk, Phys. Rev. Lett. 26 Ž1971. 642. w22x R.W. Collins, M.A. Paesler, W. Paul, Solid State Commun. 34 Ž1980. 833. w23x Y. Kanemitsu, M. Iiboshi, T. Kushida, Appl. Phys. Lett. 76 Ž2000. 2200. w24x Y. Kanemitsu, T. Kushida, Appl. Phys. Lett. 77 Ž2000. 3550. w25x T. Matsumoto, T. Futagi, H. Mimura, Y. Kanemitsu, Phys. Rev. B 47 Ž1993. 13876. w26x Y. Kanemitsu, Phys. Rev. B 48 Ž1993. 12357. w27x Y. Kanemitsu, Y. Fukunishi, T. Kushida, Appl. Phys. Lett. 77 Ž2000. 211. w28x E. Bustrarret, I. Mihalcescu, M. Ligeon, R. Romestain, J.C. Vial, F. Madeore, J. Lumin. 57 Ž1993. 105. w29x M.E. Raikh, S.D. Baranovskii, B.I. Shklovskii, Phys. Rev. B. 41 Ž1990. 7701. w30x H.V. Nguyen, Y. Lu, S. Kim, M. Wakagi, R.W. Collins, Phys. Rev. Lett. 74 Ž1995. 3880. w31x M.J. Estes, G. Moddel, Phys. Rev. B 54 Ž1996. 14633. w32x S. Ambros, R. Carius, H. Wagner, J. Non-Cryst. Solids 137r138 Ž1991. 555.
Quantum confinement and Anderson localization of carriers in semiconductor nanoparticles: toward design of molecular electronics materials Yoshihiko KanemitsuU , Yunosuke Fukunishi Graduate School of Materials Science, Nara Institute of Science and Technology, Ikoma, Nara 630-0101, Japan
Abstract We have studied the photoluminescence ŽPL. process in amorphous silicon Ža-Si. and crystalline silicon Žc-Si. nanoparticles in order to understand the quantum confinement and localization of electron wave functions in nanometer and molecular scale materials. The a-Si and c-Si nanoparticles were prepared by electrochemical etching of hydrogenated a-Si films and c-Si wafers. The PL spectra of a-Si and c-Si nanoparticles are blueshifted from those of bulk a-Si and c-Si. The global PL spectrum of a-Si nanoparticles is similar to that of c-Si nanoparticles. However, the characteristics of resonantly excited PL spectra and PL decay dynamics of a-Si nanoparticles are different from those of c-Si nanoparticles. Luminescence properties of a-Si and c-Si nanoparticles are discussed in terms of the quantum confinement and the Anderson localization of electron wave functions in nanoscale materials. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Nanoparticles; Molecular electronics; Quantum confinement; Anderson localization
1. Introduction Recently, considerable interest has been focused on optical and electronic properties of semiconductor nanoparticles, because they exhibit a wealth of quantum phenomena and their size-dependent optical and electrical properties open a field of applications including fluorescent biological labels, single-electron transistors, and so on w1,2x. Since electrons and excitons are strongly confined in a small volume, nanoparticles behave as molecules: nanoparticles have a discrete energy spectrum and their electronic properties are sensitive to the size of nanocrystals and the physical properties of surrounding materials. It is expected that semiconductor nanoparticles are one of the most promising U
Corresponding author. Tel.: q81-743-72-6011; fax: q81-743-726011. E-mail address: [email protected] ŽY. Kanemitsu..
materials for nanoscale and molecular electronics devices w3,4x. In nanoscale and molecular-scale materials, the coherence of electron wave functions is an essential factor for the control of the optical and electronic properties. If the wave functions of electrons and excitons are delocalized over nanoparticles or molecules, the optical and electronic properties are very sensitive to the size of nanoparticles and molecules. The quantum confinement effects determine the size-dependent electronic properties. However, the structural disorder causes the Anderson localization of electrons and excitons. If the electron wave functions are strongly localized in a small volume within nanoparticles, the optical and electronic properties are not sensitive to the size of nanoparticles. The local structure determines the optical and electronic properties of nanoparticles. Therefore, the understanding of quantum confinement and Anderson localization of electrons are very important
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 1 1 1 1 - 7
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for the design and development of nanoscale materials and devices. An elemental semiconductor, silicon, is a good material for the fabrication of very small structures, because there is no composition fluctuation in the nanoparticle interior w5x. In addition, we can prepare crystalline Si Žc-Si. and amorphous Si Ža-Si. nanoparticles using electrochemical etching techniques. c-Si nanoparticles fabricated by electrochemical etching of c-Si wafers, so called porous c-Si, show efficient light emission in the visible spectral region at room temperature. The typical size of c-Si nanoparticles in porous c-Si samples is in the range of 2᎐5 nm w5᎐7x. Porous a-Si also shows visible luminescence at room temperature w8᎐12x. The typical size of a-Si nanoparticles in the porous layer is in the range 3᎐5 nm w12x. The typical size of nanoparticles in the porous a-Si layer is very similar to that in the porous c-Si layer. These c-Si and a-Si nanoparticles gives a new opportunity for the study of the quantum confinement and localization of carriers in nanoscale materials. In this work, we have studied photoluminescence ŽPL. properties of a-Si and c-Si nanoparticle samples and discuss the quantum confinement and the Anderson localization of carriers in nanoparticles. 2. Experiment The a-Si and c-Si nanoparticle samples were fabricated by electrochemical etching of a-Si films and c-Si wafers. The details of sample preparation and characterization were shown in Wehrsphon et al. w10,11x for a-Si and in Kanemitsu and Okamoto w13x for c-Si. The a-Si nanoparticles samples were fabricated at EcolePolytechnique. The 1% B-doped a-Si:H films were deposited on optically polished stainless steel by rf-plasma decomposition of silane, diborate and hydrogen gases in a capacitively coupled reactor at 13.56 MHz. The electrochemical anodization of 1% B-doped a-Si:H films was carried out in HF-ethanol solution ŽHFrH 2 OrC 2 H 5 OH s 1:1:2. at a constant current density of 10 mArcm2 . For comparison, c-Si nanoparticle samples were prepared from c-Si wafers Žp-type, 3᎐5 ⍀ cm. under the same anodization conditions. Surface morphology of a-Si nanoparticle samples was studied using an atomic force microscopy ŽAFM. system ŽTopometrix, TMX-2100.. The average height change on the surface is approximately 5 nm and a homogeneous porous layer is formed on the a-Si film. Since the device-grade a-Si films were used as starting materials, luminescence of these samples is spatially homogeneous, compared with the previous samples w11x. It is considered that the spatially homogeneous and stable PL from a-Si nanoparticle samples is related to the homogenous surface morphology of the samples. For global PL measurements in the visible and nearinfrared spectral region, the PL signals under 325-nm
or 488-nm laser excitation were dispersed by a 27-cm monochromator and detected by a cooled Ge diode detector or a cooled CCD detector. For resonantly excited PL and visible PL measurements, a wavelength-tunable Ti:Al 2 O 3 laser was used, and the PL spectra were measured by a 50-cm double-grating monochromator and detected by a photomultiplier. Time-resolved PL spectra were measured using a streak camera and a single photon counting technique under frequency-doubled picosecond Ti:A 2 O 3 laser excitation. The spectral sensitivity of the measuring systems was calibrated using a tungsten standard lamp. The samples were mounted on the cold finger of a temperature-variable closed-cycle He gas cryostat during the measurements. 3. Results and discussion Fig. 1 shows global PL spectra of Ža. undoped a-Si:H, Žb. a-Si nanoparticles, Žc. bulk c-Si and Žd. c-Si nanoparticles in the visible and near-infrared spectral region under non-resonant excitation at 13 K. Undoped a-Si:H samples show a broad PL near 1.35 eV. This broad PL is due to the transition between conduction and valence band-tail states w14x. However, in our 1% B-doped a-Si:H films Žstarting materials., PL bands are not observed in the 350᎐1700-nm spectral region. By forming nanoparticles from heavily doped a-Si:H films, the a-Si nanoparticle samples show visible luminescence near 1.6 eV. The PL peak energy in the a-Si nanoparticle sample Ž; 1.6 eV. is blueshifted from that of bulk a-Si:H Ž; 1.35 eV.. In addition, the 0.8᎐0.9-eV PL related to defects in B-doped Si:H is not observed in our nanoparticle samples. The observed PL spectrum of the a-Si nanoparticle sample is similar to that of the c-Si nanoparticle sample. It is known that the luminescence efficiency of bulk
Fig. 1. Visible and near-infrared luminescence spectra of: Ža. undoped a-Si film, Žb. a-Si nanoparticles, Žc. bulk c-Si and Žd. c-Si nanoparticles at 13 K.
Y. Kanemitsu, Y. Fukunishi r Thin Solid Films 393 (2001) 103᎐108
a-Si:H depends on doping amount of acceptors or donors. Radiative recombination occurs at localized states near the band edge Žthe band-tail state. and non-radiative recombination occurs at midgap states. Heavily doped a-Si:H is a poor luminescent material even at low temperatures, because midgap states due to defects are formed by doping. However, our experiments show that a-Si nanoparticles fabricated from heavily doped a-Si films clearly show luminescence. By fabricating nanostructures, the midgap states acting as non-radiative recombination centers would decrease. This is related to the formation of porous layer. The electrochemical etching of Si skeleton occurs preferentially at defects w15x, and it is considered that a-Si nanoparticles in the porous layer Žrest material. behave as undoped a-Si:H, a good luminescent material. In fact, the 0.8᎐0.9-eV PL related to defects is not experimentally observed in a-Si nanoparticles, as shown in Fig. 1. Visible luminescence is clearly observed in a-Si nanoparticles, as a consequence of the reduction of the defect luminescence and the non-radiative recombination of carriers. The a-Si and c-Si nanoparticle samples show broad PL in the visible spectral region and their PL spectra are similar to each other. In order to clarify the origin of the broad PL spectrum, we applied resonant excitation spectroscopy to the a-Si and c-Si samples, because resonant excitation at energies within the PL band results in fine structures. Fig. 2 shows PL spectra of a-Si and c-Si nanoparticle samples at 8 K under resonant excitation at energies within the red PL band, where the zero on the abscissa scale corresponds to the excitation energy. The fine structures in the PL spectrum are observed in both a-Si and c-Si samples under resonant excitation. In the c-Si nanoparticle sample wcurve Žd. in Fig. 2x, the step-like structures appear in the spectrum. The TO Ž ⌬ . and TA Ž ⌬ . phonon energies of bulk c-Si are shown by the arrows in the figure, where TO Ž ⌬ . and TA Ž ⌬ . are the transverse optical phonon and the transverse acoustic phonon at the conduction-bandminimum ⌬ point in bulk c-Si w16᎐19x. PL fine structures in c-Si nanoparticles can be explained by the momentum-conserving phonon-assisted luminescence processes. In addition, the spectral shape of the resonantly excited PL of the c-Si sample depends on the excitation laser energy w18x. The broad PL spectrum is due to the size and shape distribution of c-Si nanoparticles in the sample w18x. Even in the a-Si nanoparticle samples, fine structures are observed under resonant laser excitation. The observed peak energy in the a-Si nanoparticle sample wcurves Ža᎐c. in Fig. 2x is equal to the TO phonon energy in bulk a-Si:H. The observed phonon-related structures in a-Si nanoparticles are very similar to the Raman spectrum in the vicinity of the TO phonon
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Fig. 2. Resonantly excited luminescence spectra of Ža᎐c. a-Si nanoparticles and Žd. c-Si nanoparticles at the low-energy side of the excitation energies at 8 K: Ža. 1.592, Žb. 1.662, Žc. 1.711 and Žd. 1.543 eV. The zero on the abscissa scale corresponds to the excitation laser energy. The TO Ž ⌬ . and TA Ž ⌬ . phonon energies correspond to the transverse optical phonon and the transverse acoustic phonon at the conduction-band-minimum ⌬ point in bulk c-Si, respectively.
modes near 480 cmy1 in a-Si:H films w20,21x. In addition, the spectral shape of the phonon-related structures in a-Si nanoparticles does not depend on the excitation laser energy wsee, curves Ža᎐c. in Fig. 2x. Therefore, it is considered that these phonon-related signals are due to the Raman process, rather than the luminescence process. Moreover, the intensity of the resonantly excited PL in a-Si nanoparticles is much weaker that that in c-Si nanoparticles. The weak intensity of the resonantly excited PL suggests that visible PL comes from localized states rather than the extended state with a large density of states. The characteristics of resonantly excited PL in a-Si nanoparticles are completely different from those of c-Si nanoparticles: The exciton recombination mechanism in a-Si nanoparticles is different from that in c-Si nanoparticles. Fig. 3 shows the temperature dependence of the PL intensity in a-Si and c-Si nanoparticles and bulk a-Si and c-Si under cw laser excitation. Bulk c-Si is an indirect gap semiconductor and its PL intensity abruptly decreases with an increase of temperature. In bulk undoped a-Si, there exit non-radiative recombination centers related to structural disorder and dangling bonds. At high temperatures, carriers trapped in the band-tail state are thermally excited to the extended state. The mobile carries in the extended state are captured at the non-radiative recombination centers. In a-Si, the thermal quenching of the PL intensity is determined by the thermally activated process of carriers from the band-tail state to the extended state
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Fig. 3. Temperature dependence of the total PL intensity of a-Si nanoparticles Ž䢇., bulk a-Si Ž'., c-Si nanoparticles Ž`. and bulk c-Si Ž^..
w14,22x. Then, the PL intensity of a-Si films abruptly decreases with an increase of temperature. Therefore, both bulk c-Si and bulk a-Si do not show luminescence at room temperature. However, in c-Si and a-Si nanoparticle samples, visible PL is observed even at room temperature and the PL intensities in both a-Si and c-Si nanoparticle samples are insensitive to the measurement temperature, compared with the cases of bulk a-Si and bulk c-Si. This implies that the non-radiative recombination of carriers is drastically reduced by the confinement of carriers in a small volume, similar to the case of a-Si based quantum wells w23,24x. The size reduction to a few nanometers cause the blueshift of the PL spectrum and the reduction of the thermal quenching of the PL intensity in a-Si and c-Si materials. In order to discuss the luminescence mechanism in nanoparticles, we study PL dynamics of the fast-decay component of the a-Si and c-Si nanoparticle samples in the nanosecond time region. The study of decay dynamics of luminescence provides direct information on the radiative and non-radiative recombination processes in nanoparticles w25,26x. The PL decay profile consists of two components, the fast-decay and slow-decay components in both a-Si and c-Si nanoparticles w25᎐28x. The PL decay dynamics at the initial stage strongly reflect the difference in the carrier relaxation processes between a-Si and c-Si nanoparticle samples w27x. Fig. 4 shows PL decay profiles of the a-Si nanoparticle sample at different emission energies wŽa. 1.91, Žb. 1.80, Žc. 1.65, and Žd. 1.55 eVx under 3.10-eV and 1.1-ps laser excitation at 10 K. The PL decay curves show
Fig. 4. PL decay profiles of the a-Si nanoparticle sample at different emission energies: Ža. 1.91, Žb. 1.80, Žc. 1.65 and Žd. 1.55 eV. The decay dynamics was measured under 3.10-eV and 1.1-ps laser excitation at 10 K. The PL decay curves in the fast component are fitted by two exponential functions Žsolid lines..
non-exponential even in the nanosecond time region. The PL decay profiles of the fast component, I F Ž t ., are approximately fitted by two exponential components Žsolid curves in Fig. 4.. In the fast-decay component of the a-Si and c-Si samples, the decay profile, I F Ž t ., has essentially the same non-exponential shape at different emission energies. Therefore, in order to compare the PL decay dynamics between the a-Si and c-Si samples, the mean PL lifetime of the fast-decay component, PL , is defined by, PL s
1 IF Ž0.
HI
F
Ž t . dt
where I F Ž0. is the initial PL intensity of the fast component just after pulsed laser excitation. The mean PL decay rate y1 PL at 10 K is summarized as a function of the emission phonon energy in Fig. 5. In both a-Si and
Fig. 5. PL decay rate y1 PL of a-Si and c-Si nanoparticles as a function of the emission photon energy at 10 K.
Y. Kanemitsu, Y. Fukunishi r Thin Solid Films 393 (2001) 103᎐108
c-Si nanoparticle samples, the PL decay rate depends on the emission photon energy at low temperatures. In c-Si nanoparticles, the wave functions of electrons and holes are delocalized over the 3᎐5-nm nanoparticles, because in bulk c-Si the Bohr radius of free excitons is approximately 4.3 nm w4x. It is considered that the exciton recombination rate in c-Si nanoparticles is sensitive to the nanoparticle size. In c-Si nanoparticles, the spectral shape of the resonantly excited PL depends on the excitation laser energy, as mentioned above. Since the bulk c-Si shows a narrow PL spectrum Žsee Fig. 1., a single c-Si nanoparticle will show a narrow PL spectrum. Then, it is concluded that the broad PL spectrum is mainly due to the size fluctuation of nanoparticles in the sample. Since there is a correlation between the emission photon energy and the nanoparticle size w7x, the observed energy-dependence of the PL lifetime mainly reflects the size dependence of the PL lifetime. However, in a-Si, the localization length of carriers is estimated to be 1 nm or less w29᎐31x. This is smaller than the size of a-Si nanoparticles Ž; 3᎐5 nm. w10᎐12x. It is believed that the electron wavefunction is strongly localized within nanoparticles and the PL lifetime is not sensitive to the size of a-Si nanoparticles. Moreover, bulk a-Si shows a broad PL spectrum even at low temperatures, as shown in Fig. 1. It is considered that the broad PL spectrum of a-Si nanoparticles is due to the radiative recombination in the band-tail state of nanoparticles, rather than the size fluctuation of a-Si nanoparticles w27x. The single a-Si nanoparticle will show a broad PL spectrum, because broad luminescence in a-Si is due to the radiative transitions in the band-tail state. In addition, in the band-tail emission, the PL lifetime becomes longer with a decrease of the emission photon energy, because the average distance of electrons and holes for the radiative tunneling becomes longer at deeper localized state. In a-Si nanoparticles, visible PL is attributed to the radiative recombination of carriers localized in the band-tail state. In a-Si based materials, one usually considers the mostly delocalized state Žthe extended state. and the weakly localized state Žthe band-tail state. in the light absorption and emission processes. With a decrease of the nanoparticle size, the extended state shifts to higher energy, but the deep localized state Žthe strongly localized state. does not change. Therefore, it is expected that in a-Si nanoparticle the quantum confinement of carriers causes the spreading of the band tail. In fact, the PL bandwidth of a-Si nanoparticles is larger than that of bulk a-Si, as shown in Fig. 1. The spreading of the band tail reduces the thermal emission rate of carriers localized in the band-tail state and then sup-
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presses the thermal quenching of the PL intensity in a-Si nanoparticles, as shown in Fig. 3. Moreover, in a-Si nanoparticles, the PL lifetime is very short even at low temperatures, compared with the case of bulk a-Si w32x. At low temperatures, the dominant recombination is radiative tunneling in a-Si based materials w14x. In a-Si nanoparticles, the average tunneling distance for radiative recombination decreases and then the average PL lifetime becomes shorter. The radiative recombination rate is enhanced in a-Si nanoparticles, because the electrons and holes are confined in a small volume. The short lifetime of carriers reduces the energy relaxation of carriers into lowerenergy states and then increases the average energy of carriers for radiative recombination in the band-tail state. Because of the short lifetime of carriers confined in a small volume and the spreading of the band tail, we can observe the blueshift of the PL peak energy in a-Si nanoparticles. The formation of nanoparticles causes the strong modification of luminescence properties of both a-Si and c-Si materials. The blueshift of the PL spectrum and the remarkable reduction of the thermal quenching of the PL intensity are observed in both a-Si and c-Si nanoparticles. However, the PL mechanism is different from each other. In c-Si nanoparticles, quantum confinement effects play an essential role in the modification of band structures and optical responses. In a-Si nanoparticles, the Anderson localization determines the carrier dynamics and the luminescence is due to the radiative recombination in the band-tail states. The non-radiative recombination centers exist in a-Si nanoparticles due to the structural disorder. It is believed that the crystalline nanoparticle is a better luminescence material and the crystallinity of the interior state of nanoparticles is very important even in nanoscale and molecular scale materials. 4. Conclusion We have studied luminescence properties of a-Si and c-Si nanoparticles by means of resonantly excited PL spectra and time-resolved PL decay dynamics measurements. The formation of nanoparticles cause the blueshift of the PL spectrum and the remarkable reduction of the thermal quenching of the PL intensity in both a-Si and c-Si materials. In a-Si nanoparticles the electron wave functions do not extend over nanoparticles, but luminescence properties of nanoparticles are completely different from those of bulk a-Si. Luminescence properties of amorphous materials can be modified by changing the size of nanostructures. It is demonstrated that optical responses of nanoparticles are modified by the spatial confinement of carriers in
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amorphous materials and the quantum confinement of carriers in crystalline materials. Acknowledgements The authors would like to thank Dr J.-N. Chazalviel, Dr R.B. Wehrspohn and Dr M. Gros-Jean of CNRS´ cole-Polytechnique for providing porous a-Si samples, E Professor T. Kushida for discussion and M. Kobayashi of NAIST for technical assistance with AFM. This work was partly supported by a Grant-In-Aid for Scientific Research ŽB. from The Japan Society for the Promotion of Science Ž噛 11440095., The Yamada Science Foundation, The Kawasaki Steel 21st Century Foundation, The Kansai Research Foundation for Technology Promotion and The Yazaki Memorial Foundation for Science and Technology. References w1x L.E. Brus, A. Efros, T. Itoh ŽEds.., Spectroscopy of Isolated and Assembled Semiconductor Nanocrystals, J. Lumin 76 Ž1996.. w2x J.R. Heath ŽEd.., Nanoscale Materials, Acc. Chem. Res, 32Ž5. Ž1999. Special Issue. w3x T. Ogawa, Y. Kanemitsu ŽEds.., Optical Properties of Low-Dimensional Materials, World Scientific, Singapore, 1995. w4x Y. Kanemitsu, in: D.J. Lockwood ŽEd.., Light Emission in Silicon, Semiconductors and Semimetals, 49, Academic Press, New York, 1998, p. 157. w5x Y. Kanemitsu, Phys. Rep. 263 Ž1995. 1 and references therein. w6x A. Cullis, L.T. Canham, L. Calcott, J. Appl. Phys. 82 Ž1997. 909 and references therein. w7x Y. Kanemitsu, S. Okamoto, Mater. Sci. Eng. B 48 Ž1997. 108. w8x E. Bustarret, M. Ligeon, L. Ortega, Solid State Commun. 83 Ž1992. 461. w9x E. Bustarret, E. Sauvaian, M. Ligeon, M. Rosenbauer, Thin Solid Films 276 Ž1996. 134.
w10x R.B. Wehrspohn, J.-N. Chazalviel, F. Ozanam, I. Solomon, Phys. Rev. Lett. 77 Ž1996. 1885. w11x R.B. Wehrspohn, J.-N. Chazalviel, F. Ozanam, I. Solomon, European Phys. J. B 8 Ž1999. 179. w12x E. Bustarret, E. Sauvaian, M. Ligeon, Phil. Mag. Lett. 75 Ž1997. 35. w13x Y. Kanemitsu, S. Okamoto, Phys. Rev. B 56 Ž1997. R1696. w14x R.A. Street, Hydrogenated Amorphous Silicon, Cambridge University Press, Cambridge, 1991. w15x P. Schmuki, L.E. Erickson, D.J. Lockwood, Phys. Rev. Lett. 80 Ž1998. 4060. w16x P.D.J. Calcott, K.J. Nash, L.T. Canham, M.J. Kane, D. Brumhead, J. Phys. Condens. Matter 5 Ž1993. L91. w17x P.D.J. Calcott, K.J. Nash, L.T. Canham, M.J. Kane, D. Brumhead, J. Lumin. 57 Ž1994. 271. w18x Y. Kanemitsu, S. Okamoto, Phys. Rev. B 58 Ž1998. 9652. w19x D. Kovalev, H. Heckler, M. Ben-Chorin, G. Polisski, M. Schwartzkopff, F. Koch, Phys. Rev. Lett. 81 Ž1998. 2803. w20x M.H. Brodsky, in: M. Cardona ŽEd.., Light Scattering in Solids, Springer, Berlin, 1975, p. 208. w21x J.E. Smith Jr., M.H. Brodsky, B.L. Crowder, M.I. Nathan, A. Pinczuk, Phys. Rev. Lett. 26 Ž1971. 642. w22x R.W. Collins, M.A. Paesler, W. Paul, Solid State Commun. 34 Ž1980. 833. w23x Y. Kanemitsu, M. Iiboshi, T. Kushida, Appl. Phys. Lett. 76 Ž2000. 2200. w24x Y. Kanemitsu, T. Kushida, Appl. Phys. Lett. 77 Ž2000. 3550. w25x T. Matsumoto, T. Futagi, H. Mimura, Y. Kanemitsu, Phys. Rev. B 47 Ž1993. 13876. w26x Y. Kanemitsu, Phys. Rev. B 48 Ž1993. 12357. w27x Y. Kanemitsu, Y. Fukunishi, T. Kushida, Appl. Phys. Lett. 77 Ž2000. 211. w28x E. Bustrarret, I. Mihalcescu, M. Ligeon, R. Romestain, J.C. Vial, F. Madeore, J. Lumin. 57 Ž1993. 105. w29x M.E. Raikh, S.D. Baranovskii, B.I. Shklovskii, Phys. Rev. B. 41 Ž1990. 7701. w30x H.V. Nguyen, Y. Lu, S. Kim, M. Wakagi, R.W. Collins, Phys. Rev. Lett. 74 Ž1995. 3880. w31x M.J. Estes, G. Moddel, Phys. Rev. B 54 Ž1996. 14633. w32x S. Ambros, R. Carius, H. Wagner, J. Non-Cryst. Solids 137r138 Ž1991. 555.