- Email: [email protected]
Surface recombination model of visible luminescence in porous silicon
Journal of Non-Crystalline Solids 227–230 Ž1998. 1053–1057
Surface recombination model of visible luminescence in porous silicon Zoltan ´ Hajnal, Peter ´ Deak ´
)
Department of Atomic Physics, TU Budapest, Budafoki ut ´ 8, H-1111, Hungary
Abstract The most favourite candidate to explain visible photoluminescence ŽPL. of porous silicon ŽPS. is quantum confinement. It has been shown theoretically that decreasing size of silicon particles leads to the widening of the gap Žphysical confinement.. According to calculations, red luminescence requires particle sizes that are too small to be directly observed in PS. On the other hand, chemical effects, other than etching, seem to affect the PL frequency. These effects indicate similarities to the PL of siloxene which is due to isolation of Si 6 rings by oxygen atoms Žchemical confinement.. Using self-consistent semi-empirical calculations, we have shown that the observed correlation between shift of the PL and Raman bands in PS can only be explained by chemical effects. Therefore, we suggest a surface recombination model of PL in PS, where the emission is determined primarily by physical confinement in features with nanometer dimensions on the surface of microcrystallites, while chemical substitutions tune the PL into the red. Empirical tight binding calculations on such particles show quantitative agreement with observed PL energies. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Nanostructures; Silicon; Quantum confinement; Surface recombination
1. Introduction Although visible, room-temperature photoluminescence ŽPL. in porous silicon ŽPS. is investigated since its discovery w1,2x, a consistent theoretical explanation of this phenomenon is still missing. Physical quantum confinement ŽPQC. of the carriers within wires or crystallites is accepted as the main reason for the increase of the band gap. The size range, theoretically required Žsee e.g., Refs. w3,4x. to show visible PL is F 2 nm. Experimental determination of particle sizes in porous materials is difficult and hindered by ambiguities. Small angle X-ray scatter)
Corresponding author. Tel.: q36-1 463 1393; fax: q36-1 463 4357; e-mail: [email protected].
ing shows w5x a bimodal distribution of sizes, crystallites smaller than 3 nm and much larger wires. The smallest entities are claimed w6x to be responsible for the luminescence, but the average crystallite diameters observed are over 3 nm Žsee Fig. 6 in Ref. w6x.. We have previously shown, that correlation between the shift of the PL peak and the displacement of the characteristic Raman band with decreasing crystallite sizes also contradicts the predicted anticorrelation of the quantum confinement models w7x. Similarities of PL and IR spectra of PS and siloxene, and the small exciton radii observed in both materials by ODMR w8x provided the basis for the chemical quantum confinement ŽCQC. model. Here, the confinement of the carriers is due to the chemical isolating effect of oxygen bridges between Si 6 rings. This
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 2 4 2 - 7
1054
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057
model predicts the correlation of the PL with the Raman peak correctly and explains the tuning of the PL peak with chemical treatments w9x. Siloxene itself is not detected in PS, however. It has been suggested by Koch w10x that PL in PS occurs due to radiative recombination on the surface after excitation of crystallites with basically bulk-like electronic structure. The recombination center has, however, not been identified. Models based on the excitation and recombination of hydrogenated surfaces have been proposed w11,12x, but these do not explain the sustained PL after oxidation. Based on semi-empirical model calculations, we have shown w13x that small bulges Ž‘buds’. on the surface of silicon microcrystals result in localized resonances in the valence and conduction bands of the microcrystals. The localization of these resonances is increased by incorporation of oxygen atoms into the backbone or substitution of the surface terminators of the buds. In the present work, we show that the localization of the resonances increases with increasing aspect ratio of the buds. While a microcrystal can still have an indirect band gap in the infrared, these resonances serve as carrier traps after direct transitions have been excited in the visible or near UV. They act as radiative recombination centers emitting photons with an energy that is larger than the band gap of the crystallite. The energy of recombination can then be tuned by chemical substitution of the terminator atoms on the surface, along with a parallel shift in the Raman band.
various ‘buds’ are built upon this slab by substituting six surface hydrogens by the ‘bud’. The base of every ‘bud’ is the same: it covers 1r6 of the surface. The diameter is 0.88 nm, while the distance to the next ‘bud’ Žbecause of the periodicity along the surface. is 1.54 nm. ‘Buds’ containing 9, 13, 19, 32, 41 and 45 silicon atoms Žwith hydrogens to saturate dangling bonds. represent aspect ratios of 0.35, 0.62, 0.71, 1.06, 1.41 and 1.68. Fig. 1 shows the ‘buds’
2. Constraints on theory Our preliminary semi-empirical quantum chemical calculations w13x were limited to show only the possibility for the surface recombination mechanism. To investigate the behaviour of the proposed structures, the microcrystal will be simulated with a sufficiently thick, two-dimensionally periodic SiŽ111. slab terminated by hydrogen atoms. We have chosen a slab with eight silicon layers Ž1.5-nm thick.. To diminish interactions between ‘buds’, a 6 = 6 surface unit cell has been chosen and cyclic boundary conditions have been applied. This results in a crystallite model containing 288 Si and 72 H atoms. The
Fig. 1. ‘Buds’ on the Si Ž111. surface consisting of 9, 13, 19, 32, 41 and 45 Si atoms.
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057
1055
Table 1 Calculated and experimental w15x electronic energies ŽeV. of bulk c-Si, H 2 , SiH 4 and Si 2 H 6 c-Si State
Calculated
Experimental
State
Calculated
Experimental
State
Calculated
Experimental
G1 G 25X G 15 G 2X
y17.88 y5.35 y2.17 y1.36
y17.91 y5.35 y2.00 y1.20
X 1v X4 X 1c X3
y13.11 y8.54 y3.79 y0.28
y13.10 y8.25 y4.22
L2 L 1v L 3X L 1c L3
y15.61 y11.86 y6.69 y4.19 y2.04
y14.69 y12.17 y6.57 y3.30 y1.44
H2 s s)
y15.45 y2.27
y15.45
SiH 4 a1 t2 t2 a1
y18.68 y12.56 y0.79 y0.67
y18.02 y12.67
Si 2 H 6 a 1g a 2u eu eg a 1g a 1g a 2u eg a 2u eu
y19.38 y16.12 y13.13 y11.99 y10.34 y2.93 y2.07 y1.23 0.50 0.64
y19.84 y16.5 y12.9 y12.0 y10.53
together with the top two silicon layers of the slab. The bond lengths and angles have been fixed at standard values. For modelling on a realistic size scale, ab initio, or even a semi-empirical approximation to the self-consistent solution of the Schrodinger ¨ equation is extremely demanding on computational capacity. To calculate the electronic states of these very large systems, we are left to computationally inexpensive methods such as the empirical tight binding ŽETB. approximation. This non-self-consistent method has been proven useful for calculating band structures of tetrahedral solids. Since we have no deviation from the usual bonding here, we may expect a reasonable semi-quantitative agreement. To achieve the necessary accuracy, while keeping the computational work down, we needed a good ETB band structure for crystalline silicon with a minimal basis. Because of the terminating H atoms, the ionization energies of Si and H containing molecules have to be reproduced as well. Since this is a rare combination of requirements, we have not found an appropriate parametrization in the literature. So we determined the matrix elements according to the classical Slater–Koster formalism. The parametrization was done in two steps. The first and second neighbour Hamiltonian matrix elements between Si s
X
and p orbitals have been fitted to the band structure of bulk Si w14x. The conduction band ŽCB. minimum of the resulting bulk band structure is at 0.77 on the G –X axis, 0.94 eV above the valence band ŽVB. edge. ŽThe experimental values are 0.81 and 1.1 eV.. We have only used high symmetry points in the Brillouin-zone Ž G , X, L. to achieve a fit with an RMS error of 0.36 eV. The diagonal elements have been chosen to give the experimental ionization threshold of bulk Si, 5.35 eV w15x. Next, the first and second neighbour Si–H, and H–H parameters were fitted to the experimental ionization energies of the molecules H 2 , SiH 4 , and Si 2 H 6 w15x. The RMS error here was 0.28 eV. The results of our fit are compared with experimental data in Table 1.
3. Results Applying this ETB scheme to the unperturbed slab of 1.5-nm thickness results in an indirect gap of 1.34 eV in the two dimensional band structure Žcf. the 0.94 eV gap for the bulk.. The direct gap is 1.36 eV. The hydrogen terminators do not contribute to the states near the band edges.
1056
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057
states provide a recombination center in the visible redryellow range, even when only a small amount of oxygen is present in the system.
5. Conclusions
Fig. 2. Wave function contribution of VB and CB resonances to near band-gap eigenstates.
The electronic states localized on the various ‘buds’ are depicted in Fig. 2. The probability of finding the electron of a given eigenstate on the ‘bud’ are shown ŽLocalization. as a function of energy and aspect ratio. The VB and CB edges of the slab are at y5.5 and y4.2 eV, respectively. As can be seen, for ‘buds’ with an aspect ratio above 1, weakly localized resonances appear at about 1 eV below the VB edge. At the same time, strongly localized states near the slab CB edge can be found Žstill above the bulk CB edge.. The nature of the resonances corresponds to those found in the semiempirical SCF calculations w13x, namely the lowest lying CB states have an antibonding s )-like behaviour between Si atoms, while the VB states are bonding within the ‘bud’ and antibonding to the slab.
Our ETB calculations show that small bulges with sizes in the order of 1 nm, and aspect ratio over 1, on the surface of silicon microcrystals give rise to localized resonances in the valence and conduction bands of the microcrystallites. Increasing aspect ratio shifts the energy of the resonances towards the bulk band edges and increases their localization. Presence of oxygen enhances these effects. The resonances serve as carrier traps and allow for radiative recombination with larger than band gap energy. The energy of recombination can be tuned towards the red by chemical substitution of the terminator atoms on the surface, along with a parallel shift in the Raman peak. Thus, we provided an atomistic model for the bulk-like excitation-surface recombination model w10x for the explanation of strong visible luminescence in porous silicon.
Acknowledgements This work has been supported by the COPERNICUS grant No. 7839. Discussion with members of our COPERNICUS consortium are gratefully acknowledged.
4. Discussion References With increasing aspect ratio, the localization of the resonances increases and the energy separation between VB and CB resonances decreases. For ‘buds’ with aspect ratio higher than 1, the energy of the minimum energy transition between VB and CB resonances is 2.2 eV. As we have shown previously w13x, substitution of the surface hydrogens of the ‘bud’ with more electronegative ligands Že.g., H ™ OH. further decreases this transition energy. Thus, irrespective of the precise electronic structure for the microcrystal Žfor which our 1.5-nm thick, two-dimensionally infinite slab is only a model., these
w1x w2x w3x w4x
L.T. Canham, Appl. Phys. Lett. 57 Ž1990. 1046. V. Lehmann, U. Gosele, Appl. Phys. Lett. 58 Ž1991. 856. ¨ M.S. Hybertsen, Phys. Rev. Lett. 72 Ž1994. 1514. C. Delerue, M. Lannoo, G. Allan, E. Martin, Thin Solid Films 255 Ž1995. 27. w5x M. Binder, T. Edelmann, T.H. Metzger, G. Mauckner, G. Goerigk, J. Peisl, Thin Solid Films 276 Ž1996. 65. w6x 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. Chaban, P.F. Szajowski, S.B. Christman, P.H. Citrin, Phys. Rev. B 52 Ž1995. 4910. w7x P. Deak, ´ Z. Hajnal, M. Stutzmann, H.D. Fuchs, Thin Solid Films 255 Ž1995. 241.
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057 w8x M. Stutzmann, M.S. Brandt, M. Rosenbauer, H.D. Fuchs, S. Finkbeiner, J. Weber, P. Deak, ´ J. Lumin. 57 Ž1993. 321. w9x S.M. Prokes, O.J. Glembocki, V.M. Bermudez, R. Kaplan, Phys. Rev. B 45 Ž1992. 13788. w10x F. Koch, Mater. Res. Soc. Symp. Proc. 298 Ž1993. 319. w11x Y. Takeda, S. Hyodo, N. Suzuki, T. Motohiro, T. Hioki, S. Noda, J. Appl. Phys. 73 Ž1993. 1924.
1057
w12x R.J. Baierle, M.J. Caldas, S. Ossicini, Solid State Commun. 102 Ž1997. 545. w13x P. Deak, ´ Z. Hajnal, J. Miro, ´ Thin Solid Films 276 Ž1996. 290. w14x D.R. Masovic, F.R. Vukajlovic, S. Zelkovic, J. Phys. C 16 Ž1983. 6731. w15x P. Deak, ´ Int. J. Quantum Chem. 23 Ž1983. 1165.
Surface recombination model of visible luminescence in porous silicon Zoltan ´ Hajnal, Peter ´ Deak ´
)
Department of Atomic Physics, TU Budapest, Budafoki ut ´ 8, H-1111, Hungary
Abstract The most favourite candidate to explain visible photoluminescence ŽPL. of porous silicon ŽPS. is quantum confinement. It has been shown theoretically that decreasing size of silicon particles leads to the widening of the gap Žphysical confinement.. According to calculations, red luminescence requires particle sizes that are too small to be directly observed in PS. On the other hand, chemical effects, other than etching, seem to affect the PL frequency. These effects indicate similarities to the PL of siloxene which is due to isolation of Si 6 rings by oxygen atoms Žchemical confinement.. Using self-consistent semi-empirical calculations, we have shown that the observed correlation between shift of the PL and Raman bands in PS can only be explained by chemical effects. Therefore, we suggest a surface recombination model of PL in PS, where the emission is determined primarily by physical confinement in features with nanometer dimensions on the surface of microcrystallites, while chemical substitutions tune the PL into the red. Empirical tight binding calculations on such particles show quantitative agreement with observed PL energies. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Nanostructures; Silicon; Quantum confinement; Surface recombination
1. Introduction Although visible, room-temperature photoluminescence ŽPL. in porous silicon ŽPS. is investigated since its discovery w1,2x, a consistent theoretical explanation of this phenomenon is still missing. Physical quantum confinement ŽPQC. of the carriers within wires or crystallites is accepted as the main reason for the increase of the band gap. The size range, theoretically required Žsee e.g., Refs. w3,4x. to show visible PL is F 2 nm. Experimental determination of particle sizes in porous materials is difficult and hindered by ambiguities. Small angle X-ray scatter)
Corresponding author. Tel.: q36-1 463 1393; fax: q36-1 463 4357; e-mail: [email protected].
ing shows w5x a bimodal distribution of sizes, crystallites smaller than 3 nm and much larger wires. The smallest entities are claimed w6x to be responsible for the luminescence, but the average crystallite diameters observed are over 3 nm Žsee Fig. 6 in Ref. w6x.. We have previously shown, that correlation between the shift of the PL peak and the displacement of the characteristic Raman band with decreasing crystallite sizes also contradicts the predicted anticorrelation of the quantum confinement models w7x. Similarities of PL and IR spectra of PS and siloxene, and the small exciton radii observed in both materials by ODMR w8x provided the basis for the chemical quantum confinement ŽCQC. model. Here, the confinement of the carriers is due to the chemical isolating effect of oxygen bridges between Si 6 rings. This
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 2 4 2 - 7
1054
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057
model predicts the correlation of the PL with the Raman peak correctly and explains the tuning of the PL peak with chemical treatments w9x. Siloxene itself is not detected in PS, however. It has been suggested by Koch w10x that PL in PS occurs due to radiative recombination on the surface after excitation of crystallites with basically bulk-like electronic structure. The recombination center has, however, not been identified. Models based on the excitation and recombination of hydrogenated surfaces have been proposed w11,12x, but these do not explain the sustained PL after oxidation. Based on semi-empirical model calculations, we have shown w13x that small bulges Ž‘buds’. on the surface of silicon microcrystals result in localized resonances in the valence and conduction bands of the microcrystals. The localization of these resonances is increased by incorporation of oxygen atoms into the backbone or substitution of the surface terminators of the buds. In the present work, we show that the localization of the resonances increases with increasing aspect ratio of the buds. While a microcrystal can still have an indirect band gap in the infrared, these resonances serve as carrier traps after direct transitions have been excited in the visible or near UV. They act as radiative recombination centers emitting photons with an energy that is larger than the band gap of the crystallite. The energy of recombination can then be tuned by chemical substitution of the terminator atoms on the surface, along with a parallel shift in the Raman band.
various ‘buds’ are built upon this slab by substituting six surface hydrogens by the ‘bud’. The base of every ‘bud’ is the same: it covers 1r6 of the surface. The diameter is 0.88 nm, while the distance to the next ‘bud’ Žbecause of the periodicity along the surface. is 1.54 nm. ‘Buds’ containing 9, 13, 19, 32, 41 and 45 silicon atoms Žwith hydrogens to saturate dangling bonds. represent aspect ratios of 0.35, 0.62, 0.71, 1.06, 1.41 and 1.68. Fig. 1 shows the ‘buds’
2. Constraints on theory Our preliminary semi-empirical quantum chemical calculations w13x were limited to show only the possibility for the surface recombination mechanism. To investigate the behaviour of the proposed structures, the microcrystal will be simulated with a sufficiently thick, two-dimensionally periodic SiŽ111. slab terminated by hydrogen atoms. We have chosen a slab with eight silicon layers Ž1.5-nm thick.. To diminish interactions between ‘buds’, a 6 = 6 surface unit cell has been chosen and cyclic boundary conditions have been applied. This results in a crystallite model containing 288 Si and 72 H atoms. The
Fig. 1. ‘Buds’ on the Si Ž111. surface consisting of 9, 13, 19, 32, 41 and 45 Si atoms.
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057
1055
Table 1 Calculated and experimental w15x electronic energies ŽeV. of bulk c-Si, H 2 , SiH 4 and Si 2 H 6 c-Si State
Calculated
Experimental
State
Calculated
Experimental
State
Calculated
Experimental
G1 G 25X G 15 G 2X
y17.88 y5.35 y2.17 y1.36
y17.91 y5.35 y2.00 y1.20
X 1v X4 X 1c X3
y13.11 y8.54 y3.79 y0.28
y13.10 y8.25 y4.22
L2 L 1v L 3X L 1c L3
y15.61 y11.86 y6.69 y4.19 y2.04
y14.69 y12.17 y6.57 y3.30 y1.44
H2 s s)
y15.45 y2.27
y15.45
SiH 4 a1 t2 t2 a1
y18.68 y12.56 y0.79 y0.67
y18.02 y12.67
Si 2 H 6 a 1g a 2u eu eg a 1g a 1g a 2u eg a 2u eu
y19.38 y16.12 y13.13 y11.99 y10.34 y2.93 y2.07 y1.23 0.50 0.64
y19.84 y16.5 y12.9 y12.0 y10.53
together with the top two silicon layers of the slab. The bond lengths and angles have been fixed at standard values. For modelling on a realistic size scale, ab initio, or even a semi-empirical approximation to the self-consistent solution of the Schrodinger ¨ equation is extremely demanding on computational capacity. To calculate the electronic states of these very large systems, we are left to computationally inexpensive methods such as the empirical tight binding ŽETB. approximation. This non-self-consistent method has been proven useful for calculating band structures of tetrahedral solids. Since we have no deviation from the usual bonding here, we may expect a reasonable semi-quantitative agreement. To achieve the necessary accuracy, while keeping the computational work down, we needed a good ETB band structure for crystalline silicon with a minimal basis. Because of the terminating H atoms, the ionization energies of Si and H containing molecules have to be reproduced as well. Since this is a rare combination of requirements, we have not found an appropriate parametrization in the literature. So we determined the matrix elements according to the classical Slater–Koster formalism. The parametrization was done in two steps. The first and second neighbour Hamiltonian matrix elements between Si s
X
and p orbitals have been fitted to the band structure of bulk Si w14x. The conduction band ŽCB. minimum of the resulting bulk band structure is at 0.77 on the G –X axis, 0.94 eV above the valence band ŽVB. edge. ŽThe experimental values are 0.81 and 1.1 eV.. We have only used high symmetry points in the Brillouin-zone Ž G , X, L. to achieve a fit with an RMS error of 0.36 eV. The diagonal elements have been chosen to give the experimental ionization threshold of bulk Si, 5.35 eV w15x. Next, the first and second neighbour Si–H, and H–H parameters were fitted to the experimental ionization energies of the molecules H 2 , SiH 4 , and Si 2 H 6 w15x. The RMS error here was 0.28 eV. The results of our fit are compared with experimental data in Table 1.
3. Results Applying this ETB scheme to the unperturbed slab of 1.5-nm thickness results in an indirect gap of 1.34 eV in the two dimensional band structure Žcf. the 0.94 eV gap for the bulk.. The direct gap is 1.36 eV. The hydrogen terminators do not contribute to the states near the band edges.
1056
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057
states provide a recombination center in the visible redryellow range, even when only a small amount of oxygen is present in the system.
5. Conclusions
Fig. 2. Wave function contribution of VB and CB resonances to near band-gap eigenstates.
The electronic states localized on the various ‘buds’ are depicted in Fig. 2. The probability of finding the electron of a given eigenstate on the ‘bud’ are shown ŽLocalization. as a function of energy and aspect ratio. The VB and CB edges of the slab are at y5.5 and y4.2 eV, respectively. As can be seen, for ‘buds’ with an aspect ratio above 1, weakly localized resonances appear at about 1 eV below the VB edge. At the same time, strongly localized states near the slab CB edge can be found Žstill above the bulk CB edge.. The nature of the resonances corresponds to those found in the semiempirical SCF calculations w13x, namely the lowest lying CB states have an antibonding s )-like behaviour between Si atoms, while the VB states are bonding within the ‘bud’ and antibonding to the slab.
Our ETB calculations show that small bulges with sizes in the order of 1 nm, and aspect ratio over 1, on the surface of silicon microcrystals give rise to localized resonances in the valence and conduction bands of the microcrystallites. Increasing aspect ratio shifts the energy of the resonances towards the bulk band edges and increases their localization. Presence of oxygen enhances these effects. The resonances serve as carrier traps and allow for radiative recombination with larger than band gap energy. The energy of recombination can be tuned towards the red by chemical substitution of the terminator atoms on the surface, along with a parallel shift in the Raman peak. Thus, we provided an atomistic model for the bulk-like excitation-surface recombination model w10x for the explanation of strong visible luminescence in porous silicon.
Acknowledgements This work has been supported by the COPERNICUS grant No. 7839. Discussion with members of our COPERNICUS consortium are gratefully acknowledged.
4. Discussion References With increasing aspect ratio, the localization of the resonances increases and the energy separation between VB and CB resonances decreases. For ‘buds’ with aspect ratio higher than 1, the energy of the minimum energy transition between VB and CB resonances is 2.2 eV. As we have shown previously w13x, substitution of the surface hydrogens of the ‘bud’ with more electronegative ligands Že.g., H ™ OH. further decreases this transition energy. Thus, irrespective of the precise electronic structure for the microcrystal Žfor which our 1.5-nm thick, two-dimensionally infinite slab is only a model., these
w1x w2x w3x w4x
L.T. Canham, Appl. Phys. Lett. 57 Ž1990. 1046. V. Lehmann, U. Gosele, Appl. Phys. Lett. 58 Ž1991. 856. ¨ M.S. Hybertsen, Phys. Rev. Lett. 72 Ž1994. 1514. C. Delerue, M. Lannoo, G. Allan, E. Martin, Thin Solid Films 255 Ž1995. 27. w5x M. Binder, T. Edelmann, T.H. Metzger, G. Mauckner, G. Goerigk, J. Peisl, Thin Solid Films 276 Ž1996. 65. w6x 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. Chaban, P.F. Szajowski, S.B. Christman, P.H. Citrin, Phys. Rev. B 52 Ž1995. 4910. w7x P. Deak, ´ Z. Hajnal, M. Stutzmann, H.D. Fuchs, Thin Solid Films 255 Ž1995. 241.
Z. Hajnal, P. Deak ´ r Journal of Non-Crystalline Solids 227–230 (1998) 1053–1057 w8x M. Stutzmann, M.S. Brandt, M. Rosenbauer, H.D. Fuchs, S. Finkbeiner, J. Weber, P. Deak, ´ J. Lumin. 57 Ž1993. 321. w9x S.M. Prokes, O.J. Glembocki, V.M. Bermudez, R. Kaplan, Phys. Rev. B 45 Ž1992. 13788. w10x F. Koch, Mater. Res. Soc. Symp. Proc. 298 Ž1993. 319. w11x Y. Takeda, S. Hyodo, N. Suzuki, T. Motohiro, T. Hioki, S. Noda, J. Appl. Phys. 73 Ž1993. 1924.
1057
w12x R.J. Baierle, M.J. Caldas, S. Ossicini, Solid State Commun. 102 Ž1997. 545. w13x P. Deak, ´ Z. Hajnal, J. Miro, ´ Thin Solid Films 276 Ž1996. 290. w14x D.R. Masovic, F.R. Vukajlovic, S. Zelkovic, J. Phys. C 16 Ž1983. 6731. w15x P. Deak, ´ Int. J. Quantum Chem. 23 Ž1983. 1165.