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Shedding light on the growth of amorphous, polymorphous, protocrystalline and microcrystalline silicon thin films
Thin Solid Films 383 Ž2001. 161᎐164
Shedding light on the growth of amorphous, polymorphous, protocrystalline and microcrystalline silicon thin films A. Fontcuberta i MorralU , P. Roca i Cabarrocas Laboratoire de Physique des Interfaces et des Couches Minces (UMR 7647 CNRS), Ecole Polytechnique, 91128 Palaiseau Cedex, France
Abstract We focus here on a study of the growth of polymorphous and protocrystalline silicon materials with respect to the well-established amorphous and microcrystalline silicon. Protocrystalline films correspond to a slow crystallisation process, in which the films grow densely in the first monolayers, but their porosity and roughness increase with thickness, allowing the nucleation of crystallites, and finally the formation of a microcrystalline phase. On the contrary, polymorphous films remain dense, independent of their thickness. The control of the temperature gradient between the RF electrode and the substrate holder allows a switch from microcrystalline to polymorphous silicon growth, which strongly supports our hypothesis of polymorphous films being formed by simultaneous contributions of silicon radicals and clusters to the growth. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Microcrystalline silicon; Polymorphous silicon; Protocrystalline silicon; Clusters
1. Introduction Plasma-enhanced chemical vapour deposition allows the production of a wide range of silicon thin films with varying degrees of disorder. The optimisation of plasma conditions used for the growth of amorphous and microcrystalline silicon thin films has led to renewed interest in materials produced near the onset of crystallisation, often referred to as paracrystalline or protocrystalline silicon w1,2x. Moreover, study of the formation of powders in silane plasmas w3x has led to the development of polymorphous silicon films, presenting improved electronic and transport properties with respect to a-Si:H w4,5x. While polymorphous and protocrystalline films share some features, such as the presence of nanometer-sized crystallites, the details of their growth processes are still a matter of debate, and
U
Corresponding author. Tel.: q33-1-69-33-32-11; fax: q33-1-6933-30-06. E-mail address: [email protected] ŽA. Fontcuberta i Morral..
no clear distinction has so far been drawn between them. The purpose of this work is to determine what the differences are, if any, between the two materials, and to compare them to give a better understanding of amorphous and microcrystalline silicon thin films. 2. Experimental set-up Amorphous Ža-Si:H., polymorphous Žpm-Si:H., protocrystalline and microcrystalline Žc-Si:H. silicon have been deposited by radio frequency Ž13.56 MHz. plasma-enhanced chemical vapour deposition ŽPECVD. using a mixture of SiH 4 and H 2 in a monochamber reactor at 250⬚C. Amorphous silicon was deposited by the dissociation of pure silane Ž10 sccm. at 4.5 Pa with an RF power of 6 W. Polymorphous, protocrystalline and microcrystalline silicon films were produced by the dissociation of silane at 3 sccm diluted in hydrogen at 140 sccm under an RF power of 20 W. The transition from c- to pm-Si:H was achieved by increasing the total gas pressure in the range 75᎐250 Pa. The transition to polymorphous phase takes place between 121
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 0 . 0 1 5 9 6 - 0
162
A. Fontcuberta i Morral, P. Roca i Cabarrocas r Thin Solid Films 383 (2001) 161᎐164
and 131 Pa. The transition could also be achieved by changing the temperature gradient between the electrodes, supporting our hypothesis of silicon clusters contributing to the growth of pm-Si:H. The thickness and composition of the films, and their evolution during growth, were deduced from in situ ellipsometry measurements. We used the Bruggeman effective medium model ŽBEMA. w6x to analyse the amorphous and microcrystalline spectra. As a reference in the BEMA model, we used the dielectric function of amorphous silicon given by Aspnes w7x and of fine-grained polycrystalline silicon given by Jellison et al. w8x. As no reference files exist for polymorphous silicon, we used a Tauc᎐Lorentz w9x dispersion law to simulate the complex refractive index. The spectra of amorphous and protocrystalline samples were also analysed with this dispersion law, in order to compare the refractive indices of the three materials. 3. Results Fig. 1 shows the spectra of the imaginary part of the pseudo-dielectric function ² 2 : of a microcrystalline, an amorphous and a polymorphous film. Although the deposition conditions are relatively close for the cand pm-Si:H films, the shape of the spectra is quite different. Two shoulders can be seen in the microcrystalline spectrum, corresponding to a convolution of direct electronic transitions in the UV region of the crystalline silicon w10x. The results of the analysis of the c-Si:H film by BEMA are given in the inset of Fig. 1. The spectra of a-Si:H and pm-Si:H samples have the same shape, but are clearly distinct from that of cSi:H, even if some nanocrystallites are present in the case of pm-Si:H w11x. These crystallites might be too small to have the same optical transitions of the infinite crystal, or their concentration too low to be detectable by ellipsometry. The shift of the spectra towards higher energy in the case of pm-Si:H could be related to the
Fig. 1. Spectra of the imaginary part of the pseudo-dielectric function ² 2 : of a-, pm- and c-Si:H samples.
presence of crystallites, or more likely to a higher hydrogen content. In order to study the growth of the films, we plot in Fig. 2a the evolution of the maximum value of ² 2 : at approximately 3.55 eV. There is a clear distinction between the films deposited below and those above 133 Pa, or under standard a-Si:H conditions. The value of ² 2 : decreases for materials deposited at low pressures, corresponding to the development of a crystalline phase. The faster the decrease in ² 2 :, the faster the increase in the crystalline fraction, as seen in Fig. 2b. For materials deposited at pressures higher than 133 Pa, the value of ² 2 : remains almost constant during growth. As shown in Fig. 2b, the increase in pressure results in a delayed crystallisation process; i.e. the thickness of the incubation phase before the formation of the first stable crystallites increases with pressure w12x. Indeed, in the case of the film deposited at 123 Pa, the crystalline fraction is very low, even for a 350-nm thick film. This crystallisation is even slower in the case of the film deposited at 133 Pa with a cold RF electrode.
Fig. 2. Ža. Evolution of the maximum of the ² 2 : during the growth of materials deposited at a substrate holder and RF electrode temperature of 250 ⬚C under different pressures. Note the change in the growth at 133 Pa when the RF electrode is not heated. Žb. Evolution of the crystalline fraction of the films deposited at different pressures.
A. Fontcuberta i Morral, P. Roca i Cabarrocas r Thin Solid Films 383 (2001) 161᎐164
163
Fig. 3. Refractive index of amorphous, polymorphous, protocrystalline and microcrystalline silicon.
This means that, under these conditions, the incubation phase of c-Si:H is very long. The films deposited under such slow crystallisation conditions have been analysed in terms of evolutionary phase diagrams w1x and referred to as protocrystalline silicon. However, as shown in Fig. 2b, protocrystalline silicon films can only be obtained up to a given thickness, which depends on the plasma conditions and substrate. The thickness of the incubation phase increases with pressure, and for films deposited above 123 Pa we do not observe the transition to c-Si:H, but we obtain pm-Si:H films. It could be argued that films deposited above 123 Pa have an infinite incubation phase, and therefore are the same as protocrystalline silicon. However, the amplitude of ² 2 : for films deposited above 123 Pa remains constant, and is characteristic of a dense material. Indeed, the surface roughness of these films Ž0.2 nm. is extremely small, even smaller than that of a-Si:H Ž1.5 nm.. To prove that pm-Si:H films are distinct from protocrystalline silicon, we analysed their refractive index and compare it with that of a-Si:H and c-Si:H films ŽFig. 3.. 4. Discussion The above results show that polymorphous and protocrystalline silicon are two different materials. Thus, the question is what makes polymorphous silicon different? Effects of the growth pressure presented in this study can be discussed in terms of the enhancement of secondary reactions leading to the formation of powders. The effect of the temperature of the RF electrode presented in Fig. 2 suggests that thermophoresis is an important factor in pm-Si:H deposition. Thus, we varied ⵜT by changing the electrode and radio-frequency temperature, as well as the interelectrode distance. The results shown in Table 1 indicate that, for a gradient above 50⬚Crcm, c-Si:H is formed, while for lower values of ⵜT we obtain pm-
Si:H. Thus, when the substrate holder is hotter than the RF electrode, silicon clusters andror crystallites are pushed away from the substrate by thermophoresis and pm-Si:H cannot be produced. In order to support the contribution of clusters to deposition, let us consider the forces acting on them. w13x: ÝF s Fg q FE q Fqq Fv q Fth
Ž1.
where Fg is the gravity, FE is the electrostatic, Fq the ion drag, Fv the viscous gas drag and Fth the thermophoresis force. In the case of pm-Si:H deposition, we assume that, because of their small size, the clusters are neutral. Thus, two relevant forces have to be considered, the viscous gas drag and the thermophoresis: 2
ÝF s FT q FV s 32r15⭈ Ž rp . r¨ o m ⭈ K T ⭈ ⵜT q 1.86⭈ n o ⭈ m o ⭈ ¨om ⭈ ⭈ rp2 ⭈ u o
Ž2.
where rp is the radius of the nanoparticle, ¨om the average thermal velocity, n o and m o the gas density and mass, respectively, and K T is the translational part of the thermal conductivity of H 2 . As both forces depend on Ž rp . 2 , the condition of equilibrium ⌺F s 0 does not depend on the size of the particle. At a Table 1 Structure of films deposited as a function of the thermal gradient between the RF electrode and the substrate holder a Sample
90317C 90325B 90317B 90318A 91012A 91111A a
Temperature Ž⬚C. RF
Substrate
d Žcm.
200 150 100 50 50 50
150 150 150 150 150 250
2 2 2 2 2.7 2.7
is the inter-electrode distance.
ⵜT Ž⬚rcm.
Material
q25 0 y25 y50 y39 y74
pm-Si:H pm-Si:H pm-Si:H c-Si:H pm-Si:H c-Si:H
164
A. Fontcuberta i Morral, P. Roca i Cabarrocas r Thin Solid Films 383 (2001) 161᎐164
constant flow rate, ⌺F s 0 only depends on the temperature gradient ⵜT. For our conditions, we found that the thermal gradient for which both forces equilibrate is 50⬚C, in excellent agreement with the experimental results of Table 1. 5. Conclusion In situ ellipsometry studies of the growth of amorphous, polymorphous, protocrystalline and microcrystalline silicon films show clear differences in the growth dynamics and structure of the materials. Protocrystalline silicon films correspond to the incubation phase of microcrystalline, which can extend over a thickness of ; 1 m. On the other hand, polymorphous silicon films result from a different growth process, governed by the incorporation of silicon clusters in the amorphous matrix. Furthermore, we have shown that it is the thermal gradient between the two electrodes that governs the transport of these clusters to the substrate changing the growth of either protocrystalline or polymorphous silicon.
References w1x J Koh, A.S. Ferlauto, P.I. Rovira, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 75 Ž1999. 2286. w2x S. Guha, J. Yang, D.L. Williamson, Y. Lubianiker, J.D. Cohen, A.H. Mahan, Appl. Phys. Lett. 74 Ž1999. 1860. w3x P. Roca i Cabarrocas, S. Hamma, S.N. Sharma, J. Costa, E. Bertran, J. Non-Cryst. Solids 227᎐230 Ž1998. 871. w4x M. Meaudre, R. Meaudre, R. Butte, ´ S. Vignoli, C. Longeaud, J.P. Kleider, P. Roca i Cabarrocas, J. Appl. Phys. 86 Ž1999. 946. w5x C. Longeaud, J.P. Kleider, P. Roca i Cabarrocas, S. Hamma, R. Meaudre, M. Meaudre, J. Non-Cryst. Solids 227᎐230 Ž1999. 96. w6x D.A.G. Bruggeman, Ann. Phys. ŽLeipzig. 24 Ž1935. 636. w7x D.E. Aspnes, Thin Solid Films 89 Ž1982. 249. w8x G.E. Jellison Jr, M.F. Chisholm, S.M. Gorbatkin, Appl. Phys. Lett. 62 Ž1993. 3348. w9x G.E. Jellison Jr, F.A. Modine, Appl.Phys.Lett. 69 Ž1996.. w10x L.Van Hove, Phys. Rev. B 89 Ž1959. 1189. w11x A. Fontcuberta i Morral, R. Brenot, E.A.G. Hamers, R. Vanderhagen, P. Roca i Cabarrocas, J. Non-Cryst. Solids, in press. w12x S. Hamma, D. Colliquet, P. Roca i Cabarrocas, Mater. Res. Soc. Symp. Proc. 507 Ž1998. 505. w13x J. Perrin, P. Molinas-Mata, P. Belenguer, J. Phys. D: Appl. Phys. 27 Ž1994. 2499.
Shedding light on the growth of amorphous, polymorphous, protocrystalline and microcrystalline silicon thin films A. Fontcuberta i MorralU , P. Roca i Cabarrocas Laboratoire de Physique des Interfaces et des Couches Minces (UMR 7647 CNRS), Ecole Polytechnique, 91128 Palaiseau Cedex, France
Abstract We focus here on a study of the growth of polymorphous and protocrystalline silicon materials with respect to the well-established amorphous and microcrystalline silicon. Protocrystalline films correspond to a slow crystallisation process, in which the films grow densely in the first monolayers, but their porosity and roughness increase with thickness, allowing the nucleation of crystallites, and finally the formation of a microcrystalline phase. On the contrary, polymorphous films remain dense, independent of their thickness. The control of the temperature gradient between the RF electrode and the substrate holder allows a switch from microcrystalline to polymorphous silicon growth, which strongly supports our hypothesis of polymorphous films being formed by simultaneous contributions of silicon radicals and clusters to the growth. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Microcrystalline silicon; Polymorphous silicon; Protocrystalline silicon; Clusters
1. Introduction Plasma-enhanced chemical vapour deposition allows the production of a wide range of silicon thin films with varying degrees of disorder. The optimisation of plasma conditions used for the growth of amorphous and microcrystalline silicon thin films has led to renewed interest in materials produced near the onset of crystallisation, often referred to as paracrystalline or protocrystalline silicon w1,2x. Moreover, study of the formation of powders in silane plasmas w3x has led to the development of polymorphous silicon films, presenting improved electronic and transport properties with respect to a-Si:H w4,5x. While polymorphous and protocrystalline films share some features, such as the presence of nanometer-sized crystallites, the details of their growth processes are still a matter of debate, and
U
Corresponding author. Tel.: q33-1-69-33-32-11; fax: q33-1-6933-30-06. E-mail address: [email protected] ŽA. Fontcuberta i Morral..
no clear distinction has so far been drawn between them. The purpose of this work is to determine what the differences are, if any, between the two materials, and to compare them to give a better understanding of amorphous and microcrystalline silicon thin films. 2. Experimental set-up Amorphous Ža-Si:H., polymorphous Žpm-Si:H., protocrystalline and microcrystalline Žc-Si:H. silicon have been deposited by radio frequency Ž13.56 MHz. plasma-enhanced chemical vapour deposition ŽPECVD. using a mixture of SiH 4 and H 2 in a monochamber reactor at 250⬚C. Amorphous silicon was deposited by the dissociation of pure silane Ž10 sccm. at 4.5 Pa with an RF power of 6 W. Polymorphous, protocrystalline and microcrystalline silicon films were produced by the dissociation of silane at 3 sccm diluted in hydrogen at 140 sccm under an RF power of 20 W. The transition from c- to pm-Si:H was achieved by increasing the total gas pressure in the range 75᎐250 Pa. The transition to polymorphous phase takes place between 121
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 0 . 0 1 5 9 6 - 0
162
A. Fontcuberta i Morral, P. Roca i Cabarrocas r Thin Solid Films 383 (2001) 161᎐164
and 131 Pa. The transition could also be achieved by changing the temperature gradient between the electrodes, supporting our hypothesis of silicon clusters contributing to the growth of pm-Si:H. The thickness and composition of the films, and their evolution during growth, were deduced from in situ ellipsometry measurements. We used the Bruggeman effective medium model ŽBEMA. w6x to analyse the amorphous and microcrystalline spectra. As a reference in the BEMA model, we used the dielectric function of amorphous silicon given by Aspnes w7x and of fine-grained polycrystalline silicon given by Jellison et al. w8x. As no reference files exist for polymorphous silicon, we used a Tauc᎐Lorentz w9x dispersion law to simulate the complex refractive index. The spectra of amorphous and protocrystalline samples were also analysed with this dispersion law, in order to compare the refractive indices of the three materials. 3. Results Fig. 1 shows the spectra of the imaginary part of the pseudo-dielectric function ² 2 : of a microcrystalline, an amorphous and a polymorphous film. Although the deposition conditions are relatively close for the cand pm-Si:H films, the shape of the spectra is quite different. Two shoulders can be seen in the microcrystalline spectrum, corresponding to a convolution of direct electronic transitions in the UV region of the crystalline silicon w10x. The results of the analysis of the c-Si:H film by BEMA are given in the inset of Fig. 1. The spectra of a-Si:H and pm-Si:H samples have the same shape, but are clearly distinct from that of cSi:H, even if some nanocrystallites are present in the case of pm-Si:H w11x. These crystallites might be too small to have the same optical transitions of the infinite crystal, or their concentration too low to be detectable by ellipsometry. The shift of the spectra towards higher energy in the case of pm-Si:H could be related to the
Fig. 1. Spectra of the imaginary part of the pseudo-dielectric function ² 2 : of a-, pm- and c-Si:H samples.
presence of crystallites, or more likely to a higher hydrogen content. In order to study the growth of the films, we plot in Fig. 2a the evolution of the maximum value of ² 2 : at approximately 3.55 eV. There is a clear distinction between the films deposited below and those above 133 Pa, or under standard a-Si:H conditions. The value of ² 2 : decreases for materials deposited at low pressures, corresponding to the development of a crystalline phase. The faster the decrease in ² 2 :, the faster the increase in the crystalline fraction, as seen in Fig. 2b. For materials deposited at pressures higher than 133 Pa, the value of ² 2 : remains almost constant during growth. As shown in Fig. 2b, the increase in pressure results in a delayed crystallisation process; i.e. the thickness of the incubation phase before the formation of the first stable crystallites increases with pressure w12x. Indeed, in the case of the film deposited at 123 Pa, the crystalline fraction is very low, even for a 350-nm thick film. This crystallisation is even slower in the case of the film deposited at 133 Pa with a cold RF electrode.
Fig. 2. Ža. Evolution of the maximum of the ² 2 : during the growth of materials deposited at a substrate holder and RF electrode temperature of 250 ⬚C under different pressures. Note the change in the growth at 133 Pa when the RF electrode is not heated. Žb. Evolution of the crystalline fraction of the films deposited at different pressures.
A. Fontcuberta i Morral, P. Roca i Cabarrocas r Thin Solid Films 383 (2001) 161᎐164
163
Fig. 3. Refractive index of amorphous, polymorphous, protocrystalline and microcrystalline silicon.
This means that, under these conditions, the incubation phase of c-Si:H is very long. The films deposited under such slow crystallisation conditions have been analysed in terms of evolutionary phase diagrams w1x and referred to as protocrystalline silicon. However, as shown in Fig. 2b, protocrystalline silicon films can only be obtained up to a given thickness, which depends on the plasma conditions and substrate. The thickness of the incubation phase increases with pressure, and for films deposited above 123 Pa we do not observe the transition to c-Si:H, but we obtain pm-Si:H films. It could be argued that films deposited above 123 Pa have an infinite incubation phase, and therefore are the same as protocrystalline silicon. However, the amplitude of ² 2 : for films deposited above 123 Pa remains constant, and is characteristic of a dense material. Indeed, the surface roughness of these films Ž0.2 nm. is extremely small, even smaller than that of a-Si:H Ž1.5 nm.. To prove that pm-Si:H films are distinct from protocrystalline silicon, we analysed their refractive index and compare it with that of a-Si:H and c-Si:H films ŽFig. 3.. 4. Discussion The above results show that polymorphous and protocrystalline silicon are two different materials. Thus, the question is what makes polymorphous silicon different? Effects of the growth pressure presented in this study can be discussed in terms of the enhancement of secondary reactions leading to the formation of powders. The effect of the temperature of the RF electrode presented in Fig. 2 suggests that thermophoresis is an important factor in pm-Si:H deposition. Thus, we varied ⵜT by changing the electrode and radio-frequency temperature, as well as the interelectrode distance. The results shown in Table 1 indicate that, for a gradient above 50⬚Crcm, c-Si:H is formed, while for lower values of ⵜT we obtain pm-
Si:H. Thus, when the substrate holder is hotter than the RF electrode, silicon clusters andror crystallites are pushed away from the substrate by thermophoresis and pm-Si:H cannot be produced. In order to support the contribution of clusters to deposition, let us consider the forces acting on them. w13x: ÝF s Fg q FE q Fqq Fv q Fth
Ž1.
where Fg is the gravity, FE is the electrostatic, Fq the ion drag, Fv the viscous gas drag and Fth the thermophoresis force. In the case of pm-Si:H deposition, we assume that, because of their small size, the clusters are neutral. Thus, two relevant forces have to be considered, the viscous gas drag and the thermophoresis: 2
ÝF s FT q FV s 32r15⭈ Ž rp . r¨ o m ⭈ K T ⭈ ⵜT q 1.86⭈ n o ⭈ m o ⭈ ¨om ⭈ ⭈ rp2 ⭈ u o
Ž2.
where rp is the radius of the nanoparticle, ¨om the average thermal velocity, n o and m o the gas density and mass, respectively, and K T is the translational part of the thermal conductivity of H 2 . As both forces depend on Ž rp . 2 , the condition of equilibrium ⌺F s 0 does not depend on the size of the particle. At a Table 1 Structure of films deposited as a function of the thermal gradient between the RF electrode and the substrate holder a Sample
90317C 90325B 90317B 90318A 91012A 91111A a
Temperature Ž⬚C. RF
Substrate
d Žcm.
200 150 100 50 50 50
150 150 150 150 150 250
2 2 2 2 2.7 2.7
is the inter-electrode distance.
ⵜT Ž⬚rcm.
Material
q25 0 y25 y50 y39 y74
pm-Si:H pm-Si:H pm-Si:H c-Si:H pm-Si:H c-Si:H
164
A. Fontcuberta i Morral, P. Roca i Cabarrocas r Thin Solid Films 383 (2001) 161᎐164
constant flow rate, ⌺F s 0 only depends on the temperature gradient ⵜT. For our conditions, we found that the thermal gradient for which both forces equilibrate is 50⬚C, in excellent agreement with the experimental results of Table 1. 5. Conclusion In situ ellipsometry studies of the growth of amorphous, polymorphous, protocrystalline and microcrystalline silicon films show clear differences in the growth dynamics and structure of the materials. Protocrystalline silicon films correspond to the incubation phase of microcrystalline, which can extend over a thickness of ; 1 m. On the other hand, polymorphous silicon films result from a different growth process, governed by the incorporation of silicon clusters in the amorphous matrix. Furthermore, we have shown that it is the thermal gradient between the two electrodes that governs the transport of these clusters to the substrate changing the growth of either protocrystalline or polymorphous silicon.
References w1x J Koh, A.S. Ferlauto, P.I. Rovira, C.R. Wronski, R.W. Collins, Appl. Phys. Lett. 75 Ž1999. 2286. w2x S. Guha, J. Yang, D.L. Williamson, Y. Lubianiker, J.D. Cohen, A.H. Mahan, Appl. Phys. Lett. 74 Ž1999. 1860. w3x P. Roca i Cabarrocas, S. Hamma, S.N. Sharma, J. Costa, E. Bertran, J. Non-Cryst. Solids 227᎐230 Ž1998. 871. w4x M. Meaudre, R. Meaudre, R. Butte, ´ S. Vignoli, C. Longeaud, J.P. Kleider, P. Roca i Cabarrocas, J. Appl. Phys. 86 Ž1999. 946. w5x C. Longeaud, J.P. Kleider, P. Roca i Cabarrocas, S. Hamma, R. Meaudre, M. Meaudre, J. Non-Cryst. Solids 227᎐230 Ž1999. 96. w6x D.A.G. Bruggeman, Ann. Phys. ŽLeipzig. 24 Ž1935. 636. w7x D.E. Aspnes, Thin Solid Films 89 Ž1982. 249. w8x G.E. Jellison Jr, M.F. Chisholm, S.M. Gorbatkin, Appl. Phys. Lett. 62 Ž1993. 3348. w9x G.E. Jellison Jr, F.A. Modine, Appl.Phys.Lett. 69 Ž1996.. w10x L.Van Hove, Phys. Rev. B 89 Ž1959. 1189. w11x A. Fontcuberta i Morral, R. Brenot, E.A.G. Hamers, R. Vanderhagen, P. Roca i Cabarrocas, J. Non-Cryst. Solids, in press. w12x S. Hamma, D. Colliquet, P. Roca i Cabarrocas, Mater. Res. Soc. Symp. Proc. 507 Ž1998. 505. w13x J. Perrin, P. Molinas-Mata, P. Belenguer, J. Phys. D: Appl. Phys. 27 Ž1994. 2499.