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The vibrational local modes of the metastable threefold coordinated oxygen in hydrogenated amorphous silicon oxide
Journal of Non-Crystalline Solids 266±269 (2000) 850±853
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The vibrational local modes of the metastable threefold coordinated oxygen in hydrogenated amorphous silicon oxide Shu-Ya Lin * Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30043, Taiwan, Republic of China
Abstract The theoretical cluster-Bethe-lattice method is used to study the vibrational local modes of the threefold coordinated oxygen site in amorphous silicon oxide. There is no vibrational mode in the region between 800 and 1000 cmÿ1 for the oxygen site with normal twofold coordination. The vibrational densities of states for the pyramidal O3 bonding con®guration with various vertex angles are calculated. There is a new vibrational mode induced in the region between 800 and 1000 cmÿ1 . The valence alternation model is used to explain the existence of the metastable, O3 , bonding structure. When the hydrogenated amorphous silicon oxide is subject to annealing, the hydrogen will euse and break Si±H bonds. The threefold coordinated Si will re-bond with the O of the neighboring Si±O±Si bond to form a threefold coordinated metastable O3 bond. The O3 bonding structure can induce an 880 cmÿ1 vibrational mode found in experiment. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Amorphous silicon dioxide ®lms are usually grown by thermal treatment or plasma enhanced chemical vapor deposition method [1,2]. There are defect states in a-SiO2 [3±5]. The defect structures can be identi®ed by the electron spin resonance (ESR) [3±5] or optical measurement [3]. The most well known defect in a-SiO2 is the E0 center [6,7], which is a threefold coordinated silicon bonded with three oxygen (ºSiá). The dot denotes the unpaired electron. There are also Si±Si bonds, nonbridging oxygen hole centers (NBOHC,ºSi±Oá), and peroxyl radical centers (ºSi±O±Oá) in a-SiO2 . Oxygen, like chalcogen elements Se and S, has six valence electrons, two of which are s-electrons,
*
Tel.: +886-3 574 2589; fax: +886-3 571 5971. E-mail address: [email protected] (S.-Y. Lin).
and the remaining four are p-electrons. Two of the p-electrons are in non-bonding p states, which are usually located at the top of the valence band and the remaining two p-electrons bond with electrons of the neighboring atoms. In chalcogenide, the valence alternation model [8] is used to explain the existence of diamagnetic defect centers. The threefold metastable O3 sites are assumed to exist in a-SiO2 . But, their concentration could be so small that an infrared (IR) band is not detectable [9]. The study in this paper will show that the threefold metastable O3 can have a density detectable by IR spectroscopy. The IR absorption is an eective way to study local bonding structures in amorphous materials. In the plasma-enhanced chemical vapor deposited (PECVD) a-SiOx :H 0 6 x 6 2, a vibrational mode at 880 cmÿ1 has been reported [10]. This mode is ascribed to the Si±H bond-bending mode of the HSi±(OSi)3 bonding con®guration [10,11]. In the
0022-3093/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 8 5 4 - 6
S.-Y. Lin / Journal of Non-Crystalline Solids 266±269 (2000) 850±853
dc magnetron sputtered a-SiOx :H ®lms [12], the amplitude of the 880 cmÿ1 mode was found to increase after annealing up to 500°C. The amplitude of this mode decreased for higher-temperature annealing and vanished at 900°C. The assignment of this mode was to the (SiO)6 ring [12]. These two dierent aspects of the 880 cmÿ1 vibrational mode of a-SiOx :H have their origins in the parameters of ®lm depositions and depend on whether there was a thermal treatment after deposition. In this paper, a proposal is made that the 880 cmÿ1 vibrational mode is due to the O3 bonding con®guration. The theoretical calculations are used to identify the vibrational mode induced by the O3 bond. The cluster-Bethe-lattice method [13], which is an eective method employed for studying the vibrational and electronic properties of disordered solids, is adopted in this study.
2. Theoretical method The cluster-Bethe-lattice method [13,14] is used to investigate this problem. The GreenÕs function, G, is used to set up the equations of motion. The equation of motion can be written as x2 G 1 DG;
1
where x is the vibrational frequency and D is the dynamical matrix. A valence-force-®eld representation of the near-neighbor interactions [13,15] is used to generate the dynamical matrices. The vibrational local density of states (DOS) can be obtained from the calculated GreenÕs function. The eective ®eld (or transfer matrix) method can be employed to solve the equations of motion to obtain the GreenÕs function and hence the density of states. The mathematical development can be found in Refs. [13,16]. To study the vibrational local modes of aSiOx :H, the SiO2 Bethe lattice must be built ®rst. Details about the SiO2 Bethe lattice used in this study can be found in Ref. [17]. The eective ®elds for this Bethe lattice are calculated. A major work in this study is to identify if the increase in the 880 cmÿ1 mode in a-SiOx :H, after the ®lm is annealed,
851
is due to the O3 bond. The threefold coordinated pyramidal, O3 , bonding con®gurations of various vertex angles are then connected to the SiO2 Bethe lattice. Eq. (1) is used to set up the equations. The vibrational modes induced by the O3 bonding con®guration can be recognized after the equations are solved and the vibrational local DOS are obtained.
3. Results and discussion 3.1. Si±H bond Fig. 1(a) presents the vibrational DOS for the hydrogen of the HSi±(OSi)3 bonding con®guration with C3 symmetry. There is a Si±H bond-bending mode at 876 cmÿ1 and a Si±H bond-stretching mode at 2265 cmÿ1 . Replacing hydrogen by deuterium, the vibrational DOS for the deuterium of the DSi±(OSi)3 bonding con®guration is presented in Fig. 1(b). There is a Si±D bond-bending mode at 617 cmÿ1 and a bond-stretching mode at 1632 cmÿ1 . The scaling factors of 1.39 (2265/1632) and 1.41 (876/617) are close to the square root of the mass ratio of deuterium and hydrogen. The calculated results are in general agreement with experimental data [2]. When there is no C3 symmetry
Fig. 1. Vibrational DOS functions for (a) hydrogen atom of the H±Si(OSi)3 conformation, (b) deuterium of the D±Si(OSi)3 conformation, and (c) bulk SiO2 .
852
S.-Y. Lin / Journal of Non-Crystalline Solids 266±269 (2000) 850±853
for the HSi±(OSi)3 , the Si±H bond-bending mode splits [14]. In the PECVD a-SiOx :H ®lms [2], the amplitudes of the 876 cmÿ1 and 2265 cmÿ1 modes increased with increase of the oxygen content in aSiOx :H. Also shown in the ®gure is the averaged DOS, for density of states, SiO2 . The bending modes are at about 800 cmÿ1 and the stretching modes are in the range of 1000±1200 cmÿ1 . 3.2. O3 bond For the dc magnetron sputtered a-SiOx :H [12], when the ®lms were annealed at 500°C, the Si±H bond-stretching mode decreased, but the 880 cmÿ1 mode increased. In this case, the 880 cmÿ1 mode is not a Si±H related mode. Fig. 2 presents the vibrational DOS for the pyramidal O3 bonding con®guration with dierent vertex angles. There are two vibrational modes induced. The lower one, which is the bond-bending mode, changes from 956 to 785 cmÿ1 and the upper one, which is the bond-stretching mode, changes from 990 to 1043 cmÿ1 as the vertex angle changes from 95° to 115°.
The bending mode decreases in frequency while the stretching mode increases in frequency as the vertex angle increases. These two modes are degenerate at 973 cmÿ1 for the bonding con®guration with vertex angle of 90°. An 880 cmÿ1 mode is induced for a bonding con®guration with vertex angle of 104°. There is a range for the O3 bonding con®guration with various vertex angles, which have vibrational mode in the range between 800 and 1000 cmÿ1 . I have calculated the vibrational DOS for the (SiO)6 regular ring of a-quartz. There is no vibrational mode in the range between 800 and 1000 cmÿ1 . In fact, there are (SiO)6 rings everywhere in a-quartz and there is no vibrational mode in the range between 800 and 950 cmÿ1 [16]. The possibility of the 880 cmÿ1 mode due to the (SiO)6 ring can be ruled out. The 880 cmÿ1 vibrational mode is due to the O3 bonding structure. In chalcogenide, the valence alternation model [8] is used to explain the phenomena of the metastable bonding states. The normal twofold coordinated chalcogen elements can become threefold (C3 ) or onefold (C1 ) coordinated in chalcogenide. They can be either charged or neutral. Lucovsky [18] used the intermediate valence-alternation-pair (IVAP) model and introduced the concept of C 3 and Cÿ 1 pairs in vitreous silicon dioxide (v-SiO2 ). This was the beginning of the concept of threefold coordinated O3 bonds in v-SiO2 . OÕReilly and Robertson [9] studied the defects in v-SiO2 . They ÿ showed that the existence of the O 3 and O1 pairs could give a shallow state in the gap near the bottom of the conduction band. But, the creation energy for the O 3 site is greater than the similar metastable states in chalcogenide glass. The concentration of O 3 is too small to be IR detectable in regular ®lms. Under annealing, the evolution of hydrogen can break the Si±H bonds in a-SiOx :H and allow the formation of the O3 bonding sites. The reaction can be written as Si
Si ÿ O ÿ Si
j
Si ÿ H ! Si ÿ O ÿ Si
1 H2 : 2
2
Fig. 2. Vibrational DOS functions for the threefold coordinated O bonding con®gurations of various vertex angles. The dashed lines are for oxygen and silicon atoms of the bulk SiO2 .
The binding energy of Si±H is smaller than H2 [19]. The change from Si±H to H2 is exothermic. The concentration of the defect sites is proportional to
S.-Y. Lin / Journal of Non-Crystalline Solids 266±269 (2000) 850±853
exp()DG/kT), where DG is the free energy for creating a point defect. Though the creation energy of O3 sites is about 2.6 eV [9], the energy released from the above process can reduce the potential barrier to form O3 sites. The concentration of O3 sites can increase and the detection of IR absorption may be possible. The glass transition temperature (Tg ) of SiO2 is about 1350 K. This O3 metastable state may be frozen if the cooling rate is large enough near Tg [18]. As the annealing temperature increases, the metastable O3 is activated to break one of its Si±O bonds and changes to a more energetically stable Si±O±Si bond. The reaction can be written as Si j
Si ÿ O ÿ Si ! Si ÿ O ÿ Si áSi : 3 The threefold coordinated Si can re-bond with the other unsaturated bonded atoms. These possible processes indicate that the intensity of the 880 cmÿ1 mode will diminish after high temperature annealing. 4. Conclusion This study has shown that an 880 cmÿ1 vibrational mode due to the threefold coordinated, O3 , sites in amorphous silicon oxide is possible. This mode is infrared invisible in the as-deposited ®lms due to the high creation energy for the O3 structure. Annealing breaks the Si±H bonds and may provide sucient energy to overcome the potential barrier to increase the concentration of the O3 bonding con®guration. The glass transition temperature of
853
a-SiO2 makes this metastable state stable. However, higher-temperature annealing can destroy this metastable bonding state. Acknowledgements This research was supported by the National Science Council, the Republic of China under contract no. NSC 87-2215-E-007-026. References [1] J. Batey, E. Tierney, J. Appl. Phys. 60 (1986) 3136. [2] D.V. Tsu, G. Lucovsky, B.N. Davidson, Phys. Rev. B 40 (1989) 1795. [3] D.L. Griscom, J. Non-Cryst. Solids 73 (1985) 51. [4] W.L. Warren, P.M. Lenahan, B. Robinson, J.H. Stathis, Appl. Phys. Lett. 53 (1988) 482. [5] W.L. Warren, E.H. Poindexter, M. Oenberg, W. M ullerWarmuth, J. Electrochem. Soc. 139 (1992) 872. [6] R.A. Weeks, J. Appl. Phys. 27 (1956) 1376. [7] C.M. Nelson, R.A. Weeks, J. Am. Ceram. Soc. 43 (1960) 396. [8] M. Kastner, D. Adler, H. Fritzsche, Phys. Rev. Lett. 37 (1976) 1504. [9] E.P. OÕReilly, J. Robertson, Phys. Rev. B 27 (1983) 3780. [10] L. He, T. Inokuma, Y. Kurata, S. Hasegawa, J. Non-Cryst. Solids 185 (1995) 249. [11] S.Y. Lin, Appl. Phys. Lett. 70 (1997) 203. [12] M. Zacharias, D. Dimova-Malinovska, M. Stutzmann, Philos. Mag. B 73 (1996) 799. [13] G. Lucovsky, W.B. Pollard, J.D. Joannopoulos, G. Lucovsky, The Physics of Hydrogenated Amorphous Silicon II, Springer, Berlin, 1984, p. 302. [14] S.Y. Lin, J. Appl. Phys. 82 (1997) 5976. [15] R.M. Martin, Phys. Rev. B 1 (1970) 4005. [16] R.B. Laughlin, J.D. Joannopoulos, Phys. Rev. B 16 (1977) 2942. [17] S.Y. Lin, Mater. Chem. Phys. 58 (1998) 156. [18] G. Lucovsky, Philos. Mag. B 39 (1979) 513. [19] C.G. Van de Walle, Phys. Rev. B 49 (1994) 4579.
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The vibrational local modes of the metastable threefold coordinated oxygen in hydrogenated amorphous silicon oxide Shu-Ya Lin * Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30043, Taiwan, Republic of China
Abstract The theoretical cluster-Bethe-lattice method is used to study the vibrational local modes of the threefold coordinated oxygen site in amorphous silicon oxide. There is no vibrational mode in the region between 800 and 1000 cmÿ1 for the oxygen site with normal twofold coordination. The vibrational densities of states for the pyramidal O3 bonding con®guration with various vertex angles are calculated. There is a new vibrational mode induced in the region between 800 and 1000 cmÿ1 . The valence alternation model is used to explain the existence of the metastable, O3 , bonding structure. When the hydrogenated amorphous silicon oxide is subject to annealing, the hydrogen will euse and break Si±H bonds. The threefold coordinated Si will re-bond with the O of the neighboring Si±O±Si bond to form a threefold coordinated metastable O3 bond. The O3 bonding structure can induce an 880 cmÿ1 vibrational mode found in experiment. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Amorphous silicon dioxide ®lms are usually grown by thermal treatment or plasma enhanced chemical vapor deposition method [1,2]. There are defect states in a-SiO2 [3±5]. The defect structures can be identi®ed by the electron spin resonance (ESR) [3±5] or optical measurement [3]. The most well known defect in a-SiO2 is the E0 center [6,7], which is a threefold coordinated silicon bonded with three oxygen (ºSiá). The dot denotes the unpaired electron. There are also Si±Si bonds, nonbridging oxygen hole centers (NBOHC,ºSi±Oá), and peroxyl radical centers (ºSi±O±Oá) in a-SiO2 . Oxygen, like chalcogen elements Se and S, has six valence electrons, two of which are s-electrons,
*
Tel.: +886-3 574 2589; fax: +886-3 571 5971. E-mail address: [email protected] (S.-Y. Lin).
and the remaining four are p-electrons. Two of the p-electrons are in non-bonding p states, which are usually located at the top of the valence band and the remaining two p-electrons bond with electrons of the neighboring atoms. In chalcogenide, the valence alternation model [8] is used to explain the existence of diamagnetic defect centers. The threefold metastable O3 sites are assumed to exist in a-SiO2 . But, their concentration could be so small that an infrared (IR) band is not detectable [9]. The study in this paper will show that the threefold metastable O3 can have a density detectable by IR spectroscopy. The IR absorption is an eective way to study local bonding structures in amorphous materials. In the plasma-enhanced chemical vapor deposited (PECVD) a-SiOx :H 0 6 x 6 2, a vibrational mode at 880 cmÿ1 has been reported [10]. This mode is ascribed to the Si±H bond-bending mode of the HSi±(OSi)3 bonding con®guration [10,11]. In the
0022-3093/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 8 5 4 - 6
S.-Y. Lin / Journal of Non-Crystalline Solids 266±269 (2000) 850±853
dc magnetron sputtered a-SiOx :H ®lms [12], the amplitude of the 880 cmÿ1 mode was found to increase after annealing up to 500°C. The amplitude of this mode decreased for higher-temperature annealing and vanished at 900°C. The assignment of this mode was to the (SiO)6 ring [12]. These two dierent aspects of the 880 cmÿ1 vibrational mode of a-SiOx :H have their origins in the parameters of ®lm depositions and depend on whether there was a thermal treatment after deposition. In this paper, a proposal is made that the 880 cmÿ1 vibrational mode is due to the O3 bonding con®guration. The theoretical calculations are used to identify the vibrational mode induced by the O3 bond. The cluster-Bethe-lattice method [13], which is an eective method employed for studying the vibrational and electronic properties of disordered solids, is adopted in this study.
2. Theoretical method The cluster-Bethe-lattice method [13,14] is used to investigate this problem. The GreenÕs function, G, is used to set up the equations of motion. The equation of motion can be written as x2 G 1 DG;
1
where x is the vibrational frequency and D is the dynamical matrix. A valence-force-®eld representation of the near-neighbor interactions [13,15] is used to generate the dynamical matrices. The vibrational local density of states (DOS) can be obtained from the calculated GreenÕs function. The eective ®eld (or transfer matrix) method can be employed to solve the equations of motion to obtain the GreenÕs function and hence the density of states. The mathematical development can be found in Refs. [13,16]. To study the vibrational local modes of aSiOx :H, the SiO2 Bethe lattice must be built ®rst. Details about the SiO2 Bethe lattice used in this study can be found in Ref. [17]. The eective ®elds for this Bethe lattice are calculated. A major work in this study is to identify if the increase in the 880 cmÿ1 mode in a-SiOx :H, after the ®lm is annealed,
851
is due to the O3 bond. The threefold coordinated pyramidal, O3 , bonding con®gurations of various vertex angles are then connected to the SiO2 Bethe lattice. Eq. (1) is used to set up the equations. The vibrational modes induced by the O3 bonding con®guration can be recognized after the equations are solved and the vibrational local DOS are obtained.
3. Results and discussion 3.1. Si±H bond Fig. 1(a) presents the vibrational DOS for the hydrogen of the HSi±(OSi)3 bonding con®guration with C3 symmetry. There is a Si±H bond-bending mode at 876 cmÿ1 and a Si±H bond-stretching mode at 2265 cmÿ1 . Replacing hydrogen by deuterium, the vibrational DOS for the deuterium of the DSi±(OSi)3 bonding con®guration is presented in Fig. 1(b). There is a Si±D bond-bending mode at 617 cmÿ1 and a bond-stretching mode at 1632 cmÿ1 . The scaling factors of 1.39 (2265/1632) and 1.41 (876/617) are close to the square root of the mass ratio of deuterium and hydrogen. The calculated results are in general agreement with experimental data [2]. When there is no C3 symmetry
Fig. 1. Vibrational DOS functions for (a) hydrogen atom of the H±Si(OSi)3 conformation, (b) deuterium of the D±Si(OSi)3 conformation, and (c) bulk SiO2 .
852
S.-Y. Lin / Journal of Non-Crystalline Solids 266±269 (2000) 850±853
for the HSi±(OSi)3 , the Si±H bond-bending mode splits [14]. In the PECVD a-SiOx :H ®lms [2], the amplitudes of the 876 cmÿ1 and 2265 cmÿ1 modes increased with increase of the oxygen content in aSiOx :H. Also shown in the ®gure is the averaged DOS, for density of states, SiO2 . The bending modes are at about 800 cmÿ1 and the stretching modes are in the range of 1000±1200 cmÿ1 . 3.2. O3 bond For the dc magnetron sputtered a-SiOx :H [12], when the ®lms were annealed at 500°C, the Si±H bond-stretching mode decreased, but the 880 cmÿ1 mode increased. In this case, the 880 cmÿ1 mode is not a Si±H related mode. Fig. 2 presents the vibrational DOS for the pyramidal O3 bonding con®guration with dierent vertex angles. There are two vibrational modes induced. The lower one, which is the bond-bending mode, changes from 956 to 785 cmÿ1 and the upper one, which is the bond-stretching mode, changes from 990 to 1043 cmÿ1 as the vertex angle changes from 95° to 115°.
The bending mode decreases in frequency while the stretching mode increases in frequency as the vertex angle increases. These two modes are degenerate at 973 cmÿ1 for the bonding con®guration with vertex angle of 90°. An 880 cmÿ1 mode is induced for a bonding con®guration with vertex angle of 104°. There is a range for the O3 bonding con®guration with various vertex angles, which have vibrational mode in the range between 800 and 1000 cmÿ1 . I have calculated the vibrational DOS for the (SiO)6 regular ring of a-quartz. There is no vibrational mode in the range between 800 and 1000 cmÿ1 . In fact, there are (SiO)6 rings everywhere in a-quartz and there is no vibrational mode in the range between 800 and 950 cmÿ1 [16]. The possibility of the 880 cmÿ1 mode due to the (SiO)6 ring can be ruled out. The 880 cmÿ1 vibrational mode is due to the O3 bonding structure. In chalcogenide, the valence alternation model [8] is used to explain the phenomena of the metastable bonding states. The normal twofold coordinated chalcogen elements can become threefold (C3 ) or onefold (C1 ) coordinated in chalcogenide. They can be either charged or neutral. Lucovsky [18] used the intermediate valence-alternation-pair (IVAP) model and introduced the concept of C 3 and Cÿ 1 pairs in vitreous silicon dioxide (v-SiO2 ). This was the beginning of the concept of threefold coordinated O3 bonds in v-SiO2 . OÕReilly and Robertson [9] studied the defects in v-SiO2 . They ÿ showed that the existence of the O 3 and O1 pairs could give a shallow state in the gap near the bottom of the conduction band. But, the creation energy for the O 3 site is greater than the similar metastable states in chalcogenide glass. The concentration of O 3 is too small to be IR detectable in regular ®lms. Under annealing, the evolution of hydrogen can break the Si±H bonds in a-SiOx :H and allow the formation of the O3 bonding sites. The reaction can be written as Si
Si ÿ O ÿ Si
j
Si ÿ H ! Si ÿ O ÿ Si
1 H2 : 2
2
Fig. 2. Vibrational DOS functions for the threefold coordinated O bonding con®gurations of various vertex angles. The dashed lines are for oxygen and silicon atoms of the bulk SiO2 .
The binding energy of Si±H is smaller than H2 [19]. The change from Si±H to H2 is exothermic. The concentration of the defect sites is proportional to
S.-Y. Lin / Journal of Non-Crystalline Solids 266±269 (2000) 850±853
exp()DG/kT), where DG is the free energy for creating a point defect. Though the creation energy of O3 sites is about 2.6 eV [9], the energy released from the above process can reduce the potential barrier to form O3 sites. The concentration of O3 sites can increase and the detection of IR absorption may be possible. The glass transition temperature (Tg ) of SiO2 is about 1350 K. This O3 metastable state may be frozen if the cooling rate is large enough near Tg [18]. As the annealing temperature increases, the metastable O3 is activated to break one of its Si±O bonds and changes to a more energetically stable Si±O±Si bond. The reaction can be written as Si j
Si ÿ O ÿ Si ! Si ÿ O ÿ Si áSi : 3 The threefold coordinated Si can re-bond with the other unsaturated bonded atoms. These possible processes indicate that the intensity of the 880 cmÿ1 mode will diminish after high temperature annealing. 4. Conclusion This study has shown that an 880 cmÿ1 vibrational mode due to the threefold coordinated, O3 , sites in amorphous silicon oxide is possible. This mode is infrared invisible in the as-deposited ®lms due to the high creation energy for the O3 structure. Annealing breaks the Si±H bonds and may provide sucient energy to overcome the potential barrier to increase the concentration of the O3 bonding con®guration. The glass transition temperature of
853
a-SiO2 makes this metastable state stable. However, higher-temperature annealing can destroy this metastable bonding state. Acknowledgements This research was supported by the National Science Council, the Republic of China under contract no. NSC 87-2215-E-007-026. References [1] J. Batey, E. Tierney, J. Appl. Phys. 60 (1986) 3136. [2] D.V. Tsu, G. Lucovsky, B.N. Davidson, Phys. Rev. B 40 (1989) 1795. [3] D.L. Griscom, J. Non-Cryst. Solids 73 (1985) 51. [4] W.L. Warren, P.M. Lenahan, B. Robinson, J.H. Stathis, Appl. Phys. Lett. 53 (1988) 482. [5] W.L. Warren, E.H. Poindexter, M. Oenberg, W. M ullerWarmuth, J. Electrochem. Soc. 139 (1992) 872. [6] R.A. Weeks, J. Appl. Phys. 27 (1956) 1376. [7] C.M. Nelson, R.A. Weeks, J. Am. Ceram. Soc. 43 (1960) 396. [8] M. Kastner, D. Adler, H. Fritzsche, Phys. Rev. Lett. 37 (1976) 1504. [9] E.P. OÕReilly, J. Robertson, Phys. Rev. B 27 (1983) 3780. [10] L. He, T. Inokuma, Y. Kurata, S. Hasegawa, J. Non-Cryst. Solids 185 (1995) 249. [11] S.Y. Lin, Appl. Phys. Lett. 70 (1997) 203. [12] M. Zacharias, D. Dimova-Malinovska, M. Stutzmann, Philos. Mag. B 73 (1996) 799. [13] G. Lucovsky, W.B. Pollard, J.D. Joannopoulos, G. Lucovsky, The Physics of Hydrogenated Amorphous Silicon II, Springer, Berlin, 1984, p. 302. [14] S.Y. Lin, J. Appl. Phys. 82 (1997) 5976. [15] R.M. Martin, Phys. Rev. B 1 (1970) 4005. [16] R.B. Laughlin, J.D. Joannopoulos, Phys. Rev. B 16 (1977) 2942. [17] S.Y. Lin, Mater. Chem. Phys. 58 (1998) 156. [18] G. Lucovsky, Philos. Mag. B 39 (1979) 513. [19] C.G. Van de Walle, Phys. Rev. B 49 (1994) 4579.