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Dynamic phase diagram for a-Si in rapid thermal processes
Journal of Non-Crystalline Solids 164-166 (1993) 239-242 North-Holland
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"' ~ l
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Dynamic Phase Diagram for a-Si in Rapid Thermal Processes Akio Kitagawa, Shungo Kanai and Masakuni Suzuki Department of Electrical and Computer Engineering, Faculty of Technology, Kanazawa University, Kodatsuno 2-40-20, Kanazawa 920, Japan
The heating rate dependent crystallization temperature of a-Si was calculated from the transient period of the crystallization processes in isothermal conditions. A model for the glass transition in a-Si was proposed based on the continuous random network model. Results are summarized in a phase diagram describing transient phases and their transition temperatures as a function of the heating rate.
1. I N T R O D U C T I O N There has been growing interest in the thermodynamic properties of the a-Si because rapid thermal processes using intense incoherent and coherent light and electron beam are expected to be successfully used for high quality siliconon-insulator (SOI) structures covering large area. In non-isothermal ramp annealing, some problems still remain. For example, the appearance of supercooled liquid state [1, 2], and the heating rate dependent transition temperatures [3, 4], etc. present questions which need to be addressed, Thus, it is important to study transition temperatures as a function of the heating rate or cooling rate. We have developed a procedure estimating the heating rate dependent transition temperature from the transient time associated with nucleation in the phase transition in isothermal conditions. In addition, a model for the glass transition in a-Si is proposed based on the continuous random network model. Results are summarized in a "Dynamic Phase Diagram" of a-Si which makes it possible to investigate the melting and crystallization behavior with respect to the heating rate.
by the formation of clusters of the new phase. The free energy of formation of a cluster is initially positive and goes through a maximum as the cluster size is increased, so clusters need to exceed a critical size to grow into nuclei. As a resuit, there exists the induction time for nucleation or the incubation period in the phase transition [7-11]. Although it is hard to detect experimentally the strict onset of the transition, the induction time or the incubation period for nucleation tin, may be estimated, for example, by plotting the crystalline fraction vs annealing time in the isothermal condition [7, 11]. In the case of the phase transition from a-Si to the crystalline Si, experimental results of the transient period observed in a series of isothermal annealings are all expressed as [7-11], /
lr~ "x
\J:l/
2. T H E H E A T I N G R A T E D E P E N D E N T TRANSITION TEMPERATURE
where E is the activation energy, T is the isotherreal annealing temperature, and 7"0 is the preexponential factor. Although the inverse Arrhenius form of eq.(1) would involve, more or less, some portion of the growth processes of crystallites after nucleation, tt~(T) may be approximated to be tin(T).
2.1. T r a n s i e n t t i m e o f n u c l e a t i o n Transient behavior in the phase transition has been investigated by many authors [5-7]. In the classical theory, nucleation is assumed to occur
2.2. F o r m u l a t i o n t o e s t i m a t e t h e c r y s t a l lization temperature A non-isothermal ramp annealing is regarded as a medley of successive isothermal annealings
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved.
240
A. Kitagawa et al. / Dynamic phase diagramfor a-Si in rapid thermal processes
as shown in Fig.1. Then, the effective incubation period in the phase transition during a ramp annealing can be estimated phenomenologieally from tin(T), assuming that nucleation processes at each new temperature in a medley of successive isothermal annealings are inherited from the previoustannealings) in such a way that the inherited time from the previous annealing plus the annealing time Atk at Tk is reduced to ~(e) ~k+l which is succeeded to the annealing at Tk+l ( : Tk + AT) as given below,
~k+ll(e) = 7(T) tin (T k + AT) (t~*) + Ark) tin(Tk)
a K/s /
a~ c~
I'"
Ttr .~ . . . . . . . . . . . . . . T k + AT _ _ ~ /
a~ t
(2)
A t k ,~t k+l
|n where 7(T) is the correction factor reflecting nonlinear characters of nucleation processes. 7(T) is tentatively taken to be unity at present. The system reaches the transition temperature Ttr, when the sum of the reduced annealing time reaches tin(Ttr). These situations are expressed by the following equation,
~ tiT,T,~ tin(T ) o~ d T =
1
(3)
where Ti is the initial temperature at which the rate scan annealing starts and a is the heating rate. This equation provides the relation between the transient temperature Ttr and the heating rate a. The calculation of eq.(3) can be carried out using eq.(1) of the Arrhenius form. A solid curve T¢ in Fig.2 is the crystallization temperature calculated from data in ref.[ll] which are expected to include little portion of growth processes of crystallites after nucleation. Calculated Tc is valid for the temperature below the glass transition temperature 7"9. We have no data regarding nucleation processes to calculate Tc above T9 at present. The glass transition phenomena are discussed in the next section, 2.3. S u p e r c o o l e d liquid s t a t e a n d t h e glass t r a n s i t i o n of a-Si The transition from a-Si to the crystalline Si involves a fundamental change in bonding from the
ANNEALING TIME Figure 1. Non-isothermal rate scan annealing consisting of a medley of successive isothermal annealings. (At ---, 0)
covalent ,-~4-fold coordination to the metallic ~6 or ,,~12-fold coordination [12, 13], so the transition is discontinuous and first order [4, 14]. The supercooled metallic liquid (ml) phase was observed above--d400 K by measurements of time-resolved reflectance and conductance [2, 15, 16], but further low melting temperatures around 1200 K have been suggested [1, 17, 18]. In addition, a deeper supercooled phase is strongly suggested to be -~4-fold coordination by the experimental fact that disk-shaped Si flakes having amorphous cores were observed in the fine-grained poly-Si produced by electron beam pulse heating [18]. The transition from the solid amorphous phase to the deeper supercooled phase could be identifled with the glass transition. The glass transition has not been definitely observed for the 4-fold coordinated amorphous solids. However, it appears to be possible that the 4-fold coordinated a-Si behaves like fluid as follows. The a-Si involves a high density of dangling bonds [19] and weak bonds [20]. The a-Si is, therefore, expected to dissociate into amorphous fragments at high temperature if crystallization does not intervene. Those fragments may
A. Kitagawa et al. / Dynamic phase diagram for a-Si in rapid thermal processes
metallic liq. Tm
~" 1.5
supercooled metallic liq.
cryst.
"-"
> Tml /:)-. . . . . . . . supercooled / ; semicond, l i q . . . / / 5 " Tg . . ."/. . . . .
~" :~1 .C T / / ~
,
........
amorphous :~ (I) ,, (II) t ,~ . . . . . . 10° HEATING RATE (K/s)
,, (III)..__, i , , , , 101°
Figure 2. Dynamic phase diagram of a-Si in the rate scan annealing
be called pseudo-molecules, of which sizes could be estimated to be similar to those dimensions of Polk's continuous random network model of a-Si, having no dangling bond inside [21]. If the heating rate is high enough, pseudo-molecular-solids would turn to van der Waals (VDW) fluid at a certain temperature assigned to the glass transition temperature. The VDW fluid of pseudomolecules must be a semieonductive (sl) liquid, since constituents of the fluid are ,~4-fold coordination, Although the supercooling down to 1170 K should be taken to the glass transition temperature Tg for the heating process at around 109 K/s [1], Tg at 0.67 K/s is higher than at least 1010 K since Tc at 0.67 K/s was reported to be 1010 K [22]. Taking into account the weak heating rate dependence of Tg, a point of intersection of Tg with T¢, a triple point in the dynamic phase diagram is tentatively placed at about 1100 K. Thus, we obtained two transition temperatures: T a and Trot, the transition temperature from the supercooled sl-Si to the supercooled ml-Si, Numerical calculation of eq.(3) above Tg can not be performed at present because of the lack of data about tlm(T) in the supercooled sl-Si. Time-
241
resolved reflectance measurements, however, provide useful data. For example, heating rates around 106 K/s using cw Ar + ion laser irradiation produced not the supercooled ml-Si but polySi, and Tc was estimated to be lower than 1300 K [23]. On the other hand, the supercooled mlSi was produced by pulsed dye laser irradiation when a is higher than --- 108 K/s [15]. We, thus, obtained the broken curve for 7~ above Tg from 2 ~ 3 x 1 0 t o , ~ l x 10s K/s. To, Tg and T,~t of a-Si as a function of the heating rate are illustrated in Fig.2. The behavior of a-Si in the non-isothermal rate scan annealing is categorized in three regions. In the region (I), solid-phase crystallization exclusively takes place at T¢. In the region (II), a-Si turns to the supercooled sl-phase at Ta and then crystallizes at T~. Explosive crystallization may occur because of the short tim(T) and the accerelation effects due to the sharp exothermic peak at To. In the region (III), crystallization does not occur, the aSi goes into the supercooled ml-phase through the supercooled sl-phase. Tg and T¢ in the region (II) and T,~z in Fig.2 include some ambiguity since they were estimations obtained from a few data over a wide range of a. T¢ in the region (I) may also somewhat be modified when the detection level of the transient period is elevated. Characteristic features of the dynamic phase diagram, however, will be held, even if modified. Similar phase diagrams for other amorphous solids will be obtained applying similar procedures. Phase diagrams for the cooling processes could also be developed.
3. C O N C L U D I N G
SUMMARY
Transient phases and their transition temperatures of a-Si were found to be expressed as a function of the heating rate, so that the behavior of a-Si in the non-isothermal rate scan anhealing can be categorized in three regions with respect to the heating rate. The appearence of the supercooled semiconductive liquid state of aSi was understood in termes of van der Waals fluid of pseudo-molecules. These resnlts were summarized in a "Dynamic Phase Diagram".
242
A. Kitagawa et al. / Dynamic phase diagram for a-Si in rapid thermal processes
ACKNOWLEDGEMENTS The authors wish to thank Dr. S. Usui and Dr. D. P. Gosain of Sony Central Research Lab. and Dr. S. Tsuda and Mr. S. Noguchi of Sanyo Functional Mater. Res. Center for their useful discussions and encouragement. The authors also thank to Prof. M. Kitao of Shizuoka university for providing useful data and helpful discussion. This work was partially supported by Betsukawa Fundation and Iketani Science Fundation.
REFERENCES 1. P. Baeri, G. Foti, J. M. Poate and A . G . Cullis, Phys. Rev. Lett. 45 (1980) 2036. 2. M.O. Thompson, G. J. Galvin, J. W. Mayer, P. S. Peercy, J. M. Poate, D. C. Jacobson, A. G. Cullis and N. G. Chew, Phys. Rev. Lett. 52 (1984) 2360. 3. S. R. Stiffler, M. O. Thompson and P. S. Peercy, Phys. Rev. B 43 (1991) 9851. 4. B.G. Bagley and H. S. Chen, AIP Conf. Proc. 50 (1979) 97. 5. D. Kashchiev, Surf. Sci. 14 (1969) 209. 6. K . F . Kelton, A. L. Greer and C. V. Thompson, J. Chem. Phys 79 (1983) 6261. 7. R. B. Iverson and R. Reif, J. Appl. Phys. 62 (1987) 1675. 8. N. A. Blum and C. Feldman, J. Non-cryst. Solids, 11 (1972) 242. 9. U. USester, Phys. Star. Sol. (a) 48 (1978) 313. 10. R. Bisaro, J. Magarifio, K. Zellama, S. Squelard, P. Germain and J. F. Morhange, Phys. Rev. B 31 (1985) 3568. 11. M. Suzuki, M. Hiramoto, M. Ogiura, W. Kamisaka and S. Hasegawa, Jpn. J. Appl. Phys. 27 (1988) L1380. 12. H. C. Gerritsen, H. van Brug, F. Bijkerk, K. Murakami and M. J. van der Wiel, J. Appl. Phys. 60 (1986) 1774. 13. E. P. Donovan, F. Spaepen, D. Turnbull, J. M. Poate and D. C. Jacobson, J. Appl. Phys. 57 (1985) 1795. 14. F. Spaepen and D. Turnbull, AIP Conf. Proc. 50 (1979) 73. 15. G. L. Olson, J. A. Roth, E. Nygren, A. P. Pogany and J. S. Williams, Mat. Res. Soc.
Symp. Proc. 74 (1987) 109. 16. P. S. Peercy, M. O. Thompson and J. Y. Tsao, Mater. Res. Soc. Symp. Proc. 74 (1987) 15. 17. J. J. P. Bruines, R. P. M. van Hal, B. H. Hoek, M . P . A . Viegers and H. M. J. Boots, Mater. Res. Soc. Symp. Proc. 74 (1987) 91. 18. D. H. Lowndes, S. J. Pennycook, G. E. Jellison,Jr., S. P. Withrow and D. N. Mashburn, J. Mater. Res. 2 (1987) 648. 19. M. It. Brodski, R. S. Title, K. Weiser and G. D. Pettit, Phys. Rev. B 1 (1970) 2632. 20. T. Motooka and O. H. Holland, Appl. Phys. Lett. 61 (1992) 3005. 21. D. E. Polk, J. Non-cryst. Solids, 5 (1971) 365. 22. J. C. C. Fan and C. H. Anderson, Jr., J. Appl. Phys. 52 (1981) 4003. 23. S. A. Kokorowski, G. L. Olson, J. A. Roth and L. D. Hess, Phys. Rev. Lett. 48 (1982) 498.
~
S
"' ~ l
~
Dynamic Phase Diagram for a-Si in Rapid Thermal Processes Akio Kitagawa, Shungo Kanai and Masakuni Suzuki Department of Electrical and Computer Engineering, Faculty of Technology, Kanazawa University, Kodatsuno 2-40-20, Kanazawa 920, Japan
The heating rate dependent crystallization temperature of a-Si was calculated from the transient period of the crystallization processes in isothermal conditions. A model for the glass transition in a-Si was proposed based on the continuous random network model. Results are summarized in a phase diagram describing transient phases and their transition temperatures as a function of the heating rate.
1. I N T R O D U C T I O N There has been growing interest in the thermodynamic properties of the a-Si because rapid thermal processes using intense incoherent and coherent light and electron beam are expected to be successfully used for high quality siliconon-insulator (SOI) structures covering large area. In non-isothermal ramp annealing, some problems still remain. For example, the appearance of supercooled liquid state [1, 2], and the heating rate dependent transition temperatures [3, 4], etc. present questions which need to be addressed, Thus, it is important to study transition temperatures as a function of the heating rate or cooling rate. We have developed a procedure estimating the heating rate dependent transition temperature from the transient time associated with nucleation in the phase transition in isothermal conditions. In addition, a model for the glass transition in a-Si is proposed based on the continuous random network model. Results are summarized in a "Dynamic Phase Diagram" of a-Si which makes it possible to investigate the melting and crystallization behavior with respect to the heating rate.
by the formation of clusters of the new phase. The free energy of formation of a cluster is initially positive and goes through a maximum as the cluster size is increased, so clusters need to exceed a critical size to grow into nuclei. As a resuit, there exists the induction time for nucleation or the incubation period in the phase transition [7-11]. Although it is hard to detect experimentally the strict onset of the transition, the induction time or the incubation period for nucleation tin, may be estimated, for example, by plotting the crystalline fraction vs annealing time in the isothermal condition [7, 11]. In the case of the phase transition from a-Si to the crystalline Si, experimental results of the transient period observed in a series of isothermal annealings are all expressed as [7-11], /
lr~ "x
\J:l/
2. T H E H E A T I N G R A T E D E P E N D E N T TRANSITION TEMPERATURE
where E is the activation energy, T is the isotherreal annealing temperature, and 7"0 is the preexponential factor. Although the inverse Arrhenius form of eq.(1) would involve, more or less, some portion of the growth processes of crystallites after nucleation, tt~(T) may be approximated to be tin(T).
2.1. T r a n s i e n t t i m e o f n u c l e a t i o n Transient behavior in the phase transition has been investigated by many authors [5-7]. In the classical theory, nucleation is assumed to occur
2.2. F o r m u l a t i o n t o e s t i m a t e t h e c r y s t a l lization temperature A non-isothermal ramp annealing is regarded as a medley of successive isothermal annealings
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved.
240
A. Kitagawa et al. / Dynamic phase diagramfor a-Si in rapid thermal processes
as shown in Fig.1. Then, the effective incubation period in the phase transition during a ramp annealing can be estimated phenomenologieally from tin(T), assuming that nucleation processes at each new temperature in a medley of successive isothermal annealings are inherited from the previoustannealings) in such a way that the inherited time from the previous annealing plus the annealing time Atk at Tk is reduced to ~(e) ~k+l which is succeeded to the annealing at Tk+l ( : Tk + AT) as given below,
~k+ll(e) = 7(T) tin (T k + AT) (t~*) + Ark) tin(Tk)
a K/s /
a~ c~
I'"
Ttr .~ . . . . . . . . . . . . . . T k + AT _ _ ~ /
a~ t
(2)
A t k ,~t k+l
|n where 7(T) is the correction factor reflecting nonlinear characters of nucleation processes. 7(T) is tentatively taken to be unity at present. The system reaches the transition temperature Ttr, when the sum of the reduced annealing time reaches tin(Ttr). These situations are expressed by the following equation,
~ tiT,T,~ tin(T ) o~ d T =
1
(3)
where Ti is the initial temperature at which the rate scan annealing starts and a is the heating rate. This equation provides the relation between the transient temperature Ttr and the heating rate a. The calculation of eq.(3) can be carried out using eq.(1) of the Arrhenius form. A solid curve T¢ in Fig.2 is the crystallization temperature calculated from data in ref.[ll] which are expected to include little portion of growth processes of crystallites after nucleation. Calculated Tc is valid for the temperature below the glass transition temperature 7"9. We have no data regarding nucleation processes to calculate Tc above T9 at present. The glass transition phenomena are discussed in the next section, 2.3. S u p e r c o o l e d liquid s t a t e a n d t h e glass t r a n s i t i o n of a-Si The transition from a-Si to the crystalline Si involves a fundamental change in bonding from the
ANNEALING TIME Figure 1. Non-isothermal rate scan annealing consisting of a medley of successive isothermal annealings. (At ---, 0)
covalent ,-~4-fold coordination to the metallic ~6 or ,,~12-fold coordination [12, 13], so the transition is discontinuous and first order [4, 14]. The supercooled metallic liquid (ml) phase was observed above--d400 K by measurements of time-resolved reflectance and conductance [2, 15, 16], but further low melting temperatures around 1200 K have been suggested [1, 17, 18]. In addition, a deeper supercooled phase is strongly suggested to be -~4-fold coordination by the experimental fact that disk-shaped Si flakes having amorphous cores were observed in the fine-grained poly-Si produced by electron beam pulse heating [18]. The transition from the solid amorphous phase to the deeper supercooled phase could be identifled with the glass transition. The glass transition has not been definitely observed for the 4-fold coordinated amorphous solids. However, it appears to be possible that the 4-fold coordinated a-Si behaves like fluid as follows. The a-Si involves a high density of dangling bonds [19] and weak bonds [20]. The a-Si is, therefore, expected to dissociate into amorphous fragments at high temperature if crystallization does not intervene. Those fragments may
A. Kitagawa et al. / Dynamic phase diagram for a-Si in rapid thermal processes
metallic liq. Tm
~" 1.5
supercooled metallic liq.
cryst.
"-"
> Tml /:)-. . . . . . . . supercooled / ; semicond, l i q . . . / / 5 " Tg . . ."/. . . . .
~" :~1 .C T / / ~
,
........
amorphous :~ (I) ,, (II) t ,~ . . . . . . 10° HEATING RATE (K/s)
,, (III)..__, i , , , , 101°
Figure 2. Dynamic phase diagram of a-Si in the rate scan annealing
be called pseudo-molecules, of which sizes could be estimated to be similar to those dimensions of Polk's continuous random network model of a-Si, having no dangling bond inside [21]. If the heating rate is high enough, pseudo-molecular-solids would turn to van der Waals (VDW) fluid at a certain temperature assigned to the glass transition temperature. The VDW fluid of pseudomolecules must be a semieonductive (sl) liquid, since constituents of the fluid are ,~4-fold coordination, Although the supercooling down to 1170 K should be taken to the glass transition temperature Tg for the heating process at around 109 K/s [1], Tg at 0.67 K/s is higher than at least 1010 K since Tc at 0.67 K/s was reported to be 1010 K [22]. Taking into account the weak heating rate dependence of Tg, a point of intersection of Tg with T¢, a triple point in the dynamic phase diagram is tentatively placed at about 1100 K. Thus, we obtained two transition temperatures: T a and Trot, the transition temperature from the supercooled sl-Si to the supercooled ml-Si, Numerical calculation of eq.(3) above Tg can not be performed at present because of the lack of data about tlm(T) in the supercooled sl-Si. Time-
241
resolved reflectance measurements, however, provide useful data. For example, heating rates around 106 K/s using cw Ar + ion laser irradiation produced not the supercooled ml-Si but polySi, and Tc was estimated to be lower than 1300 K [23]. On the other hand, the supercooled mlSi was produced by pulsed dye laser irradiation when a is higher than --- 108 K/s [15]. We, thus, obtained the broken curve for 7~ above Tg from 2 ~ 3 x 1 0 t o , ~ l x 10s K/s. To, Tg and T,~t of a-Si as a function of the heating rate are illustrated in Fig.2. The behavior of a-Si in the non-isothermal rate scan annealing is categorized in three regions. In the region (I), solid-phase crystallization exclusively takes place at T¢. In the region (II), a-Si turns to the supercooled sl-phase at Ta and then crystallizes at T~. Explosive crystallization may occur because of the short tim(T) and the accerelation effects due to the sharp exothermic peak at To. In the region (III), crystallization does not occur, the aSi goes into the supercooled ml-phase through the supercooled sl-phase. Tg and T¢ in the region (II) and T,~z in Fig.2 include some ambiguity since they were estimations obtained from a few data over a wide range of a. T¢ in the region (I) may also somewhat be modified when the detection level of the transient period is elevated. Characteristic features of the dynamic phase diagram, however, will be held, even if modified. Similar phase diagrams for other amorphous solids will be obtained applying similar procedures. Phase diagrams for the cooling processes could also be developed.
3. C O N C L U D I N G
SUMMARY
Transient phases and their transition temperatures of a-Si were found to be expressed as a function of the heating rate, so that the behavior of a-Si in the non-isothermal rate scan anhealing can be categorized in three regions with respect to the heating rate. The appearence of the supercooled semiconductive liquid state of aSi was understood in termes of van der Waals fluid of pseudo-molecules. These resnlts were summarized in a "Dynamic Phase Diagram".
242
A. Kitagawa et al. / Dynamic phase diagram for a-Si in rapid thermal processes
ACKNOWLEDGEMENTS The authors wish to thank Dr. S. Usui and Dr. D. P. Gosain of Sony Central Research Lab. and Dr. S. Tsuda and Mr. S. Noguchi of Sanyo Functional Mater. Res. Center for their useful discussions and encouragement. The authors also thank to Prof. M. Kitao of Shizuoka university for providing useful data and helpful discussion. This work was partially supported by Betsukawa Fundation and Iketani Science Fundation.
REFERENCES 1. P. Baeri, G. Foti, J. M. Poate and A . G . Cullis, Phys. Rev. Lett. 45 (1980) 2036. 2. M.O. Thompson, G. J. Galvin, J. W. Mayer, P. S. Peercy, J. M. Poate, D. C. Jacobson, A. G. Cullis and N. G. Chew, Phys. Rev. Lett. 52 (1984) 2360. 3. S. R. Stiffler, M. O. Thompson and P. S. Peercy, Phys. Rev. B 43 (1991) 9851. 4. B.G. Bagley and H. S. Chen, AIP Conf. Proc. 50 (1979) 97. 5. D. Kashchiev, Surf. Sci. 14 (1969) 209. 6. K . F . Kelton, A. L. Greer and C. V. Thompson, J. Chem. Phys 79 (1983) 6261. 7. R. B. Iverson and R. Reif, J. Appl. Phys. 62 (1987) 1675. 8. N. A. Blum and C. Feldman, J. Non-cryst. Solids, 11 (1972) 242. 9. U. USester, Phys. Star. Sol. (a) 48 (1978) 313. 10. R. Bisaro, J. Magarifio, K. Zellama, S. Squelard, P. Germain and J. F. Morhange, Phys. Rev. B 31 (1985) 3568. 11. M. Suzuki, M. Hiramoto, M. Ogiura, W. Kamisaka and S. Hasegawa, Jpn. J. Appl. Phys. 27 (1988) L1380. 12. H. C. Gerritsen, H. van Brug, F. Bijkerk, K. Murakami and M. J. van der Wiel, J. Appl. Phys. 60 (1986) 1774. 13. E. P. Donovan, F. Spaepen, D. Turnbull, J. M. Poate and D. C. Jacobson, J. Appl. Phys. 57 (1985) 1795. 14. F. Spaepen and D. Turnbull, AIP Conf. Proc. 50 (1979) 73. 15. G. L. Olson, J. A. Roth, E. Nygren, A. P. Pogany and J. S. Williams, Mat. Res. Soc.
Symp. Proc. 74 (1987) 109. 16. P. S. Peercy, M. O. Thompson and J. Y. Tsao, Mater. Res. Soc. Symp. Proc. 74 (1987) 15. 17. J. J. P. Bruines, R. P. M. van Hal, B. H. Hoek, M . P . A . Viegers and H. M. J. Boots, Mater. Res. Soc. Symp. Proc. 74 (1987) 91. 18. D. H. Lowndes, S. J. Pennycook, G. E. Jellison,Jr., S. P. Withrow and D. N. Mashburn, J. Mater. Res. 2 (1987) 648. 19. M. It. Brodski, R. S. Title, K. Weiser and G. D. Pettit, Phys. Rev. B 1 (1970) 2632. 20. T. Motooka and O. H. Holland, Appl. Phys. Lett. 61 (1992) 3005. 21. D. E. Polk, J. Non-cryst. Solids, 5 (1971) 365. 22. J. C. C. Fan and C. H. Anderson, Jr., J. Appl. Phys. 52 (1981) 4003. 23. S. A. Kokorowski, G. L. Olson, J. A. Roth and L. D. Hess, Phys. Rev. Lett. 48 (1982) 498.