Comparison of growth characteristics of sapphire and silicon ribbon produced by EFG

316

Journal of Crystal Growth 65 (1983) 316-323 North-Holland, Amsterdam

COMPARISON OF GROWTH CHARACTERISTICS OF SAPPHIRE AND SILICON RIBBON PRODUCED BY EFG

J.P. KALEJS Mobil Solar Energy Corporation, Waltham, Massachusetts 02254, USA

and H.M. ETTOUNEY and R.A. BROWN Department of Chemical Engineering, Massachusetts Insitute of Technology, Cambridge, Massachusetts 02139, USA

Finite dement analysis of heat transfer and meniscus shape is used to compare the operating conditions for Edge-defined Film-fed Growth (EFG) of silicon and sapphire (A1203) sheets. The relationships between sheet thickness and growth velocity are predicted for both systems with varying ambient thermal conditions. More effective radiative heat transfer between the melt and surroundings makes the A1203 growth less sensitive to growth rate variations and leads to more convex (with respect to the melt) melt/solid interface shapes than for Si sheets grown from a die with the same dimensions. Considering capillarity alone would lead to the opposite conclusion for the sensitivity of sheet thickness to growth rate.

1. Introduction

Edge-defined Film-fed Growth (EFG) was first applied to the growth of sapphire (A1203) and has been developed for production of diverse crystal shapes used in many applications [1], most notably for the growth of thin silicon ribbon for use as a substrate for photovoltaic devices [2]. Although experimental aspects of the EFG process have been extensively investigated [3,4], detailed theoretical understanding of the interactions of capillarity and heat transfer in setting the operating conditions for steady-state growth has not progressed at a comparable rate for either EFG or other meniscus-defined techniques for crystal growth. In a recent paper [5], we reported a computeraided algorithm based on the finite-element method for solving two-dimensional heat transfer models for the temperature fields in melt, crystal and die and the location of the melt/crystal interface simultaneously with the Young-Laplace equation for meniscus shape. This analysis was used in ref. [5] to predict the variation of thickness of a silicon sheet with changes in growth rate and ambient

heat transfer conditions, and so coupled the meniscus shape and temperature distribution of the sheet directly to control parameters in the actual growth system. In the present study, we extend the analysis to the growth of AI203 sheets from a molybdenum die and compare steady-state growth of AI203 to the previous results for Si sheets. Emphasis is placed on differences in the sensitivity of the growth of A1203 and Si to changes in process conditions that arise from the differences in the thermophysical properties of the two materials. This comparison is made possible by considering the growth of A1203 and Si from dies of the same dimension and in growth with similar heating and cooling configurations. The equations governing heat transfer and meniscus shape are presented in detail in ref. [5] and only parameters that are relevant to the present study are reviewed in section 2. The description of the finite-element solution of these equations is left entirely to ref. [5]. The comparisons of the variation of crystal thickness and melt/solid interface shape with growth rate and ambient heat transfer conditions for A1203 and Si are presented in section 3.

0022-0248/83/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

317

J.P. Kalejs et al. / Growth characteristics of sapphire and Si ribbon

v't

2. Models for Si and A1203 growth We model the growth of Si and A1203 sheets with thickness 2t that are continuously pulled and solidified from a die at the velocity Vs. The die geometry used in both systems is shown in fig. 1 and has the same dimensions as reported in table 1 of ref. [5]. The die is made of graphite for Si growth and of molybdenum for the A1203 system. The heat transfer models used here and in ref. [5] assume that conduction is the dominant mode of heat transfer in both melt and crystal and account for convection simply by incorporating uniform velocities in the melt, VL, and crystal, Vs, in the growth direction. Heat is transported through the die only by conduction. The transparency of the Si and A1203 is neglected. Radiation through solid A1203 is a more significant mechanism for heat transfer than for Si [6]. It is esimated that up to 80% of the radiation emitted at the A1203 interface will be transmitted through the solid, as compared to about 20% for silicon. While silicon transparency is confined to infrared frequencies, the transmission through A1203 is so pervasive that the growth interface can be visually observed during growth. Some uncertainty exists in the reported thermal conductivity of crystalline A1203, and the value used here may already partially include effects of crystal transparency. Heat transfer in the melt, crystal and die and the role of surface tension in determining the shape of the m e l t / g a s meniscus are parameterized b y a number of dimensionless groups listed in

t

SHEET

I MELT/SOLID INTERFACE ~

F

2t .7

MENIS

s ~3 -

~

I-

~3

I

x

|

F 2-4

Fig. 1. Cross-sectional schematic of EFG system used in this study.

Table 1 Dimensionless groups for modeling Si and A1203 systems Dimensionless group

~5

Biot numbers, Bii ---hL*/ki, i = L, S, d Radiation number, R L ---ociL*T*3/kL Melting temperature, Tm= 1"rn/T* Stefan number, St ~- AHf/c_ T* Bond number, Bo ---gL*2A;/~y Static heat, Heff ---heff/L* Surrounding temperature, Too =-J'~/ T*

Si 0 7.2x10 -4 0.95 1.0 2.1x10 -3 20 0.2

A1203 0 7.2x10 -3 1.30 0.47 2.6x10 -3 20 0.2

Reference temperature, T* (K) Reference length, L* = 213 (cm)

1783 0.025

1783 0.025

318

J.P. Kalejs et al. / Growth characteristics of sapphire and Si ribbon

Table 2 Thermophysical properties for silicon and A1203 systems Property Melt Thermal conductivity, k L (W/cm-K) Density, PL (g/cm3) Specific heat, cpL (J/g. K) Emissivity, ¢ Crystal Thermal conductivity, k s (W/cm. K) Density, Ps (g/cm3) Specific heat, cps (J/g. K) Emissivity, ¢ Interfaces Melting temperature, 2Pm (K) Latent heat, AHf (J/g) Melt contact angle with die, Ca (deg) Melt/gas surface tension, ~ (dyn/cm) Melt/crystal growth angle (orientation) (deg)

Si

A1203

0.64 2.42 1.00 0.64

0.1 3.05 1.26 0.9

0.22 2.30 1.00 0.64

0.1 4.00 1.26 0.9

1683 1800 30 720 11

2316 1046 26 700 17 ((0001))

35 ((10i0)) Property

Graphite

Molybdenum

Die Thermal conductivity, k a (W/cm-K) Density, Pa (g/cm3) Specific heat, cpa (J/g. K)

0.43 2.1 1.7

0.84 10.2 0.4

table 1. These groups arise naturally in the dimensionless form of the governing equations (see ref. [5]) when the reference temperature is taken as T* and the reference length scale is identified as L*. The values of these parameters listed in table 1 were calculated using the estimates for thermophysical properties of Si and A1203 given in table 2 with T* = 1783 K and L* = 0.025 cm. The Biot and radiation numbers listed in table 1 characterize the importance of convective and radiative heat transfer, respectively, from the die/crystal/melt system to an ambient at the uniform dimensionless temperature, Too, according to the boundary condition -(n.

wT/) = B i i ( T , - T o o ) + R i ( T i 4 - T4),

i = L,S'd,

(1)

where n is the unit vector normal to a surface separating die (i = d), melt (i = L), or crystal (i = S) from the surroundings. All solutions presented here are for Bi i = 0. The higher melting tempera-

ture of A1203 results in a greater portion of heat being transmitted by radiation to the surroundings than for silicon. This is accounted for in our model by the larger dimensionless temperatures in the A1203 system; compare the melting temperatures in table 1. Radiative heat transfer to the surroundings also represents a larger portion of the heat lost from the melt in the A1203 system because of the much lower thermal conductivity in this system as compared to silicon; this effect is described quantitatively by the order-of-magnitude increase in R L for A1203 over the radiation number for molten Si. The radiation numbers for the crystal and die for both Si and AI203 are computed by scaling R L with the appropriate thermal conductivity ratio. The molybdenum die used in the A1203 system is more conductive relative to the melt ( k d / k L = 8.4) than the graphite die in the silicon system ( k d / k L = 0.67) and this difference causes the shape of the isotherms near the die top to vary significantly between the two systems. Although reported surface tensions of Si and

J.P. Kalejs et al. / Growth characteristics of sapphire and Si ribbon

0.055

"~

I

I

I

I

I

I

~.. \ ~ ,

o.o3o

o "; ,,, 0.020 ,ez

,:\ \ ' X \\ \ \ \

to

~\

~ ~

", ,,

~¢o:170\

",,

o

I-to 0.010 >-

o.-

0.005

oooo

~

5i

'v5 ,5 ~.~

,

0.00

\\

~

0.02

, 0.0~

,,

\0.5

'\',X

~. , \ \ ,

0.01

f 0.5 cm

0.04

\.

"',

\,

,

0.05

0.06

',

,.07

H E I G H T , s (cm)

MENISCUS

Fig. 2. Relationship between crystal thickness 2 t and meniscus height s for a range of static heads h~ff. Growth angles @o are for Si (11 °) and for <0001> (17 °) and <1010} (35 °) grown A1203.

0.055

I

I

I

I

I

~

,\

3.1. Operating sensitivity

0.025

'x}

d 0.020

\

Z v (.9

C~)

'\ ~ \ .

-r 0.015 t-,.J

0.010 >-

0.005

0.000

\\ x \4j'k "%. \ \x

! -(!) O.

A1203 melts are similar, the thickness of an A1203 crystal is much more sensitive to meniscus height because of the larger wetting angle @0 at the melt/gas/crystal junction. Values of @0 are listed in table 3 for sapphire. These vary between 17 ° and 35 ° , depending on the crystal orientation [7]. Crystal thicknesses 2t predicted by solution of the Young-Laplace equation are shown in fig. 2 as a function of meniscus height, s, and the height of the die top above the level of the melt, heff, for wetting angles typical of the A1203 and Si systems. The operating conditions for the EFG system are characterized by the pull rate of the sheet, Vs, the ambient temperature of the surroundings, ]~oo, and a set-point temperature, I"0, for the melt entering at the bottom of the die. Calculations were performed to set the ranges of these parameters where steady-state operation is possible and to compare the sensitivity of crystal thickness to changes in the parameters for A1203 and Si. In the calculations presented here, all other control parameters were held at the values given in table 1, unless changes are explicitly mentioned.

3. Comparison of Ai 203 and Si sheet growth

I

%

0.030

319

ib) I

2.

~ (d) (c)

(e) "'~.. (g) (h) (m)

I

I I I 6. 8. I0. RATE, Vs(cm/min)

4. GROWTH

'~(i) I 12.

14.

Fig. 3. Operating curves of crystal thickness as a function of growth rate for Si and A1203 sheets grown in the systems described in table 1. Curves (a)-(i) are for Si with set-point temperatures varying from (a) 1793 to (i) 1713 K in 10 K increments. Curves (j)-(m) are for A1203 growth with different combinations of @0 and ~r0; (j) 17 °, 2675 K; (k) 17 °, 2585 K; (1) 17 °, 2496 K; (m) 35 °, 2585 K.

Increasing the growth rate at constant set-point and ambient temperatures increases the amount of sensible and latent heat that must be dissipated and causes the interface to rise. As demonstrated in fig. 2, the meniscus height increase results in thinner sheets. Variations of crystal thickness with growth rate for Si and A1203 ribbon are compared in fig. 3 for several set-point temperatures; ]'oo = 357 K for all cases. The most striking feature of these results is the order-of-magnitude greater sensitivity of t to Vs for Si than for A1EOa, as measured by the slope d t / d V s, for the range of growth rates and die set-point temperatures considered. The slope estimates for linear interpolations of the curves in fig. 3 are listed separately in table 3. Comparable differences are found in the slopes of t versus heff curves, but they are not reproduced here. In both systems, decreasing the set-point tem-

320

J.P. Kalejs et aL / Growth characteristics of sapphire and Si ribbon 0.12

Table 3 Comparison of sensitivity of crystal thickness to growth rate for A1203 and Si; 213 = 0.025 cm A

I

I

O.lO

Material

I"o (K)

I"oo(K)

d t / d V s (min)

A1203, 4o = 17°

2496 2585 2675 2585 2585 2496

357 357 357 714 1783 1783

1.62 × 10- 3 1.51 × 10- 3 1.47 X 10- 3 1.51 × 10- 3 1.71 × 1 0 - 3 2.72 x 10- 3

A 1 2 0 3 , #do = 35°

2496 2585

357 357

2.19X 10 -3 1.96X 10 -3

~ 0.04 -

Si, g'o = 11°

1793 1783 1773 1763

357 357 357 357

1.77 x 10 -2 1.27 x 10 -2 9.30x 10 -3 7.60 × 10- 3

u 0.02 -

2585

357

2.23 x 10 -3

A1203, q>o= 17 ° , R L = 3.6 x 10 -3

I

~-oJ ta0

to w r-

0.08 0.06

-r

>er

o.o0

~

0

.

0

2

I

o.

5

I

I

2 4 6 GROWTH RATE,Vi(cm/min)

Fig. 4. Operating curves for A1203 sheets grown from dies with three gaps; ~P~ = 357 K and 1"0= 2585 K. p e r a t u r e To c a u s e d t h e m e l t t o s o l i d i f y c l o s e r t o t h e die, a n d t h e o p e r a t i n g c u r v e w a s t r a n s l a t e d t o h i g h e r v a l u e s o f 2t. F o r b o t h Si a n d A 1 2 0 3, t h e crystal thickness was slightly more sensitive to c h a n g e s i n g r o w t h r a t e a t l o w e r v a l u e s o f 7"o; see t a b l e 3. T h e s l o p e ( d t / d V s ) i n c r e a s e d o n l y 30% f o r A 1 2 0 3 g r o w t h w i t h ~0 = 35° o v e r g r o w t h w i t h ~o = 17 °. I n t h e c a s e w h e r e t h e A 1 2 0 3 m e l t t h e r m a l conductivity was increased by a factor of two

( d a t a f o r R L = 3.6 X l 0 - 3 i n t a b l e 3), t h e s h e e t t h i c k n e s s s e n s i t i v i t y t o Vs i n c r e a s e d b y 40%. T h e e n h a n c e d r a d i a t i v e h e a t t r a n s f e r to t h e surroundings and the low melt thermal conductivity in the A120 3 system are responsible for the observed reduced sensitivity of crystal thickness to g r o w t h r a t e v a r i a t i o n s . F o r A 1 2 0 3, t h e s e n s i b l e h e a t i n c r e a s e d u e t o i n c r e a s i n g Vs is lost t o t h e

Table 4 Melt temperature gradients at the center of the melt/crystal interface Material

7"o(K)

Si, 213 = 0.025 cm

1763 1763 1763 1763

A1203, 213 = 0.025 cm A1203, 213 = 0.1 cm

2P~ (K)

Vs (cm/min)

d l ' / d y (K/cm)

357 357 357 357

1 2 3 4

-

2585 2585 2585

357 357 357

0 1.5 3.0

- 6.90 X 103 -6.13 x 103 - 5.35 × 103

2585 2585 2585 2585 2585 2585 2585

357 357 357 1783 1783 1783 1783

1.5 3 4.5 0 1.5 3.0 4.5

-2.54× -2.03 x - 1.41 x - 2.60 x - 1.98 x - 1.40 x - 9.69 x

5.93 x 5.99 x 6.69 x 8.08 x

102 102 102 102

103 103 103 103 103 103 102

J.P. Kalejs et al. / Growth characteristics of sapphire and Si ribbon

surroundings by a small increase in surface area of the meniscus at the expense of a slight decrease in crystal thickness. This is not the case for silicon. As discussed in ref. [5], the bulk of the heat transferred from a silicon melt conducts through the melt/crystal interface into the crystal; then any increase in meniscus height caused by increasing Vs decreases the effectiveness of this axial conduction by decreasing the cross-sectional area of the crystal. Increasing the thickness of the A1203 ribbon by widening the die-gap, 213, increased the sensitivity of the crystal thickness to changes in Vs, as shown in fig. 4 for ir0 = 2585 K and I"o0= 357 K. The slope d t / d V s for 0.1 cm thick A1203 sheets was similar to the values predicted for Si growth with 213 = 0.025 cm. In all three cases shown in fig. 4, the melt solidified at the die top for low growth rates. Raising the ambient temperature Too increased the height of the melt and magnified the sensitivity of the thickness to the growth rate; for 7"~ = 1783 K, dt/dVs = -1.41 × 10 -2 min, compared to -1.20 X 10 -z for 7"~ = 357 K. A static (Vs = 0) sheet in contact with its melt was possible for this higher i"~ with a crystal thickness of 27 = 0.091 cm. Table 4 compares the axial temperature gradi005 o ..c i x

I.l.I ,'vLLI I-Z

I

1

I

I

[

I

004

oo ,is 002

-

~

=

001 0 ).-...I I.IJ

Tc0 = 1 7 8 5

0.00

-0.0

I 0.0

I 0.1

I 0.2

I 0.5 X

I 0.4

I 0.5

K

I 0.6

0.7

COORDINATE

Fig. 5. Variation of AI203 m e l t / c r y s t a l interface shape with a m b i e n t temperature T~; V~ = 0, To = 2585 K and 2/3 = 0.025 cm.

321

ent in the melt evaluated along the centerline of the sheet at the solidification front for Si and A1203 and shows the difference in thermal response of these two systems. For the range of operating conditions examined, the temperature gradient d]'/d)7 for silicon increased with increas, ing growth velocity, whereas the gradient for A1203 decreased. The gradients in both systems are much higher than usually are realized in practice because thermal stresses caused by growing a crystal under these conditions can lead to cracking of the sheet. Temperature gradients of under 500 K / c m are approached, however, by increasing the ambient temperature to values nearer the melting point, as shown by the calculations for A1203with 2/3 = 0.1 cm. Tailoring the ambient heat transfer conditions to an actual growth furnace and proper accounting of radiation through the crystal will lead to realistic temperature gradients and to growth conditions that are more sensitive to crystal thickness.

3.2. Melt/crystal interface shapes for A1203 The direction and extent of the curvature of the melt/solid interface is a major factor in setting the distribution of dopants and impurities across the thickness of the sheet [8-10]. Interface shapes for A120 a ribbon in the limit of zero growth rate (Vs = 0) are shown in fig. 5 as a function of the lateral coordinate scaled with 2/3 = 0.025 cm, for ~'0 = 2585 K and three values of the ambient temperature T~. For the lower two values of T~ the interfaces were convex (with respect to the melt) near the center of the crystal, and concave close to the edge of the sheet; the maximum interface deflection was less than 10% of the crystal halfthickness in both cases. Increasing the ambient temperature to 7"o= 1783 K increased the height of the melt and resulted in an entirely concave melt/solid interface. The convex-to-concave transition in interface shape observed for low ambient temperatures becomes more pronounced as the thickness of the A1203 sheet is increased by widening the die gap; the trend for thicker ribbon is shown in fig. 6. Interfaces with the convex-to-concave transition are the result of a temperature field in the melt with a maximum that follows an inclined ridge-line

322

J.P. Kalejs et at,. / Growth characteristics of sapphire and Si ribbon 0.09

i

I

i

0.1

I

I

I

I

I

I

0.07

0.0

x J= uJ (j, h t'r LI.I I"Z

0.05

0.05

Q J 0 (/) 0,0 I J LIJ -0.0 I 0.0

-O.I

?/IIoo2 I 0.4

I 0.8 X

I 1.2

I 1,6

z a -0.2

3 I 2.0

COORDINATE

-0.3 0.0

I

I

I

I

I

0.4

0.8

1.2

1.6

2.0

X

COORDINATE

Fig. 6. Variation of AI203 m e l t / c r y s t a l interface shape with die gap 213; Vs =1.5 c m / m i n , ~Po= 2585 K and 7"~ = 357 K.

Fig. 7. Variation of AI203 m e l t / c r y s t a l interface shape with growth rate Vs; To = 2585 K, 2l 3 = 0.1 cm, and T~ = 357 K.

from the entering melt at the die top to an elevation in the crystal where the maximum intersects the surface. This maximum is equal to Tm at the point of maximum elevation of the melt/crystal interface. The two-dimensional structure of the temperature field is a result of interaction between heat transfer in the die and melt and was observed in ref. [5] for silicon grown from a graphite die. This structure disappears and the solidification front becomes entirely concave if the ambient temperature is increased so that the maximum interface temperature in the melt lies on the crystal centerline. Increasing the pull rate of the crystal increases the latent and sensible heat that must be transported through the melt and inverts the melt/crystal interface to concave; this transition is displayed in fig. 7 for 2l 3 = 0.1 cm, 7"0= 2585 K, and ]~ = 357 K.

stability of the system. Several authors [11] have used simplified heat transfer models to examine analytically the stability of meniscus-defined growth systems. These studies predict that the interaction of meniscus and thermal effects can enhance capillary stability and extend the range of control parameters for stable growth. Our results for the sensitivity of 2t to changes in heat transfer are consistent with these analyses and now allow the identification of the influence of system specific parameters (e.g., T0 and T~) that govern the sensitivity of an EFG growth system. Full stability analysis of the model for EFG used here is feasible by combining new finite-element methods [12] with computer-aided techniques for nonlinear analysis [13]. Results of this analysis will be reported later. The melt/solid interfaces shown in figs. 6 and 7 for 2l 3 = 0.1 cm have qualitatively the same shape as those observed experimentally [3], but appear not to be as deformed. This quantitative difference may be partially a result of neglecting the transparency of the crystal, and partially due to the use of operating variables in the modeling different from those in the experiments. Radiation into the crystals will act like a heat sink along the solidification front. This causes the interface to be more convex near the center of the melt. We have mod-

4. Discussion

Simultaneous modeling of heat transfer and capillarity is necessary for predicting the differences in the sensitivity of A1203 and Si growth to changes in growth parameters and is the first step toward a comprehensive understanding of the

J.P. Kalejs et al. / Growth characteristics of sapphire and Si ribbon

eled this effect by simply introducing a heat sink along the m e l t / c r y s t a l interface and produced even more exaggerated curves than shown, for example, for 273 = 0.1 cm in fig. 6. M e l t / c r y s t a l interfaces with high curvature near t h e ribbon surfaces are consistent with shapes required for preferential formation of sheet microvoids observed in A1203 growth at these locations [3,14]. They arise for m a n y combinations of ribbon thickness, growth speed, die set-point and ambient temperatures (see figs. 5 to 7). As has been demonstrated [8,9], segregated impurities tend to concentrate near concave portions of the interface. I m p u r i t y concentrations will reach levels high enough to produce constitutional supercooling and localized interface b r e a k d o w n initially in the near-surface concave regions under conditions where the rest of the solidification front is stable [14]. The appearance of A120 3 sheet microvoids is first observed to occur at locations approximately 1 0 0 / t m from the crystal surfaces as growth speed is increased above a threshold of the order of 0.05 c m / m i n [3,15]. Detailed information on operating conditions or melt impurity levels is not available for these cases. Factors such as material shrinkage u p o n solidification and melt dissociation have been proposed in addition to constitutional supercooling in order to explain variations in void size and distribution patterns as a function of changes in operating parameters. The experimental observations do not at this time favor a specific mechanism for void formation nor do they rule out that several m a y be simultaneously operative. In the cases modeled here, the large interface temperature gradients predicted (table 4) are likely to

323

effectively suppress constitutional supercooling in the absence of high melt impurity concentrations.

Acknowledgement We wish to thank H.E. LaBelle, Jr., for providing details on experimental aspects of A I 2 0 3 ribbon growth.

References [1] H.E. LaBelle, Jr., J. Crystal Growth 50 (1980) 8. [2] F.V. Wald, in: Crystals: Growth, Properties and Applications, Vol. 5 (Springer, Berlin, 1981). [3] R.E. Novak, R. Metzl, A. Dreeben and S. Berkman, J. Crystal Growth 50 (1980) 143. [4] D.O. Bergin, J. Crystal Growth 50 (i980) 381. [5] H.M. Ettouney, R.A. Brown and J.P. Kalejs, J. Crystal Growth 62 (1983) 230. [6] P.I. Antonov, S.I. Bakholdin, E.A. Tropp and V.S. Yeferev, J. Crystal Growth 50 (1980) 62. [7] A. B. Dreeben, K.M. Kim and A. Schujko, J. Crystal Growth 50 (1980) 126. [8] H.M. Ettouney and R.A. Brown, J. Crystal Growth 58 (1982) 313. [9] J.P. Kalejs, L.-Y. Chin and F.M. Carlson, J. Crystal Growth 61 (1983) 473. [10] H.M. Ettouney and R.A. Brown, J. Appl. Phys., in press. [11] T. Surek, B. Chalmers and S. Coriell, J. Crystal Growth 50 (1980) 21; V.A. Tatarchenko and E.A. Brener, J. Crystal Growth 50 (1980) 33. [12] H.M. Ettouney and R.A. Brown, J. Computat. Phys. 49 (1983) 118. [13] L.H. Ungar, H.M. Ettourney and R.A. Brown, Phys. Rev. B, in press. [14] V.A. Tatarchenko, T.N. Yalovets, G.A. Satunkin, L.M. Zatulovsky, L.P. Egorov and D. Ya. Kravetsky, J. Crystal Growth 50 (1980) 335. [15] K. Wada and K. Hoshikawa, J. Crystal Growth 50 (1980) 151.