- Email: [email protected]
Full encapsulation by molten salts during the Bridgman growth process
j........ C R Y S T A L QROWT H
ELSEVIER
Journal of Crystal Growth 179 (1997) 356-362
Full encapsulation by molten salts during the Bridgman growth process T. Duffar a'*, J.M. Gourbil a, P. Boiton a, P. Dusserre a, N. E u s t a t h o p o u l o s b a CEREM/DEM/SPCM, Commissariat ~ l"Energie Atomique, 17, Avenue des Mar~rs. F-38054 Grenoble, France b LTPCM, ENSEEG, Domaine Universitaire, BP 75. F-38042 Saint Martin d'Heres, France
Received 27 November 1996; accepted 7 February 1997
Abstract Full encapsulation of liquid semiconductors during Bridgman growth helps to improve the crystal quality by decreasing the nucleation of grains and the dislocation density. An experimental and theoretical study has been undertaken in order to better understand the phenomena and to determine the necessary conditions to be achieved. In the case of the LiC1-KC1 encapsulant in silica crucibles, surface energy calculations predict a stable salt layer between the molten semiconductor and the crucible. For GaAs growth with B203 encapsulant, surface energies are not strong enough and it is shown that the oxide layer is due to the high viscosity of the encapsulant which prevents it flowing upward. It is then mandatory to have a good wetting of the crucible walls by the boron oxide before the melting of the semiconductor. Keywords:
Bridgman growth; Encapsulation
1. Introduction The vertical Bridgman method is gaining more and more interest for the growth of large size I I I - V semiconductor crystals. It has been ascertained by numerous studies that, due to the low thermal gradients which can be achieved, the dislocation density is significantly decreased compared to crystals obtained by the classical Czochralski process. Furthermore, the method is easy to monitor and gives perfectly cylindrical crystals.
* Corresponding author. E-mail: [email protected].
Nevertheless, a couple of problems are remaining, related to the inherent presence of the crucible in contact with the sample all along the process. This often initiates nucleation of grain boundaries at the periphery of the crystal. Internal stresses due to differential contraction between the crucible and the crystal during cooling are also generated, either because the crucible contracts more than the crystal or because the crystal sticks on the crucible. Liquid encapsulation by B203, already used for a long time in Czochralski pulling of I I I - V compounds, was introduced by Blum [1] as an improvement of the gradient freeze growth of G a P in pyrolytic boron nitride (p-BN) crucibles in order to
0022-0248/97/$17.00 Copyright @ 1997 Elsevier Science B.V. All rights reserved PII S0022-0248(97)00 1 45-0
T. Duffar et al. / Journal o f C~stal Growth 179 (1997) 356-362
prevent phosphorus evaporation. The method was then applied to the growth of CulnSe2 and InP in silica crucibles [2-], to the growth of InP in p-BN [3-], and for GaAs in p-BN in a vertical zone melt method I-4]. Two simultaneous papers have reported on full encapsulation of the crystal by the encapsulant. Hoshikawa [5], after encapsulated growth of GaAs in p-BN, found a B2Oa layer between the crucible and the crystal, all along the pulling length. In some places where this layer was absent, grain nucleation occurred as a consequence of crystal-crucible interaction. Garandet [6-] got also a continuous layer of salt between the crystal and the crucible after the growth of GaSb in silica crucibles with the LiC1-KC1 eutectic as encapsulant; the dislocation density in these crystals was practically zero. Bourret 1-7] studied the full encapsulation of GaAs by B203 in p-BN which effectively prevents the occurrence of grain nucleations. It was found that, in order to get a homogeneous oxide layer, the B203 lumps must be mixed with the GaAs or that the crucible inner wall must be oxidized, prior to the growth experiment, by heating under oxygen flow; the effect of water content in the B203 is also discussed. The fully encapsulated GaAs Bridgman growth was also used by Althaus [8] in p-BN and silica crucibles but did not work when a pyrolytic carbon layer was deposited on silica. Amon [9] has extensively employed pre-oxidised p-BN crucibles for the growth of GaAs. The fully encapsulated vertical Bridgman and gradient freeze processes were also used for the growth of InP in silica [10] or p-BN [11-], with B203, and are used in our laboratory to grow two inch GaSb crystals in silica crucibles with the LiC1-KCI eutectic as full encapsulant 1,12]. All papers report on the great advantage associated with the encapsulant layer which remains liquid far below the solidification point of the semiconductor and prevents any contact with the crucible, with the consequence of dramatic decrease of dislocation density and grain nucleations. The classical properties of a good encapsulant are the following [13]: • Melting temperature and solid expansion coefficient lower than the crystal. • Thermal stability, low vapor pressure.
357
• Specific mass lower than the liquid semiconductor. • Chemical inertia: no dissolution of the sample, of the crucible and no added impurity. • Easy removal of the crystal after growth. Obviously, it is highly desirable that, furthermore, the sample/crucible/encapsulant system presents the full encapsulation phenomena. Till now, it was vaguely supposed to be related to wetting properties [5, 6-] but no clear explanation and leading parameters were given. For the molding of silicon bricks in graphite under molten MgF2, Minster 1-14] found that the liquid silicon was supported by SiC whiskers growing in the MgF2 layer, but this is a very specific case which cannot be taken as a rule for the fully encapsulated processes of interest. This paper reports on an experimental and theoretical research program with the aim of better understanding how the full encapsulation phenomenon works when using LiC1-KC1 eutectic or B203.
2. Experimental procedure 2.1. LiCI-KCI film thickness durin9 the 9rowth of antimonides in silica The fact that, when cold, solid salt is found between the crystal and the crucible is not in itself evidence that a liquid salt layer was present when the semiconductor was liquid and even when it solidified. We can for example imagine that the salt is all located above the liquid semiconductor during the process and that it flows afterwards down in the gap created, during cooling down, between the crucible and the sample because of the great difference of expansion coefficients between silica and GaSb. In order to answer this question, we have heated to 800°C, in closed 14 mm silica tubes under vacuum, GaSb alone and a cylinder of GaSb with a piece of LiC1-KC1 eutectic (58% LIC1-42% KC1, in moles) on top. By quickly removing the tubes from the furnace, after 15 h of heating, it was possible to glance at the molten samples. Some bubbles were present on the walls. Without salt, the edge of the bubble is sharp, showing a well defined contact
l~ Duffar et al. / Journal of C~stal Growth 179 (1997) 356-362
358
angle. With salt, the boundary of the bubble is diffuse, without a definitely marked border line. The same observations were made at the top of the G a S b melt, which separates from the silica with a well defined line only in the absence of salt. These observations ascertained the fact that the liquid salt flows down, when it melts, between the crucible and the solid sample and stays in steady state when the semiconductor is molten. The thickness of the layer between the cold crystal and the silica can hardly be measured directly because the salt is very hygroscopic. We have then used a differential method. The inner diameter of the crucibles were measured, before crystal growth, by pouring molten tin inside and measuring the outer diameter of the cylindrical tin rod which is easily removed from the crucible after careful directional solidification. Contraction of the tin and of the silica from the melting point of tin to ambient was taken into account in order to get the inner diameter of the cold crucible. After fully encapsulated crystal growth, the outer diameter of the crystals is measured and the layer thickness is obtained by difference (the expansion coefficients,/L of
90
GaSb, SiO 2 and Sn are, respectively, 7× 10 -6, 0.2× 10 -6 and 15× 10-6 K - l ) . Measurements of the layer thickness versus GaSb depth have been performed on crucibles 10 and 14 m m in diameter with G a S b melt depths up to 50 mm. Polycrystalline growth up to 160 m m was also investigated, but shrinkage of the tin at the end of solidification prevented having a perfect overlapping for depths smaller than 50 mm. Results are plotted on Fig. 1, the error on the thickness was estimated to be + 9 lam in the worse cases. F r o m 0 to 60 mm, the thickness decreases. Beyond 60 m m from the top of the GaSb, the thickness is constant and equal to the differential contraction between silica and GaSb, from the melting point of G a S b to ambient, which depends on the diameter of the tube. 2.2. Surface energy measurements
We will see in Section 3 that the results can be discussed in terms of interfacial energy. Some values of interest for the two studied systems can be found in the literature, but some were lacking.
I
80
I eDiam. 10 -Diam. 14 I
70 A 6O E ..,m
o
"g 50 ~ 40 ._~ i-- 30
m
•
20
w
O--
•
•
10
0
I
I
I
I
20
40
60
80
E
100
I
120
140
Liquid Depth (mm) Fig. 1. Thickness of the salt layer versus depth of GaSb melt, for several 10 and 14 mm diameter tubes. Lines correspond to the differential contraction, from 706°C to ambient, of GaSb versus silica for both diameters. Broken line corresponds to Eq. (7) for a diameter of 10 mm and a growth angle of 20".
I2 Duffar et al. / Journal of C~stal Growth 179 (1997) 356-362
359
silica, p-BN and glassy carbon: the contact angles decreased with temperature then remained constant between 1000°C and 1200°C. The unknown surface energies were obtained from the measured contact angles and from known values with the classical Young-Dupre equation: c o s 0 = (asv - a s 0 / a l v ,
(1j
where Gv is the solid-vapor interfacial energy, asl the solid liquid interfacial energy, a~v the liquid-vapor energy (surface tension of the liquid) and 0 the contact angle. Table 1 gives the contact angles and surface tensions relevant for the present study.
3. Discussion
3.1. Encapsulation of GaSb and InSb by LiCI-KC1
3 Fig. 2. W e t t i n g of the L i C I - K C 1 eutectic o n silica. (al 500"C, Ib) 5 5 0 C , (c) 600~C.
We have measured the missing surface tensions by the sessile drop method with the apparatus and data treatment already described in Ref. El4]. The wetting of the LiC1-KC1 eutectic on polished silica and solid GaSb was investigated by melting 0.1 g of salt under argon. At 400°C, the wetting angle is 90 ° but it vanishes quickly with temperature on both substrates to reach practically 0 ° at the melting temperature of GaSb (see Fig. 2). We have tried to measure the contact angle of molten GaSb on silica immersed in the salt, but the molten drop glided on the silica which made the measurement very difficult and the contrast on the pictures was very bad so that we got only approximate results. We have also measured the wetting behaviour of BzOs on
The observations and measurements reported in Section 2.1 suggest that a liquid film exists between the semiconductor and the crucible and that, after solidification of the semiconductor, the gap between the crucible and the crystal increases due to differential contraction and is continuously filled by liquid salt from the top. For depths greater than 60 mm, the original thickness is negligible compared to the differential contraction. In order to understand why this layer exists, we will compare the energy associated with the two configurations shown on Fig. 3. If Soy1is the inner lateral area of the cylinder along the GaSb depth and Sbo, the area of the bottom of the crucible, then E a - - E b = (Soy I + Sbot)(O's/C - - OIE/C - - O'E/S)
(2)
with as/c, aE/c and CrE/s, respectively, the liquid-semiconductor/crucible, encapsulant/crucible and encapsulant/liquid-semiconductor surface tensions. This can also be written, taking into account the Young-Dupr6 Eq. (1): E a - - E b = (Scy I -[- S b o t ) ( c o s 0EO" E - - COS 0sO" S - - 6E/S) ,
(3)
where 0E and 0s are the contact angles of the encapsulant and of the semiconductor on the crucible
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T Duffar et al. / Journal o f C~stal Growth 179 (1997) 356-362
Table 1 Surface and wetting properties of the semiconducteur/salt/crucibles systems at the melting temperature of the semiconductor System
Contact angle (°degree)
Reference
System
Surface tension (J m - 2)
Reference
GaSb/SiO2 LiCI-KCI/SiO2 GaAs/SiO2 B203/SiO 2 GaAs/BN B203/BN GaAs/C B203/C
122 + 2 0-10 120 + 5 10 + 2 155 + 5 59 + 2 120 _+ 5 79 _+ 2
[15] this work [19] this work [19] this work [19] this work
GaSb LiC1-KCI GaAs
0.45 + 0.03 0.21 + 0.05 0.4 + 0.06 0.1 0.31 + 0.03 0.5
[15] [16] [18] [20] this work [17]
Crucible
I Salt
Salt Semiconductor
B203 GaSb/LiC1-KC1 GaAs/B203
~t
Liquid
Semiconductor
/ a)
b)
Fig. 3. The two configurations discussed in Section 3.1. (a) normal encapsulation, (b) full encapsulation.
and o"E and as the surface tensions of the encapsulant and semiconductor. With the values of Table 1, we obtain, for the system GaSb/ LiC1-KC1/SiO2: AO" = E a - - E b / ( S c y I q- Sbot) ----0.13
L)
B
R
< / / /
Salt ~-
Solid
+ 0.11 J m -2.
Then, configuration ( a ) h a s a greater energy than configuration (b) and the stable state of the system corresponds to the presence of a layer of salt between the molten semiconductor and the crucible. In order to get an estimation of the thickness of the layer, e, as observed after growth, the following mechanism is suggested. As a consequence of the very good wetting of the salt on both GaSb and SIO2, a thin wetting film of salt exists between the molten semiconductor and the crucible. During solidification, due to the growth angle ~ typical of
e Fig. 4. Details of the solid/liquid/salt triple point region during growth of a fully encapsulated semiconductor.
semiconductors, the lateral surface of the crystal grows at an increased distance from the wall (see Fig. 4) and, during cooling down, this gap increases again because of the differential contraction between the crucible and the sample. Joanny and de Gennes studied the thickness of wetting films and found values less than one
T. Duffar et al. / Journal of Crystal Growth 179 (1997) 356-362
micrometer, even in the case of strong Van der Walls or ionic interactions [21]. The thickness of the initial layer is then supposed to be negligible. In order to estimate the gap generated by the solidification process, we will refer to Fig. 4. For a first approximation, it will be supposed that the hydrostatic pressure does not change significantly along the little meniscus created between the solid/ liquid/salt triple line A and the point B where the liquid semiconductor is parallel to the crucible. In this case the meniscus is an arc of circle and the Laplace equation gives:
R = aE/s/Ap gh
(4)
with R the radius of curvature (the second radius of curvature has the order of magnitude of the radius of the crucible and is negligible), Ap the difference of density between GaSb and the salt (6100 1600 = 4500 kg/m3), g the gravity and h the GaSb depth. From Fig. 4 it follows that -
e = R(1 -- cos ~)
(5)
following results are obtained:
2
for p-BN.
Aa = - 0.20 _+ 0.10 J m -2,
for silica.
Aa = - 0.28 + 0.08 J m-2, on silica.
for pyrolytic carbon
Aa = - 0.09 _+ 0.08 J m -
These negative values indicate that a layer of B 2 0 3 is not likely to exist between GaAs and any kind of crucible. Nevertheless, except for the case of carbon [8], full encapsulation was observed. Despite the fact that the water content of the boron oxide [7] or stoichiometry of GaAs [18] might have an effect on the surface properties and then increase the chance of full encapsulation, another explanation must be found. The viscosity of B 2 0 3 at the melting point of GaAs is 3.6 Pa s [22] (to be compared to LiC1-KCI at 700°C: 9.6 x 10 .3 Pa s). The flow of a liquid under a pressure gradient between two plates is given by [23] (
or
e = aE/S(1 - - COS or)lApgh.
(6)
Taking into account the differential contraction between silica and GaSb from the melting point, Tfus, to ambient, Ta, the thickness of the gap becomes e = r(flGaSb - - f l s i o ) ( T f u s - - Za)
(7)
with r the radius of the crucible. This result is shown by the dotted line on Fig. 1. Of course the growth angle of GaSb immersed in the molten eutectic is not known and the value of 20 °, typical of antimonides under inert gas, has been chosen for the calculations. Despite the strong approximations performed, this coarse expression gives a good estimation of the variation of the thickness of the layer.
3.2. Encapsulation of GaAs by B 2 0 3 If Eq. (3) is applied to the case of GaAs with taking the numerical data from Table 1, the
B203,
d2V
dP
PE dx 2
dz
)
PEg dV = 0
(8)
with #E the dynamic viscosity of boron oxide, V the velocity of the liquid along the vertical axis, P the pressure, x the radial coordinate, g the gravity and PE the density of the B 2 0 3 . The hydrostatic pressure of the molten GaAs on the B203 layer is, with Ps the density of the molten GaAs: dP dz
-
+ 6E/S(1 -- COS ~)/Ap gh
361
-
z
From
V(x)
(Ps - PE)9.
(9)
integration of Eqs. (8) and (9) it follows that
ps-- 2P~ ( ~ - -
(10)
and the mean value of the velocity is 17 - Ps - 2pE e2 ' 12/~E
(11)
For a layer 10 gm thick, this gives a mean velocity of 22.5 gm h - 1 (0.2 gm h - 1 for 1 gm, 2.2 mm h - 1 for 100 ~m).Then, for a typical growth process (about 100 h), the encapsulation phenomenon must be as follows: the B203 melts before GaAs and wets the walls of the crucible. For SiO2,
362
• Duffar et al. /Journal of C~stal Growth 179 (1997) 356-362
the wetting is good, but for p-BN, it is necessary to help this wetting either by mixing the GaAs and boron oxide lumps or, best, by pre-oxidation of the crucible, as reported by several authors I-7-9]. Then the GaAs melts and its hydrostatic pressure pushes the boron oxide layer upward in order to get the configuration shown on Fig. 3a. Due to the high viscosity of the layer, the steady state cannot be reached at the time scale of a growth process. For the case of pyrolytic carbon, the bad wetting of boron oxide prevents to obtain a homogeneous layer before melting the GaAs. During growth, increase of the gap thickness by the mechanism described in Section 3.1 occurs but it is difficult to estimate the thickness of the initial layer of the encapsulant.
4. Conclusions The full encapsulation phenomena occurring during encapsulated Bridgman growth of semiconductors can be explained as follows. For GaSb/LiCI-KC1, the salt layer which prevents contact between the sample and the crucible corresponds to a steady state energetic configuration due to the very good wetting of both the silica crucible and the semiconductor by the eutectic (contact angles practically zero). For GaAs/B203, with a worse wetting behaviour, an initial boron oxide film must be established before the melting of GaAs and it is the high viscosity of this layer which prevents it from flowing upward. During solidification, a mechanism specific to semiconductors increases the thickness of the encapsulant layer. For the case oflnP and GaP encapsulated by B 2 0 3 , the lack of physical data prevents the drawing of a firm conclusion and surface tension measurements would be of interest, as well as determination of layer thicknesses. It is then possible to give drawbacks for the choice of an encapsulant in order not only to prevent evaporation, but also to enhance the crystal quality: it must wet the crucible and the semiconductor as much as possible and a high viscosity helps the full encapsulation.
Acknowledgements This work has been performed in the frame work of the GRAMME agreement between the Commissariat fi l'Energie Atomique and the Centre National d'Etudes Spatiales.
References [ 1] S.E. Blum, R.J. Chicotka, J. Elecrochem. Soc. 120 (4) (1973) 588. [2] T.F. Ciszek, C.D. Evans, J. Crystal Growth 91 (1988) 533. [3] E.M. Monberg, H. Brown, C.E. Bonner, J. Crystal Growth 94 (1989) 109. [4] E.M. Swiggard, J. Crystal Growth 94 (1989) 556. [5] K. Hoshikawa, H. Nakanishi, H. Kohda, M. Sasaura, J. Crystal Growth 94 (1989) 643. [6] J.P. Garandet, T. Duffar, J.J. Favier, J. Crystal Growth 96 (1989) 888. [7] E.D. Bourret, E.C. Merk, J. Crystal Growth 110(1991) 395. [8] M. Althaus, K. Sonnenberg, E. Ki.issel, R. Naeven, J. Crystal Growth 166 (1996) 566. [9] J. Amon, W. Auer, D. Zemke, G. Miiller, DGKK annual meeting, K61n, 1996; J. Crystal Growth 166 (1996) 646. [10] R. Fornari, M. Curti, R. Magnanini, G. Mignoni, G. Zuccalli, Crystal Prop. Preparation 3638 (19911 306. [11] F. Matsumoto, Y. Okano, I. Yonenaga, K. Hoshikawa, T. Fukuda, J. Crystal Growth 132 i1993) 348. [12] P. Boiton, Doctoral thesis, Universit6 Montpellier-III, 1996. [13] B. Pamplin, Crystal Growth, Int. Ser. Sci. Solid State, vol. 16, Pergamon, Oxford, 1980. [14] O. Minster, Doctoral Thesis, Inst. Nat. Polytechnique, Grenoble, 1984. [15] I. Harter, P. Dusserre, T. Duffar, J.P. Nabot, N. Eusthatopoulos, J. Crystal Growth 131 (1993) 157. [16] A.R. Ubbelhode, The Molten State of Matter, Wiley, New York, 1978. [17] M.D. Amashukeli, V.V. Karataev, M.G. Kekua, M.G. Mil'vidskii, D.V. Khantadze, Neorg. Mater. 17 (1982) 2126. [18] R. Rupp, G. Miiller, J. Crystal Growth 113 (1991) 131. [19] R. Shetty, R. Balasubramanian, W.R. Wilcox, J. Crystal Growth 100 (1990) 58. [20] E.E. Shipirrain, K.A. Yakimovitch, A.F. Tsitsarkin, D.N. Kagan, L.S. Barkhatov, V.A. Fomin, Y. Tsignkhagen, Fluid Mech. Sov. Res. 3 (4) (1974) 29. [21] J.F. Joanny, P.G. de Gennes, C.R. Acad. Sci. Paris 299, serie II, (7) (19841 279. [22] P. Sabhapathy, M.E. Salcudean, J. Crystal Growth 113 (19911 164. [23] E. Guyon, J.P. Hulin, L. Petit, Hydrodynamique Physique, Editions du CNRS, 1991, p. 159.
ELSEVIER
Journal of Crystal Growth 179 (1997) 356-362
Full encapsulation by molten salts during the Bridgman growth process T. Duffar a'*, J.M. Gourbil a, P. Boiton a, P. Dusserre a, N. E u s t a t h o p o u l o s b a CEREM/DEM/SPCM, Commissariat ~ l"Energie Atomique, 17, Avenue des Mar~rs. F-38054 Grenoble, France b LTPCM, ENSEEG, Domaine Universitaire, BP 75. F-38042 Saint Martin d'Heres, France
Received 27 November 1996; accepted 7 February 1997
Abstract Full encapsulation of liquid semiconductors during Bridgman growth helps to improve the crystal quality by decreasing the nucleation of grains and the dislocation density. An experimental and theoretical study has been undertaken in order to better understand the phenomena and to determine the necessary conditions to be achieved. In the case of the LiC1-KC1 encapsulant in silica crucibles, surface energy calculations predict a stable salt layer between the molten semiconductor and the crucible. For GaAs growth with B203 encapsulant, surface energies are not strong enough and it is shown that the oxide layer is due to the high viscosity of the encapsulant which prevents it flowing upward. It is then mandatory to have a good wetting of the crucible walls by the boron oxide before the melting of the semiconductor. Keywords:
Bridgman growth; Encapsulation
1. Introduction The vertical Bridgman method is gaining more and more interest for the growth of large size I I I - V semiconductor crystals. It has been ascertained by numerous studies that, due to the low thermal gradients which can be achieved, the dislocation density is significantly decreased compared to crystals obtained by the classical Czochralski process. Furthermore, the method is easy to monitor and gives perfectly cylindrical crystals.
* Corresponding author. E-mail: [email protected].
Nevertheless, a couple of problems are remaining, related to the inherent presence of the crucible in contact with the sample all along the process. This often initiates nucleation of grain boundaries at the periphery of the crystal. Internal stresses due to differential contraction between the crucible and the crystal during cooling are also generated, either because the crucible contracts more than the crystal or because the crystal sticks on the crucible. Liquid encapsulation by B203, already used for a long time in Czochralski pulling of I I I - V compounds, was introduced by Blum [1] as an improvement of the gradient freeze growth of G a P in pyrolytic boron nitride (p-BN) crucibles in order to
0022-0248/97/$17.00 Copyright @ 1997 Elsevier Science B.V. All rights reserved PII S0022-0248(97)00 1 45-0
T. Duffar et al. / Journal o f C~stal Growth 179 (1997) 356-362
prevent phosphorus evaporation. The method was then applied to the growth of CulnSe2 and InP in silica crucibles [2-], to the growth of InP in p-BN [3-], and for GaAs in p-BN in a vertical zone melt method I-4]. Two simultaneous papers have reported on full encapsulation of the crystal by the encapsulant. Hoshikawa [5], after encapsulated growth of GaAs in p-BN, found a B2Oa layer between the crucible and the crystal, all along the pulling length. In some places where this layer was absent, grain nucleation occurred as a consequence of crystal-crucible interaction. Garandet [6-] got also a continuous layer of salt between the crystal and the crucible after the growth of GaSb in silica crucibles with the LiC1-KC1 eutectic as encapsulant; the dislocation density in these crystals was practically zero. Bourret 1-7] studied the full encapsulation of GaAs by B203 in p-BN which effectively prevents the occurrence of grain nucleations. It was found that, in order to get a homogeneous oxide layer, the B203 lumps must be mixed with the GaAs or that the crucible inner wall must be oxidized, prior to the growth experiment, by heating under oxygen flow; the effect of water content in the B203 is also discussed. The fully encapsulated GaAs Bridgman growth was also used by Althaus [8] in p-BN and silica crucibles but did not work when a pyrolytic carbon layer was deposited on silica. Amon [9] has extensively employed pre-oxidised p-BN crucibles for the growth of GaAs. The fully encapsulated vertical Bridgman and gradient freeze processes were also used for the growth of InP in silica [10] or p-BN [11-], with B203, and are used in our laboratory to grow two inch GaSb crystals in silica crucibles with the LiC1-KCI eutectic as full encapsulant 1,12]. All papers report on the great advantage associated with the encapsulant layer which remains liquid far below the solidification point of the semiconductor and prevents any contact with the crucible, with the consequence of dramatic decrease of dislocation density and grain nucleations. The classical properties of a good encapsulant are the following [13]: • Melting temperature and solid expansion coefficient lower than the crystal. • Thermal stability, low vapor pressure.
357
• Specific mass lower than the liquid semiconductor. • Chemical inertia: no dissolution of the sample, of the crucible and no added impurity. • Easy removal of the crystal after growth. Obviously, it is highly desirable that, furthermore, the sample/crucible/encapsulant system presents the full encapsulation phenomena. Till now, it was vaguely supposed to be related to wetting properties [5, 6-] but no clear explanation and leading parameters were given. For the molding of silicon bricks in graphite under molten MgF2, Minster 1-14] found that the liquid silicon was supported by SiC whiskers growing in the MgF2 layer, but this is a very specific case which cannot be taken as a rule for the fully encapsulated processes of interest. This paper reports on an experimental and theoretical research program with the aim of better understanding how the full encapsulation phenomenon works when using LiC1-KC1 eutectic or B203.
2. Experimental procedure 2.1. LiCI-KCI film thickness durin9 the 9rowth of antimonides in silica The fact that, when cold, solid salt is found between the crystal and the crucible is not in itself evidence that a liquid salt layer was present when the semiconductor was liquid and even when it solidified. We can for example imagine that the salt is all located above the liquid semiconductor during the process and that it flows afterwards down in the gap created, during cooling down, between the crucible and the sample because of the great difference of expansion coefficients between silica and GaSb. In order to answer this question, we have heated to 800°C, in closed 14 mm silica tubes under vacuum, GaSb alone and a cylinder of GaSb with a piece of LiC1-KC1 eutectic (58% LIC1-42% KC1, in moles) on top. By quickly removing the tubes from the furnace, after 15 h of heating, it was possible to glance at the molten samples. Some bubbles were present on the walls. Without salt, the edge of the bubble is sharp, showing a well defined contact
l~ Duffar et al. / Journal of C~stal Growth 179 (1997) 356-362
358
angle. With salt, the boundary of the bubble is diffuse, without a definitely marked border line. The same observations were made at the top of the G a S b melt, which separates from the silica with a well defined line only in the absence of salt. These observations ascertained the fact that the liquid salt flows down, when it melts, between the crucible and the solid sample and stays in steady state when the semiconductor is molten. The thickness of the layer between the cold crystal and the silica can hardly be measured directly because the salt is very hygroscopic. We have then used a differential method. The inner diameter of the crucibles were measured, before crystal growth, by pouring molten tin inside and measuring the outer diameter of the cylindrical tin rod which is easily removed from the crucible after careful directional solidification. Contraction of the tin and of the silica from the melting point of tin to ambient was taken into account in order to get the inner diameter of the cold crucible. After fully encapsulated crystal growth, the outer diameter of the crystals is measured and the layer thickness is obtained by difference (the expansion coefficients,/L of
90
GaSb, SiO 2 and Sn are, respectively, 7× 10 -6, 0.2× 10 -6 and 15× 10-6 K - l ) . Measurements of the layer thickness versus GaSb depth have been performed on crucibles 10 and 14 m m in diameter with G a S b melt depths up to 50 mm. Polycrystalline growth up to 160 m m was also investigated, but shrinkage of the tin at the end of solidification prevented having a perfect overlapping for depths smaller than 50 mm. Results are plotted on Fig. 1, the error on the thickness was estimated to be + 9 lam in the worse cases. F r o m 0 to 60 mm, the thickness decreases. Beyond 60 m m from the top of the GaSb, the thickness is constant and equal to the differential contraction between silica and GaSb, from the melting point of G a S b to ambient, which depends on the diameter of the tube. 2.2. Surface energy measurements
We will see in Section 3 that the results can be discussed in terms of interfacial energy. Some values of interest for the two studied systems can be found in the literature, but some were lacking.
I
80
I eDiam. 10 -Diam. 14 I
70 A 6O E ..,m
o
"g 50 ~ 40 ._~ i-- 30
m
•
20
w
O--
•
•
10
0
I
I
I
I
20
40
60
80
E
100
I
120
140
Liquid Depth (mm) Fig. 1. Thickness of the salt layer versus depth of GaSb melt, for several 10 and 14 mm diameter tubes. Lines correspond to the differential contraction, from 706°C to ambient, of GaSb versus silica for both diameters. Broken line corresponds to Eq. (7) for a diameter of 10 mm and a growth angle of 20".
I2 Duffar et al. / Journal of C~stal Growth 179 (1997) 356-362
359
silica, p-BN and glassy carbon: the contact angles decreased with temperature then remained constant between 1000°C and 1200°C. The unknown surface energies were obtained from the measured contact angles and from known values with the classical Young-Dupre equation: c o s 0 = (asv - a s 0 / a l v ,
(1j
where Gv is the solid-vapor interfacial energy, asl the solid liquid interfacial energy, a~v the liquid-vapor energy (surface tension of the liquid) and 0 the contact angle. Table 1 gives the contact angles and surface tensions relevant for the present study.
3. Discussion
3.1. Encapsulation of GaSb and InSb by LiCI-KC1
3 Fig. 2. W e t t i n g of the L i C I - K C 1 eutectic o n silica. (al 500"C, Ib) 5 5 0 C , (c) 600~C.
We have measured the missing surface tensions by the sessile drop method with the apparatus and data treatment already described in Ref. El4]. The wetting of the LiC1-KC1 eutectic on polished silica and solid GaSb was investigated by melting 0.1 g of salt under argon. At 400°C, the wetting angle is 90 ° but it vanishes quickly with temperature on both substrates to reach practically 0 ° at the melting temperature of GaSb (see Fig. 2). We have tried to measure the contact angle of molten GaSb on silica immersed in the salt, but the molten drop glided on the silica which made the measurement very difficult and the contrast on the pictures was very bad so that we got only approximate results. We have also measured the wetting behaviour of BzOs on
The observations and measurements reported in Section 2.1 suggest that a liquid film exists between the semiconductor and the crucible and that, after solidification of the semiconductor, the gap between the crucible and the crystal increases due to differential contraction and is continuously filled by liquid salt from the top. For depths greater than 60 mm, the original thickness is negligible compared to the differential contraction. In order to understand why this layer exists, we will compare the energy associated with the two configurations shown on Fig. 3. If Soy1is the inner lateral area of the cylinder along the GaSb depth and Sbo, the area of the bottom of the crucible, then E a - - E b = (Soy I + Sbot)(O's/C - - OIE/C - - O'E/S)
(2)
with as/c, aE/c and CrE/s, respectively, the liquid-semiconductor/crucible, encapsulant/crucible and encapsulant/liquid-semiconductor surface tensions. This can also be written, taking into account the Young-Dupr6 Eq. (1): E a - - E b = (Scy I -[- S b o t ) ( c o s 0EO" E - - COS 0sO" S - - 6E/S) ,
(3)
where 0E and 0s are the contact angles of the encapsulant and of the semiconductor on the crucible
360
T Duffar et al. / Journal o f C~stal Growth 179 (1997) 356-362
Table 1 Surface and wetting properties of the semiconducteur/salt/crucibles systems at the melting temperature of the semiconductor System
Contact angle (°degree)
Reference
System
Surface tension (J m - 2)
Reference
GaSb/SiO2 LiCI-KCI/SiO2 GaAs/SiO2 B203/SiO 2 GaAs/BN B203/BN GaAs/C B203/C
122 + 2 0-10 120 + 5 10 + 2 155 + 5 59 + 2 120 _+ 5 79 _+ 2
[15] this work [19] this work [19] this work [19] this work
GaSb LiC1-KCI GaAs
0.45 + 0.03 0.21 + 0.05 0.4 + 0.06 0.1 0.31 + 0.03 0.5
[15] [16] [18] [20] this work [17]
Crucible
I Salt
Salt Semiconductor
B203 GaSb/LiC1-KC1 GaAs/B203
~t
Liquid
Semiconductor
/ a)
b)
Fig. 3. The two configurations discussed in Section 3.1. (a) normal encapsulation, (b) full encapsulation.
and o"E and as the surface tensions of the encapsulant and semiconductor. With the values of Table 1, we obtain, for the system GaSb/ LiC1-KC1/SiO2: AO" = E a - - E b / ( S c y I q- Sbot) ----0.13
L)
B
R
< / / /
Salt ~-
Solid
+ 0.11 J m -2.
Then, configuration ( a ) h a s a greater energy than configuration (b) and the stable state of the system corresponds to the presence of a layer of salt between the molten semiconductor and the crucible. In order to get an estimation of the thickness of the layer, e, as observed after growth, the following mechanism is suggested. As a consequence of the very good wetting of the salt on both GaSb and SIO2, a thin wetting film of salt exists between the molten semiconductor and the crucible. During solidification, due to the growth angle ~ typical of
e Fig. 4. Details of the solid/liquid/salt triple point region during growth of a fully encapsulated semiconductor.
semiconductors, the lateral surface of the crystal grows at an increased distance from the wall (see Fig. 4) and, during cooling down, this gap increases again because of the differential contraction between the crucible and the sample. Joanny and de Gennes studied the thickness of wetting films and found values less than one
T. Duffar et al. / Journal of Crystal Growth 179 (1997) 356-362
micrometer, even in the case of strong Van der Walls or ionic interactions [21]. The thickness of the initial layer is then supposed to be negligible. In order to estimate the gap generated by the solidification process, we will refer to Fig. 4. For a first approximation, it will be supposed that the hydrostatic pressure does not change significantly along the little meniscus created between the solid/ liquid/salt triple line A and the point B where the liquid semiconductor is parallel to the crucible. In this case the meniscus is an arc of circle and the Laplace equation gives:
R = aE/s/Ap gh
(4)
with R the radius of curvature (the second radius of curvature has the order of magnitude of the radius of the crucible and is negligible), Ap the difference of density between GaSb and the salt (6100 1600 = 4500 kg/m3), g the gravity and h the GaSb depth. From Fig. 4 it follows that -
e = R(1 -- cos ~)
(5)
following results are obtained:
2
for p-BN.
Aa = - 0.20 _+ 0.10 J m -2,
for silica.
Aa = - 0.28 + 0.08 J m-2, on silica.
for pyrolytic carbon
Aa = - 0.09 _+ 0.08 J m -
These negative values indicate that a layer of B 2 0 3 is not likely to exist between GaAs and any kind of crucible. Nevertheless, except for the case of carbon [8], full encapsulation was observed. Despite the fact that the water content of the boron oxide [7] or stoichiometry of GaAs [18] might have an effect on the surface properties and then increase the chance of full encapsulation, another explanation must be found. The viscosity of B 2 0 3 at the melting point of GaAs is 3.6 Pa s [22] (to be compared to LiC1-KCI at 700°C: 9.6 x 10 .3 Pa s). The flow of a liquid under a pressure gradient between two plates is given by [23] (
or
e = aE/S(1 - - COS or)lApgh.
(6)
Taking into account the differential contraction between silica and GaSb from the melting point, Tfus, to ambient, Ta, the thickness of the gap becomes e = r(flGaSb - - f l s i o ) ( T f u s - - Za)
(7)
with r the radius of the crucible. This result is shown by the dotted line on Fig. 1. Of course the growth angle of GaSb immersed in the molten eutectic is not known and the value of 20 °, typical of antimonides under inert gas, has been chosen for the calculations. Despite the strong approximations performed, this coarse expression gives a good estimation of the variation of the thickness of the layer.
3.2. Encapsulation of GaAs by B 2 0 3 If Eq. (3) is applied to the case of GaAs with taking the numerical data from Table 1, the
B203,
d2V
dP
PE dx 2
dz
)
PEg dV = 0
(8)
with #E the dynamic viscosity of boron oxide, V the velocity of the liquid along the vertical axis, P the pressure, x the radial coordinate, g the gravity and PE the density of the B 2 0 3 . The hydrostatic pressure of the molten GaAs on the B203 layer is, with Ps the density of the molten GaAs: dP dz
-
+ 6E/S(1 -- COS ~)/Ap gh
361
-
z
From
V(x)
(Ps - PE)9.
(9)
integration of Eqs. (8) and (9) it follows that
ps-- 2P~ ( ~ - -
(10)
and the mean value of the velocity is 17 - Ps - 2pE e2 ' 12/~E
(11)
For a layer 10 gm thick, this gives a mean velocity of 22.5 gm h - 1 (0.2 gm h - 1 for 1 gm, 2.2 mm h - 1 for 100 ~m).Then, for a typical growth process (about 100 h), the encapsulation phenomenon must be as follows: the B203 melts before GaAs and wets the walls of the crucible. For SiO2,
362
• Duffar et al. /Journal of C~stal Growth 179 (1997) 356-362
the wetting is good, but for p-BN, it is necessary to help this wetting either by mixing the GaAs and boron oxide lumps or, best, by pre-oxidation of the crucible, as reported by several authors I-7-9]. Then the GaAs melts and its hydrostatic pressure pushes the boron oxide layer upward in order to get the configuration shown on Fig. 3a. Due to the high viscosity of the layer, the steady state cannot be reached at the time scale of a growth process. For the case of pyrolytic carbon, the bad wetting of boron oxide prevents to obtain a homogeneous layer before melting the GaAs. During growth, increase of the gap thickness by the mechanism described in Section 3.1 occurs but it is difficult to estimate the thickness of the initial layer of the encapsulant.
4. Conclusions The full encapsulation phenomena occurring during encapsulated Bridgman growth of semiconductors can be explained as follows. For GaSb/LiCI-KC1, the salt layer which prevents contact between the sample and the crucible corresponds to a steady state energetic configuration due to the very good wetting of both the silica crucible and the semiconductor by the eutectic (contact angles practically zero). For GaAs/B203, with a worse wetting behaviour, an initial boron oxide film must be established before the melting of GaAs and it is the high viscosity of this layer which prevents it from flowing upward. During solidification, a mechanism specific to semiconductors increases the thickness of the encapsulant layer. For the case oflnP and GaP encapsulated by B 2 0 3 , the lack of physical data prevents the drawing of a firm conclusion and surface tension measurements would be of interest, as well as determination of layer thicknesses. It is then possible to give drawbacks for the choice of an encapsulant in order not only to prevent evaporation, but also to enhance the crystal quality: it must wet the crucible and the semiconductor as much as possible and a high viscosity helps the full encapsulation.
Acknowledgements This work has been performed in the frame work of the GRAMME agreement between the Commissariat fi l'Energie Atomique and the Centre National d'Etudes Spatiales.
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