Transient analysis of LE-VGF
growth of compound
Yasunori Okano, Susumu Sakai, Takahiro Morita
and Jun Shimizu
Department of Materials Science and Chemical Engineering, Shizuoka
University, Johoku, Hamamatsu, Japan
Bulk single crystals of compound semiconductors such as GaAs and InP are
very important materials for the substrates of various electronic devices. The
Czochralski technique is widely used for the growth of these crystals. However,
container crystal growth techniques, i.e. the vertical gradient freezing (VGF)
and vertical Bridgman (VB) techniques are very promising because they can
grow crystals without diameter control in a lower axial-thermal-gradient than
that of the Czochralski method.
Components of compound semiconductor melts such as As and P are very
easy to evaporate. Therefore, in order to grow high-quality crystals, it is
required to suppress the volatilization and maintain the stoichiometry of the
components during growth. From this point of view, the liquid encapsulated
vertical Bridgman (LE-VB) technique and the liquid encapsulated vertical
gradient freezing (LE-VGF) technique have been proposed. Recently,
Matsumoto et al. have successfully grown twin-free bulk single crystals of
InP by the LE-VB technique with a flat bottom crucible and Okada et al. have
grown ZnSe single crystals by the LE-VB technique.
In order to grow high-quality single crystals, it is necessary to control the flow
and temperature fields which affect the melt/crystal interface shape and
segregation phenomena during crystal growth. However, it is impossible to
observe and measure these phenomena during crystal growth because the crystal
is grown in a crucible under high pressure. Therefore, numerical simulation is
attractive for the establishment of the optimum furnace design and growth
conditions, and many numerical studies have been reported. A pseudo steady-
state has been assumed in numerous studies[7-16]. Recently, three-dimensional
calculations on the VB crystal growth system have been reported[17,18].
Kim and Brown have performed a transient analysis on the VGF and
VB[20,21] crystal growth systems by the finite element method. Kuppurao et al.
Received August 1997
Revised December 1997
Accepted March 1998
This work was partially supported by the Assistance of International Information Exchanges,
TEPCO Research Foundation, and a Grant-in-Aid for Scientific Research (B) (No. 07305060) from
the Japanese Ministry of Education, Science and Culture. The authors wish to thank S. Nishino for
his help with the computer calculations.
International Journal of Numerical
Methods for Heat & Fluid Flow
Vol. 8 No. 8, 1998, pp. 956-968.
© MCB University Press, 0961-5539