Numerical simulation of thermal and mass transport during Czochralski crystal growth of sapphire

Abstract

The thermal and flow transport in an inductively heated Czochralski crystal growth furnace during a crystal growth process is investigated numerically. The temperature and flow fields inside the furnace, coupled with the heat generation in the iridium crucible induced by the electromagnetic field generated by the RF coil, are computed. The results indicate that for an RF coil fixed in position during the growth process, although the maximum value of the magnetic, temperature and velocity fields decrease, the convexity of the crystal-melt interface increases for longer crystal growth lengths. The convexity of the crystal-melt interface and the power consumption can be reduced by adjusting the relative position between the crucible and the induction coil during growth.

Numerical simulation of heat and fluid flows for sapphire single crystal growth by the Kyropoulos method

“…It is obvious that during the growth process, flow motion inside the melt is laminar, and the effect of buoyancy convection is dominant. Following Lu and Chen [1,3,8], Chen and Lu [2] and Lu et al [7], convexity is defined by the height difference of the crystal-melt interface in the vertical direction. Fig.…”

“…In the present system, we use T out ¼300 K and T w ¼ 450 K. In these equations, T amb,l , T amb,c and T amb,s indicate the effective ambient temperatures corresponding to the melt surface, the crystal surface and the solid surface in vacuum, respectively. In this system, T amb is given by [5,6,8,15] where A j , e j and T j are the area, emissivity and temperature of surface j, respectively, and G j-k is Gebhart's absorption factor. To count G j-k , the view factor between each surface in the vacuum space should be calculated.…”

“…In order to produce a perfect single crystal, it is important to obtain precise information about the heat transfer and flow motion inside the KY furnace during the growth process. The heat and fluid transport phenomena of Czochralski (CZ) and heat-exchanger methods have been studied numerically by several investigators [1][2][3][4][5][6][7][8]. However, the numerical simulation of KY sapphire single crystal has been investigated by only a few researchers.…”

Effect of power arrangement on the crystal shape during the Kyropoulos sapphire crystal growth process

“…The Newton-Raphson method is chosen in order to solve the resultant nonlinear discrete equations. The solidifying crystal is treated as a liquid with a very large viscosity [1,2,[8][9][10][11]. The viscosity of both the liquid and crystal phases is assumed to be constant.…”

“…Information related to heat transfer and fluid motion during the crystal growth process inside the furnace is very important for the production of high quality sapphire single crystals. Numerical simulations [1][2][3][4][5][6][7][8][9][10][11] are thus frequently used to predict these transport phenomena.…”