Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth

Abstract

For the seeding process of oxide Czochralski crystal growth, influence of the crucible bottom shape on the heat generation, temperature and flow field of the system and the seed-melt interface shape have been studied numerically using the finite element method. The configuration usually used in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and seed crystal. At first, the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF-coil was calculated. Using this heat generation in the crucible wall as a source the fluid flow and temperature field of the entire system as well as the seed-melt interface shape were determined. We have considered two cases, flat and rounded crucible bottom shape. It was observed that using a crucible with a rounded bottom has several advantages such as: (i) The position of the heat generation maximum at the crucible side wall moves upwards, compared to the flat bottom shape. (ii) The location of the temperature maximum at the crucible side wall rises and as a result the temperature gradient along the melt surface increases. (iii) The streamlines of the melt flow are parallel to the crucible bottom and have a curved shape which is similar to the rounded bottom shape. These important features lead to increasing thermal convection in the system and influence the velocity field in the melt and gas domain which help preventing some serious growth problems such as spiral growth.

Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

“…Anselmo A P et al [14] and Tavakoli M H et al [15] showed that a cylindrical crucible with a curved bottom has advantages for crystallization. Therefore, it is proposed recently by Mokhtari F et al [16,17,18] to modify the device as a cylindro-spherical system (figure 1).…”

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

“…From the 80s until the mid-90s, Kobayashi [1], Derby [2][3][4] and Tsukada [5] successfully applied two-dimensional numerical analysis to compute the temperature distribution, the flow field and the melt-gas interface in a CZ system. However, recent studies performed by Tsukada [6][7], Imaishi [8][9], Wilke [10][11], Banerjee [12] and Tavakoli [13][14][15] have shown that specific global, three-dimensional and unsteady features of the melt flow can make a significant contribution to the heat and mass transfer near the melt-crystal interface, and may even govern the formation of the crystallization front for large-diameter crystal growth. Induction heating is frequently used in the CZ crystal growth process.…”

“…Tavakoli and Wilke [13][14][15] conducted a series of numerical simulation studies of CZ sapphire crystal growth. First, they performed a two-dimensional numerical simulation of heat generation and heat transport in a real Czochralski system without any crystal and melt, to investigate the effect of the insulation and the gap between the crucible and the afterheater on the air flow and temperature field.…”

“…Brandon and his co-workers [21][22][23][24] tried to simplify the problem by using artificially enhanced thermal conductivity, including the internal radiative effect inside the grown crystal during the directional melt-growth process. Several previous studies [14][15][16] have employed this method of performing numerical simulation of the growth of optically thick CZ-sapphire crystal. In this study, we also use this method, including the effect of the internal radiation.…”

The effect of crucible bottom deformation on the quality of Nd:GGG crystals grown by Czochralski method

“…Particularly, the crucible bottom shape can influence the fluid flow and heat transfer process during the seeding. A computer modeling [13] shows that a crucible with the round corners at the bottom has several differences with a flat bottom crucible, such as increasing the velocity of melt flow, thermal convection and ____________________ lifting the melt's maximum temperature upward. However, no experimental investigation has been reported in this study to verify these theoretical findings.…”