Computer simulation of liquid encapsulated vertical bridgman crystal growth: pseudo steady‐state calculations

Abstract

A pseudo steady‐state model is developed to study heat transfer, fluid flow, and the interface shape in the liquid encapsulated vertical Bridgman crystal growth. The model, which is governed by momentum, heat, and overall mass balances in the system, is solved by a finite‐volume/Newton method. Flow and temperature fields, as well as unknown melt/crystal and melt/encapsulant interfaces, are calculated simultaneously. Sample calculations are mainly conducted for the GaAs/B2O3/PBN system. Calculated results for the Germanium/graphite system are compared with finite element calculations by Adornato and Brown, and they are in good agreement. The effects of some process parameters, including the growth speed, ambient temperature profile and heat transfer conditions, on flow patterns, temperature fields and the interface shape are illustrated through calculated results. Interface inversion from concave to convex, by modifying the ambient temperature profile, is also demonstrated through computer simulation. Particularly, through an inverse problem approach, a flat interface can be easily obtained for various operation conditions.

A visualization and computational study of horizontal Bridgman crystal growth

“…To reduce the concavity of the growth interface further, a typical way for Bridgman growth is to lower the cold zone temperature or to increase the thermal gradient near the interface [10,16]. The results are shown in Fig.…”

Effects of axial vibration on vertical zone-melting processing

“…For puri®cation, mixing is also important on its eciency. In general, tuning the furnace con®gurations to control the melt ¯ow and thus the interface shape and mixing is typical, but it is usually dicult and less ¯exible [2,3]. Therefore, using external forces to control crystal growth has been widely adopted [ 4± 15].…”

Transient analysis of LE‐VGF growth of compound semiconductors

“…Therefore, numerical simulation is attractive for the establishment of the optimum furnace design and growth conditions, and many numerical studies have been reported [6]. A pseudo steadystate has been assumed in numerous studies [7][8][9][10][11][12][13][14][15][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 [19] and VB [20,21] crystal growth systems by the finite element method.…”