Dynamic global simulation of the Czochralski process. I. Principles of the method

A very efficient numerical method to simulate the time-dependent Czochralski growth of semiconductor crystals is presented. Heat transfer by conduction and diffuse grey radiation, in and between all the furnace constituents, is taken into account. Transient effects induced by the heat capacity of all the bodies, the inertia of the solid-liquid interface, and by all the geometrical changes related to the growth of the crystal are considered. Convection in the melt is not taken into account (this effect will be addressed in a subsequent paper). Two kinds of time-dependent problems are defined: the inverse problem, which consists in calculating the heater power required to grow a crystal of a given shape, and the direct problem, which consists in calculating the crystal shape resulting from given heater power and pull rate histories. Solid-liquid, solid-gas, and liquid-gas interfaces are unknown in the direct problem. Our method is illustrated by the simulation of the pulling of a germanium crystal. More detailed examples will be investigated in following papers.

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