Modelling InSb Czochralski Growth

Abstract

The dominant technique for producing large defect free crystals is known as the Czochralski method. Developed in 1916 by Jan Czochralski as a method of producing crystals of rare metals, this method is now used to produce most of the semiconductor wafers in the electronics industry.

Many aspects of this process have been investigated to gain a greater insight of the physical processes involved. We begin with the heat problem, first as a one dimensional model, then extending to a second dimension. This analysis indicates
that the temperature of the gas surrounding the crystal has a major impact on both the thermal stress experienced by the crystal and the shape of the crystal/melt interface. In contrast,variations in the heat
flux from the melt have much less of an effect.

Having investigated the temperature profiles, the analysis then focuses on the behaviour of the fluid. Scaling arguments are used to estimate the thickness of the various boundary layers and explain the main flow patterns that are experimentally observed.

Next, the shape of the meniscus is determined for various rotation rates. This analysis shows that the shape of the meniscus is relatively invariant at least at low rotation rates yet the actual vertical position of the meniscus changes readily with the rate of rotation.

After analyzing the fluid flow patterns, a model is developed for the height of the melt as a function of time. This indicates that for a crystal of constant radius the proportion of the effective pull rate due to the falling fluid level remains essentially constant over the complete growing time of the crystal. This no longer remains true if the radius of the crystal is allowed to increase at a constant rate.