Three-dimensional numerical simulation of crystal growth using TSM under g-jitter conditions

Abstract

The goal of this thesis is to study the effect of residual gravity on crystal growth of Silicon Germanium GE0.98 Si0.02 using the Traveling Heater Method (THM). This method has proven to be one of the most efficient techniques to grow high-quality crystals because it can be grown at relatively low temperatures compared to existing crystal growth techniques. Yet, because of natural convection due to earth's gravity, imperfection in terms of silicon distribution along the growth interface occurs. By growing crystals in a space environment, residual gravity represented by a static microgravity component and a sinusoidal component would decrease the intensity of the convective flow, which in return would lead to a more uniform silicon distribution. However, g-jitter fluctuation has proven to have a noticeable effect on the silicon distribution. Therefore, as an initial step to understand the behavior of crystal growth in space, each component of the g-jitter force will be studied thoroughly. The momentum, mass and energy equations, representing the 3D TSM model, were solved using finite element means. The preliminary results indicate that the complexity and the intensity of the silicon distribution along the growth interface are proportional to the convective flow, that partially controls the migration of silicon. Therefore, the quality of the crystal growth is assessed based on the behavior of the flow along the solvent regime. Based on the imposed static gravity in the range of 10-6 go to 10-3 go, the flow was determined to be in a diffusion mode with a velocity ranging from 10-6 cm/sec to 10-3 cm/sec. As a matter of fact, the flow intensity was noted to be positively proportional to the dominant component of both the static and the amplitude of the imposed g-jitter and negatively proportional to the frequency of the sinusoidal g-jitter. Consequently, realistic space growth conditions have proven to be an effective way of producing a homogeneous crystal since a flawless crystal silicon distribution is obtained at the growth interface.

The Modeling of growth process on the surface of crystal

“…This means that the substances involved in the growth of the film are considered as some mass distributed in volume. This method is convenient when one of the substances is in a liquid (solution or melt) state [7].…”