Simulation of the growth rate and layer thickness for liquid phase epitaxy (LPE) under slider-induced convection

Abstract

The effect of slider velocity on growth rate and epi-layer thickness for the liquid phase epitaxial (LPE) growth has been studied numerically by means of a finite analytic method for the first time. The simulation shows that three growth mechanisms occur during the liquid phase epitaxy. In the initial period of epitaxial growth, the slider motion introduces disturbance in the melt; convective mass-transfer process predominates and the epi-layer grows rapidly. After the melt is settled, the mass-transfer rate is controlled by diffusion and a concentration gradient is established to maintain the diffusion. The time required for a disturbance to decay is a function of Reynolds number. However, this settling time depends only weakly on the slider velocity. As the constituent in the growth melt becomes eventually depleted by the crystal growth, the concentration gradient decreases to zero, as does the growth rate. By applying this method to GaAs LPE growth, very good agreement with published experimental data is obtained in the diffusion-limited region. As for the convection-limited region, a sliding effect has to be taken into account for the agreement with reported data. The slider-induced convection increases the growth rate in the initial transient; however, it also introduces the layer thickness non-uniformity. Higher slider velocity increases the growth rate, but decreases the uniformity of the epi-layer, especially at the edge of the wafer.