Internal radiation effect on semiconductor β-Ga2O3 crystals grown by the VB Method and anisotropic thermal stress

Abstract

Gallium oxide crystals are semitransparent semiconductors with good optical and electrical properties, which allow their use for several technological applications. During the growth process of β-${\mathrm{Ga}}_2{O}_3$ crystals, internal radiation plays a crucial role that affects the growth process and then the crystal quality. In this work, the effect of the melt and the crystal transparency on the vertical Bridgman growth of β-${\mathrm{Ga}}_2{O}_3$ oxide is thoroughly studied. Using a global 2D/3D finite element model, temperature, melt flow, melt-crystal interface, and three-dimensional anisotropic thermal stress are computed at different growth stages. At each stage, four cases are considered, namely, opaque melt and crystal, semi-transparent melt and opaque crystal, semitransparent crystal and opaque melt, and finally semitransparent melt and crystal. The role of internal radiation in each case at different growth stages is then highlighted separately and then coupled together. It was found that the melt-crystal interface is shifted from a convex shape at the early stage to a nearly plane and then to a concave shape at the last stage. The melt flow is then changed from two rolls pattern at the beginning to a single-roll structure at the last stage. Thermal stress of the as-grown ingot is decreased during the growth due to the decrease of temperature non-linearities. Internal radiation inside the crystal acts to increase the melt-crystal interface convexity at the early and middle stages of the growth process and leads to a decrease in its concavity at the final stage. However, the melt transparency leads to the opposite effects, i.e., it decreases the interface convexity at the early stage and increases the interface concavity at the final stage. As a result, for semitransparent crystal and melt, the interface is between the two previous cases. The calculated thermal stresses are found to be more affected by the transparency of the crystal than the melt as the absorption coefficient of β-${\mathrm{Ga}}_2{O}_3$ crystal is smaller than that of the melt. At all stages, the thermal stresses are found to be larger for the opaque case due to the increase of temperature non-linearities in the crystal. Large values are found at the bottom and the lower part of the periphery. Furthermore, internal radiation inside the melt plays a major role during the early growth stage due to the large liquid volume. It reduces the melt flow intensity close to the free surface where the shear stress is combined with the buoyant force and leads to the flattening of the interface decreasing then the radial temperature gradients, which leads to small attenuation of the thermal stress. At the final stage, the transparency of the melt plays the opposite role due to the increase of the interface concavity which leads to an increase in both of the temperature gradients and the thermal stress inside the crystal. Due to the crystal anisotropy, and especially to the large thermal expansion coefficient in the [0 1 0] direction, the 3D thermal stress values are found to be larger in this direction, especially in the bottom part of the ingot. Comparisons with available experimental and numerical works are provided in this paper.