Vertical Concentration Distribution of Impurities in Horizontal Zone Melting

Abstract

Vertical concentration distribution of impurities in ingot grown by resistance heating horizontal zone melting method is investigated. For the analysis of experimental data, Abe's model-natural convection due to temperature gradient perpendicular to vertical solid-melt interface is the most important factor that determines effective distribution coefficient of impurities; expressbile by Saunders' first approximation-is revised as follows. The rate of natural convective flow over the upper half of solid-melt interface in molten zone can be calculated by Saunders' theory, but over the lower half, the flow rate is smaller than the value expected from his theory owing to the effect of bottom; it is assumed a priori that the flow rate over the lower half of interface can be expressed symmetrically to that over the upper half of interface.
Measurement of vertical resistivity distribution is made on <111> grown Ge single crystal doped with Li, As, Sb, Bi, Zn, Ga, In, and TI by zone levelling for which a travelling resistance furnace is used. According to the revised model, if the distribution coefficient is smaller than unity, the impurity concentration in lower part of the ingot becomes larger than in upper part when the growth rate becomes larger, the temperature difference in molten zone smaller and the diffusion constant of impurity in melt smaller, and the results obtained experimentally can be explained more or less numerically if we assume D_As≈D_Sb≈D_BI≈D_In≈D_TI≈6×10^-5cm²/sec and D_Ga≈1.4×10^-4cm²/sec. The revised model explains also why the forced convection effected by the application of D. C. current and static magnetic field method or travelling magnetic field method causes homogenization of resistivity in vertical derection.