Calculation of composition variation of In1−vGavAs ternary crystals for diffusion and electromigration limited growth from a temperature graded solution with source material

A theoretical model was proposed to calculate composition variation of III-V ternary crystals during growth. In this model, for the first time, phase equilibrium between crystal and growth solution is maintained together with constancy between the transported and incorporated mass or solute atoms at the crystal/solution interface at the same time. This model can be applied to the calculation of the diffusion and electromigration limited growth in a temperature-graded solution with source material such as the source-current-controlled (SCC) growth method. The composition variation of In_1−vGa_vAs crystals grown by diffusion and electromigration was calculated by this model. Incorporation of two kinds of solute elements, Ga and As, into crystals through the crystal/solution interface was considered on the basis of the laws of the phase equilibrium and the constancy of mass. In comparison of the experimental results with the calculated ones, it is found that in the In-Ga-As solution the diffusion coefficient of Ga, D_Ga, is about two times as large as that of As, D_As, and μ_Ga is larger than μ_As. The calculated results of the composition variation show that the composition uniformity in In_1−vGa_vAs crystals can be largely improved by controlling the growth parameters such as temperature gradient in the solution, solution length, existence of source material, and electric field.