On the pressure difference ranges which assure a specified gap size for semiconductor crystals grown in terrestrial dewetted Bridgman

Abstract

The complexity of the dewetting phenomenon on the ground consists mainly in the presence of the hydrostatic pressure which should be counterbalanced by a supplementary gas pressure difference Δ P = P c - P h between the cold and hot sides of the sample. The experiments have shown that using uncoated and coated crucibles, detached and partially detached growth can be obtained; dewetting became unsuccessful when the liquid–solid interface changed its shape—phenomenon which proved connection between the meniscus shape, pressure difference and stable dewetting. Because the interest is to grow crystals with specified gap size, the Δ P limits and the corresponding menisci shapes for which dewetting is feasible are first established, on the base of the theoretical and computational investigations. Then, for the obtained menisci, the static stability via the conjugate point criterion of the calculus of variations is studied in the cases of the classical semiconductors grown in (i) uncoated crucibles (i.e., the wetting angle θ c and growth angle α e satisfy the inequality θ c + α e < 180 ∘ ) and (ii) coated crucibles or pollution ( θ c + α e ≥ 180 ∘ ). In this way, gap thickness limitations for which the menisci are physically realizable are obtained. Numerical results are performed for InSb crystal grown in uncoated ampoule, and for Ge crystal grown in coated ampoule.