Mathematical and Numerical Analysis of Capillarity Problems and Processes

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

“…In the case of terrestrial growth, for crucibles with a reasonable practical radius (larger than the melt capillary constant), the curvature of the upper free liquid surface is very small, and hence the term 2/b can be neglected [11,14]. The axisymmetric solution z ¼ zðrÞ has to verify the boundary conditions:…”

“…According to [12][13][14], the dewetting is feasible only for convexo-concave meniscus (i.e., convexo-concave seen from the gas) and globally concave meniscus. For investigating the statically stability (instability) of these menisci shapes, Sturm majorant (Sturm minorant) equations are used (Appendixes A and B).…”

“…According to [14,15], in the case of coated ampoules (or pollution) the wetting angle and growth angle satisfy the inequality y c þ a e Z 180 3 , and the dewetting is feasible only if the menisci present convex parts (i.e., globally convex, concaveconvex and convexo-concave).…”

“…These experimental results in dewetting proved necessity of theoretical studies, in order to find the pressure difference ranges which assure menisci shapes feasible for a detached stable growth on the ground. Thus, starting from the Young-Laplace equation of a capillary surface in equilibrium in the presence of the gas pressure, on the basis of a mathematical model able to describe the meniscus surface z ¼ zðrÞ and the angle f ¼ fðrÞ between tangent to the meniscus and the horizontal axis (dz=dr ¼ tanf), the DP limits for which dewetted is feasible were established [12][13][14][15]. The analysis showed that small changes of the wetting and growth angles which occur, from one material to the other, lead to important modifications of the meniscus shape and consequently of the process stability and crystal diameter.…”

Comment on the paper “Contribution to the stability analysis of the dewetted Bridgman growth under microgravity conditions”

“…Then the curvature of the meniscus at the solid-liquid interface is totally fixed. Analytical expressions of the gap thickness e have been established [2,3] for two different cases.…”