Dependence of the meniscus shape on the pressure difference in the dewetted Bridgman process

Dewetted Bridgman crystal growth: practical stability over a bounded time period in a forced regime

“…where t denotes the time, n is the number of unknown functions (which depends on the crystallization technique), c denotes a set of crystallization parameters (thermophysical and other constants of the substance being crystallized, see for example [4,7,11,12,[18][19][20][21]), (i 1 , . .…”

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

“…Evaluating numerically the inequality (10) for InSb, it is obtained that the globally concave menisci are statically stable for gaps in the range eA ð0; 0:00123 m. On the other hand, according to [12], the computed gap range for which the meniscus has concave shape is eA ð0; 0:00143 m [12]. Comparing these two gap ranges can be concluded that globally concave menisci are statically stable, with possible exception in the case of a larger gap.…”

“…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).…”

“…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.…”

Non-Lyapunov Type Stability in a Model of the Dewetted Bridgman Crystal Growth Under Zero Gravity Conditions

“…One of them is originated in the Lyapunov stability theory of the shaped crystal growth process developed by Tatarchenko (1993) and it consists in finding a simplified autonomous set of differential equations for the radius, crystallization-front level and possibly other process parameters. Then, the mathematical description reduces to a first order nonlinear system of differential equations (see for example Duffar et al 1997Duffar et al , 2000Bizet and Duffar 2004;Fiederle et al 2004;Palosz et al 2005;Braescu 2008;Balint et al 2008). The second mathematical description is originated in the Bridgman growth theory initiated by Chang and Brown (1983), Adornato and Brown (1987), and it consists in finding the numerical solution of the system of partial differential equations which describes fluid-flow, heat and mass transport, and meniscus shape in order to be able to simulate the dynamics of the detached Bridgman process for testing the mechanical instabilities (see for example Stelian et al 2009a, b).…”