On the capillary stability of the crystal–crucible gap during dewetted Bridgman process

Existence, stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity

“…By linearizing Eq. (2) (see, e.g., Epure et al [30]) it can be shown that growth is stable when the meniscus is convex at the TPL, and unstable when it is concave there. The onset of instability occurs when an inflection point appears in the meniscus at the TPL, which is characterized by a change in sign of dc=dr:…”

“…Since the crystal growth velocity is zero under this scenario, the result is not relevant to the primary issue in detached growth that of shape stability during growth. To deduce a qualitative picture of shape stability, Epure et al [30] have applied linear stability analysis under various limiting scenarios. These results suggest that gravity can act as a stabilizing influence.…”

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

“…1; see also [10][11][12]14]. This is an over-specified boundary-value problem which has no solution for arbitrary p and h. The main objective, formulated in terms of p, is to find the range of p and h for which the above problem has an approximate solution, i.e.…”

“…19-167] to numerical solutions of discretized partial differential equations [8,9]. On this basis, several papers have been devoted to the study of the stability of dewetting, all based on Lyapunov's theory as usually applied to crystal growth [7]: simple approaches considering only the capillary effect [10,11] as well as more thorough analyses taking into account coupling between capillarity, heat transfer, and pressure fluctuations [12,13]. However, such analyses consider the stability on an infinite time period and do not allow studying the time scale of perturbation recovery, nor the acceptable amplitude of the perturbations.…”

Thermodynamics of (Ga, In)‐Sb‐O‐Si and impact on dewetting process

“…It is in fact the controlling parameter in the process, which can be monitored by an external gas circuit [4] or by changing the temperature of the gases at the hot and cold sides [5]. Dynamic stability analyses of the process [2,[6][7][8][9][10][11] predict that it is stable if the inequality θ + α > 180° (1) is satisfied, which means that the meniscus is convex (seen from the gas, figure 1-I). This has been verified experimentally in the case of the growth of gallium antimonide in silica crucibles, and it was shown that the gap between the crystal and the crucible, of the order of some tens of micrometers, remains constant on several centimetres [12][13][14].…”