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

Abstract

Dewetted Bridgman crystal growth: practical stability over a bounded time period in a forced regimeSt. Balint · S. Epure · T. Duffar · L. Braescu Abstract The concept of practical stability is applied to the case of dewetted Bridgman crystal growth on Earth, in a simplified configuration. Taking into account both heat transfer and capillarity, it is formally demonstrated that the process is stable in case of convex menisci, provided that pressure fluctuations remain in a range which can be computed. The theoretical concepts are illustrated by examples involving InSb and GaSb crystal growth. It is concluded that practical stability gives valuable knowledge of the dynamics of the studied technique and could be usefully applied to other crystal-growth processes, especially those involving capillary shaping.Keywords Dewetted Bridgman technique · Non-Lyapunov stability · Nonlinear system · Semiconductors · Single crystal growth model 1 Introduction "Dewetting" refers to a phenomenon that has occurred spontaneously during many experiments of Bridgman solidification of semiconductors in space (see reviews [1,2]). It also refers to a process developed for crystal growth on Earth (see review in [3]). In both cases, the crystal is grown without interaction with the crucible, which considerably improves the structural quality of the material: less residual stresses, dislocations, spurious nucleation or twins. The origin of the gap between the crystal and the crucible comes from a small liquid meniscus at the level of the solid-liquid interface [4]. While the phenomenon is spontaneous under microgravity conditions, because of the lack of hydrostatic pressure, it has been adapted on Earth by applying on the liquid a gas pressure difference,

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

“…The function ψ (r c , p) obtained for an arbitrary l 0 and h 0 coincides with that obtained applying the same steps for any l = l 0 , l∈(0,H a ) (see Balint et al 2011).…”

“…It can be shown that the following statement holds (see Balint et al 2011): Statement 1 For 0 < e 1 < e 2 < r a , h ∈ e 2 tan π 2 − α e , e 2 tan θ c − π 2 and p satisfying: there exists r c ∈ [r a − e 2 , r a − e 1 ], l (t) ∈ [l(t) + h − e 2 tan (θ c − π 2 ), l(t) + h − e 1 tan( π 2 − α e )] and a convex solution z(r) (i.e., d 2 z dr 2 > 0) of the initial value problem:…”

Experimental investigation of dewetting models

“…Stability analyses, generally based on Lyapunov's approach [17], have been performed for the three models. Simple approaches considering only the capillary effect [9,10] as well as more thorough analyses taking into account coupling between capillarity, heat transfer and pressure fluctuations [18][19][20][21][22][23] give the same result: dewetting is stable only when the meniscus is convex at the liquid-crystal-gas triple line, which means that abnormally high values of y should be considered in order to fulfil relation (1). In the case of model 3, stability also depends on the transport of gas dissolved in the liquid [21].…”