Detached growth represents a radical change from classical Bridgman crystal growth. In this process, first observed in space-based growth experiments, the melt dewets the ampoule wall, allowing the crystal to pull away from it. Detached growth eliminates deleterious interactions between the growing crystal and the ampoule, dramatically improving crystal quality. However, the promising early results of microgravity experiments have been difficult to advance in terrestrial growth systems due to a number of instabilities that can be manifest during growth.
As a basis for better understanding the physics underpinning this process, we develop and apply a thermocapillary model to study the existence, stability, and nonlinear dynamics of detached melt crystal growth in a vertical Bridgman system under zero gravity conditions. The model incorporates time-dependent heat, mass, and momentum transport, and accounts for temperature-dependent surface tension effects at the meniscuses bounding the melt. The positions of the meniscus and phase-change boundary are computed to satisfy the conservation laws rigorously. In addition, we examine the capability of a capillary statics model developed by Duffar et al. for explaining shape stability in this system.
A rich bifurcation structure in gap width versus pressure difference is uncovered, demarcating conditions under which growth with a stable gap is feasible. Thermal effects shift the bifurcation diagram to a slightly different pressure range, but do not alter its general structure. Necking and freeze-off are shown to be two different manifestations of the same instability mechanism. Supercooling of melt at the meniscus and low thermal gradients in the melt ahead of the crystal-melt-gas trijunction, either of which may be destabilizing, are both observed under some conditions. The role of wetting and growth angles in dynamic stability is clarified.
We also discuss the dynamics, operability limits, and tuning of several feedback controllers to stabilize detached vertical Bridgman crystal growth. Proportional and proportional-integral control can stabilize unstable growth, but only within tight operability limits imposed by the narrow range of allowed meniscus shapes. Substantially better performance is shown to arise from a nonlinear, model-based control.
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Supported in part by DOE/NNSA, DE-FG52-08NA28768, the content of which does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred. |