Meniscus-defined melt crystal growth processes in which the meniscus is confined to a small region, such as detached Bridgman growth (DVB), edge-defined film fed growth (EFG), horizontal ribbon growth (HRG), and micropull crystal growth (MPG), are low to intermediate Bond number systems in which there often exists several meniscus shapes that can satisfy the local force balance. Consequently these systems exhibit a variety of dynamical bifurcations, signaling existence of multiple steady solutions as well as time-periodic behavior. Bifurcations of the saddle node, pitchfork, transcritical, and Hopf types can occur depending on the growth configuration, particularly the manner in which the meniscus is confined at its ends. Thermal effects often play a role, either instigating or modulating the bifurcation. Commonly, solutions are found to exist only within a narrow range of operating parameters, posing problems to both physical operation and computer simulation of these systems.
We investigate these systems using thermal-capillary models which rigorously conserve mass, energy, and momentum within the meniscus and solidification regions. Steady state model equations are solved on deforming grids by the Galerkin finite element method. Locations of the growth front, triple-phase line, and meniscuses are all computed to satisfy appropriate physics at these interfaces. An inverse solution strategy based on constrained parameter continuation proves essential to identifying regions of solution existence. Solution stability is assessed by nonlinear transient analysis.
The nature of the end condition imposed on the meniscus, namely whether it meets a smooth surface at the wetting angle, or is pinned at a sharp corner, has a profound influence on system behavior. Saddle node limit points are commonly observed in pinned systems such as MPG and HRG. Symmetry-breaking pitchfork bifurcations are observed in systems of a planar geometry having two pinned menisci, such as planar EFG. Perhaps most unusual, however, is the appearance of a transcritical bifurcation in the detached vertical Bridgman system which marks a loss of solution stability above a critical wetting angle of melt on crucible. This bifurcation presents a limit on stability but none on existence, making it possible to employ an active control strategy based on controlling the pressure below the meniscus. In particular, this feature is discussed with respect to making the growth of cadmium zinc telluride (CZT), an important material for radiation detection, practical in a detached Bridgman system.