Toward an integrated analysis of czochralski growth

Crystal Pulling from the Melt

“…A number of simulation experiments have been performed by Schwabe and Metzger [67] which appear to demonstrate that Marangoni flow in a Czochralski melt is very significant. This conclusion is supported by a number of numerical simulations [68].…”

“…Following this pioneering work, Brown and co-workers [68] have made an extensive modelling study of this, so-called TCM (thermal-capillary model) to include heat transfer through the crucible, convection in the melt, heat transfer through the meniscus and from the cooling crystal to a convecting gas ambient. However, the computing demands made by such a model are such that it has not yet been possible to model the convective flow up to realistic values of the Grashof number.…”

A Review of the Automation of the Czochralski Crystal Growth Process

“…Then one is confronted with the problem of numerically solving a set of time dependent 2D/3D partial dierential equations with free boundary conditions. Even though powerful nite element methods for solving such problems exist, and computational performance has dramatically increased in the last years this still is one of the most challenging tasks [79]. The situation gets even worse if feed-forward trajectories need to be rescheduled in real time during growth, for instance in order to react to some perturbations [80].…”

Computer Modelling of Bulk Crystal Growth

“…Several models of melt growth have been developed that include detailed calculations of furnace radiation, starting with Brown and coworkers [35,38,39]. Two of these efforts have led to commercial codes, FEMAG [40] and CrysVUN [41,42].…”