Numerical simulations of bulk crystal growth on different scales: silicon and GeSi

Abstract

Numerical modelling has become an important tool for improving or introducing new processes in bulk crystal growth. For a complete description, scales ranging from atomistic ones up to those of industrial furnaces have to be considered. This article presents methods used on different scales for the Czochralski growth of silicon as well as of Ge1–xSix alloys and for ingot casting of silicon. It shows the recent developments for the different scales and the attempts at coupling the approaches.

Numerical study on transport phenomena in a directional solidification process in the presence of travelling magnetic fields

“…[5]), but mostly on the lab-scale sizes of equipment, where laminar steady models can well describe the melt flow [1,2]. With increasing crucible size the flow becomes unsteady and more complex.…”

Simulating Interface Growth and Defect Generation in CZT – Simulation State of the Art and Known Gaps

“…Although the issue of developing models and modeling approaches to crystal growth based on multiscale modeling approaches has been addressed [41,42], we feel that this is inadequate. In particular, these methods do not contain sufficient detail that a mesoscale model of CZT growth, such as that discussed in Section 3.2, can be created containing the correct physical mechanisms.…”

Numerical studies of flow patterns during Czochralski growth of square-shaped Si crystals

“…Due to the high Reynolds numbers for such Czochralski system the flow computation is still challenging (see e.g. [5]). We use the large eddy simulations (LES) as it has become common for computing the flow in Czochralski growth of silicon [6,7].…”