Modeling and bulk crystal growth processes: What is to be learned?

Abstract

Modeling is an important tool to better understand crystal growth. This assertion is discussed via examples of classical models that have proven to be enlightening. The discussion continues with a brief primer on the mathematical governing equations of continuum and interfacial phenomena important in crystal growth processes and several techniques that can be applied to these equations for analysis, including scaling and numerical methods. Finally, some examples of modeling a melt growth system are presented to illustrate modern applications.

Anomalous segregation during electrodynamic gradient freeze growth of cadmium zinc telluride

“…This non-classical segregation behavior arises from the very strong influence of convection on mass transfer in the melt, especially flows near the melt-solid interface. Although the influence of quasi-steady, incomplete mixing near the interface has been long known [13][14][15], the effect of timeevolving, multi-cellular flow transitions on producing such complexity of segregation patterns during growth has not been theoretically demonstrated before (other than the effect of highfrequency striations produced by oscillating or turbulent flows [40][41][42]). Another important factor at play here is the propensity of CZT flows to rearrange themselves as a function of a changing thermal environment.…”

“…Both behaviors exhibit monotonic axial concentration distributions that either steadily increase or decrease in the direction of growth, according, respectively, to cases where the distribution coefficient of the segregated species is greater than or less than unity. A more complete picture of segregation emerged, with the appreciation of the effects of interface shape and incomplete mixing on radial segregation, from the careful application of numerical models for convection and solidification; see, e.g., the overviews [13][14][15].…”

Thermal-capillary analysis of the horizontal ribbon growth of silicon crystals

“…This approach is discussed in more depth by Yeckel and Derby [26] and is appropriate as long as the kinetics of phase change are sufficiently fast [27], which is usually the case for semiconductor melt growth.…”

Fluid dynamics in crystal growth: The good, the bad, and the ugly

“…mass × acceleration Net force (1) where the bold characters indicate vector quantities. This simple form is applicable to a rigid body.…”

“…The literature on flows in crystal growth is vast, and no attempt will be made to present a comprehensive summary of it. Some recent reviews on this topic include those of Derby et al [1], Kakimoto and Gao [2], Tsukada [3], Vizman [4], and Capper and Zharikov [5]. In this chapter, we will first focus on some essentials on flows and their effects, followed by a series of examples of interesting and important flows in crystal growth systems.…”