Transient analysis of surface supersaturation after crystal face submersion using the analytical and transmission-line matrix (TLM) methods

The time-dependent equation of Burton, Cabrera and Frank (BCF) is analytica lly solved for transient-state growth conditions occurring immediately afte r submersion of crystal face in supersaturated solution. The time-dependent BCF model is also solved using the transmission-line matrix (TLM) numerica l method. We find that the time necessary to attain the steady-state value of surface supersaturation does not depend on bulk supersaturation but incr eases with increasing interstep distance. Calculated results obtained by th e two methods are shown to be in excellent agreement, indicating a promisin g potential of the TLM method for solving analytically intractable problems of interest. (C) 1999 Elsevier Science B.V. All rights reserved.