A microscopic kinetic theory of crystal growth
Abstract
We reexamine the ratedetermining kinetic process that is used in the BurtonCabreraFrank (BCF) theory of crystal growth using the FokkerPlanck equation to describe the diffusion of molecules along terraces. We show that the use of the diffusion equation with Fick's law to relate the surface concentration and flux requires the use of a modified surface diffusion coefficient which has the form D' _{s} = D_{s}(1 + o( β)). Here D_{s} is the surface diffusion coefficient in the absence of adsorption and desorption from and to the bulk, and β = 1/ ξτ_{D}, the ratio of relaxation times characterizing surface diffusion (1/ξ) and desorption (τ _{D} and is generally a small quantity. We also present explicit results for the molecular flux entering and exiting the steps. The latter results cannot be determined in the diffusion equation description on which the BCF theory is based.
 Publication:

Journal of Crystal Growth
 Pub Date:
 September 1989
 DOI:
 10.1016/00220248(89)902121
 Bibcode:
 1989JCrGr..97..319H
 Keywords:

 Crystal Growth;
 Kinetic Theory;
 Surface Diffusion;
 Diffusion Coefficient;
 FokkerPlanck Equation;
 Molecular Diffusion;
 SolidState Physics