A theoretical analysis and computer simulation of the growth of epitaxial films

Equations are derived which describe the growth of epitaxial islands on a crystalline substrate subject to certain restrictions, and an attempt is made to define the limits of their application in a physical system. For an initial random distribution of point nuclei, the growth of islands which instantaneously coalesce to a fixed shape obeys equations of the form : In ( N / N 0 ) = -2 N ⅓ 0 A V -⅔ T ⅔ for N 0 > N > 10 -2 N 0 and P = P 0 (1- N / N 0 ) for all N , where 0.5 < P 0 < 0.6. In these equations the island distribution is described in terms of three parameters: the island density N , the fractional surface coverage P and the mean thickness T . The constants A and V are fixed by the shape of an island of size r , such that the volume is Vr 3 and the interface area is Ar 2 .