SURFACE-DIFFUSION ON A STEPPED SURFACE

Surface diffusion of an adatom on a vicinal surface is investigated, u sing site-dependent hopping rates based on a model surface-potential p rofile of a regularly stepped surface. We solved analytically the coup led rate equations for the occupation probability of an adatom at a su fficiently long time, in analogy to the tight-binding theory of electr onic structure. From this, the general relation between the hopping ra tes and the diffusion coefficient is derived. Formulas of both surface diffusion coefficients, parallel and perpendicular to a step edge dir ection, are obtained as functions of related atomic hopping rates at a terrace site, an upper edge site, and a lower edge site and of the st ep spacing. The fundamental mechanism determining the crucial role of step arrays on surface diffusion is clarified. No difference was found between step-up diffusion and step-down diffusion, even in the absenc e of inversion symmetry on the surface-potential profile. With Monte C arlo simulation, the effect of kink sites on surface diffusion is stud ied. Kinks greatly suppress the parallel diffusion coefficient, while they suppress only weakly the perpendicular diffusion coefficient.