Formulas for the force dipole interaction of surface line defects in homoepitaxy

Abstract

Abstract. By use of asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between curved line defects (steps) of the same sign in homoepitaxy. Our starting point is continuum linear elasticity in accordance with the classic model by Marchenko and Parshin (1981 Soviet Phys. JETP 52 129). We consider geometries that stem from perturbations of concentric circular steps (radial case). In the radial case, we define a small geometric parameter, δ 2 , expressing the smallness of interstep distance relative to the circle radii. We invoke the Mellin transform with respect to δ 2 and derive systematically an approximation for the requisite integral. This technique offers an alternative to an exact evaluation in terms of elliptic integrals. We then demonstrate the use of the Mellin transform when calculating the force dipole interaction energy between smoothly, slowly varying steps that form perturbations of circles. We discuss conditions by which the force dipole interaction may favor the modulation of closed step profiles.