VELOCITY FUNCTION MODELS OF STEP DYNAMICS - THEORY OF CURRENT-INDUCEDSTEP BUNCHING ON SI(111) SURFACES

We study two-dimensional models of step flow in which the local veloci ty of a step is expressed as a function of its neighboring terrace wid ths and the local curvature of the step. Repulsive step interactions m odify the velocity functions at short distances and prevent step cross ing. When the velocity of a step depends mainly on the width of the te rrace behind, the resulting asymmetry in the velocity functions can ma ke the uniform step train unstable towards step bunching. Typically, d uring growth or evaporation, the surface will develop characteristic p atterns where slowly moving fairly straight bunches coexist with fast- moving, strongly bent single steps that cross from one bunch to anothe r. The bunching and debunching processes happen simultaneously. These general features have been seen in recent experiments on the current-i nduced step bunching of Si(111) surfaces. The same qualitative behavio r persists in a wide class of microscopic models that require a much m ore complicated description.