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Nonequilibrium Interface Dynamics:
Theory and Simulation from Atomistic to Continuum Scales

CSIC Building (#406), Seminar Room 4122.
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Distribution of Step Spacing on Misoriented Surfaces: Fermion in 1D, From Simple Models to Random Matrix Theory

Dr. Theodore L. Einstein

Department of Physics, University of Maryland

Abstract:   The continuum step model has proved remarkably successful in bridging length scales and describing—in terms of step stiffness, step interaction strength, and the appropriate generalized step mobility—a wide variety of phenomena on stepped surfaces, such as step fluctuations, cluster diffusion, step kinetics, electromigration, and mound decay. From the terrace-width (called l) distribution [TWD], one can gauge the magnitude A of the typically dominant elastic interactions, which vary like A/l2 (like the entropic repulsion due to non-crossing of steps). Much progress can be made by mapping the configurations of steps on vicinal surfaces into the world lines of fermions in 1-D, evolving in time. The simplest mean field approximation is the familiar problem of a quantum mechanical problem of a particle in a 1-D box or a parabolic well. More sophisticated analyses can be made, culminating in the use of results from random-matrix theory, in particular the generalized Wigner surmise—a gamma distribution in l2 rather than the customary Gaussian—to describe the TWD. The model TWDs are compared with experimental data (esp. vicinal Si and Cu), numerical simulations (mostly Monte Carlo, some transfer matrix), and exact results. When surface states also mediate the step interaction, the situation is more complicated. Non-equilibrium effects can severely alter the TWDs.

Work supported by NSF MRSEC at U. of Maryland, done in collaboration with H.L. Richards, O. Pierre-Louis, Hailu Gebremariam, S.D. Cohen, R.D. Schroll, N.C. Bartelt, E.D. Williams, and others at Maryland, with M. Giesen and H. Ibach at FZ-Jülich (via Humboldt Foundation), and with J.-J. Métois at Marseilles