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Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the diffusion of adatoms on terraces with boundary conditions at sharp steps, as first studied by Burton, Cabrera and Frank (BCF). Recent electromigration experiments on vicinal Si surfaces suggest the need for more general boundary conditions in a BCF approach. We study a discrete 1D hopping model that takes into account asymmetry in the hopping rates in the region around a step and the finite probability of incorporation into the solid at the step site. By expanding the continuous concentration field in a Taylor series evaluated at discrete sites near the step, we relate the kinetic coefficients and permeability rate in general sharp step models to the physically suggestive parameters of the hopping models. In particular we find that both the kinetic coefficients and permeability rate can be negative when diffusion is faster near the step than on terraces. These ideas are used to provide an understanding of recent electromigration experiment on Si(001) surfaces where step bunching is induced by an electric field directed at various angles to the steps.
We propose a two-dimensional phase-field-crystal model for the (2$times$1)-(1$times$1) phase transitions of Si(001) and Ge(001) surfaces. The dimerization in the 2$times$1 phase is described with a phase-field-crystal variable which is determined by
We study current-induced step bunching and wandering instabilities with subsequent pattern formations on vicinal surfaces. A novel two-region diffusion model is developed, where we assume that there are different diffusion rates on terraces and in a
For more than three decades, measurement of terrace width distributions (TWDs) of vicinal crystal surfaces have been recognized as arguably the best way to determine the dimensionless strength $tilde{A}$ of the elastic repulsion between steps. For su
The practical difficulties to use graphene in microelectronics and optoelectronics is that the available methods to grow graphene are not easily integrated in the mainstream technologies. A growth method that could overcome at least some of these pro
Single-layer atom or vacancy clusters in the presence of electromigration are studied theoretically assuming an isotropic medium. A variety of distinctive behaviors distinguish the response in the three standard limiting cases of periphery diffusion