We formulate a phase-field description of step dynamics on vicinal surfaces that makes use of a single dynamical field, at variance with previous analogous works in which two coupled fields are employed, namely, a phase-field proper plus the physical adatom concentration. Within an asymptotic sharp interface limit, our formulation is shown to retrieve the standard Burton-Cabrera-Frank model in the general case of asymmetric attachment coefficients «Ehrlich-Schwoebel effect». We confirm our analytical results by means of numerical simulations of our phase-field model. Our present formulation seems particularly well adapted to generalization when additional physical fields are required.
Keywords: Theory and models of crystal growth; physics of crystal growth, crystal morphology, and orientation, Interface structure and roughness, Molecular, atomic, ion, and chemical beam epitaxy,….
Physical Review E. Volume: 79 Issue: 2 Pages: 021601-1-021601-8
DOI reference: 10.1103/PhysRevE.79.021601
Published on paper: February 2009.
M. Castro, A. Hernández-Machado, R. Cuerno. Single-phase-field model of stepped surfaces. Physical Review E. vol. 79, no. 2, pp. 021601-1-021601-8, February 2009.