Conserved Growth on Vicinal Surfaces

TL;DR

This paper models crystal growth on vicinal surfaces using an anisotropic conserved KPZ equation, showing that growth dynamics are similar to isotropic cases under certain conditions, relevant for molecular beam epitaxy.

Contribution

It introduces an anisotropic conserved KPZ equation for vicinal surface growth and demonstrates the universality of growth exponents through renormalization group analysis.

Findings

Dynamical exponent matches isotropic case

Roughness exponent matches isotropic case

Applicable to molecular beam epitaxy conditions

Abstract

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo, and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A one--loop dynamical renormalization group calculation yields the values of the dynamical exponent and the roughness exponent which are shown to be the same as in the isotropic case. The results presented here should apply in particular to growth under conditions which are typical for molecular beam epitaxy.