Motion of Contact Line of a Crystal Over the Edge of Solid Mask in Epitaxial Lateral Overgrowth

TL;DR

This paper presents a mathematical model for tracking crystal growth at the edge of a solid mask during epitaxial lateral overgrowth, considering anisotropic energies and interface diffusion, with numerical methods to handle complex edge geometries.

Contribution

It introduces a comprehensive model that accounts for anisotropic interfacial energies and mask surface inhomogeneities, along with a numerical approach to address ill-posedness in interface evolution.

Findings

Contact line slows near sharp mask edges.

Model captures effects of surface energy anisotropy.

Numerical method overcomes ill-posedness issues.

Abstract

Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor interface) flux from the vapor phase and by the interface diffusion. The model accounts for possibly inhomogeneous energy of the mask surface and for strong anisotropies of crystal-vapor interfacial energy and kinetic mobility. Results demonstrate that the motion of the crystal-mask contact line slows down abruptly as radius of curvature of the mask edge approaches zero. Numerical procedure is suggested to overcome difficulties associated with ill-posedness of the evolution problem for the interface with strong energy anisotropy. Keywords: Thin films, epitaxy, MOCVD, surface diffusion, interface dynamics, contact lines, rough surfaces, wetting, regularization of ill-posed evolution problems.