Modeling elastic effects in epitaxial growth - stress induced instabilities of epitaxially grown surfaces

摘要

The paper addresses the fundamental problem of strained epitaxial surface growth on the basis of a front capturing approach. The particular problem arising in this context is the correct handling of (1) asymmetric attachment kinetics as well as (2) proper inclusion of energetic terms to model the elastic effects. The latter has not been included in most previous work concerned with the modeling of epitaxial surface growth. In the case of front capturing (1) and (2) pose fundamental challenges. In contrast to this, front tracking offers the possibility of a direct translation of the kinetics and the dynamics under consideration into a coupled set of free boundary equations to simulate. However, their numerical realization is troublesome. A numerical procedure is presented to overcome the technical problems arising in the case of front tracking as a benchmark for the front capturing model without elastic contributions. Developing the front tracking model further to include elastic effects remains an open challenge. In contrast front capturing allows for a straightforward extension to elastic driving forces based on variational principles of irreversible thermodynamics. The extended front capturing model is successfully applied to experiments by Dorsch et al. [J. Cryst. Growth 183, 305 (1998)]. The respective numerical study elucidates the question why these experiments contradict previous experimental findings with respect to final surface morphologies.