Eur. Phys. J. B (2013) 86: 175
https://doi.org/10.1140/epjb/e2013-31053-1

Regular Article

A study of pyramidal islands formation in epitaxy within the generalized phase-field model

¹ Institute of Applied Physics, National Academy of Sciences of Ukraine, 58 Petropavlovskaya St., 40000 Sumy, Ukraine
² Sumy State University, 2 Rimskii-Korsakov St., 40007 Sumy, Ukraine

^a e-mail: dikh@ipfcentr.sumy.ua
^b e-mail: vasiliy@ipfcentr.sumy.ua

Received: 20 November 2012
Received in final form: 15 February 2013
Published online: 22 April 2013

Abstract

We study epitaxial growth of pyramidal patterns in a framework of the phase-field model generalized by introduction of temperature field dynamics and an assumption of interacting adsorbate due to elastic effects. We have shown that in the system with different rates of the phase-field change oscillatory dynamics of surface pattern formation can be realized. Analytical results are verified by numerical simulations. We compare properties of surface structures within the framework of the standard phase-field model and proposed a generalized model of epitaxial growth using statistical approach. It is shown that in the generalized model pyramidal patterns can be sustained by thermodynamical force governing flux of interacting adsorbate.