Phase boundary between ripple and hut in the initial roughening stage in heteroepitaxy

Abstract

A regularly undulating surface topography has been observed during growth of heteroepitaxial layers such as Si1-xGex/Si-2 and InxGa1-xAs/GaAs5. We present a modified evolution mechanism of this ripple structure, which consists of initial roughening and evolving stages. A theoretical relationship is derived through energy minimization, which indicates that the ratio of the amplitude to the square of the period of the ripple structure is constant in the evolving stage. Also derived is a criterion for determining the phase boundary between the ripple and hut phases in the Stranski-Krastanov growth.