Anisotropic stability analysis of surface undulations of strained lattice-mismatched layers

The anisotropic linear stability analysis of surface undulations in a strai ned layer on a semi-infinite solid is presented here. The free energy of th e system is taken to be the sum of the surface free energy and the elastic strain energy. The calculation is performed under the assumptions that the system is in equilibrium and that the total volume of the system is constan t, which correspond to the circumstances in annealing rather than those in crystal growth. Firstly, by estimating the difference between the free ener gy for the system with a flat surface and the free energy for the system wi th an undulating surface, we showed that the [100] undulations are more Lik ely to be formed than the [100] undulations. Secondly, we compared the crit ical layer thickness for misfit dislocation formation with the layer thickn ess range where surface undulations always decay. Numerical results for the Si1-xGex/Si systems show that misfit dislocation generations tend to occur for x < 0.5 and surface undulations do for x > 0.5. These tendencies are i n agreement with the experimentally observed features of surface morphology in the literature. (C) 1999 Elsevier Science S.A. All rights reserved.