Stress-driven surface evolution in heteroepitaxial thin films: Anisotropy of the two-dimensional roughening mode

We have analyzed the anisotropic behavior of surface roughening in Si_1−xGe_x/Si(001) heterostructures by use of methods of elastic analysis of undulated surfaces and perturbation analysis on the basis of global energy variations associated with surface evolution. Both methods have shown that the two-dimensional stage of surface roughening preferentially takes place in the form of ridges aligned along the two orthogonal 〈100〉 type directions. This prediction has been confirmed by ex situ experimental observations of surface evolution by use of atomic force microscopy and transmission electron microscopy in both subcritically and supercritically thick Si_1−xGe_x films grown on Si(001) substrates. Further experiments in supercritically thick films have revealed a remarkable interplay between defect formation and surface evolution: the formation of a network of 〈110〉?misfit dislocations in the latter stages alters the evolution process by rotating the ridge formations toward the 〈110〉 type directions.