We present an approach in equilibrium theory for strain relaxation in heteroepitaxial semiconductor structures, which includes surface relaxation effects and elastic interactions between straight misfit dislocations. The free-surface boundary conditions are satisfied by placing an image dislocation outside the crystal so that its stress field cancels that of the real interface misfit dislocation at the surface. The effect of the Airy stress function that removes the fictitious shear and normal stresses at the surface is discussed. This image method provides an equilibrium theory, which correctly predicts experimentally observed values of critical strained layer thickness and completely describes the elastic and plastic strain relief and work hardening in lattice-mismatched SiGe epilayers. It is shown that the elastic coherency stress of the strained material is really affected by a large surface relaxation stress. This is essential for experimental determination of the Ge content of extremely thin films as a function of the tetragonal distortion of the cubic lattice cells. The equilibrium theory is also used to define the degree of strain relaxation and to predict the incomplete strain relief at the end of thermal relaxation process of metastable SiGe/Si heterostructures. © 1996 The American Physical Society.

• Received 6 May 1996

DOI:https://doi.org/10.1103/PhysRevB.54.8761