Computation of equilibrium surface fluctuations in strained epitaxial films due to interface misfit dislocations

In practice, it is now possible to grow strained epitaxial films of extremely high quality by a number of techniques. However, the question of whether or not that quality can be retained during subsequent processing, including thermal cycling, has major practical implications. This paper deals with the relevant issue of strained film quality degradation by formation of surface roughness in high-temperature processing due to the presence of interface misfit dislocations. It is assumed that initially the layer thickness is uniform and that the strain field is uniform. Thus, the chemical potential is constant along the surface. The strain is then partially relieved by formation of interface misfit dislocations resulting in an inhomogeneous strain field along the surface which, in turn, implies a chemical potential gradient along the surface. Gradients of chemical potential constitute a thermodynamic force and cause a drift of surface atoms from regions of high potential to regions of low potential, and a net change in shape of the surface occurs. It has been observed that, for some material systems, the surface shape can take the form of ridges or waviness which correlate with the positions of underlying misfit dislocations. A numerical method is developed which leads to an estimate of the magnitude and profile of surface waviness under conditions of thermodynamic equilibrium. Starting from some initial configuration, a full transient problem is solved numerically to describe relaxation to a stable equilibrium shape with a constant chemical potential along the surface.