Factors affecting the formation, uniformity, and density of misfit and threading dislocation arrays during heteroepitaxial growth

An improved theory relating the separation of misfit dislocations in a heteroepitaxial thin film undergoing a continuous process of strain relaxation by the introduction of dislocations is presented. Because it provides a quantitative relationship between the dislocation spacing, misfit, total system energy, and film thickness, a number of quantities such as energy gain on formation of the dislocation network as a function of dislocation spacing can be estimated. The model allows calculation of useful thermodynamic quantities such as the compressibility of the misfit array which are useful for determining the average spacing of dislocations, the thickness at which dislocations are introduced (the critical thickness), and the dispersion in dislocation spacings in arrays.