Scaling laws for the reduction of threading dislocation densities in homogeneous buffer layers

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Abstract
In the heteroepitaxial growth of films with large misfit with the underlying substrate (linear mismatch strains in excess of 1%–2%) the generation of misfit dislocations and threading dislocations (TDs) is ubiquitous for thicknesses well in excess of the equilibrium critical thickness. Experimental data suggest that the TD density in relaxed homogeneous buffer layers can be divided into three regimes: (i) an entanglement region near the film/substrate interface corresponding to TD densities of ∼1010–1012 cm−2; (ii) a falloff in TD density that is inversely proportional to the film thickness h, applicable to densities in the range ∼107–109 cm−2; and (iii) saturation or weak decay of the TD density with further increase in film thickness. Typical saturation densities are on the order of ∼106–107 cm−2. In this article, we show that the TD reduction may be described in terms of effective lateral motion of TDs with increasing film thickness. An analytic model is developed that successfully predicts both the 1/h scaling behavior and the saturation of TD densities. Long-range fluctuations in the net Burgers vector content of the local TDs is a cause for saturation behavior. These models are supported by computer simulations.