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For the design and analysis of a strained-layer semiconductor device structure, the equilibrium strain profile may be determined numerically by energy minimization but this method is computationally intense and non-intuitive. Here we present an electric circuit model approach for the equilibrium analysis of an epitaxial stack, in which each sublayer may be represented by an analogous configuration involving a current source, a resistor, a voltage source, and an ideal diode. The resulting node voltages in the analogous electric circuit correspond to the equilibrium strains in the original epitaxial structure. This new approach enables analysis using widely accessible circuit simulators, and an intuitive understanding of electric circuits may be translated to the relaxation of strained-layer structures. In this paper, we describe the mathematical foundation of the electrical circuit model and demonstrate its application to epitaxial layers of Si 1 −x Ge x grown on a Si (001) substrate.

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Several simple models have been developed for the threading dislocation behavior in heteroepitaxial semiconductor materials. Tachikawa and Yamaguchi [Appl. Phys. Lett., 56, 484 (1990)] and Romanov et al. [Appl. Phys. Lett., 69, 3342 (1996)] described models for the annihilation and coalescence of threading dislocations in uniform-composition layers, and Kujofsa et al. [J. Electron. Mater., 41, 2993 (2013)] extended the annihilation and coalescence model to compositionally-graded and multilayered structures by including the misfit dislocation-threading dislocation interactions. However, an important limitation of these previous models is that they involve empirical parameters. The goal of this work is to develop a predictive model for annihilation and coalescence of threading dislocations which is based on the dislocation interaction length Lint. In the first case if only in-plane glide is considered the interaction length is equal to the length of misfit dislocation segments while in the second case glide and climb are considered and the interaction length is a function of the distance from the interface, the length of misfit dislocations, and the density of the misfit dislocations. In either case the interaction length may be calculated using a model for dislocation flow. Knowledge of the dislocation interaction length allows predictive calculations of the threading dislocation densities in metamorphic device structures and is of great practical importance. Here we demonstrate the latter model based on glide and climb. Future work should compare the two models to determine which is more relevant to typical device heterostructures.