Strain relaxation in large lattice-mismatched epitaxial films, such as Ge and III-V materials on Si, introduces high threading dislocation densities (TDDs). A thermodynamic model of TDD dependence on film thickness is developed. According to this model, the quasiequilibrium TDD of a given strain-relaxed film scales down with the inverse square of its thickness. The quasiequilibrium TDDs in both Ge and GaAs films follow this model consistently. Our model predicts the lowest possible TDD of a large lattice-mismatched film on Si (100), which is determined by the dislocation glide activation energy and the film thickness.
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