Calculation of critical layer thickness versus lattice mismatch for Ge_xSi_1−x/Si strained-layer heterostructures

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A calculation of the critical layer thickness h_c for growth of Ge_xSi_1−x strained layers on Si substrates is presented for 0x1.0. The present results are obtained assuming misfit dislocation generation is determined solely by energy balance. This approach differs therefore from previous theories (e.g., Matthews et al.), in which the absence of mechanical equilibrium for grown-in threading dislocations determines the onset of the generation of interfacial misfit dislocations. It is assumed that interfacial misfit dislocations will be generated when the areal strain energy density of the film exceeds the energy density associated with the formation of a screw dislocation at a distance from the free surface equal to the film thickness h. For films thicker than this critical value, screw (and edge) dislocations will be generated at the film/substrate interface. Values obtained for the critical thickness versus lattice mismatch are in excellent agreement with measurements of h_c for Ge_xSi_1−x strained layers on Si substrates. Applied Physics Letters is copyrighted by The American Institute of Physics.