We present a two-dimensional analysis of the in-plane misfit stress and its elastic relaxation in rectangular patterned heteroepitaxial multilayer structures on rigid substrate. Based on the generally acknowledged model of relaxing film stress we calculate the distribution of the misfit stress versus distance from the free surface of a multilayered mesa edge. By superposition of the isolated stress fields of the mesa edges, we obtain the biaxial misfit stress distribution in a finite heteroepitaxial thin film structure on thick substrate. The formalism developed permits the determination of the variation of stress values as a function of material and size characteristics of the patterned multilayer-substrate system. The theoretical analysis will be applied to the SiGe/Si strained layer epitaxy and III-V compound semiconductor integration with Si or Ge.
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Fischer, A., Richter, H. Biaxial State of Stress in SiGe Epilayers on Patterned Si Substrates. MRS Online Proceedings Library 318, 703–708 (1993). https://doi.org/10.1557/PROC-318-703