Elastic misfit stress relaxation in heteroepitaxial SiGe/Si mesa structures

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Abstract
We present a two-dimensional analysis of the in-plane misfit stress and its elastic relaxation in rectangular patterned heteroepitaxial SiGe structures on the Si 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 mesa edge. By superposition of the isolated stress fields of the mesa edges, we obtain the biaxial misfit stress distribution in a finite heteroepitaxial SiGe mesa on silicon substrate. The formalism developed permits the determination of the variation of stress values as a function of material and size characteristics of the patterned layer-substrate system. A main result of this letter is that the elastic misfit stress is relaxed appreciably in small square SiGe/Si mesa structures, but not in a narrow/long pattern. Furthermore, the theoretical analysis can be applied to most of the pseudomorphic and heteroepitaxial material systems of current interest.