Elastic strain reduction of finite germanium(x) silicon(1-x)/silicon structures

The focus of this dissertation is a rigorous examination the elastic, intrinsic behavior of stress/strain for epitaxial Si_1−xGe _x/Si (100) structures having finite dimensions. Existing models predict that the behavior is governed primarily by geometry, which can have a profound effect should the ratio of half-width to height (l/h) be less than 50. Two main aspects of existing theories were pressed: first, the role of geometry for a fixed Si_1−xGe_x composition and therefore strain (ϵ = 0.42%) and second, the role of misfit stress for a fixed l/b ratio of 0.5. Strict control of the fabrication process necessitated selective epitaxial growth via gas-source molecular beam epitaxy. Though experimental combinations of various thickness (50, 100, 140, and 200 nm) and variable pitch (0.09–25 μm) a wide range of l/b values was obtained (0.5–500). As the selectively grown structures are arranged into a periodic array, where the period is repeated over a large distance (mm), in addition to dynamical diffraction, Fraunhoffer diffraction was also observed. These two complementary mechanisms of diffraction were used to determine the stress distribution within these structures. Ensemble with transmission electron microscopy, a qualitative assessment of elastic strain reduction mechanisms—local curvature effects and tangential forces—was possible. The main conclusions of this dissertation are as follows: (A) An analytical reciprocal space construction was developed to facilitate the interpretation of experimental x-ray diffraction data. (B) As a corollary, arbitrary positioning and movement in reciprocal space are described, which in practice is applied to capturing scattered intensity parallel to the surface. (C) Facet growth in SiGe selective epitaxy was investigated. One key result is the persistence of a {lcub}113{rcub} facet with increasing thickness, as the {lcub}111{rcub} facet is anticipated. (D) In examining the role of geometry, elastic lattice distortions were only observed for l/ b ratios 1.25, 0.8, and 0.5. Experimentally, a strong dependence of applied stress was observed. Overall, these results strongly deviate from the predictions, which brings to light the limitations of the models—namely, the role of tangential forces for single crystal films and the role of curvature.