Relaxation of a strained quantum well at a cleaved surface. Part Ⅱ: Effect of cubic symmetry

摘要

In a previous paper [J. H. Davies, D. M. Bruls, J. W. A. M. Vugs, and P. M. Koenraad, J. Appl. Phys. 91, 4171 (2002). Part Ⅰ.] we compared theory and experiment for the relaxation at a cleaved surface of a strained quantum well of InGaAs in GaAs. The measurements were taken with a scanning tunneling microscope and the analytic calculation used classical elastic theory for a linear, isotropic, homogeneous medium. Qualitative agreement was good but the theory gave only about 80% of the observed displacement. We have therefore extended the calculation to explore the effect of cubic symmetry and the orientation of the cleaved surface. The "strain suppression" method reduces the problem to the response of a half space to traction on its surface. We have calculated this for orthotropic symmetry, which includes the common orientations of orthorhombic, tetragonal, hexagonal, and cubic crystals. Anisotropy has no effect on the shape of the relaxed surface but the magnitude of relaxation changes. For cubic material there is no effect on the strain along the direction of growth if the cleaved surface is a {001} plane and a reduction of a few percent for a {011} plane, which is the case of experimental interest. The outward relaxation is reduced by about 20% due to cubic symmetry for a {001} plane because the shear stiffness of GaAs is higher than in the isotropic model, and is a further 10% smaller for a {011} plane. Thus the results for cubic symmetry lie further from the measurements than those calculated for isotropic material. Interfacial forces may contribute to this discrepancy but we suggest that nonlinear elasticity is probably responsible.