CALCULATION OF STRAIN DISTRIBUTIONS AT THE EDGE OF STRAINED-LAYER STRUCTURES

A method for calculating stress/strain distributions in structures containing one or more strained layers is presented. The theory, which is based on that presented by Treacy et al, is applied to the mesa laser structure containing either a single 3.5 nm strained layer or four evenly spaced 3.5 nm strained layers of In0.7Ga0.3As grown on InGaAsP (lattice matched to InP). The theory includes the anisotropy of elastic constants in full. Cases of structures containing four strained layers are examined where the separation between the centre of the layers is 7.0 nm, 10.0 nm and 16.5 nm. The maximum shear strain in the case of the single layer is found to occur at the layer/barrier interface, clsoe to the edge of the sample. This is, therefore, the region where dislocations are likely to nucleate. The shear strain is about 1.3% for the mesa structure which has a mismatch of 0.009. The presence of four closely spaced strained layers does not significantly affect the magnitude of the shear strain in the region of its maximum. Both the in-plane and perpendicular components of the strain, epsilon-yy and epsilon-xx respectively, show relaxation at the edge of the structure with the largest relaxation occurring close to, but not at, the edge. For the case of four strained layers, each layer has a strain distribution similar to that for the single layer, but, for layer-to-layer separations of 10.0 nm and 7.0 nm, the material between the layers becomes significantly strained near the edge of the sample. At a layer separation of 16.5 nm the strain distributions in each layer are nearly independent of their neighbours. If the elastic constants are assumed to be isotropic, the results differ only slightly (less than 6%) from those obtained from the full anisotropic calculation. For the isotropic case, the maximum shear strain for a strained layer of Poisson's ratio-nu and mismatch f is found to be 0.68f(1 + nu)/(1 - nu). The minimum value of the strain relaxation perpendicular to the plane of the layer, epsilon-xx, is f(0.10-0.82-nu)(1 + nu)/(1-nu) while the maximum value of the in-plane strain relaxation, epsilon-yy, is f(0.90-1.19-nu)(1 + nu)/(1-nu).