Strain and piezoelectric fields in arbitrarily oriented semiconductor heterostructures. I. Multiple quantum wells

We present a theoretical study of the strain and piezoelectric fields of semiconductor multiple quantum wells (superlattices), which are either free-standing or coherent with respect to an arbitrarily oriented thick substrate crystal. The strain-tensor components are calculated by minimization of the strain-energy density and by imposing the commensurability constraint at the heterointerfaces (coherent interface condition) of the different semiconductor materials of cubic symmetry. In order to match correctly the deformed unit cells of the different materials at the heterointerfaces, the asymmetric part of the strain tensor is also considered. The symmetry of the distorted crystal is investigated in detail as a function of the interface orientation. We obtain a tetragonal deformation for the high-symmetry surfaces [001], [110], and [111], while for all the other surface orientations a monoclinic lattice of deformation is obtained. These findings are confirmed for superlattices which are either free-standing or coherent with respect to a thick substrate crystal. In zinc-blende heterostructures, according to some interface orientations, these strain fields can generate high internal electric fields, which are due to the piezoelectric effect. A comparison between the theoretical predictions of our model and those obtained by other authors reveals differences in the predicted values of the internal strain-induced electric fields as great as 60% for low-symmetry heterointerface orientations. Our model can be used for semiconductor quantum-well structures made of III-V as well as II-VI compounds. Here, for example, the strain and piezoelectric fields are studied for an ${\mathrm{In}}_{0.20}$ ${\mathrm{Ga}}_{0.80}$As/GaAs multiple-quantum-well structure.