BEM calculation of strain energy density and relative strain energy in QWR nanostructures

In this paper, we propose a bimaterial boundary element method (BEM) for the calculation of the strain energy density and the relative strain energy in quantum wire (QWR) nanostructures. We first derive the bimaterial Green's functions in terms of the Stroh formalism. We then discretize the boundary of the problem with constant elements for which the involved Green's function kernels can be exactly integrated. Our bimaterial BEM program is finally applied to calculate the strain energy density and relative strain energy in free-standing/embedded InAs QWR on/in GaAs substrate. For a square InAs (1 1 1) QWR, it is found that the magnitude of the relative strain energy increases with increasing depth of the QWR with respect to the surface of the GaAs (1 1 1) substrate. For an isosceles triangle of InAs (1 1 1) QWR free-standing on the surface of the GaAs (1 1 1) substrate, we found that the magnitude of the relative strain energy increases with increasing base angle of the triangle QWR. Strain energy density inside the InAs QWR is also plotted to show its strong dependence on the QWR shape. These results could be useful to the control of the QWR shape and size in epitaxial growth