Inclusion of nonlinear strain effects in the Hamiltonian for nanoscale semiconductor structures

Lassen, B., Willatzen, M. and Melnik, R.V.N.

Journal of Computational and Theoretical Nanoscience, 3(4), 588-597, 2006


In this paper a general method of treating Hamiltonians of deformed nanoscale semiconductor structures based on a Taylor series expansion(1) is used to derive two second-order approximations with respect to a known deformation, one based on the weak formulation and one based on the strong formulation of the problem. In the case of the strong formulation of the problem appropriate interface boundary conditions are derived. In addition, a second-order approximation with respect to a known strain tensor is derived. As a model example, energies for a one-dimensional Kronig-Penney potential are calculated with an exact, a first-order and a second-order strain Hamiltonian. Also, the more realistic example of a rectangular quantum dot is studied. In this example the strain tensor is found using linear isotropic strain theory and the resulting strain tensor is used to study the influence of including first- and second-order strain contributions in electronic band-structure calculations.