Accurate quadratic-response approximation for the self-consistent pseudopotential of semiconductor nanostructures

Abstract

Quadratic-response theory is shown to provide a conceptually simple but accurate approximation for the self-consistent one-electron potential of semiconductor nanostructures. Numerical examples are presented for GaAs/ AlAs and In 0.53 Ga 0.47 As/ InP ͑001͒ superlattices using the local-density approximation to densityfunctional theory and norm-conserving pseudopotentials without spin-orbit coupling. When the reference crystal is chosen to be the virtual-crystal average of the two bulk constituents, the absolute error in the quadraticresponse potential for ⌫ 15 valence electrons is about 2 meV for GaAs/ AlAs and 5 meV for In 0.53 Ga 0.47 As/ InP. Low-order multipole expansions of the electron density and potential responses are shown to be accurate throughout a small neighborhood of each reciprocal-lattice vector, thus providing a further simplification that is confirmed to be valid for slowly varying envelope functions. Although the linear response is about an order of magnitude larger than the quadratic response, the quadratic terms are important both quantitatively ͑if an accuracy of better than a few tens of meV is desired͒ and qualitatively ͑due to their different symmetry and long-range dipole effects͒.

Electronic states and wavefunctions of diatomic donor molecular ions in silicon: multi-valley envelope function theory

“…The single-particle impurity potential V imp (r) includes the charge screening caused by the electron density surrounding the donor nucleus. This potential can be modeled using an approximate expression for the dielectric function [16] or can be derived using the first-principles non-linear response theory proposed by Foreman [26,27].…”

“…Taking into account the spherical symmetry of the Coulomb potential and the symmetry of the periodic Bloch functions (35a)-(35c), the central-cell potential in equation (27) can be decomposed as follows:…”