Position-dependent effective mass for inhomogeneous semiconductors.

Abstract

A systematic approach is adopted to extract an effective low-energy Hamiltonian for crystals with a slowly varying inhomogeneity, resolving several controversies. It is shown that the effective mass m(R) is, in general, position dependent, and enters the kinetic energy operator as -\ensuremath{\nabla}[m${(\mathrm{R})}^{\mathrm{\ensuremath{-}}1}$]\ensuremath{\nabla}/2. The advantage of using a basis set that exactly diagonalizes the Hamiltonian in the homogeneous limit is emphasized.