Energy and coordinate dependent effective mass and confined electron states in quantum dots

We present a theoretical study of the electron energy states in narrow gap semiconductor quantum dots (QDs). For a finite height hard-wall 3D confinement potential the problem was solved by using of the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, and the Ben Daniel–Duke boundary condition. To solve the 3D Schrödinger equation, we employ a numerical scheme by using the finite difference method and the QR algorithm. Our results show that the parabolic band approximation is applicable only for relatively thin cylindrical QDs or for the dots with large radius. We show that the electron wave function localization plays an important role in the dependency of the energy and the electron effective mass. For the excited states, the non-parabolicity effect has been found to be stronger than it at ground state.