We present a theoretical study of the electron energy states in narrow gap
semiconductor quantum dots (QDs). For a finite height hard-wall 3D confinem
ent potential the problem was solved by using of the effective one electron
ic band Hamiltonian, the energy and position dependent electron effective m
ass approximation, and the Ben Daniel-Duke boundary condition. To solve the
3D Schrodinger 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 th
e electron effective mass. For the excited states, the non-parabolicity eff
ect has been found to be stronger than it at ground state. (C) 2001 Elsevie
r Science Ltd. All rights reserved.