Random potential perturbation effect on a one dimensional parabolic quantum dot

The traditional approximation of treating a doped region as a uniform charge density is inadequate in nanoscale heterostructure semiconductor quantum dots. However, it can be treated as a randomly positioned ion in the doped layer which gives rise to a random potential. Because of the discreteness and smallness of the ion potential in nanoscale devices, a perturbation treatment of the random potential is presented in this paper. The first and second order correction energies have been calculated for all electrons confined in a one dimensional parabolic well.