Computer simulation of electron energy levels for different shape InAs/GaAs semiconductor quantum dots

A computational technique for the energy levels calculation of an electron confined by a 3D InAs quantum dot (QD) embedded in GaAs semiconductor matri x is presented. Based on the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, a fin ite height hard-wall 3D confinement potential, and the Ben Daniel-Duke boun dary conditions, the problem is formulated and solved for the disk, ellipso id, and conical-shaped InAs/GaAs QDs. To calculate the ground state and fir st excited state energy levels, the nonlinear 3D Schrodinger is solved with a developed nonlinear iterative algorithm to obtain the final self-consist ent solutions. In the iteration loops, the Schrodinger equation is discreti zed with a nonuniform mesh finite difference method, and the corresponding matrix eigenvalue problem is solved with the balanced and shifted QR method . The proposed computational method has a monotonically convergent property for all simulation cases. The computed results show that for different qua ntum dot shapes, the parabolic band approximation is applicable only for re latively large dot volume. For the first excited states the non-parabolicit y effect also has been found to be stronger than it at ground state. The QD model and numerical method presented here provide a novel way to calculate the energy levels of QD and it is also useful to clarify principal depende ncies of QD energy states on material band parameter and QDs size for vario us QD shapes. (C) 2001 Elsevier Science B.V. All rights reserved.