We develop schemes of subpixel smoothing for the multiband Luttinger–Kohn and Burt–Foreman Hamiltonians of semiconductor nanostructures. With proper procedures of parameter averages at abrupt interfaces, computational errors of envelope functions due to the discontinuity of heterostructures are significantly reduced. Two smoothing approaches are presented. One is based on eliminations of the first-order perturbation in energy, and the other is an application of the Hellmann–Feynman theorem. Using the finite-difference method, we find that while the procedure of perturbation theory seems to be more robust than that of Hellmann–Feynman theorem, the errors of both schemes are (considerably) lower than that without smoothing or with direct but unjustified averages of untransformed parameters. The proposed approaches may enhance numerical accuracies and reduce computational cost for the modeling of nanostructures.
['Chi-Ti Hsieh', 'Tung-Han Hsieh', 'Shu-Wei Chang']
Improving accuracy using subpixel smoothing for multiband effective-mass Hamiltonians of semiconductor nanostructures