Based on the finite difference method, linear optical susceptibility, photoluminescence peak and binding energies of three first states of an exciton trapped by a positive charge donor-impurity ( ) confined in InN/AlN quantum well are investigated in terms of well size and impurity position. The electron, heavy hole free and bound excitons allowed eigen-values and corresponding eigen-functions are obtained numerically by solving one-dimensional time-independent Schrödinger equation. Within the parabolic band and effective mass approximations, the calculations are made considering the coupling of the electron in the n-th conduction subband and the heavy hole in the m-th valence subband under the impacts of the well size and impurity position. The obtained results show clearly that the energy, binding energy and photoluminescence peak energy show a decreasing behavior according to well size for both free and bound cases. Moreover, the optical susceptibility associated to exciton transition is strongly red-shift (blue-shifted) with enhancing the well size (impurity position).
The dependence of the exciton binding energies on quantum well widths of the donor doped GaAs/AlGaAs QW influencing on the intersubband transition
