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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).

In this paper, we study the hydrogen-like donor-impurity binding energy of the ground-state change as a function of the well width under the effect of temperature, size, and impurity position. Within the framework of the effective mass approximation, the Schrodinger-Poisson equation has been solved taken account an on-center hydrogen-like impurity in double QWs with rectangular finite confinement potential profile for 10% of indium concentration in the (well region). The eigenvalues and their correspondent eigenvectors have been obtained by the fined element method (FEM). The obtained results are in good agreement with the literature and show that the temperature, size, and the impurity position have a significant impact on the binding energy of a hydrogen-like impurity in symmetric double coupled quantum wells based on non-polar wurtzite (In,Ga) N/GaN core/Shell.