Effects of charge density on the luminescence energy shift of GaN quantum wells: A variational approach

The influence of free-carrier screening on the luminescence energy shift in GaN quantum wells (QWs) mainly in relation to a quantum-confined Stark effect is investigated theoretically. This effect substantially modifies the electronic states in the QW and the emission energy in the photoluminescence (PL) spectra. In this paper, the influence of the built-in electric field on the PL emission is calculated by considering a variational electron and hole wave function to obtain the ground-energy transitions inside the active region in QW. Furthermore, the contribution between the interaction of the electron with the charge distribution of electrons and holes in the QW is taken into account in the Schrödinger equation, and this energy potential also satisfies the Poisson's equation with the charge density in the ground-state subband as the source term. The transition energy calculations between the confined electron and hole states as a function of the carrier density and the well thickness are in agreement with the PL experiments reported in the literature.