Design of a GaN White Light-Emitting Diode Through Envelope Function Analysis

In this paper, we present an envelope function analysis technique for the design of the emission spectra of a white quantum-well light-emitting diode (QWLED). The nanometric heterostructure that we are dealing with is a multiple QW, consisting of periods of three single QWs with various well thicknesses. With the aid of 6 × 6 Luttinger Hamiltonian, we employ the combination of two methods, k·p perturbation and the transfer matrix method, to acquire the electron and hole wave functions numerically. The envelope function approximation was considered to obtain these wave functions for a special basis set. While adjacent valence sub-bands have been determined approximately, the conduction bands are approximated as parabolic. The effect of Stokes shift has also been taken into account. The dipole moment matrix elements for interband atomic transitions are evaluated via the correlation between the electron and hole envelope functions, for both orthogonal polarizations, thus simplifying the calculation of the photoluminescence intensity. Spatial variations in the hole/electron wave functions have been examined with the introduction of piezoelectric and spontaneous polarization internal fields. We theoretically establish the possibility of a highly efficient InGaN red emitter, resulting in a uniform luminescence in red, green, and blue emissions from a white light emitting diode by adjusting the material composition, internal field, and well thickness.