  In this paper, we present an envelope function analysis in order to design
the emission spectra of a white quantum well light emitting diode. The
nanometric heterostructure that we are dealing with is a multiple quantum well,
consisting periods of three single quantum wells with various well thicknesses.
With the aid of 6x6 Luttinger Hamiltonian, we employ the combination of two
methods, k.p perturbation and transfer matrix method, to acquire electron and
hole wavefunctions analytically. The envelope function approximation was
considered to obtain these wavefunctions for a special basis set. While
adjacent valence subbands have been studied exactly, the conduction bands are
approximated as parabolic. The effect of Stokes shift has been also taken into
account. The dipole moment matrix elements for interband atomic transitions are
evaluated via correlation between electron and hole envelope functions, for
both orthogonal polarizations. This has simplified the calculation of
photoluminescence intensity. Spatial variations in hole/electron wavefunctions
have been examined with the introduction of piezoelectric and spontaneous
polarizations internal field. We theoretically establish the possibility of a
highly efficient InGaN red emitter, resulting in a uniform luminescence in red,
green and blue emissions from the while light emitting diode, through adjusting
material composition, potential slope, and thickness.
