Boundary conditions for the electron wavefunction in GaInNAs-based quantum wells and modelling of the temperature-dependent effective bandgap

The boundary conditions were investigated for the electron wavefunction in Ga_1-xIn_xN_yAs_1-y-based heterostructures described by the band anticrossing model. Among other advantages, the utilisation of these boundary conditions simplifies the calculation of, for example, transition energies in quantum wells. The derived equations were applied to model the temperature-dependence of the effective bandgap in Ga_1-xIn_xN_yAs_1-y/GaAs quantum well structures with high indium concentration. From a fit to the experimental photoreflectance data, evidence was found to show that the nitrogen level E_N in the band anticrossing Hamiltonian, measured with respect to the valence band edge, shifts to higher energies with decreasing temperature. This extends similar results reported in the literature for low indium content epilayers.