A Comparison Of Calculated Impurity Wavefunctions With GaP:N Luminescence

Abstract

Luminescence spectra due to impurities in a semiconductor contain contributions from both direct and indirect electronic transitions. In the indirect transition, a momentum conserving phonon is emitted or absorbed simultaneously with the emission of a photon. Because such transitions occur in all parts of the B illouin zone where the impurity wavefunction is non-vanishing, much information about the wavefunction (in k-space) can, in principle, be obtained from the phonon sidebands of the luminescence spectrum. In this paper, we derive an expression for the luminescence intensity due to indirect transitions, as a function of energy, and relate it to the k-space charge density, |ψ(k)|2, of the impurity level. This expression can then be used to test the accuracy of particular theoretical models of localized wavefunctions and energy levels. A charge density in k-space is calculated by the use of a theoretical model, and the corresponding spectrum is then calculated according to our expression. We compare this with the measured luminescence spectrum, which has first been treated to remove configuration coordinate electron-phonon interactions.(1)