We can also rule out the effect of change in excitation density as just a local temperature increase under the electron beam, because the position of the free exciton does not change with beam current varying over two orders of magnitude. Therefore, the cause of the observed peak-shift is not a change of physical properties with depth. Instead, a pronounced exponential band tail with Urbach energies of 30 meV for GaN and up to 200 meV for the Al x Ga 1-x N alloys has been found. This could originate from structural disorder, or could be caused by point defects, alloy fluctuations, or impurities creating shallow defects such as silicon or oxygen. The Urbach parameter E Urb has units of energy and is assumed to be related to disorder in the material.
R depends on the beam-energy and the density of the material.
Matsukawa et al. The peak shift could be expected to be strongest for lines with large FWHM in the order of the Urbach energy. It also shows, that due to the higher absorption, the peak amplitude is reduced when beam energy is increased. This explains why the peak with lower photon energy becomes stronger for an increasing beam energy at the same time. In order to compare the measured peak-shift with the simulations, the position of the peak maximum as a function of beam energy is calculated in Figure 6 for different E Urb .