Low-temperature photoluminescence spectra of nominally undoped high quality AlN layers on SiC and Al2O3 substrates are reported. Under high excitation conditions, we observe several bands that increase superlinearly with the excitation density. Based on temperature and excitation level dependences recorded on different samples, we identify a band 36 meV below the free A-exciton transition as due to exciton-exciton scattering (P2 band) and a second band down-shifted from the A-exciton transition by 27 meV as due to biexciton recombination. The combined data yield an exciton binding energy of 48 meV.
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