We present data on the carrier concentration dependence of the absorption, luminescence and Raman spectra for InN grown by MBE on (0 0 0 1) sapphire in the carrier concentration region where superconductivity was observed. The carrier concentration was changed from 2 x 10(19) to 7 x 10(20) cm(-3) by Mg and Dy doping. The band gap energy increased as the carrier concentration increased, but the luminescence peak remained at around 0.8 eV. We attempt to interpret the Raman spectra using a Fano resonance. There was an optimum carrier concentration region for which the InN superconductivity occurred. (C) 2004 Elsevier B.V. All rights reserved.