Detailed analysis of the dielectric function for wurtzite InN and In-rich InAlN alloys

A detailed analysis of the dielectric function (DF) for wurtzite InN as well as for In-rich InAlN alloys is presented. The experimental data, covering the energy range from 0.72 up to 9.5 eV, were obtained by ellipsometric studies of an (11 (2) over bar0) a-plane InN film and low carrier density (0001) c-plane films. Model calculations of the imaginary part of the DF around the band gap provide direct insight how to determine the energetic position of the Fermi energy from the experimental results. Then, taking into account both, band gap renormalization and Burstein-Moss shift, the values of the gaps at zero carrier density are calculated. The dependence of the InAlN band gap on the alloy composition is described by a bowing parameter of 4.0 eV. The a-plane film exhibits a characteristic optical anisotropy below 1 eV which is attributed to the polarization dependence of transition probabilities from the three valence bands at the Gamma point of the Brillouin zone into the conduction band. The splitting of 25 meV between the absorption edges for the two polarization directions can be well explained by a crystal field energy of 19 (24) meV if a calculated spin-orbit energy of 13 (5) meV is assumed. All results emphasize a band gap value of wurtzite InN of about 0.68 eV. By fitting the third derivatives of the dielectric function up to 9.5 eV we determine the compositional dependences of the transition energies for at least three critical points of the band structure. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.