Dielectric function and Van Hove singularities for In-rich InxGa1- xN alloys : Comparison of N-and metal-face materials

Spectroscopic ellipsometry is applied in order to determine the complex dielectric function (DF) for In-rich ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ alloys with N-face polarity from near-infrared into the vacuum ultraviolet spectral region. The results are compared to corresponding data for metal-face films. The optical properties of both types of hexagonal films agree in the essential features which emphasizes that the extracted DFs do not depend on the polarity but represent therefore bulk characteristics. Besides the band gap, five critical points of the band structure are clearly resolved within the composition range of $1\ensuremath{\geqslant}x\ensuremath{\geqslant}0.67$. Their transition energies are determined by a fit of the third derivative of the DF. With increasing Ga content, all transitions undergo a continuous shift to higher energies characterized by small bowing parameters. Model calculations of the imaginary part of the DF close to the band gap that take the influence of band filling and conduction-band nonparabolicity into account are presented. A comparison to the experimental data yields the position of the Fermi energy. With the calculated values for the carrier-induced band-gap renormalization and the Burstein-Moss shift, the zero-density values for the fundamental band gaps are obtained. Their dependence on the alloy composition is described by a bowing parameter of $b=1.72\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.