Influence of defects on the absorption edge of InN thin films: The band gap value

We investigate the optical-absorption spectra of InN thin films whose electron density varies from $\ensuremath{\sim}{10}^{17}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}\ensuremath{\sim}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The low-density films are grown by molecular-beam-epitaxy deposition while highly degenerate films are grown by plasma-source molecular-beam epitaxy. The optical-absorption edge is found to increase from $0.61\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.90\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ as the carrier density of the films is increased from low to high density. Since films are polycrystalline and contain various types of defects, we discuss the band gap values by studying the influence of electron degeneracy, electron-electron, electron-ionized impurities, and electron-LO-phonon interaction self-energies on the spectral absorption coefficients of these films. The quasiparticle self-energies of the valence and conduction bands are calculated using dielectric screening within the random-phase approximation. Using one-particle Green's function analysis, we self-consistently determine the chemical potential for films by coupling equations for the chemical potential and the single-particle scattering rate calculated within the effective-mass approximation for the electron scatterings from ionized impurities and LO phonons. By subtracting the influence of self-energies and chemical potential from the optical-absorption edge energy, we estimate the intrinsic band gap values for the films. We also determine the variations in the calculated band gap values due to the variations in the electron effective mass and static dielectric constant. For the lowest-density film, the estimated band gap energy is $\ensuremath{\sim}0.59\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, while for the highest-density film, it varies from $\ensuremath{\sim}0.60\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}\ensuremath{\sim}0.68\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ depending on the values of electron effective mass and dielectric constant.