Optical properties and temperature dependence of the interband transitions of cubic and hexagonal GaN

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Abstract
The optical properties of cubic and hexagonal GaN thin films, grown by electron-cyclotron resonance microwave plasma-assisted molecular-beam epitaxy on silicon and sapphire substrates, respectively, have been studied at photon energies up to 25 eV with conventional and synchrotron-radiation spectroscopic ellipsometry. The fundamental gaps of the two polytypes are located at different energies, namely at 3.25 and 3.43 eV for cubic and hexagonal GaN. Analysis of the dielectric function of the two phases in the region 4.5–9.5 eV with appropriate models yields the energy location and broadening of the observed critical points. These critical points are assigned to specific points in the zinc-blende and wurtzite Brillouin zones, respectively, making use of the latest published band-structure studies and a comparison is made between the corresponding results for GaN, GaAs, and GaP. Measurements in the temperature range from 80 to 650 K provide the temperature dependence of these parameters. The features observed in the reflectivity spectra of hexagonal GaN are discussed in relation to other works. Kramers-Kronig analysis of the reflectivity between 0 and 33 eV of the hexagonal polytype verifies the existence of a broad feature centered at 14 eV. Finally, average properties, such as the effective ir dielectric constant and the effective number of valence electrons per atom are calculated for the two polytypes and compared to GaAs and GaP.