We use a combined generalized spectroscopic ellipsometry and density functional theory approach to determine and analyze the anisotropic dielectric functions of an α-Ga2O3 thin film. The sample is grown epitaxially by plasma-assisted molecular beam epitaxy on m-plane sapphire. Generalized spectroscopic ellipsometry data from multiple sample azimuths in the spectral range from 0.73 eV to 8.75 eV are simultaneously analyzed. Density functional theory is used to calculate the valence and conduction band structure. We identify, for the indirect-bandgap material, two direct band-to-band transitions with M0-type van Hove singularities for polarization perpendicular to the c axis, E0,⊥=5.46(6) eV and E0,⊥=6.04(1) eV, and one direct band-to-band transition with M1-type van Hove singularity for polarization parallel to E0,||=5.44(2) eV. We further identify excitonic contributions with a small binding energy of 7 meV associated with the lowest ordinary transition and a hyperbolic exciton at the M1-type critical point with a large binding energy of 178 meV.
A complete set of infrared-active and Raman-active lattice modes is obtained from density functional theory calculations for single-crystalline centrosymmetric orthorhombic neodymium gallate. The results for infraredactive modes are compared with an analysis of the anisotropic long-wavelength properties using generalized spectroscopic ellipsometry. The frequency-dependent dielectric function tensor and dielectric loss function tensor of orthorhombic neodymium gallium oxide are reported in the spectral range of 80-1200 cm −1. A combined eigendielectric displacement vector summation and dielectric displacement loss vector summation approach augmented by considerations of lattice anharmonicity is utilized to describe the experimentally determined tensor elements. All infrared-active transverse and longitudinal optical mode pairs obtained from density functional theory calculations are identified by our generalized spectroscopic ellipsometry investigation. The results for Raman-active modes are compared to previously published experimental observations. Static and high-frequency dielectric constants from theory as well as experiment are presented and discussed in comparison with values reported previously in the literature.
The quasi-static anisotropic permittivity parameters of electrically insulating beta gallium oxide (β-Ga2O3) were determined by terahertz spectroscopy. Polarization-resolved frequency domain spectroscopy in the spectral range from 200 GHz to 1 THz was carried out on bulk crystals along different orientations. Principal directions for permittivity were determined along crystallographic axes c and b and reciprocal lattice direction a*. No significant frequency dispersion in the real part of dielectric permittivity was observed in the measured spectral range. Our results are in excellent agreement with recent radio frequency capacitance measurements as well as with extrapolations from recent infrared measurements of phonon mode and high-frequency contributions and close the knowledge gap for these parameters in the terahertz spectral range. Our results are important for applications of β-Ga2O3 in high-frequency electronic devices.
Mueller matrix spectroscopic ellipsometry is applied to determine anisotropic optical properties for a set of single-crystal rhombohedral structure α-(Al xGa1− x)2O3 thin films (0 [Formula: see text] x [Formula: see text] 1). Samples are grown by plasma-assisted molecular beam epitaxy on m-plane sapphire. A critical-point model is used to render a spectroscopic model dielectric function tensor and to determine direct electronic band-to-band transition parameters, including the direction dependent two lowest-photon energy band-to-band transitions associated with the anisotropic bandgap. We obtain the composition dependence of the direction dependent two lowest band-to-band transitions with separate bandgap bowing parameters associated with the perpendicular ([Formula: see text] = 1.31 eV) and parallel ([Formula: see text] = 1.61 eV) electric field polarization to the lattice c direction. Our density functional theory calculations indicate a transition from indirect to direct characteristics between α-Ga2O3 and α-Al2O3, respectively, and we identify a switch in band order where the lowest band-to-band transition occurs with polarization perpendicular to c in α-Ga2O3 whereas for α-Al2O3 the lowest transition occurs with polarization parallel to c. We estimate that the change in band order occurs at approximately 40% Al content. Additionally, the characteristic of the lowest energy critical point transition for polarization parallel to c changes from M1 type in α-Ga2O3 to M0 type van Hove singularity in α-Al2O3.
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