Temperature dependent dielectric function and the E critical points of hexagonal GaN from 30 to 690 K

Abstract

The complex dielectric function ɛ and the E0 excitonic and band-edge critical-point structures of hexagonal GaN are reported for temperatures from 30 to 690 K and energies from 0.74 to 6.42 eV, obtained by rotating-compensator spectroscopic ellipsometry on a 1.9 μm thick GaN film deposited on a c-plane (0001) sapphire substrate by molecular beam epitaxy. Direct inversion and B-splines in a multilayer-structure calculation were used to extract the optical properties of the film from the measured pseudodielectric function ⟨ɛ⟩. At low temperature sharp E0 excitonic and critical-point interband transitions are separately observed. Their temperature dependences were determined by fitting the data to the empirical Varshni relation and the phenomenological expression that contains the Bose-Einstein statistical factor.

Temperature dependence of exciton-surface plasmon polariton coupling in Ag, Au, and Al films on InxGa1−xN/GaN quantum wells studied with time-resolved cathodoluminescence

“…The measurements of e(x,T) were performed for Al x Ga 1Àx N for energies less than the bandgap and for 0 x 1 by Brunner et al, 53 which we incorporated into our calculations for the SPP dispersion of Au and Ag using e(x,T) for GaN. For the SPP dispersion of aluminum, e i (x,T) is required for energies considerably above the GaN bandgap and so we used the experimental data of Kim et al 54 In order to account for the temperature dependence of e(x) for the metal films, it is necessary to first consider existing approaches, as e(x) is usually modelled using a Drude-Lorentz approach. [50][51][52] The Drude term for nearly free valence electrons describes the intraband behavior and is given by…”

“…Using our model for e(x,T) ¼ e 0 (x,T) þ ie 00 (x,T) for Au, Ag, and Al films and the empirical functions obtained for e(x,T) of GaN, 53,54 we then solved Eq. (2) with t ¼ 20 nm and obtained the x vs k 0 SPP dispersion relation for various temperatures from $50 to 300 K, as shown in Fig.…”

Enhanced excitonic emission efficiency in porous GaN

“…Here, β  = ε 1 (ω)/ε 0 , where the dielectric constant ε 1 in the vicinity of excitonic resonances is taken equal 8 49 . L i is the depolarization factor along i -th axis, expressed via elliptic integrals.…”