Composition dependence of the infrared dielectric functions in Si-doped hexagonalAlxGa1−xNfilms onc-plane sapphire substrates

Abstract

The optical properties of hexagonal ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ ($x$ from 0.05 to 0.42) epitaxial films with Si doping concentrations up to ${10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ grown on $c$-plane sapphire substrates by metal-organic chemical vapor deposition have been investigated using infrared reflectance spectra. The dielectric functions $(\ensuremath{\epsilon}={\ensuremath{\epsilon}}_{1}+i{\ensuremath{\epsilon}}_{2})$ of the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ films are determined in the wavelength region of $1.54--50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ at room temperature. The experimental reflectance spectra are analyzed using classical harmonic Lorentz oscillators and Drude model in the transparent, reststrahlen, and free carrier absorption regions. GaN-like ${E}_{1}$ transverse-optical (TO) phonon frequency linearly decreases and its strength increases with decreasing Al composition. However, AlN-like ${E}_{1}(\mathrm{TO})$ phonon frequency shows a relatively weak composition dependence and its strength increases with increasing composition. At a wavelength of $1.54\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, ${\ensuremath{\epsilon}}_{1}$ varies between 4.86 and 5.2 when the composition $x$ changes from 0.05 to 0.42 and ${\ensuremath{\epsilon}}_{2}$ is close to zero. The longitudinal-optical phonon plasmon (LPP) coupled modes of $n$-type hexagonal ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ films are also discussed. For samples with higher concentrations beyond ${10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ the upper LPP coupled mode frequencies increase with increasing carrier concentration indicating the transition from phononlike to plasmonlike behavior.