Infrared dielectric function, phonon modes and free-charge carrier properties of high-Al-content Al$_x$Ga$_{1-x}$N alloys determined by mid-infrared spectroscopic ellipsometry and optical Hall effect

The phonon mode parameters and anisotropic mid-infrared dielectric function tensor components of high- Al-content Al$_x$Ga$_{1-x}$N alloys in dependence of the Al content $x$ are precisely determined from mid-infrared spectroscopic ellipsometry measurements for a set of high-quality Si-doped Al$_x$Ga$_{1-x}$N epitaxial layers on 4H-SiC substrates. Two-mode behavior of the $E_1$(TO) modes and one-mode behavior of the $A_1$(LO) mode are found in agreement with previous Raman scattering spectroscopy reports. The composition dependencies of the IR active phonon frequency parameters are established and a discussion on the silent $B_1$ mode that may be disorder activated is provided. The static dielectric constants in dependence of $x$ are determined by using the best-match model derived phonon mode frequency and high-frequency dielectric constant parameters and applying the Lydanne-Sachs-Teller relation. The effective mass parameter in high-Al-content Al$_x$Ga$_{1-x}$N alloys and its composition dependence are determined from mid-infrared optical Hall effect measurements. Furtheremore, the free electron concentration $N$ and mobility parameters $\mu$ of Al$_x$Ga$_{1-x}$N films with similar Si doping levels are investigated as function of the Al content, $x$ and discussed.