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The phonon mode parameters and anisotropic mid-infrared dielectric functiontensor components of high- Al-content Al$_x$Ga$_{1-x}$N alloys in dependence ofthe Al content $x$ are precisely determined from mid-infrared spectroscopicellipsometry measurements for a set of high-quality Si-doped Al$_x$Ga$_{1-x}$Nepitaxial layers on 4H-SiC substrates. Two-mode behavior of the $E_1$(TO) modesand one-mode behavior of the $A_1$(LO) mode are found in agreement withprevious Raman scattering spectroscopy reports. The composition dependencies ofthe IR active phonon frequency parameters are established and a discussion onthe silent $B_1$ mode that may be disorder activated is provided. The staticdielectric constants in dependence of $x$ are determined by using thebest-match model derived phonon mode frequency and high-frequency dielectricconstant parameters and applying the Lydanne-Sachs-Teller relation. Theeffective mass parameter in high-Al-content Al$_x$Ga$_{1-x}$N alloys and itscomposition dependence are determined from mid-infrared optical Hall effectmeasurements. Furtheremore, the free electron concentration $N$ and mobilityparameters $\mu$ of Al$_x$Ga$_{1-x}$N films with similar Si doping levels areinvestigated as function of the Al content, $x$ and discussed.

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