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We determine the anisotropic dielectric functions of rhombohedral$\alpha$-Ga$_2$O$_3$ by far-infrared and infrared generalized spectroscopicellipsometry and derive all transverse optical and longitudinal optical phononmode frequencies and broadening parameters. We also determine the highfrequency and static dielectric constants. We perform density functional theorycomputations and determine the phonon dispersion for all branches in theBrillouin zone, and we derive all phonon mode parameters at the Brillouin zonecenter including Raman-active, infrared-active, and silent modes. Excellentagreement is obtained between our experimental and computation results as wellas among all previously reported partial information from experiment andtheory. We also compute the same information for $\alpha$-Al$_2$O$_3$, thebinary parent compound for the emerging alloy of$\alpha$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$, and use results from previousinvestigations [Schubert, Tiwald, and Herzinger, Phys. Rev. B 61, 8187 (2000)]to compare all properties among the two isostructural compounds. From bothexperimental and theoretical investigations we compute the frequency shifts ofall modes between the two compounds. Additionally, we calculate overlapparameters between phonon mode eigenvectors and discuss the possible evolutionof all phonon modes into the ternary alloy system and whether modes may formsingle mode or more complex mode behaviors.

Infrared dielectric functions and Brillouin zone center phonons of $\alpha$-Ga$_2$O$_3$ compared to $\alpha$-Al$_2$O$_3$