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We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(Al_xGa_1−x)₂O₃alloys by far-infrared and infrared generalized spectroscopic ellipsometry. Single-crystalline high quality undoped thin-films grown on m-plane oriented α-Al₂O₃substrates with x =  0.18, 0.37, and 0.54 were investigated. A single mode behavior is observed for all phonon modes, i.e., their frequencies shift gradually between the equivalent phonon modes of the isostructural binary parent compounds. We also provide physical model line shape functions for the anisotropic dielectric functions. We use the anisotropic high-frequency dielectric constants for polarizations parallel and perpendicular to the lattice c axis measured recently by Hilfiker et al. [Appl. Phys. Lett. 119, 092103 (2021)], and we determine the anisotropic static dielectric constants using the Lyddane–Sachs–Teller relation. The static dielectric constants can be approximated by linear relationships between those of α-Ga₂O₃and α-Al₂O₃. The optical phonon modes and static dielectric constants will become useful for device design and free charge carrier characterization using optical techniques.