Mueller matrix spectroscopic ellipsometry is applied to determine anisotropic optical properties for a set of single-crystal rhombohedral structure α-(Al x Ga 1− x ) 2 O 3 thin films (0 [Formula: see text] x [Formula: see text] 1). Samples are grown by plasma-assisted molecular beam epitaxy on m-plane sapphire. A critical-point model is used to render a spectroscopic model dielectric function tensor and to determine direct electronic band-to-band transition parameters, including the direction dependent two lowest-photon energy band-to-band transitions associated with the anisotropic bandgap. We obtain the composition dependence of the direction dependent two lowest band-to-band transitions with separate bandgap bowing parameters associated with the perpendicular ([Formula: see text] = 1.31 eV) and parallel ([Formula: see text] = 1.61 eV) electric field polarization to the lattice c direction. Our density functional theory calculations indicate a transition from indirect to direct characteristics between α-Ga 2 O 3 and α-Al 2 O 3 , respectively, and we identify a switch in band order where the lowest band-to-band transition occurs with polarization perpendicular to c in α-Ga 2 O 3 whereas for α-Al 2 O 3 the lowest transition occurs with polarization parallel to c. We estimate that the change in band order occurs at approximately 40% Al content. Additionally, the characteristic of the lowest energy critical point transition for polarization parallel to c changes from M 1 type in α-Ga 2 O 3 to M 0 type van Hove singularity in α-Al 2 O 3 .
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Infrared-active phonon modes and static dielectric constants in α -(Al x Ga 1− x ) 2 O 3 (0.18 ≤ x ≤ 0.54) alloys
We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(AlxGa1−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.
more » « less- NSF-PAR ID:
- 10363967
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 120
- Issue:
- 11
- ISSN:
- 0003-6951
- Page Range / eLocation ID:
- Article No. 112202
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The anisotropic dielectric functions (DF) of corundum structured
m -planeα -(Alx Ga1−x )2O3thin films (up tox = 0.76) grown onm -plane sapphire substrate by metalorganic CVD have been investigated. IR and visible–UV spectroscopic ellipsometry yields the DFs, while X-ray diffraction revealed the lattice parameters (a ,m ,c ), showing the samples are almost fully relaxed. Analysis of the IR DFs from 250 to 6000 cm−1by a complex Lorentz oscillator model yields the anisotropic IR active phononsE u andA 2u and the shift towards higher wavenumbers with increasing Al content. Analyzing the UV DFs from 0.5 to 6.6 eV we find the change in the dielectric limitsε ∞and the shift of the Γ-point transition energies with increasing Al content. This results in anisotropic bowing parameters forα -(Alx Ga1−x )2O3ofb ⊥= 2.1 eV andb ∣∣= 1.7 eV. -
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