Anisotropic dielectric functions, band-to-band transitions, and critical points in α -Ga2O3

Abstract

We use a combined generalized spectroscopic ellipsometry and density functional theory approach to determine and analyze the anisotropic dielectric functions of an α-Ga2O3 thin film. The sample is grown epitaxially by plasma-assisted molecular beam epitaxy on m-plane sapphire. Generalized spectroscopic ellipsometry data from multiple sample azimuths in the spectral range from 0.73 eV to 8.75 eV are simultaneously analyzed. Density functional theory is used to calculate the valence and conduction band structure. We identify, for the indirect-bandgap material, two direct band-to-band transitions with M0-type van Hove singularities for polarization perpendicular to the c axis, E0,⊥=5.46(6) eV and E0,⊥=6.04(1) eV, and one direct band-to-band transition with M1-type van Hove singularity for polarization parallel to E0,||=5.44(2) eV. We further identify excitonic contributions with a small binding energy of 7 meV associated with the lowest ordinary transition and a hyperbolic exciton at the M1-type critical point with a large binding energy of 178 meV.

Atomic‐Layer‐Ti‐Doped Ga2O3 Thin Films with Tunable Optical Properties and Wide Ultraviolet Optoelectronic Responses

“…The optical bandgap and dielectric properties are vital to effectively design and fabricate optical and electronic devices. Typically, spectroscopic ellipsometry (SE) [ 15–19 ] and absorption spectroscopy [ 20 ] have been successfully applied to evaluate and analyze the optical constants of Ga 2 O 3 bulk materials and thin films with various phases. More efforts in examining the optical constants of amorphous and nanocrystalline Ga 2 O 3 thin films are expected because these constants are significant in practical applications.…”

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

“…Most recently, Hilfiker et al performed a wide spectral range analysis determining the anisotropic dielectric functions and fundamental band-toband transitions for polarization directions parallel (||, extraordinary direction) and perpendicular (⊥, ordinary direction) to the lattice c axis in aGO using generalized spectroscopic ellipsometry from the near infrared (IR) to the vacuum ultraviolet (0.73 eV to 8.75 eV). 22 The band-to-band transi- tions for polarization perpendicular to the c axis, E 0,⊥ = 5.46 (6) eV and E 0,⊥ = 6.041 eV belong to M 0 -type van Hove singularities, whereas a M 1 -type van Hove singularity occurs for the band-to-band transition parallel to the c axis (E 0,|| = 5.442 eV). 22 Hybrid-level density functional theory was also used to elucidate the structure of both the valence and conduction bands and Γ-point effective mass parameters were provided along high symmetry directions.…”

“…22 The band-to-band transi- tions for polarization perpendicular to the c axis, E 0,⊥ = 5.46 (6) eV and E 0,⊥ = 6.041 eV belong to M 0 -type van Hove singularities, whereas a M 1 -type van Hove singularity occurs for the band-to-band transition parallel to the c axis (E 0,|| = 5.442 eV). 22 Hybrid-level density functional theory was also used to elucidate the structure of both the valence and conduction bands and Γ-point effective mass parameters were provided along high symmetry directions. As an unusual property among conventional semiconductors, such as GaAs or GaN, the highly complex and anisotropic band structure of aGO results in excitonic contributions to the anisotropic band-to-band transitions.…”

“…21 On the contrary, aGO is optically uniaxial and is characterized by only two fundamental band-to-band transitions polarized along high symmetry directions. 22 Furthermore, aGO also possesses only half the number of phonon modes in the set of Brillouin zone center lattice vibrations whose displacement directions all align with high symmetry lattice directions.…”

“…A small binding energy of 7 meV was found for the lowest ordinary transition and a hyperbolic (quasi 2-dimensional) exciton with large binding energy of 178 meV was observed for the M 1 -type (extraordinary) critical point transition. 22 In earlier work, Segura et al, 39 Kracht et al, 40 and Feneberg et al 36 reported on more limited spectroscopic investigations and obtained partial bandgap energy information in agreement with Hilfiker et al The anisotropic dielectric constant for photon energies far below the bandgap but far above optical phonon mode frequencies were obtained from IR ellipsometry measurements (ε ∞,⊥ =3.75 and ε ∞, =3.64), 26 which agreed reasonably well by extrapolation from the near IR ellipsometry analysis (ε ∞,⊥ = 3.86, ε ∞, = 3.76) and direct Cauchy model analysis (ε ∞,⊥ = 3.864, ε ∞, = 3.756) performed by Hilfiker et al 22,32 Of fundamental importance for device design and operation is precise knowledge of phonon mode properties and static dielectric constants. A complete picture for these properties has not emerged yet.…”