Mathias Schubert

Zirconia (ZrO2) thin films were fabricated using an ultra-high-vacuum electron-beam physical vapor deposition technique. Spectroscopic ellipsometry (SE) data from multiple samples with different thicknesses were acquired over a broad photon-energy range of 0.74–9.25 eV to determine the frequency-dependent complex dielectric function of ZrO2 thin films. Atomic force microscopy (AFM) analysis confirms the formation of highly uniform films with an average height variation below 2 nm across the scanned areas. In the SE-based optical analysis, a five-layer model consisting of the substrate, native oxide, ZrO2 thin film, surface roughness layer, and ambient was employed within a multi-sample analysis framework. The surface roughness layer was modeled using a 50:50 effective medium approximation of the film and ambient, yielding roughness thicknesses consistent with those obtained from AFM measurements. By parameterizing the intrinsic dielectric response using a set of oscillators, a critical-point model dielectric-function analysis was applied to identify band-to-band transition parameters. These results provide a comprehensive parameterization of the dielectric function of electron-beam-deposited ZrO2 thin films and establish a robust ellipsometry-based framework for correlating thin-film structure and optical properties in ultra-wide-bandgap oxide materials.

We present a model dielectric function composed of critical point functions in order to parameterize the temperature and wavelength dependencies of the dielectric function of InAs. This model is based on Adachi’s critical point model, with simple wavelength-dependent analytical functions whose parameters change linearly with temperature. The calculated dielectric function at room temperature is in excellent agreement with previously published data. We apply this model in the spectral range of 0.7–5 eV and in the temperature range of room temperature to 250°C with in situ spectroscopic ellipsometry measurements on an InAs substrate. Spectroscopic measurements were performed continuously while slowly ramping sample temperature in a stepwise manner in the controlled ambient environment of an atomic layer deposition system. We find that our model matches excellently with all experimental data with deviations less than 2% in pseudoepsilon. Our model permits smooth interpolation of the dielectric function of InAs for any intermediate temperature in the range studied and therefore can be used to monitor temperature, for example, during thin film deposition processes by in situ spectroscopic ellipsometry. We propose that this model can be applied to other semiconductors as well as wider temperature ranges.

We investigate the temperature-dependent complex dielectric function of bulk single-crystal In2O3 over the spectral range of 1–6 eV and temperatures from room temperature to 600 °C under high-vacuum conditions using in situ spectroscopic ellipsometry. The dielectric function was modeled using wavelength-by-wavelength and critical-point model dielectric function analyses. The dielectric function exhibits pronounced alterations with increasing temperature, attributed to thermally induced changes in the band structure and carrier dynamics. We identify direct and indirect interband transitions and excitonic contributions associated with the direct bandgap near the onset of absorption. At elevated temperatures, features in the dielectric function due to indirect transitions emerge below the direct bandgap energy, which shift toward shorter photon energies with increasing temperature. Combining our results with low-temperature data from previous reports, both observed shifts of the direct and indirect transitions can be seamlessly explained with the Bose–Einstein model. The direct transition is coupled less strong to the phonon bath (average temperature θB=512 K), leading to a smaller high-temperature slope (γ=−0.2 meV/K) than for the indirect transition (θB=360 K, γ=−1.3 meV/K). The exciton contributions diminish toward higher temperatures reflected by the decrease in amplitude and increase in broadening model parameters. Our parameter set can be used to calculate the model dielectric function In2O3 at elevated temperatures.

A set of ultrawide bandgap single-crystal NdGaO3 samples cut with crystallographic surface orientations (001), (101), and (110) are investigated by using generalized spectroscopic ellipsometry. We report the complex anisotropic dielectric functions in the spectral range from 0.73 to 9.0 eV, for polarization along directions a, b, and c of the orthorhombic unit cell. A Kramers–Kronig consistent parameterized model was utilized to identify critical point structures and their association with band-to-band transitions, and the results from density functional theory (DFT) calculations for the electronic band structure of NdGaO3 are compared. A Cauchy parameter analysis for the three refractive indices is performed in the below bandgap spectral range. Dielectric functions along lattice directions a, b, and c and their respective bandgap energy values are very similar. Below the bandgap energy, the refractive index differences for directions a and b are very small (0.34% on average) while index differences with direction c (approximately 1.25%) lead to effective positive uniaxial optical properties (nc>na≈nb) toward the phonon modes spectral range. Our ellipsometry analysis determines the lowest band-to-band transitions of NdGaO3 to occur at Ea=6.46(6)eV, Eb=6.29(5)eV, and Ec=6.77(7)eV, i.e., Ec>Ea>Eb, while our DFT calculations predict the first transition to be lowest along the a axis. We discuss our findings in light of previous reports and present all parameters of our theoretical and experimental analyses.

We determine the composition dependence of the below-bandgap anisotropic refractive indices and dielectric functions of β-(AlxGa1−x)2O3 for x up to 25% Al. We use Mueller matrix generalized spectroscopic ellipsometry and investigate a set of high quality single crystalline bulk (x=0%,5%,10%,15%,20%,25%) and thin film (4.6%, 9.7%, 12%, 15%, 16.3%, 21%) samples grown by the Czochralski method and by plasma-assisted molecular beam epitaxy, respectively. Bulk samples with 0.2% silicon doping are cut from ingots with (100) surface and the unintentionally doped thin films samples are grown pseudomorphically on (010) β-Ga2O3. The combination of ellipsometry data from both sample sets permits to fully determine the optical properties of the transparent alloys. We employ a quasi-orthorhombic approach which ignores the very small shear components induced by the monoclinic crystal structure. We also ignore the possibly small effects due to strain within the pseudomorphically grown epitaxial samples. We report indices and dielectric functions for polarization along lattice vectors a, b, and reciprocal lattice vector c⋆. All indices reduce with increasing incorporation of aluminum while the spectral range of transparency increases due to the increase in bandgap energy with composition. We use our results to predict Bragg reflector multilayer structures on b-plane β-(Al0.20Ga0.80)2O3, for use in polarization sensitive narrow-band optical filters in the short wavelength region.

Hyperbolic phonon polaritons ‐ hybridized modes arising from the ultrastrong coupling of infrared light to strongly anisotropic lattice vibrations in uniaxial or biaxial polar crystals ‐ enable to confine light to the nanoscale with low losses and high directionality. In even lower symmetry materials, such as monoclinic ‐Ga ₂ O ₃ (bGO), hyperbolic shear polaritons (HShPs) further enhance the directionality. Yet, HShPs are intrinsically supported only within narrow frequency ranges defined by the phonon frequencies of the host material. Here, we report spectral tuning of HShPs in bGO by isotopic substitution. Employing near‐field optical microscopy to image HShPs in ¹⁸ O bGO films homoepitaxially grown on a ¹⁶ O bGO substrate, we demonstrate a spectral redshift of 40 cm ⁻¹ for the ¹⁸ O bGO, compared to ¹⁶ O bGO. The technique allows for direct observation and a model‐free estimation of the spectral shift driven by isotopic substitution without the need for knowledge of the dielectric tensor. Complementary far‐field measurements and ab initio calculations ‐ in good agreement with the near‐field data ‐ confirm the effectiveness of this estimation. This multifaceted study demonstrates a significant isotopic substitution induced spectral tuning of HShPs into a previously inaccessible frequency range, creating new avenues for technological applications of such highly directional polaritons.

In this work, we derive the relationship between the states of strain and stress in pseudomorphic epitaxial layers on a substrate with differing equilibrium lattice parameters under symmetry-conserving conditions for the case of monoclinic crystal symmetry. We compare surface vectors across the template-epitaxial layer interface and impose conditions of a stress-free epitaxial layer. As a result, we demonstrate the theoretical existence of up to three possible unit cells that can establish on a given template. We demonstrate this approach for the special case of symmetry-conserving strain in a class of templates with ( h 0 l ) surface orientations. We use β - ( Al x Ga 1 − x ) 2 O 3 on ( h 0 l ) β - Ga 2 O 3 as an example. We discuss the effects of the composition x and surface orientation on the formation of three elastically stable unit cells, their strain and stress tensors, unit-cell axes, unit-cell volumes, lattice spacings, elastic potential energies, and stress-free directions. The previous paradigm for epitaxial layer growth, where the only stress-free direction is perpendicular to the growing surface, is not generally valid for low-symmetry materials. In the example here, we find that, in addition to the stress-free growth direction for crystallographic planes with low Miller indices, two possible competing domains can exist with stress-free directions oblique to the surface of the template for almost all planes ( h 0 l ) . We further demonstrate the effect of the orientation-dependent differently strained domains and calculate the strain-shifted anisotropic band-to-band transitions for β - ( Al 0.1 Ga 0.9 ) 2 O 3 on ( h 0 l ) β - Ga 2 O 3 . We also provide examples of x-ray diffraction analyses, which may help guide the search for the occurrence of such differently strained unit cells in epitaxial layers grown by experiment, here taking the ( 2 ¯ 01 ) surface orientation as case for demonstration.

The metalorganic chemical vapor deposition (MOCVD) dynamics of beta-gallium oxide (β-Ga2O3) growth using trimethylgallium (TMGa) and oxygen as precursors were investigated through both theoretical thermodynamic analysis and experimental validation in a horizontal low-pressure hot-wall reactor. Thermodynamic analysis revealed that high-purity β-Ga2O3 can be grown through the complete combustion of TMG-derived gallium and hydrocarbons. Furthermore, the complete combustion of intentionally supplied hydrogen into the growth system also prevents the degradation of β-Ga2O3 growth. Therefore, a high input VI/III ratio that ensures full combustion of gaseous species in the growth system is preferred for β-Ga2O3 MOCVD. The growth experiments were performed on 2-in. sapphire substrates under an input VI/III ratio of 250. β-Ga2O3 growth was confirmed at growth temperatures between 740 and 950 °C, with the growth rate decreasing from 0.7 to 0.5 μm/h as temperature increased. Thermodynamic analysis successfully reproduced this growth behavior under the effective VI/III ratio of 6.5. The results demonstrate that β-Ga2O3 MOCVD occurred under thermal equilibrium conditions and was thermodynamically controllable.

We report a Mueller matrix ellipsometer design using dual continuously rotating anisotropic meta wave plates, which determines the full set of Mueller matrix elements in the terahertz spectral range. The instrument operates in the frequency domain and employs a frequency tunable, solid state synthesizer based, continuous wave terahertz source with sub-MHz bandwidth. The implemented source permits operation within 82–125 and 170–250 GHz, without and with an additional frequency doubler, respectively. The rotating wave plates produce sufficient modulation of the Stokes vector components of terahertz light to use the wave plates in polarization state generator and polarization state detector devices. Fast terahertz light detection rate of a quasi-optical solid state detector permits acquisition with few microseconds temporal resolution and electronic sweeping control of the source frequency. We develop a fast frequency sweeping scheme while continuously rotating the terahertz wave plates. Subsequent sorting of measured data permits measurements of Mueller matrix elements at hundreds of different wavelengths. The Mueller matrix elements are obtained by forward numerical reduction of the measured data using an algorithm developed by Ruder et al. [Opt. Lett. 45, 3541–3544 (2020)]. The instrument is combined with a magnetocryostat capable of reaching magnetic field strengths of −8 T…8 T and sample temperatures from 4 K…400 K. Hence, the instrument is suitable to measure the full Mueller matrix of samples with magnetic resonances as demonstrated recently by Rindert et al. [Phys. Rev. B 110, 054413 (2024)]. We discuss design, calibration, and example applications.