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We describe a magnetic relation in analogy to the well-known dielectric Lyddane-Sachs-Teller relation [R. H. Lyddane , ]. This magnetic relation follows directly from the model equations for nuclear induction due to fast oscillating electromagnetic fields [F. Bloch, ] and relates the static permeability with the product over all ratios of antiresonance and resonance frequencies associated with all magnetic excitations within a given specimen. The magnetic relation differs significantly from its dielectric analog where the static properties are related to ratios of the squares of resonance frequencies. We demonstrate the validity of the magnetic Lyddane-Sachs-Teller relation using optical magnetization data from terahertz electron magnetic resonance spectroscopic ellipsometry measurements in the presence of an external magnetic field on an iron-doped semiconductor crystal of gallium nitride. 

Electron paramagnetic resonance of Cr3+ ions in β-Ga2O3 is investigated using terahertz spectroscopic ellipsometry under magnetic field sweeping, a technique that enables the polarization resolving capabilities of ellipsometry for magnetic resonance measurements. We employed a single-crystal chromium-doped β-Ga2O3 sample, grown by the Czochralski method, and performed ellipsometry measurements at magnetic field strengths ranging from 2 to 8 T, at frequencies from 82 to 125 and 190 to 230 GHz, and at a temperature of 15 K. Analysis of the frequency-field diagrams derived from all Mueller matrix elements allowed us to differentiate between the effects of electron spin Zeeman splitting and zero-field splitting and to accurately determine the anisotropic Zeeman splitting g-tensor and the zero-field splitting parameters. Our results confirm that Cr3+ ions predominantly substitute into octahedral gallium sites. Line shape analysis of Mueller matrix element spectra using the Bloch–Brillouin model provides the spin volume concentration of Cr3+ sites, showing very good agreement with results from chemical analysis by inductively coupled plasma-optical emission spectroscopy and suggesting minimal occupation of sites with inactive electron paramagnetic resonance. This study enhances our understanding of the magnetic and electronic properties of chromium-doped β-Ga2O3 and demonstrates the effectiveness of high-frequency/high-field electron paramagnetic resonance generalized spectroscopic ellipsometry for characterizing defects in ultrawide-bandgap semiconductors. 

A generalized approach derived from Bloch's equation of motion of nuclear magnetic moments is presented to model the frequency, magnetic field, spin density, and temperature dependencies in the electromagnetic permeability tensor for materials with magnetic resonances. The resulting tensor model predicts characteristic polarization signatures which can be observed, for example, in Mueller matrix element spectra measured. When augmented with thermodynamic considerations and suitable Hamiltonian description of the magnetic eigenvalue spectrum, important parameters such as density, spectral amplitude distribution, relaxation time constants, and geometrical orientation parameters of the magnetic moments can be obtained from comparing the generalized model approach to experimental data. We demonstrate our approach by comparing model calculations with full Mueller matrix element spectra measured at an oblique angle of incidence in the terahertz spectral range, across electron spin resonance quintuplet transitions observed in wurtzite-structure GaN doped with iron. Our model correctly predicts the complexity of the polarization signatures observed in the 15 independent elements of the normalized Mueller matrix for both positive and negative magnetic fields and will become useful for future analysis of frequency and magnetic field-dependent magnetic resonance measurements. Published by the American Physical Society2024 

Group-III nitrides have transformed solid-state lighting and are strategically positioned to revolutionize high-power and high-frequency electronics. To drive this development forward, a deep understanding of fundamental material properties, such as charge carrier behavior, is essential and can also unveil new and unforeseen applications. This underscores the necessity for novel characterization tools to study group-III nitride materials and devices. The optical Hall effect (OHE) emerges as a contactless method for exploring the transport and electronic properties of semiconductor materials, simultaneously offering insights into their dielectric function. This non-destructive technique employs spectroscopic ellipsometry at long wavelengths in the presence of a magnetic field and provides quantitative information on the charge carrier density, sign, mobility, and effective mass of individual layers in multilayer structures and bulk materials. In this paper, we explore the use of terahertz (THz) OHE to study the charge carrier properties in group-III nitride heterostructures and bulk material. Examples include graded AlGaN channel high-electron-mobility transistor (HEMT) structures for high-linearity devices, highlighting the different grading profiles and their impact on the two-dimensional electron gas (2DEG) properties. Next, we demonstrate the sensitivity of the THz OHE to distinguish the 2DEG anisotropic mobility parameters in N-polar GaN/AlGaN HEMTs and show that this anisotropy is induced by the step-like surface morphology. Finally, we present the temperature-dependent results on the charge carrier properties of 2DEG and bulk electrons in GaN with a focus on the effective mass parameter and review the effective mass parameters reported in the literature. These studies showcase the capabilities of the THz OHE for advancing the understanding and development of group-III materials and devices. 

We demonstrate detection and measurement of electron paramagnetic spin resonances (EPR) of iron defects in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$utilizing generalized ellipsometry at frequencies between 110 and 170 GHz. The experiments are performed on an Fe-doped single crystal in a free-beam configuration in reflection at ${45}^{\circ }$and magnetic fields between 3 and 7 T. In contrast with low-field, low-frequency EPR measurements, we observe all five transitions of the $s=5/2$high-spin state ${\mathrm{Fe}}^{3+}$simultaneously. We confirm that ferric ${\mathrm{Fe}}^{3+}$is predominantly found at octahedrally coordinated Ga sites. We obtain the full set of fourth-order monoclinic zero-field splitting parameters for both octahedrally and tetrahedrally coordinated sites by employing measurements at multiple sample azimuth rotations. The capability of high-field EPR allows us to demonstrate that simplified second-order orthorhombic spin Hamiltonians are insufficient, and fourth-order terms as well as consideration of the monoclinic symmetry are needed. These findings are supported by computational approaches based on density-functional theory for second-order and on ligand-field theory for fourth-order parameters of the spin Hamiltonian. Terahertz ellipsometry is a way to measure spin resonances in a cavity-free setup. Its possibility of varying the probe frequency arbitrarily without otherwise changing the experimental setup offers unique means of truly disentangling different components of highly anisotropic spin Hamiltonians. Published by the American Physical Society2024 

AlxGa1−xN/GaN high-electron-mobility transistor (HEMT) structures are key components in electronic devices operating at gigahertz or higher frequencies. In order to optimize such HEMT structures, understanding their electronic response at high frequencies and room temperature is required. Here, we present a study of the room temperature free charge carrier properties of the two-dimensional electron gas (2DEG) in HEMT structures with varying Al content in the AlxGa1−xN barrier layers between x=0.07 and x=0.42. We discuss and compare 2DEG sheet density, mobility, effective mass, sheet resistance, and scattering times, which are determined by theoretical calculations, contactless Hall effect, capacitance-voltage, Eddy current, and cavity-enhanced terahertz optical Hall effect (THz-OHE) measurements using a low-field permanent magnet (0.6 T). From our THz-OHE results, we observe that the measured mobility reduction from x=0.13 to x=0.42 is driven by the decrease in 2DEG scattering time, and not the change in effective mass. For x<0.42, the 2DEG effective mass is found to be larger than for electrons in bulk GaN, which in turn, contributes to a decrease in the principally achievable mobility. From our theoretical calculations, we find that values close to 0.3m0 can be explained by the combined effects of conduction band nonparabolicity, polarons, and hybridization of the electron wavefunction through penetration into the barrier layer. 

The anisotropic permittivity parameters of monoclinic single crystal lutetium oxyorthosilicate, Lu2SiO5 (LSO), have been determined in the terahertz spectral range. Using terahertz generalized spectroscopic ellipsometry (THz-GSE), we obtained the THz permittivities along the a, b, and c⋆ crystal directions, which correspond to the εa, εb, and εc⋆ on-diagonal tensor elements. The associated off diagonal tensor element εac⋆ was also determined experimentally, which is required to describe LSO's optical response in the monoclinic a–c crystallographic plane. From the four tensor elements obtained in the model fit, we calculate the direction of the principal dielectric axes in the a–c plane. We find good agreement when comparing THz-GSE permittivities to the static permittivity tensors from previous infrared and density functional theory studies. 

Electron effective mass is a fundamental material parameter defining the free charge carrier transport properties, but it is very challenging to be experimentally determined at high temperatures relevant to device operation. In this work, we obtain the electron effective mass parameters in a Si-doped GaN bulk substrate and epitaxial layers from terahertz (THz) and mid-infrared (MIR) optical Hall effect (OHE) measurements in the temperature range of 38–340 K. The OHE data are analyzed using the well-accepted Drude model to account for the free charge carrier contributions. A strong temperature dependence of the electron effective mass parameter in both bulk and epitaxial GaN with values ranging from (0.18 ± 0.02) m0 to (0.34 ± 0.01) m0 at a low temperature (38 K) and room temperature, respectively, is obtained from the THz OHE analysis. The observed effective mass enhancement with temperature is evaluated and discussed in view of conduction band nonparabolicity, polaron effect, strain, and deviations from the classical Drude behavior. On the other hand, the electron effective mass parameter determined by MIR OHE is found to be temperature independent with a value of (0.200 ± 0.002) m0. A possible explanation for the different findings from THz OHE and MIR OHE is proposed.