Cavity-enhanced optical Hall effect in two-dimensional free charge carrier gases detected at terahertz frequencies

The effect of a tunable, externally coupled Fabry-P\'{e}rot cavity to resonantly enhance the optical Hall effect signatures at terahertz frequencies produced by a traditional Drude-like two-dimensional electron gas is shown and discussed in this communication. As a result, the detection of optical Hall effect signatures at conveniently obtainable magnetic fields, for example by neodymium permanent magnets, is demonstrated. An AlInN/GaN-based high electron mobility transistor structure grown on a sapphire substrate is used for the experiment. The optical Hall effect signatures and their dispersions, which are governed by the frequency and the reflectance minima and maxima of the externally coupled Fabry-P\'{e}rot cavity, are presented and discussed. Tuning the externally coupled Fabry-P\'{e}rot cavity strongly modifies the optical Hall effect signatures, which provides a new degree of freedom for optical Hall effect experiments in addition to frequency, angle of incidence and magnetic field direction and strength

Free-charge carrier parameters of n-type, p-type and compensated InN:Mg determined by Infrared Spectroscopic Ellipsometry

Infrared spectroscopic ellipsometry is applied to investigate the free-charge carrier properties of Mg-doped InN films. Two representative sets of In-polar InN grown by molecular beam epitaxy with Mg concentrations ranging from $1.2\times10^{17}$ cm$^{-3}$ to $8\times10^{20}$ cm$^{-3}$ are compared. P-type conductivity is indicated for the Mg concentration range of $1\times10^{18}$ cm$^{-3}$ to $9\times10^{19}$ cm$^{-3}$ from a systematic investigation of the longitudinal optical phonon plasmon broadening and the mobility parameter in dependence of the Mg concentration. A parameterized model that accounts for the phonon-plasmon coupling is applied to determine the free-charge carrier concentration and mobility parameters in the doped bulk InN layer as well as the GaN template and undoped InN buffer layer for each sample. The free-charge carrier properties in the second sample set are consistent with the results determined in a comprehensive analysis of the first sample set reported earlier [Sch\"oche et al., J. Appl. Phys. 113, 013502 (2013)]. In the second set, two samples with Mg concentration of $2.3\times10^{20}$ cm$^{-3}$ are identified as compensated n-type InN with very low electron concentrations which are suitable for further investigation of intrinsic material properties that are typically governed by high electron concentrations even in undoped InN. The compensated n-type InN samples can be clearly distinguished from the p-type conductive material of similar plasma frequencies by strongly reduced phonon plasmon broadening

Electron effective mass in Al0.72_{0.72}Ga0.28_{0.28}N alloys determined by mid-infrared optical Hall effect

The effective electron mass parameter in Si-doped Al$_{0.72}$Ga$_{0.28}$N is determined to be $m^\ast=(0.336\pm0.020)\,m_0$ from mid-infrared optical Hall effect measurements. No significant anisotropy of the effective electron mass parameter is found supporting theoretical predictions. Assuming a linear change of the effective electron mass with the Al content in AlGaN alloys and $m^\ast=0.232\,m_0$ for GaN, an average effective electron mass of $m^\ast=0.376\,m_0$ can be extrapolated for AlN. The analysis of mid-infrared spectroscopic ellipsometry measurements further confirms the two phonon mode behavior of the E$_1$(TO) and one phonon mode behavior of the A$_1$(LO) phonon mode in high-Al-content AlGaN alloys as seen in previous Raman scattering studies

Anisotropy, Phonon Modes, and Free Charge Carrier Parameters in Monoclinic β-Gallium Oxide Single Crystals

We derive a dielectric function tensor model approach to render the optical response of monoclinic and triclinic symmetry materials with multiple uncoupled infrared and far-infrared active modes. We apply our model approach to monoclinic β-Ga2O3 single-crystal samples. Surfaces cut under different angles from a bulk crystal, (010) and (2̅01), are investigated by generalized spectroscopic ellipsometry within infrared and far-infrared spectral regions. We determine the frequency dependence of 4 independent β-Ga2O3 Cartesian dielectric function tensor elements by matching large sets of experimental data using a point-by-point data inversion approach. From matching our monoclinic model to the obtained 4 dielectric function tensor components, we determine all infrared and far-infrared active transverse optic phonon modes with Au and Bu symmetry, and their eigenvectors within the monoclinic lattice. We find excellent agreement between our model results and results of density functional theory calculations. We derive and discuss the frequencies of longitudinal optical phonons in β-Ga2O3. We derive and report density and anisotropic mobility parameters of the free charge carriers within the tin-doped crystals. We discuss the occurrence of longitudinal phonon plasmon coupled modes in β-Ga2O3 and provide their frequencies and eigenvectors. We also discuss and present monoclinic dielectric constants for static electric fields and frequencies above the reststrahlen range, and we provide a generalization of the Lyddane-Sachs-Teller relation for monoclinic lattices with infrared and far-infrared active modes.We find that the generalized Lyddane-Sachs-Teller relation is fulfilled excellently for β-Ga2O3

Infrared to vacuum-ultraviolet ellipsometry and optical Hall-effect study of free-charge carrier parameters in Mg-doped InN

Infrared to vacuum-ultraviolet spectroscopic ellipsometry and far-infrared optical Hall-effect measurements are applied to conclude on successful p-type doping of InN films. A representative set of In-polar Mg-doped InN films with Mg concentrations ranging from 1.2 x 10(16) cm(-3) to 3.9 x 10(21) cm(-3) is investigated. The data are compared and discussed in dependence of the Mg concentration. Differences between n-type and p-type conducting samples are identified and explained. p-type conductivity in the Mg concentration range between 1.1 x 10(18) cm(-3) and 2.9 x 10(19) cm(-3) is indicated by the appearance of a dip structure in the infrared spectral region related to a loss in reflectivity of p-polarized light as a consequence of reduced LO phonon plasmon coupling, by vanishing free-charge carrier induced birefringence in the optical Hall-effect measurements, and by a sudden change in phonon-plasmon broadening behavior despite continuous change in the Mg concentration. By modeling the near-infrared-to-vacuum-ultraviolet ellipsometry data, information about layer thickness, electronic interband transitions, as well as surface roughness is extracted in dependence of the Mg concentration. A parameterized model that accounts for the phonon-plasmon coupling is applied for the infrared spectral range to determine the free-charge carrier concentration and mobility parameters in the doped bulk InN layer as well as the GaN template and undoped InN buffer layer. The optical Hall-effect best-match model parameters are consistent with those obtained from infrared ellipsometry analysis.Funding Agencies|National Science Foundation|MRSEC DMR-0820521MRI DMR-0922937DMR-0907475EPS-1004094|Swedish Research Council (VR)|2010-3848|Swedish Governmental Agency for Innovation Systems (VINNOVA) under the VINNMER International Qualification program|2011-03486|FCT Portugal|PTDC/FIS/100448/2008|</p

Terahertz optical-Hall effect characterization of two-dimensional electron gas properties in AlGaN/GaN high electron mobility transistor structures

The free-charge carrier mobility, sheet density, and effective mass of a two-dimensional electron gas are exemplarily determined in the spectral range from 640 GHz to 1 THz in a AlGaN/GaN heterostructure using the optical-Hall effect at room temperature. Complementary midinfrared spectroscopic ellipsometry measurements are performed for analysis of heterostructure constituents layer thickness, phonon mode, and free-charge carrier parameters. The electron effective mass is determined to be (0.22 ± 0.04)m0. The high-frequency sheet density and carrier mobility parameters are in good agreement with results from dc electrical Hall effect measurements, indicative for frequency-independent carrier scattering mechanisms of the two-dimensional carrier distribution