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Maximizing the power conversion efficiency of solar cells plays a crucial role in upscaling solar energy production. Combining two or more solar cells with different bandgaps into a multi-junction tandem solar cells lowers thermalization losses and increases the power conversion efficiency. Whilst the best efficiencies have been achieved by vertically stacking solar cells, the fabrication process is technologically demanding and leads to high production costs. Novel photovoltaic materials such as organic photovoltaics allow solution processing, which enables the cost effective production of lateral multijunctions, where the single subcells are aligned side by side. To fully unlock their optimal performance, lateral tandems require careful light management, redirecting different spectral bands to the corresponding solar cell. So far, solar spectral splitters suffered from a strong angle dependency, which caused a degradation in performance at the slightest deviation from normal incidence. In this contribution, we reduce this limitation and achieve an enhancement in the conversion efficiency across a wide range of incident angles by inverse designing a solar spectral splitter comprised of two free-form microstructured surfaces on the top and bottom of a supporting glass substrate. Moreover, thanks to the versatility of our methodology, we can tailor the angle-dependent functionality of our device. As such, we also design devices that are optimized to provide enhanced performance at certain oblique angles, which correspond to different times of the day, e.g., when the unit price of energy is higher.

Previously, we reported that the doping and pressure dependence of the $T^\ast(B)$ crossover in YbRh$_2$Si$_2$ is incompatible with its interpretation as signature of a Kondo breakdown [M.-H. Schubert et al., Phys. Rev. Research 1, 032004(R) (2019)]. The comment by S. Wirth et al. [arXiv:1910.04108] refers to Hall measurements on undoped YbRh$_2$Si$_2$ and criticizes our study as incomplete and inconclusive. We thoroughly inspect these data and rebut the arguments of the comment., Comment: 4 pages, 4 figures

The heavy-fermion metal YbRh$_2$Si$_2$ realizes a field-induced quantum critical point with multiple vanishing energy scales $T_{\rm N}(B)$ and $T^\ast(B)$. We investigate their change with partial non-isoelectronic substitutions, chemical and hydrostatic pressure. Low-temperature electrical resistivity, specific heat and magnetic susceptibility of Yb(Rh$_{1-x}$T$_x$)$_2$Si$_2$ with T=Fe or Ni for $x\leq 0.1$, magnetic fields $B\leq 0.3$~T (applied perpendicular to the c-axis) and hydrostatic pressure $p\leq 1.5$~GPa are reported. The data allow to disentangle the combined influences of hydrostatic and chemical pressure, as well as non-isoelectronic substitution. In contrast to Ni- and Co-substitution, which enhance magnetic order, Fe-substitution acts oppositely. For $x=0.1$ it also completely suppresses the $T^\ast$ crossover and eliminates ferromagnetic fluctuations. The pressure, magnetic field and temperature dependences of $T^\ast$ are incompatible with its interpretation as Kondo breakdown signature., Comment: 25 pages including supplemental material; accepted for publication in Phys. Rev. Research

A combined generalized spectroscopic ellipsometry measurement and density functional theory calculation analysis is performed to obtain the complete set of infrared active phonon modes in Lu$_{2}$SiO$_{5}$ with monoclinic crystal structure. Two different crystals, each cut perpendicular to a different crystal axis are investigated. Ellipsometry measurements from 40 - 1200 cm$^{-1}$ are used to determine the frequency dependent dielectric function tensor elements. The eigendielectric displacement vector summation approach and eigendielectric displacement loss vector summation approach both augmented with anharmonic lattice broadening parameters proposed recently for low-symmetry crystal structures [A. Mock et al., Phys. Rev. B 95, 165202 (2017)] are applied for our ellipsometry data analysis. All measured and model calculated dielectric function tensor and inverse dielectric function tensor elements match excellently. 23 $\mathrm{A_{u}}$ symmetry and 22 $\mathrm{B_{u}}$ symmetry infrared active transverse and longitudinal optical modes are found. We also determine the directional limiting modes and the order of the phonon modes within the monoclinic plane. Results from density functional theory and ellipsometry measurements are compared and nearly perfect agreement is observed. We further compare our results to those obtained recently for the monoclinic crystal Y$_{2}$SiO$_{5}$, which is isostructural to Lu$_{2}$SiO$_{5}$ [A. Mock et al., Phys. Rev. B 97, 165203 (2018)]. We find that the lattice mode behavior of monoclinic Lu$_{2}$SiO$_{5}$ is qualitatively identical with Y$_{2}$SiO$_{5}$, and differs only quantitatively. We anticipate that members of the isostructural group of monoclinic symmetry oxyorthosilicates such as Dy$_{2}$SiO$_{5}$ or Yb$_{2}$SiO$_{5}$ will likely behave very similar in their phonon mode properties as reported here for Lu$_{2}$SiO$_{5}$., Comment: 18 pages, 10 figures

We report density-dependent effective hole mass measurements in undoped germanium quantum wells. We are able to span a large range of densities ($2.0-11\times10^{11}$ cm$^{-2}$) in top-gated field effect transistors by positioning the strained buried Ge channel at different depths of 12 and 44 nm from the surface. From the thermal damping of the amplitude of Shubnikov-de Haas oscillations, we measure a light mass of $0.061m_e$ at a density of $2.2\times10^{11}$ cm$^{-2}$. We confirm the theoretically predicted dependence of increasing mass with density and by extrapolation we find an effective mass of $\sim0.05m_e$ at zero density, the lightest effective mass for a planar platform that demonstrated spin qubits in quantum dots.

We present a public, open-source relational database (we name kaepora) containing a sample of 4975 spectra of 777 Type Ia supernovae (SNe Ia). Since we draw from many sources, we significantly improve the spectra by inspecting these data for quality, removing galactic emission lines and cosmic rays, generating variance spectra, and correcting for the reddening caused by both MW and host-galaxy dust. With our database, we organize this homogenized dataset by 56 unique categories of SN-specific and spectrum-specific metadata. With kaepora, we produce composite spectra of subpopulations of SNe Ia and examine how spectral features correlate with various SN properties. These composite spectra reproduce known correlations with phase, light-curve shape, and host-galaxy morphology. With our large dataset, we are also able to generate fine-grained composite spectra simultaneously over both phase and light-curve shape. The color evolution of our composite spectra is consistent with other SN Ia template spectra, and the spectral properties of our composite spectra are in rough agreement with these template spectra with some subtle differences. We investigate the spectral differences of SNe Ia that occur in galaxies with varying morphologies. Controlling for light-curve shape, which is highly correlated with host-galaxy morphology, we find that SNe Ia residing in late-type and early-type galaxies have similar spectral properties at multiple epochs. However for SNe Ia in these different environments, their spectra appear to have Ca II near-infrared triplet features that have slightly different strengths. Although this is apparent in the composite spectra and there is some difference in the populations as seen by individual spectra, this difference is not large enough to indicate differences in the underlying populations., Comment: 24 pages, 38 figures, published in MNRAS. Repository: https://github.com/msiebert1/kaepora; Database and Composite Spectra: https://msiebert1.github.io/kaepora/; Documentation: https://kaepora.readthedocs.io/en/latest/index.html

In this paper we investigate the structural and optical properties of few strain-unbalanced multiple Ge/GeSi quantum wells pseudomorphically grown on GeSi reverse-graded substrates. The obtained high epitaxial quality demonstrates that strain symmetrization is not a mandatory requirement for few quantum-well repetitions. Photoluminescence data, supported by a thorough theoretical modeling, allow us to unambiguously disentangle the spectral features of the quantum wells from those originating in the virtual substrate and to evaluate the impact on the optical properties of key parameters, such as quantum confinement, layer compositions, excess carrier density, and lattice strain. This detailed understanding of the radiative recombination processes is of paramount importance for the development of Ge/GeSi-based optical devices.

Buried-channel semiconductor heterostructures are an archetype material platform to fabricate gated semiconductor quantum devices. Sharp confinement potential is obtained by positioning the channel near the surface, however nearby surface states degrade the electrical properties of the starting material. In this paper we demonstrate a two-dimensional hole gas of high mobility ($5\times 10^{5}$ cm$^2$/Vs) in a very shallow strained germanium channel, which is located only 22 nm below the surface. This high mobility leads to mean free paths $\approx6 \mu m$, setting new benchmarks for holes in shallow FET devices. Carriers are confined in an undoped Ge/SiGe heterostructure with reduced background contamination, sharp interfaces, and high uniformity. The top-gate of a dopant-less field effect transistor controls the carrier density in the channel. The high mobility, along with a percolation density of $1.2\times 10^{11}\text{ cm}^{-2}$, light effective mass (0.09 m$_e$), and high g-factor (up to $7$) highlight the potential of undoped Ge/SiGe as a low-disorder material platform for hybrid quantum technologies.

We derive from an eigendielectric displacement vector summation approach the frequency order of the polar phonon modes and the polarization-dependent structure of the reststrahlen bands within the monoclinic plane of materials with monoclinic crystal symmetry. We show that phonon modes occur in associated pairs of transverse and longitudinal optical modes, and that pairs either belong to inner or outer phonon modes. Inner mode pairs are nested within outer mode pairs. Outer mode pairs cause polarization-dependent reststrahlen bands. Inner mode pairs cause polarization-independent reststrahlen bands. The directional limiting frequencies within the Born-Huang approach are bound to within outer mode regions not occupied by inner mode pairs. Hence, an unusual phonon mode order can occur where both lower-frequency as well as upper-frequency limits for the directional modes can be both transverse and/or longitudinal modes. We exemplify our findings using experimental data for the recently unraveled case of monoclinic symmetry $\beta$-Ga$_2$O$_3$ [Phys. Rev. B~\textbf{93}, 125209 (2016)] and demonstrate excellent agreement with results from density functional theory calculations., Comment: 5 pages, 2 figures. Submitted to Physical Review Letters

We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y$_2$SiO$_5$ using generalized spectroscopic ellipsometry from 40-1200 cm$^{-1}$. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017)], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain excellent match between all measured and model calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 A$_{\mathrm{u}}$ and 22 B$_{\mathrm{u}}$ symmetry long wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 A$_{\mathrm{u}}$ symmetry and 22 B$_{\mathrm{u}}$ transverse and longitudinal optical mode parameters and their orientation within the monoclincic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys. Rev. Lett. 117, 215502 (2016)].

We report on the temperature dependence of the dielectric tensor elements of $n$-type conductive $\beta$-Ga$_2$O$_3$ from 22$^\circ$C-500$^\circ$C in the spectral range of 1.5~eV--6.4~eV. We present the temperature dependence of the excitonic and band-to-band transition energies and their eigenpolarization vector orientations. We utilize a Bose-Einstein analysis of the temperature dependence of the observed transition energies and reveal electron coupling with average phonon temperature in excellent agreement with the average over all longitudinal phonon plasmon coupled modes reported previously [M. Schubert~\textit{et al.}, Phys. Rev. B \textbf{93}, 125209 (2016)]. We also report a linear temperature dependence of the wavelength independent Cauchy expansion coefficient for the anisotropic below-band-gap monoclinic indices of refraction.

We determine the frequency dependence of four independent CdWO$_4$ Cartesian dielectric function tensor elements by generalized spectroscopic ellipsometry within mid-infrared and far-infrared spectral regions. Single crystal surfaces cut under different angles from a bulk crystal, (010) and (001), are investigated. From the spectral dependencies of the dielectric function tensor and its inverse we determine all long wavelength active transverse and longitudinal optic phonon modes with $A_u$ and $B_u$ symmetry as well as their eigenvectors within the monoclinic lattice. We thereby demonstrate that such information can be obtained completely without physical model line shape analysis in materials with monoclinic symmetry. We then augment the effect of lattice anharmonicity onto our recently described dielectric function tensor model approach for materials with monoclinic and triclinic crystal symmetries [Phys. Rev. B, 125209 (2016)], and we obtain excellent match between all measured and modeled dielectric function tensor elements. All phonon mode frequency and broadening parameters are determined in our model approach. We also perform density functional theory phonon mode calculations, and we compare our results obtained from theory, from direct dielectric function tensor analysis, and from model lineshape analysis, and we find excellent agreement between all approaches. We also discuss and present static and above reststrahlen spectral range dielectric constants. Our data for CdWO$_4$ are in excellent agreement with a recently proposed generalization of the Lyddane-Sachs-Teller relation for materials with low crystal symmetry [Phys. Rev. Lett. 117, 215502 (2016)]., Comment: arXiv admin note: text overlap with arXiv:1512.08590

An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. In our current instrument we estimate the limit of detection for organic volumetric mass within the object plane of $\approx$ 49 fg within $\approx$ 7$\times$7~$\mu$m$^2$ object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of $\approx$ 500~pg for detection, the instrumentation demonstrated here improves sensitivity to a total mass required for detection by 4 orders of magnitude. We present further applications to detection of nanoparticles, to novel approaches for imaging chromatography, and to new contrast modalities for observations on living cells., Comment: 18 pages, 13 figures, accepted as regular article in Review of Scientific Instruments (October 2016)

Aims. Combining high-resolution and synoptic observations aims to provide a comprehensive description of flux emergence at photospheric level and of the growth process that eventually leads to a mature active region. Methods. Small active region NOAA 12118 was observed on 2014 July 18 with the 1.5-meter GREGOR solar telescope on 2014 July 18. High-resolution time-series of blue continuum and G-band images acquired in the blue imaging channel (BIC) of the GREGOR Fabry-P\'erot Interferometer (GFPI) were complemented by LOS magnetograms and continuum images obtained with the HMI onboard the SDO. Horizontal proper motions and horizontal plasma velocities were computed with local correlation tracking (LCT) and the differential affine velocity estimator, respectively. Morphological image processing was employed to measure the photometric/magnetic area, magnetic flux, and the separation profile of the EFR during its evolution. Results. The computed growth rates for photometric area, magnetic area, and magnetic flux are about twice as high as the respective decay rates. The space-time diagram using HMI magnetograms of five days traces a leaf-like structure, which is determined by the initial separation of the two polarities, a rapid expansion phase, a time when the spread stalls, and a period when the region slowly shrinks again. The separation rate of 0.26 km\s is highest in the initial stage, and it decreases when the separation comes to a halt. Horizontal plasma velocities computed at four evolutionary stages indicate a changing pattern of inflows. In LCT maps we find persistent flow patterns such as outward motions in the outer part of the two major pores, a diverging feature near the trailing pore marking the site of upwelling plasma and flux emergence, and low velocities in the interior of pores. We detected many elongated rapidly expanding granules between the two major polarities., Comment: 12 pages, 9 figures, 3 tables, accepted for publication in A&A

Accurate measurements of magnetic and velocity fields in and around solar active regions are key to unlocking the mysteries of the formation and the decay of sunspots. High spatial resolution image and spectral sequences with a high cadence obtained with the GREGOR solar telescope give us an opportunity to scrutinize 3-D flow fields with local correlation tracking and imaging spectroscopy. We present GREGOR early science data acquired in 2014 July - August with the GREGOR Fabry-P\'erot Interferometer and the Blue Imaging Channel. Time-series of blue continuum (? 450.6 nm) images of the small active region NOAA 12118 were restored with the speckle masking technique to derive horizontal proper motions and to track the evolution of morphological changes. In addition, high-resolution observations are discussed in the context of synoptic data from the Solar Dynamics Observatory., Comment: 7 pages, 4 figures, to be published in ASP Conf. Series - Coimbra solar physics meeting: Grounds-based solar observations in the space instrumentation era , I. Dorotovic, C. Fischer, and M. Temmer (eds.)

We derive a dielectric function tensor model approach to render the optical response of monoclinic and triclinic symmetry materials with multiple uncoupled infrared and farinfrared active modes. We apply our model approach to monoclinic $\beta$-Ga$_2$O$_3$ single crystal samples. Surfaces cut under different angles from a bulk crystal, (010) and ($\bar{2}$01), are investigated by generalized spectroscopic ellipsometry within infrared and farinfrared spectral regions. We determine the frequency dependence of 4 independent $\beta$-Ga$_2$O$_3$ 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 infared and farinfrared active transverse optic phonon modes with $A_u$ and $B_u$ 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 $\beta$-Ga$_2$O$_3$. 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 $\beta$-Ga$_2$O$_3$ 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 farinfrared active modes. We find that the generalized Lyddane-Sachs-Teller relation is fulfilled excellently for $\beta$-Ga$_2$O$_3$., Comment: 18 pages, 12 figures, 105 references; Presented at IWGO 2015 Nov. 4th, Kyoto, Japan

The phonon mode parameters and anisotropic mid-infrared dielectric function tensor components of high- Al-content Al$_x$Ga$_{1-x}$N alloys in dependence of the Al content $x$ are precisely determined from mid-infrared spectroscopic ellipsometry measurements for a set of high-quality Si-doped Al$_x$Ga$_{1-x}$N epitaxial layers on 4H-SiC substrates. Two-mode behavior of the $E_1$(TO) modes and one-mode behavior of the $A_1$(LO) mode are found in agreement with previous Raman scattering spectroscopy reports. The composition dependencies of the IR active phonon frequency parameters are established and a discussion on the silent $B_1$ mode that may be disorder activated is provided. The static dielectric constants in dependence of $x$ are determined by using the best-match model derived phonon mode frequency and high-frequency dielectric constant parameters and applying the Lydanne-Sachs-Teller relation. The effective mass parameter in high-Al-content Al$_x$Ga$_{1-x}$N alloys and its composition dependence are determined from mid-infrared optical Hall effect measurements. Furtheremore, the free electron concentration $N$ and mobility parameters $\mu$ of Al$_x$Ga$_{1-x}$N films with similar Si doping levels are investigated as function of the Al content, $x$ and discussed., Comment: 12 pages, 10 figures

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.

The densification and expansion of wireless networks pose new challenges on energy efficiency. With a drastic increase of infrastructure nodes (e.g. ultra-dense deployment of small cells), the total energy consumption may easily exceed an acceptable level. While most studies focus on the energy radiated by the antennas, the bigger part of the total energy budget is actually consumed by the hardware (e.g., coolers and circuit energy consumption). The ability to shutdown infrastructure nodes (or parts of it) or to adapt the transmission strategy according to the traffic will therefore become an important design aspect of future wireless architectures. Network infrastructure should be regarded as a resource that can be occupied or released on demand. However, the modeling and optimization of such systems are complicated by the potential interference coupling between active nodes. In this article, we give an overview on different aspects of this problem. We show how prior knowledge of traffic patterns can be exploited for optimization. Then, we discuss the framework of interference functions, which has proved a useful tool for various types of coupled systems in the literature. Finally, we introduce different classes of algorithms that have the objective of improving the energy efficiency by adapting the network configuration to the traffic load., Comment: accepted for publication. IEEE Signal Processing Magazine, Nov. 2014

We report on the development of the first integrated mid-infrared, far-infrared and terahertz optical Hall effect instrument, covering an ultra wide spectral range from 3 cm$^{-1}$ to 7000 cm$^{-1}$ (0.1-210 THz or 0.4-870 meV). The instrument comprises four sub-systems, where the magneto-cryostat-transfer sub-system enables the usage of the magneto-cryostat sub-system with the mid-infrared ellipsometer sub-system, and the far-infrared/terahertz ellipsometer sub-system. Both ellipsometer sub-systems can be used as variable angle-of-incidence spectroscopic ellipsometers in reflection or transmission mode, and are equipped with multiple light sources and detectors. The ellipsometer sub-systems are operated in polarizer-sample-rotating-analyzer configuration granting access to the upper left $3\times 3$ block of the normalized $4\times 4$ Mueller matrix. The closed cycle magneto-cryostat sub-system provides sample temperatures between room temperature and 1.4 K and magnetic fields up to 8 T, enabling the detection of transverse and longitudinal magnetic field-induced birefringence. We discuss theoretical background and practical realization of the integrated mid-infrared, far-infrared and terahertz optical Hall effect instrument, as well as acquisition of optical Hall effect data and the corresponding model analysis procedures. Exemplarily, epitaxial graphene grown on 6H-SiC, a tellurium doped bulk GaAs sample and an AlGaN/GaN high electron mobility transistor structure are investigated. The selected experimental datasets display the full spectral, magnetic field and temperature range of the instrument and demonstrate data analysis strategies. Effects from free charge carriers in two dimensional confinement and in a volume material, as well as quantum mechanical effects (inter-Landau-level transitions) are observed and discussed exemplarily.

A slanted cobalt sculptured columnar thin film was fabricated using glancing angle deposition, and coated subsequently with graphene using a low temperature chemical vapor deposition process. The graphene deposition process preserves shape and geometry of the sculptured thin film, which was confirmed by scanning electron microscopy. According to the Raman spectroscopy results, the graphene coating is two to three monolayers thick and has a high defect concentration. The graphene coverage within the sculptured thin film is determined from generalized spectroscopic ellipsometry using a generalized anisotropic Bruggeman effective medium approximation. The graphene coverage as well as structural parameters of the thin film agree excellently with electron microscopy and Raman observations, and suggest that the graphene coating is conformal.

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.

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.