Electron effective mass in unintentionally doped In0.33_{0.33}Ga0.67_{0.67}N determined by mid-infrared optical Hall effect

Mid-infrared optical Hall effect measurements are used to determine the free charge carrier parameters of an unintentionally doped wurtzite-structure $c$-plane oriented In$_{0.33}$Ga$_{0.67}$N epitaxial layer. Room temperature electron effective mass parameters of $m^{*}_{\bot}=(0.205 \pm 0.013)~m_0$ and $m^{*}_{\parallel}=(0.204 \pm 0.016)~m_0$ for polarization perpendicular and parallel to the $c$-axis, respectively, were determined. The free electron concentration was obtained as $(1.7 \pm 0.2)\times 10^{19}~$cm$^{-3}$. Within our uncertainty limits we detect no anisotropy for the electron effective mass parameter and we estimate the upper limit of the possible effective mass anisotropy is 7$\%$. We discuss the influence of band nonparabolicity on the electron effective mass parameter as a function of In content. The effective mass parameter is consistent with a linear interpolation scheme between the conduction band mass parameters in GaN and InN when the strong nonparabolicity in InN is included. The In$_{0.33}$Ga$_{0.67}$N electron mobility parameters were found to be anisotropic supporting previous experimental findings for wurtzite-structure GaN, InN, and Al$_{x}$Ga$_{1-x}$N epitaxial layers with $c$-plane growth orientation.Comment: 5 pages, 3 figures, 1 tabl

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

Band-to-band transitions, selection rules, effective mass and exciton binding energy parameters in monoclinic \beta-Ga2O3

We employ an eigen polarization model including the description of direction dependent excitonic effects for rendering critical point structures within the dielectric function tensor of monoclinic \beta-Ga2O3 yielding a comprehensive analysis of generalized ellipsometry data obtained from 0.75 eV--9 eV. The eigen polarization model permits complete description of the dielectric response, and we obtain single-electron and excitonic band-to-band transition anisotropic critical point structure model parameters including their polarization eigenvectors within the monoclinic lattice. We compare our experimental analysis with results from density functional theory calculations performed using a recently proposed Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, and we present and discuss the order of the fundamental direct band-to-band transitions and their polarization selection rules, the electron and hole effective mass parameters for the three lowest band-to-band transitions, and their exciton binding energy parameters, in excellent agreement with our experimental results. We find that the effective masses for holes are highly anisotropic and correlate with the selection rules for the fundamental band-to-band transitions, where the observed transitions are polarized closely in the direction of the lowest hole effective mass for the valence band participating in the transition

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 Sn-doped monoclinic single crystal β\beta-gallium oxide determined by mid-infrared optical Hall effect

The isotropic average conduction band minimum electron effective mass in Sn-doped monoclinic single crystal $\beta$-Ga$_2$O$_3$ is experimentally determined by mid-infrared optical Hall effect to be $(0.284\pm0.013)m_{0}$ combining investigations on ($010$) and ($\bar{2}01$) surface cuts. This result falls within the broad range of values predicted by theoretical calculations for undoped $\beta$-Ga$_2$O$_3$. The result is also comparable to recent density functional calculations using the Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, which predict an average effective mass of $0.267m_{0}$ (arXiv:1704.06711 [cond-mat.mtrl-sci]). Within our uncertainty limits we detect no anisotropy for the electron effective mass, which is consistent with most previous theoretical calculations. We discuss upper limits for possible anisotropy of the electron effective mass parameter from our experimental uncertainty limits, and we compare our findings with recent theoretical results

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