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Due to its low symmetry, $\beta$-Ga$_{2}$O$_{3}$ exhibits a strongly anisotropic optical response. As a result, the absorption spectra change with the polarization state of the incoming photons. To understand this phenomenon, here we calculate the complete electromagnetic wave equation solutions as a function of linear polarization angle and photon energy for $\beta$-Ga$_{2}$O$_{3}$ using its previously measured complex dielectric function tensor. The significant off-diagonal terms in this tensor can result in a non-exponential decay in the photon flux, indicating that the Beer-Lambert law is not generally valid in this anisotropic material. However, for above-band-gap spectral regions which depend on crystallographic orientations (> 5.8 eV (001 plane),>5.2 eV (010 plane)) an effective absorption coefficient well approximates the photon flux decay with depth. On the other hand, near the optical absorption edge (4.9 - 5.8 eV (001 plane),4.65 - 5.2 eV (010 plane)) the photon flux decay exhibits a sum of two exponential decays, such that two effective absorption coefficients are necessary to model the loss behavior versus the absorption depth. This behavior manifests from the presence of dichroism in $\beta$-Ga$_{2}$O$_{3}$. A single effective absorption coefficient can only be recovered for this energy range by augmenting the isotropic Beer-Lambert law with a critical penetration depth and polarization dependence. Using these results, we calculate the polarization-dependent photoresponsivity spectra for light polarized along different crystallographic directions., Comment: 28 pages, 10 figures

Polarization dependent photocurrent spectra are measured on a (001) $\beta$-Ga$_{2}$O$_{3}$ Schottky photodetector, where the linear polarization of light is rotated within the ab plane. Three spectral peaks at 4.92 eV, 5.15 eV, and 5.44 eV are observed that vary in intensity with the optical polarization direction. The peak transition energies are consistent with excitons previously reported in $\beta$-Ga$_{2}$O$_{3}$ due to interband transitions modified by the valence band p-orbital anisotropy and the electron-hole Coulombic attraction. The measured polarization-dependence of the photocurrent matches our predictions based on electromagnetic simulations of anisotropic absorption using the complex dielectric function tensor extracted from previous ellipsometry studies. These results illustrate the dominance of excitonic absorption and photocurrent in $\beta$-Ga$_{2}$O$_{3}$ both below and above the band gap, demonstrate a combined theoretical/experimental understanding of anisotropic photocarrier generation, and validate previous atomistic band structure calculations in this low-symmetry ultra-wide band gap semiconductor., Comment: 15 pages, 1 table, and 4 figure

$\beta-Ga_{2}O_{3}$ is an unusual semiconductor where large electric fields (~1-6 MV/cm) can be applied while still maintaining a dominant excitonic absorption peak below its ultra-wide bandgap. This provides a rare opportunity in the solid-state to examine exciton and carrier self-trapping dynamics in the strong-field limit at steady-state. Under sub-bandgap photon excitation, we observe a field-induced red-shift of the spectral photocurrent peak associated with exciton absorption and threshold-like increase in peak amplitude at high-field associated with self-trapped hole ionization. The field-dependent spectral response is quantitatively fit with an eXciton-modified Franz-Keldysh (XFK) effect model, which includes the electric-field dependent exciton binding energy due to the quadratic Stark effect. A saturation of the spectral red-shift with reverse bias is observed exactly at the onset of dielectric breakdown providing a spectral means to detect and quantify the local electric field and dielectric breakdown behavior. Additionally, the field-dependent responsivity provides insight to the photocurrent production pathway revealing the photocurrent contributions of self-trapped excitons (STXs) and self-trapped holes (STHs). Photocurrent and p-type transport in $\beta-Ga_{2}O_{3}$ are quantitatively explained by field-dependent tunnel ionization of excitons and self-trapped holes. We employ a quantum mechanical model of the field-dependent tunnel ionization of STX and STH to model the non-linear field-dependence of the photocurrent amplitude. Fitting to the data, we estimate an effective mass of valence band holes $(18.8 m_{0})$ and an ultrafast self-trapping time of holes (0.045 fs). This indicates that minority-hole transport in $\beta-Ga_{2}O_{3}$ can only arise through tunnel ionization of STH under strong fields., Comment: 47 pages, 12 figures

The eXciton Franz-Keldysh (XFK) effect is observed in GaN p-n junction diodes via the spectral variation of photocurrent responsivity data that redshift and broaden with increasing reverse bias. Photocurrent spectra are quantitatively fit over a broad photon energy range to an XFK model using only a single fit parameter that determines the lineshape, the local bias ($V_{l}$), uniquely determining the local electric field maximum and depletion widths. As expected, the spectrally determined values of $V_{l}$ vary linearly with the applied bias ($V$) and reveal a large reduction in the local electric field due to electrostatic non-uniformity. The built-in bias ($V_{bi}$) is estimated by extrapolating $V_{l}$ at $V=0$, which compared with independent C-V measurements indicates an overall $\pm$0.31 V accuracy of $V_{l}$. This demonstrates sub-bandgap photocurrent spectroscopy as a local probe of electric field in wide bandgap diodes that can be used to map out regions of device breakdown (hot spots) for improving electrostatic design of high voltage devices., Comment: 27 pages, 13 figures