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The anisotropic optical absorption edge of $\beta$-Ga$_2$O$_3$ follows a modified Beer-Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in $\beta$-Ga$_2$O$_3$, which arises from the anisotropy and spectral splitting of the physical absorbers i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of $\beta$-Ga$_2$O$_3$. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer-Lambert law arises from the interplay of both the dichroic and birefringent properties of $\beta$-Ga$_2$O$_3$., Comment: 11 pages, 5 figures

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

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