More than your average semiconductor: Exciton-Franz-Keldysh effect and the anisotropic Beer-Lambert law in β-Ga₂O₃

The inherent reduced symmetry of monoclinic crystals necessarily leads to non-zero off-diagonal components in many properties, including the complex dielectric tensor. This means that monoclinic semiconductors will necessarily show polarization dependent apparent band gaps, and that for light traveling along certain crystallographic directions, the EM-wave eigenmode polarization states change during propagation. Optically active (polarization functional) materials do not typically include semiconductors, probably since the vast majority of semiconductors studied to date are high symmetry. We will describe these effects in the ultra wide band gap monoclinic semiconductor β-Ga₂O₃, which displays remarkable polarization dependent optoelectronic phenomena, as well as electric field dependent absorption strongly modified by the electron-hole-lattice coupling, i.e. due to self-trapped-excitons. These phenomena enable the spectral measurement of the local electric field via photocurrent spectroscopy due to an excitonic Stark shift and reveal complex non-linear photocarrier generation pathways in the high field regime. The polarization dependent optical absorption leads to anisotropic photocurrents, which originate from the non-zero off-diagonal terms within the complex dielectric tensor. As a result, dichroism and an effective birefringence occur over the absorption depth of β-Ga₂O₃, leading to a steep departure from the Beer-Lambert law.