Measuring the Static and Dynamic Disorder in β-Ga₂O₃ Using Optical Transmission

Gallium oxide (Ga₂O₃) has an extremely wide bandgap, predicted high breakdown field, and can be produced from melt crystal growth techniques making it attractive for next-generation high-power electronics. It is well-known that the optical transitions in monoclinic β-Ga₂O₃ are anisotropic; the threshold energies for carrier generation using linearly polarized light depend on crystallographic direction. Using transmission optical spectroscopy, which probes subtly differently than e.g., ellipsometry, we have investigated the optical transitions of Fe doped [100] β-Ga₂O₃ as function of elevated temperature, and have documented the dramatic bandgap narrowing with temperature, which was recently explained using density functional theory [1]. In addition, we have done the optical transmission of Sn doped [010], [001], [-201] at room temperature and liquid nitrogen temperature.<br/>We elucidate the differences between ellipsometric and transmission measurements and demonstrate that transmission measurements in the literature have determined erroneous values for the bandgap because of very strong Urbach tails. We report on the anisotropy and doping dependencies of the disorder-induced tails in the optical absorption coefficient for β-Ga₂O₃and separate the tails into static and dynamic disorder induced by phonons. Given the low symmetry of β-Ga₂O₃ and its strong electron-phonon coupling, we observed that the Urbach energy increases at elevated temperature due to the contribution of static and dynamic disorder and exhibit significant anisotropy. However, at liquid nitrogen temperature (77K), the Urbach energy for Fe-doped crystals decreases as the dynamic disorder is suppressed but increases at elevated temperatures. We also show that in the case of room temperature and liquid nitrogen temperature for Sn doped crystal. We analyze the dynamic and static components within the model of Cody et al., [2] and find that the static disorder is actually dominant. We discuss the possible microscopic origins in terms of point and extended defects; interestingly at low absorption coefficients even imperfect surface polishing may contribute. We combine the temperature dependences of the Urbach tails from our measurements with those of the optical transitions from ellipsometry [3], [4] to extract the mean square displacement-deformation potential product for Ga2O3 along different crystal directions. These parameters play roles in optical transitions and carrier scattering and are thus critical to measure. We elucidate open questions and opportunities especially for further theory and calculation to predict the implications on multiple properties of wider interest than the Urbach tails per-se.