Fundamental limits on the electron mobility of β-Ga₂O₃

We perform first-principles calculations to investigate the electronic and vibrational spectra and the electron mobility of β-Ga₂O₃. We calculate the electron-phonon scattering rate of the polar optical phonon modes using the Vogl model in conjunction with Fermi's golden rule; this enables us to fully take the anisotropic phonon spectra of the monoclinic lattice of β-Ga₂O₃ into account. We also examine the scattering rate due to ionized impurities or defects using a Yukawa-potential-based model. We consider scattering due to donor impurities, as well as the possibility of compensation by acceptors such as Ga vacancies. We then calculate the room-temperature mobility of β-Ga₂O₃ using the Boltzmann transport equation within the relaxation time approximation, for carrier densities in the range from 10¹⁷ to 10²⁰ cm^-3. We find that the electron-phonon interaction dominates the mobility for carrier densities of up to 10¹⁹ cm^-3. We also find that the intrinsic anisotropy in the mobility is small; experimental findings of large anisotropy must therefore be attributed to other factors. We attribute the experimentally observed reduction of the mobility with increasing carrier density to increasing levels of compensation, which significantly affect the mobility.