Lattice dynamical, dielectric, and thermodynamic properties of $\beta \text{-}{\mathrm{Ga}}_2{\mathrm{O}}_3$ are investigated by first principles. The calculated phonon frequencies for the Raman-active and the infrared-active modes are assigned. The phonon dispersion curves along high symmetry lines in the Brillouin zone and the phonon density of states are also calculated. The electronic and static dielectric tensors are calculated. The calculated static dielectric constants are much larger than the electronic constants, showing the rather strong ionic contributions to static dielectric constants. These calculated results are in a good agreement with available experimental values. The thermodynamic functions are calculated by using the phonon density of states.

We present first-principles calculations for fluorine-doped zinc oxide (ZnO:F) by using density-functional theory. Under O-poor condition, fluorine substitution for oxygen $\left({\text{F}}_{\text{O}}\right)$ is energetically favorable in ZnO. ${\text{F}}_{\text{O}}$ can effectively diminish oxygen vacancies. With high fluorine concentration, fluorine interstitial $\left({\text{F}}_{\text{i}}\right)$ may appear. The high transition energies of ${\text{F}}_{\text{O}}$ and ${\text{F}}_{\text{i}}$ suggest that ${\text{F}}_{\text{O}}$ and ${\text{F}}_{\text{i}}$ could act as deep donor and acceptor which cannot provide free carriers in ZnO at room temperature. The increase of carriers and mobility in ZnO:F could not contribute from deep donor ${\text{F}}_{\text{O}}$ , but may be due to the surface passivation effect of fluorine.