Degenerate doping in β-Ga₂O₃ single crystals through Hf-doping

N type conductivity of \b{eta}-Ga2O3 grown from the melt is typically achieved using Sn and Si. In this paper, we experimentally and computationally investigate Hf doping of \b{eta}-Ga2O3 single crystals using UV-Vis-NIR absorption and Hall Effect measurements and hybrid functional calculations. Unintentionally-doped and Hf-doped samples with a nominal concentration of 0.5at% were grown from the melt using vertical gradient freeze (VGF) and Czochralski method in mixed Ar+O2 atmosphere. We demonstrate Hf dopants, predicted to incorporate on the octahedral GaII site as a shallow donor, achieve degenerate doping in \b{eta}-Ga2O3 with a measured electron concentration 2 x 10^19 cm^-3 , mobility 80-65 cm^2 /Vs, and resistivity down to 5 mOhm-cm in our samples. The concentration of Hf was measured to be 1.3 x 10^19 atoms/cm^3 using glow discharge mass spectroscopy (GDMS) on doped samples, confirming Hf to be the cause of n-type conductivity (electron concentration ~2 x 10^19 cm-3).