  Finding suitable p-type dopants, as well as reliable doping and
characterization methods for the emerging wide bandgap semiconductor
$\beta$-$Ga_2O_3$ could strongly influence and contribute to the development of
the next generation of power electronic. In this work, we combine easily
accessible ion implantation, diffusion and nuclear transmutation methods to
properly incorporate the Cd dopant into the $\beta$-$Ga_2O_3$ lattice, being
subsequently characterized at the atomic scale with the Perturbed Angular
Correlation (PAC) technique and Density Functional Theory (DFT) simulations.
The acceptor character of Cd in $\beta$-$Ga_2O_3$ is demonstrated, with Cd
sitting in the octahedral Ga site in the negative charge state, showing no
evidence of polaron deformations nor extra point defects nearby. Furthermore,
thermally activated free electrons were observed for temperatures above ~648 K
with an activation energy of 0.54(1) eV. At lower temperatures the local
electron transport is dominated by a tunneling process between defect levels
and the Cd probe.
