We have synthesized highly oxygen deficient HfO$_{2-x}$ thin films by controlled oxygen engineering using reactive molecular beam epitaxy. Above a threshold value of oxygen vacancies, p-type conductivity sets in with up to 6 times 10^{21} charge carriers per cm3. At the same time, the band-gap is reduced continuously by more than 1 eV. We suggest an oxygen vacancy induced p-type defect band as origin of the observed behavior.
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