Depletion-limited Effective Hall mobility in Micrometer-Scale High-Purity Germanium Crystals

Electrostatic effects can strongly constrain charge transport in thinned high-purity germanium (HPGe), with direct implications for radiation detectors and Ge-based electronic and quantum devices. We report a systematic experimental characterization of the thickness-dependent effective Hall mobility in bulk-grown, detector-grade HPGe at room temperature using Hall-effect measurements on n- and p-type samples sequentially thinned from 2.7~mm to 7~\textmu m. The intrinsic bulk carrier mobility remains thickness independent in this regime; the observed reduction in Hall-extracted mobility arises from electrostatic surface depletion that reduces the electrically active conducting thickness. The thickness-dependent data are accurately parameterized by an empirical extended-exponential relation, $\mu(t)=\mu_{0}[1-\exp(-(t/\tau)^{\beta})]$, where $\tau$ is a characteristic electrostatic length scale. Comparison with boundary-scattering and depletion-based models shows that Fuchs--Sondheimer scattering is negligible, while electrostatic depletion dominates the transport behavior. The hierarchy $\lambda_{D}<\tau\lesssim W_{0}$ directly links the apparent mobility reduction to long-range screening and near-surface electric fields. These results yield a simple design guideline: maintaining thicknesses $t\gtrsim 3\tau$ preserves near-bulk transport, whereas thinner structures operate in a depletion-controlled regime with strongly reduced effective conductivity.