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

TL;DR

This study systematically investigates how electrostatic surface depletion affects the effective Hall mobility in high-purity germanium crystals, revealing a thickness-dependent reduction that informs device design for radiation detection and quantum applications.

Contribution

It provides the first detailed experimental characterization of thickness-dependent mobility in HPGe, introducing an empirical model and clarifying the dominance of electrostatic depletion over boundary scattering.

Findings

Mobility remains constant in bulk but decreases with thinning due to surface depletion.

An empirical extended-exponential model accurately describes the mobility-thickness relation.

Electrostatic depletion, not boundary scattering, dominates charge transport reduction.

Abstract

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.