Thickness-Dependent Charge-Carrier Mobility in Home-Grown High-Purity Germanium Crystals

TL;DR

This work resolves how charge-carrier mobility in bulk-grown HPGe degrades as the crystal is thinned to micrometer scales at room temperature. By performing Van der Pauw Hall measurements across 2.7 mm to 7 μm and fitting the data with an extended-exponential form μ(t) = μ0[1 − exp(-(t/τ)^β)], the authors demonstrate that electrostatic depletion, controlled by Debye screening and surface-space-charge fields, governs the mobility crossover rather than classical boundary scattering. The extracted scales satisfy λ_D < τ ≲ W_0, linking mobility to fundamental electrostatic parameters and yielding a practical device rule t ≳ 3τ to preserve bulk-like transport. This framework unifies thickness-dependent transport from bulk to ultrathin Ge and offers quantitative benchmarks for Ge-on-insulator structures, fully depleted channels, and future Ge-based quantum and electronic devices. The results have direct implications for HPGe detectors and Ge-based nanoscale platforms where mobility engineering and electrostatic control are crucial.

Abstract

Understanding how charge-carrier mobility evolves as high-purity germanium (HPGe) is thinned from bulk to micrometer scale is essential for optimizing advanced radiation detectors, thin-body Ge electronics, and emerging quantum devices. We report, to our knowledge, the first systematic thickness-dependent mobility study on bulk-grown, detector-grade HPGe, performing Hall-effect measurements on $n$- and $p$-type samples thinned from $2.7~\mathrm{mm}$ down to $7~\mathrm{μm}$ at room temperature. The mobility follows an extended-exponential dependence $μ(t) = μ_0 \left[ 1 - \exp\big( - (t/τ)^β \big) \right]$ with characteristic electrostatic lengths $τ= 6$--$50~\mathrm{μm}$. Comparison with boundary-scattering and depletion-based models shows that mobility degradation is dominated not by Fuchs--Sondheimer surface scattering but by electrostatic depletion that reduces the effective conducting channel thickness. Across all samples, the hierarchy $λ_D < τ\lesssim W_0$ identifies long-range screening and near-surface electric fields as the primary mechanisms governing the mobility crossover. This connection provides a simple device-level design rule: maintaining $t \gtrsim 3τ$ preserves most of the bulk mobility, while thinner devices enter a depletion-controlled regime with sharply reduced transport. The extracted parameters thus supply quantitative benchmarks for mobility engineering in ultrathin HPGe and a predictive framework for Ge-on-insulator structures, fully depleted channels, and future Ge-based quantum and electronic technologies.

Figures (8)

• Figure 1: Representative HPGe sample mounted on a PTFE base using Crystalbond wax for mechanical stability and HF resistance during thinning.
• Figure 2: HPGe sample mounted in a Van der Pauw geometry with four indium corner contacts.
• Figure 3: Hall-effect measurement geometry. A current $I_x$ flows along the $x$-direction under a perpendicular magnetic field $B_z$, producing a transverse Hall voltage $V_H$.
• Figure 4: Electrostatic and transport length scales for USD-grown HPGe samples (P,Q,R,S,X, and Y). Symbols denote the Debye length ($\lambda_D$), depletion width ($W_0$), and fitted mobility characteristic length ($\tau$). Blue (top axis) and red (bottom axis) scales correspond to $\lambda_D$ and $W_0$. Linear fits quantify how the characteristic length $\tau$ tracks the electrostatic scales across all samples.
• Figure 5: Hole mobility for USD-grown p-type HPGe Samples (P,Q,R, and S). Symbols: measured data ($\pm 1\%$). Colored curves: individual extended-exponential fits. Black curve: global fit. All samples exhibit a smooth crossover from thin, screening-limited transport to bulk-like behavior.