arXiv:2603.02391v1 Announce Type: new
Abstract: Internal charge amplification (ICA) in cryogenic high-purity germanium (HPGe) can lower detection thresholds by providing gain inside the detector crystal, but reliable operation requires a predictive estimate of the avalanche-onset emph{critical electric field} (E_{mathrm{crit}}). We present a compact framework for (E_{mathrm{crit}}) at 77~K and 4~K (typical HPGe operating temperatures) that bridges (i) a mobility-based single-free-flight (SFF) upper bound with (ii) a physics-informed impact-ionization model incorporating energy-dependent scattering, nonparabolic (Kane) dispersion, intervalley transfer, and the high-energy “lucky-drift” tail. This unified treatment yields closed-form, design-useful relations, including (E_{mathrm{crit}}^{(mathrm{PI})}=B(T)/ln[A(T)d]), and a practical calibration workflow that maps measured low-field mobility (mu(T)) and gain curves (M(V)) (Chynoweth analysis) to device-level bias targets with propagated uncertainty bands. Example electron and hole estimates indicate that realistic transport typically lowers (E_{mathrm{crit}}) relative to SFF and increases the predicted change in (E_{mathrm{crit}}) between 77~K and 4~K. The resulting portable formulas connect materials/transport inputs to geometry, excess noise, and field shaping, providing design-ready guidance for stable, unipolar-favored ICA with controlled quenching in Ge and other cryogenic semiconductors.