Evaluating the Effective Segregation Coefficient in High-Purity Germanium (HPGe) Crystals for Ge Detector Development in Rare-Event Searches

TL;DR

This work addresses impurity segregation control during CZ growth of detector-grade HPGe by longitudinally mapping a USD-grown boule with 37 Hall-effect measurements. It applies an impurity-distribution model to extract $K_{ ext{eff}}$ and $C_0$ for B, Al+Ga, and P, and compares the results with the Burton–Prim–Slichter framework. The key findings show $K_{ ext{eff}}^{( ext{B})} o 11.41$, $K_{ ext{eff}}^{( ext{Al+Ga})} o 0.67$, and $K_{ ext{eff}}^{( ext{P})} o 0.17$, with corresponding $C_0$ values, revealing early boron enrichment and late phosphorus dominance with an intermediate aluminum/gallium behavior. This methodology establishes a robust benchmark for optimizing CZ pulling and zone refining to manufacture large-diameter, low-background HPGe detectors for rare-event searches such as dark matter and neutrinoless double-beta decay experiments.

Abstract

The performance and scalability of rare-event physics experiments depend on large-volume, detector-grade high-purity germanium (HPGe) crystals with precise control of impurity segregation during growth. We report a detailed study of impurity distribution in a single Czochralski-grown HPGe crystal produced at University of South Dakota (USD). The crystal was sectioned longitudinally into 37 segments, enabling the first high-resolution and systematic mapping of dopant profiles along the length of a detector-grade HPGe boule. Hall-effect measurements were used to extract impurity concentrations for boron (B), aluminum (Al), gallium (Ga), and phosphorus (P) in each segment. From these data, we determine effective segregation coefficients ($K_{eff}$) and initial melt concentrations ($C_0$) for the dominant dopants and compare them with classical Burton-Prim-Slichter expectations. The results provide quantitative insight into impurity transport and melt-solid partitioning under realistic detector growth conditions. These findings inform process-optimization strategies for HPGe crystal pulling, improve impurity control along the boule, and support the reliable fabrication of large, low-background HPGe detectors for next-generation rare-event searches.

Figures (9)

• Figure 1: Czochralski crystal growth chamber used at USD for high-purity germanium crystals under controlled thermal and atmospheric conditions.
• Figure 2: Schematic of the main stages of Czochralski growth for HPGe: (a) neck formation, (b) shoulder expansion, and (c) constant-diameter body growth.
• Figure 3: HPGe crystal grown at USD using the Czochralski technique. The diameter is $\sim 8$ cm near the shoulder and increases to $\sim 11$ cm toward the tail region.
• Figure 4: Impurity distribution along the length of the HPGe crystal grown at USD. Red vertical lines mark the positions where the crystal was longitudinally sectioned into 37 segments using a diamond wire saw for Hall-effect characterization. The profile shows strong boron dominance in the first $\sim 15$ cm of the crystal.
• Figure 5: Ecopia HMS-3000 Hall-effect measurement system at USD used to determine electrical properties and net impurity concentrations of HPGe samples at 77 K.