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

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.