Post-diffusion cooling effects on Hall-derived active lithium donor profiles in high-purity germanium

Abstract: Lithium (Li) diffusion is commonly used to form $n<sup>{+}$ contacts in high-purity germanium (HPGe) detectors, but the final electrically active donor profile can be sensitive to the post-diffusion thermal history. Li was introduced into HPGe coupons using a lithium-in-oil suspension and diffused for $30~\mathrm{min}$ at nominal temperatures of $240$--$310~<sup>{\circ}\mathrm{C}$. Short- and long-cooling protocols were documented by measured witness-Ge cooling histories. Sequential material removal combined with Hall-effect measurements at $77~\mathrm{K}$ was used to reconstruct difference-derived apparent Hall donor profiles. Because Hall response in a nonuniform conducting layer is mobility weighted, these profiles are operational electrically active-donor metrics rather than direct local or total-Li concentration profiles. Complementary-error-function fits were used to obtain the extrapolated apparent intercept $N_{s,\mathrm{app}}$ and the apparent profile-width parameter $D_{\mathrm{app}}$. For the coupons studied, short cooling was associated with larger $N_{s,\mathrm{app}}$ and sharper profiles, whereas long cooling was associated with lower $N_{s,\mathrm{app}}$ and broader low-concentration tails. Fit-derived concentration-threshold depths likewise extended farther into the Ge bulk for the long-cooling coupons. These results show that the complete post-diffusion thermal history should be considered when parameterizing Hall-active Li-diffused $n<sup>{+}$ contacts for HPGe detector fabrication.