Impact of Charge Trapping on the Energy Resolution of Ge Detectors for Rare-Event Physics Searches

Charge trapping degrades the energy resolution of germanium (Ge) detectors, which require to have increased experimental sensitivity in searching for dark matter and neutrinoless double-beta decay. We investigate the charge trapping processes utilizing nine planar detectors fabricated from USD-grown crystals with well-known net impurity levels. The charge collection efficiency as a function of charge trapping length is derived from the Shockley-Ramo theorem. Furthermore, we develop a model that correlates the energy resolution with the charge collection efficiency. This model is then applied to the experimental data. As a result, charge collection efficiency and charge trapping length are determined accordingly. Utilizing the Lax model (further developed by CDMS collaborators), the absolute impurity levels are determined for nine detectors. The knowledge of these parameters when combined with other traits such as the Fano factor serve as a reliable indicator of the intrinsic nature of charge trapping within the crystals. We demonstrate that electron trapping is more severe than hole trapping in a p-type detector and the charge collection efficiency depends on the absolute impurity level of the Ge crystal when an adequate bias voltage is applied to the detector. Negligible charge trapping is found when the absolute impurity level is less than 1.0$\times$10$^{11}/$cm$^{3}$ for collecting electrons and 2.0$\times$10$^{11}/$cm$^{3}$ for collecting holes.