Average Energy Expended Per Electron-Hole Pair in Germanium Detector for Dark Matter Searches

The value of $\varepsilon $, the average energy expended per electron-hole pair, plays a critical role in determining the energy threshold of a bolometer detector with germanium in dark matter searches. We propose an independent method to estimate the value of $\varepsilon $ down to milli-Kelvin range, which is the operating temperature for a SuperCDMS-like detector. A theoretical model and experimental analysis algorithm are developed in this work to estimate the value of $\varepsilon $ based on the relationship between $\varepsilon $, detector energy resolution (Fano factor) and the primary phonon energy. We also investigated the energy threshold for a SuperCDMS-like detector with the value of $\varepsilon $ calculated from our model. In this work, we present our theoretical calculation and show how to use experimental data to evaluate the value of $\varepsilon $. Subsequently, we report the temperature dependence of $\varepsilon $ and its value at 50 milli-Kelvin. This work is supported by NSF in part by the NSF OIA 1434142, DOE grant DE-FG02-10ER46709, and the State of South Dakota.