Average Energy Expended Per e-h Pair and Energy Scale Function for Germanium-Based Dark Matter Experiments

We report a new result of the temperature-dependent average energy expended per electron-hole (e-h) pair, $\varepsilon$, for germanium detectors. Applying energy partition mechanism in ionization for a given energy deposition, the Fano factor and the value of $\varepsilon$ can be determined separately. Subsequently, we illustrate the variation of $\varepsilon$ as a function of temperature. The impact of $\varepsilon$ on the energy threshold and energy scale for germanium detectors at a given temperature is evaluated. We demonstrate an absolute energy scale function of low-energy recoils for germanium detectors in the direct detection of dark matter particles.