Phonon emission in germanium and silicon by electrons and holes in applied electric field at low temperature

The cryogenic dark matter search employs Ge and Si detectors to search for weakly interacting massive particle dark matter via its elastic-scattering interactions with nuclei while discriminating against interactions of background particles. These detectors distinguish nuclear recoils from electron recoils by simultaneously measuring phonon and ionization production in semiconducting substrates at sub-kelvin temperatures. They also reconstruct event position by quadrant-segmented measurement of the phonon signal. The ionization drift field does work on the electrons and holes. The charge carriers radiate this energy as acoustic phonons. At the typical applied field of 300 V/m in Ge (400 V/m in Si), we self-consistently model the behavior of the electrons and holes using independent drifted Maxwellian distributions, each characterized by an average drift velocity and an effective temperature, and including acoustic phonon emission. We calculate the phonon power angular and frequency distributions. We find that the bias polarity affects these distributions and, therefore, the phonon collection efficiency in Ge.