Monte Carlo calculations of cryogenic photodetector readout of scintillating GaAs for dark matter detection

The recent discovery that GaAs(Si,B) is a bright cryogenic scintillator with no apparent afterglow offers new opportunities for detecting rare, low-energy, electronic excitations from interacting dark matter. This paper presents Monte Carlo calculations of the scintillation photon detection efficiencies of optical cavities using three current cryogenic photodetector technologies. In order of photon detection efficiency these are: (1) Ge/TES: germanium absorbers that convert interacting photons to athermal phonons that are readout by transition edge sensors, (2) KID: kinetic induction detectors that respond to the breaking of cooper pairs by a change in resonance frequency, and (3) SNSPD: superconducting nanowire single photon detectors, where a photon briefly transitions a thin wire from superconducting to normal. The detection efficiencies depend strongly on the n-type GaAs absolute absorption coefficient KA, which is a part of the narrow beam absorption that has never been directly measured. However, the high cryogenic scintillation luminosity of GaAs(Si,B) sets an upper limit on KA of 0.03/cm. Using that value and properties published for Ge/TES, KID, and SNSPD photodetectors, this work calculates that those photodetectors attached to opposing faces of a 1 cm3 cubic GaAs(Si,B) crystal in an optical cavity with gold mirrors would have scintillation photon detection efficiencies of 35%, 25%, and 8%, respectively. Larger values would be expected for lower values of KA.