Monte Carlo Modeling of Phonons at Crystal Interfaces

One of the strategies in the effort to directly detect dark matter particles is to measure the phonon and charge signals produced in an incidental collision of a weakly interacting massive particle with a nucleon in a crystalline detector. Proper calibration of the detected phonon energy relies on detailed models of phonon propagation through the crystal to the instrumented surface. Previous Detector Monte Carlo incorporate probabalistic anharmonic decay and mass defect scattering but neglect the mode dependent scattering at crystal boundaries. We calculate mode specific reflection and transmission at detector interfaces with a simple acoustic mismatch model. We find that mode preserving transmission is the most probable outcome at germanium-aluminum detector interfaces, but the probability of reflection is not negligible. The average phonon reflection probability at near normal angles of incidence at a Ge/Al interface is near 20 %, but grows dramatically for oblique incidence. We develop a code using Geant4, which should allow modeling extensions to all phonon mediated dark matter detection schemes. Our models are adaptable to other crystal materials and are generally useful in any phonon interface problem.