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Monte-Carlo Simulations of Superconducting Tunnel Junction Quantum Sensors for the BeEST Experiment

Superconducting Tunnel Junctions (STJs) are used as high-resolution quantum sensors to search for evidence of sterile neutrinos in the electron capture decay of $^7$Be. We are developing spatially-resolved Monte-Carlo simulations of the energy relaxation in superconductors to understand electron escape after the $^7$Be decay and distinguish details in the STJ response function from a possible sterile neutrino signal. Simulations of the charge generation and the Fano factor for different materials agree with the literature values. Initial simulations of the escape tail are consistent with observations, and contain fine structure in the line shape. The line shape will be refined as better experimental data become available.