  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.
