Spontaneous generation of athermal phonon bursts within bulk silicon causing excess noise, low energy background events and quasiparticle poisoning in superconducting sensors

Solid state phonon detectors used in the search for dark matter and coherent neutrino nucleus interactions (CE$ν$NS) require excellent energy resolution (eV-scale or below) and low backgrounds. An unknown source of phonon bursts, the low energy excess (LEE), dominates other above-threshold backgrounds and generates excess shot noise from sub-threshold bursts. In this paper, we measure these phonon bursts for 12 days after cooldown in two nearly identical 1 cm$^2$ silicon detectors that differ only in the thickness of their substrate (1 mm vs. 4 mm thick). We find that both the channel-correlated shot noise and near-threshold shared LEE relax with time since cooldown. Additionally, both the correlated shot noise and LEE rates scale linearly with substrate thickness. When combined with previous measurements of other silicon phonon detectors with different substrate geometries and mechanical support strategies, these measurements strongly suggest that the dominant source of both above and below threshold LEE is the bulk substrate. By monitoring the relation between bias power and excess phonon shot noise, we estimate that the energy scale for sub-threshold noise events is $0.68 \pm 0.38$ meV. In our final dataset, we report a world-leading energy resolution of 258.5$\pm$0.4 meV in the 1 mm thick detector. Simple calculations suggest that these silicon substrate phonon bursts are likely a significant source of quasiparticle poisoning in superconducting qubits operated in well shielded and vibration free environments.