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 or coherent neutrino nucleus interactions (CE$\nu$NS) require excellent energy resolution (eV-scale or below) and low backgrounds to meet their science objectives. Unfortunately, an unknown source of phonon bursts (the low energy excess, or ``LEE'') both dominates all other above threshold background sources and produces shot noise from sub-threshold bursts which greatly exceeds all fundamental noise sources. In this paper, we measure these phonon bursts for 12 days after cool down in two nearly identical multi-phonon sensor channel 1cm$^2$ silicon detectors which differ only in the thickness of their substrate (1 mm vs 4 mm thick). We find that both the correlated shot noise and near threshold shared LEE relax with time since cooldown. Additionally, we show that both 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 $\varepsilon = \frac{<E^2>}{<E>}$ 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 1mm thick detector. Simple calculations suggest that these Si substrate phonon bursts are likely the dominant source of quasi-particle poisoning in superconducting qubits and sensors that are operated in well shielded and vibration free environments.