Characterization of the background spectrum in DAMIC at SNOLAB.

We construct the first comprehensive radioactive background model for a dark matter search with charge-coupled devices (CCDs). We leverage the well-characterized depth and energy resolution of the DAMIC at SNOLAB detector and a detailed {\tt GEANT4}-based particle-transport simulation to model both bulk and surface backgrounds from natural radioactivity down to 50~eV$_{\text{ee}}$. We fit to the energy and depth distributions of the observed ionization events to differentiate and constrain possible background sources, for example, bulk $^{3}$H from silicon cosmogenic activation and surface $^{210}$Pb from radon plate-out. We observe the bulk background rate of the DAMIC at SNOLAB CCDs to be as low as $3.1 \pm 0.6$ counts kg$^{-1}$ day$^{-1}$ keV$_{\text{ee}}^{-1}$, making it the most sensitive silicon dark matter detector. Finally, we discuss the properties of a statistically significant excess of events over the background model with energies below 200~eV$_{\text{ee}}$.