Naturally occurring $^{32}$Si and low-background silicon dark matter detectors

The naturally occurring radioisotope $^{32}$Si represents a potentially limiting background in future dark matter direct-detection experiments. We investigate sources of $^{32}$Si and the vectors by which it comes to reside in silicon crystals used for fabrication of radiation detectors. We infer that the $^{32}$Si concentration in commercial single-crystal silicon is likely variable, dependent upon the specific geologic and hydrologic history of the source (or sources) of silicon "ore" and the details of the silicon-refinement process. The silicon production industry is large, highly segmented by refining step, and multifaceted in terms of final product type, from which we conclude that production of $^{32}$Si-mitigated crystals requires both targeted silicon material selection and a dedicated refinement-through-crystal-production process. We review options for source material selection, including quartz from an underground source and silicon isotopically reduced in $^{32}$Si. To quantitatively evaluate the $^{32}$Si content in silicon metal and precursor materials, we propose analytic methods employing chemical processing and radiometric measurements. Ultimately, it appears feasible to produce silicon detectors with low levels of $^{32}$Si, though significant assay method development is required to validate this claim and thereby enable a quality assurance program during an actual controlled silicon-detector production cycle.