  Radioactive contaminants on the surfaces of detector components can be a
problematic source of background events for physics experiments searching for
rare processes. Exposure to radon is a specific concern because it can result
in the relatively long-lived $^{210}$Pb (and progeny) being implanted to
significant subsurface depths such that removal is challenging. In this article
we present results from a broad exploration of cleaning treatments to remove
implanted $^{210}$Pb and $^{210}$Po contamination from silicon, which is an
important material used in several rare-event searches. We demonstrate for the
first time that heat treatments ("baking") can effectively mitigate such
surface contamination, with the results of a 1200 $^{\circ}$C bake consistent
with perfect removal. We also report results using wet-chemistry and
plasma-based methods, which show that etching can be highly effective provided
the etch depth is sufficiently aggressive. Our survey of cleaning methods
suggests consideration of multiple approaches during the different phases of
detector construction to enable greater flexibility for efficient removal of
$^{210}$Pb and $^{210}$Po surface contamination
