  Superconducting boron doped silicon is a promising material for integrated
silicon quantum devices. In particular, its low electronic density and moderate
disorder make it a suitable candidate for the fabrication of large inductances
with low losses at microwave frequencies. Here, we study experimentally the
electrodynamics of superconducting silicon thin layers patterned in coplanar
waveguide resonators, targeting three key properties: kinetic inductance,
internal losses, and the variation of these quantities with the read-out power.
We report the first observation in a doped semiconductor of microwave
resonances with internal quality factors of a few thousand. As expected in the
BCS framework, superconducting silicon presents a large sheet kinetic
inductance, in the 50-500 pH range comparable to strongly disordered
superconductors, whose temperature dependence is well described by
Mattis-Bardeen theory. We find, though, an unexpectedly strong non-linearity of
the complex surface impedance which cannot be explained either as a
non-linearity induced by depairing or as quasiparticle heating.
