  We present an experimental study of KIDs fabricated of atomic layer deposited
TiN films, and characterized at radiation frequencies of $350$~GHz. The
responsivity to radiation is measured and found to increase with increasing
radiation powers, opposite to what is expected from theory and observed for
hybrid niobium titanium nitride / aluminium (NbTiN/Al) and all-aluminium
(all-Al) KIDs. The noise is found to be independent of the level of the
radiation power. The noise equivalent power (NEP) improves with higher
radiation powers, also opposite to what is observed and well understood for
hybrid NbTiN/Al and all-Al KIDs. We suggest that an inhomogeneous state of
these disordered superconductors should be used to explain these observations.
