  We report on the characterization of microwave loss of thin aluminum oxide
films at low temperatures using superconducting lumped resonators. The oxide
films are fabricated using plasma oxidation of aluminum and have a thickness of
5 nm. We measure the dielectric loss versus microwave power for resonators with
frequencies in the GHz range at temperatures from 54 to 303 mK. The power and
temperature dependence of the loss is consistent with the tunneling two-level
system theory. These results are relevant to understanding decoherence in
superconducting quantum devices. The obtained oxide films are thin and robust,
making them suitable for capacitors in compact microwave resonators.
