  The electric-field noise above a layered structure composed of a planar metal
electrode covered by a thin dielectric is evaluated and it is found that the
dielectric film considerably increases the noise level, in proportion to its
thickness. Importantly, even a thin (mono) layer of a low-loss dielectric can
enhance the noise level by several orders of magnitude compared to the noise
above a bare metal. Close to this layered surface, the power spectral density
of the electric field varies with the inverse fourth power of the distance to
the surface, rather than with the inverse square, as it would above a bare
metal surface. Furthermore, compared to a clean metal, where the noise spectrum
does not vary with frequency (in the radio-wave and microwave bands), the
dielectric layer can generate electric-field noise which scales in inverse
proportion to the frequency. For various realistic scenarios, the noise levels
predicted from this model are comparable to those observed in trapped-ion
experiments. Thus, these findings are of particular importance for the
understanding and mitigation of unwanted heating and decoherence in
miniaturized ion traps.
