Trapping of two-dimensional electrons in substrate potentials

We report preliminary measurements of high (ripplon-limited) electron mobility on helium films supported by a hydrogen-coated glass substrate. From the smooth dependence of the mobility as a function of helium film thickness we deduce that no polaron transition occurs on films thicker than 500 Å at T>1 K. On poorer quality substrates we observe a rapid drop in the mobility at a substrate-dependent critical film thickness. We interpret these drops as due to localization in variations in the substrate potential.