We present transport measurements of surface-state electrons on liquid helium films in confined geometry. The measurements are taken using split-gate devices similar to a field effect transistor. The number of electrons passing between the source and drain areas of the device can be precisely controlled by changing the length of the voltage pulse applied to the gate electrode. We find evidence that the effective driving potential depends on electron-electron interactions, as well as the electric field applied to the substrate. Our measurements indicate that the mobility of electrons on helium films can be high and that microfabricated transistor devices allow electron manipulation on length scales close to the interelectron separation. Our experiment is an important step toward investigations of surface-state electron properties at much higher densities, for which the quantum melting of the system to a degenerate Fermi gas should be observed.
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