  We present transport measurements of electrons on the surface of liquid
helium in a microchannel device in which a constriction may be formed by a
split-gate electrode. The surface electron current passing through the
microchannel first decreases and is then completely suppressed as the
split-gate voltage is swept negative. The current decreases in a steplike
manner, due to changes in the number of electrons able to pass simultaneously
through the constriction. We investigate the dependence of the electron
transport on the AC driving voltage and the DC potentials applied to the sample
electrodes, in order to understand the electrostatic potential profile of the
constriction region. Our results are in good agreement with a finite element
modeling analysis of the device. We demonstrate that the threshold of current
flow depends not only on the applied potentials but also on the surface
electron density. The detailed understanding of the characteristics of such a
device is an important step in the development of mesoscopic experiments with
surface electrons on liquid helium.
