Electrons bound to the surface of superfluid helium form a clean two-dimensional (2D) electron gas owing to the smooth helium surface and the electrons' isolation inside the vacuum. Because of this, the electrons on helium system has been utilized by experimentalists to better understand 2D physics for the last fifty years. Much of this work has been done with thick helium (depths of a micron or more) because thicker films keep the electrons farthest away from the imperfect surfaces below the helium. The study of electrons on thin films of helium is a subject that is less explored, especially in the case of a metallic substrate. This is because, with metallic substrates, surface roughness reduces the otherwise high electron mobility and leads to tunneling of electrons through the helium. However, there are many reasons that overcoming these limitations and investigating such a system is desirable, including the possibility of observing quantum melting of the 2D Wigner crystal and initializing electron spins via interactions with Johnson noise currents for some implementations of quantum computers.

In this thesis, we make use of unique substrate materials to further our understanding of these surface-state electrons on thin helium films. The materials used are amorphous metal alloys which arc deposited into ultra-smooth layers to be used as the substrate under the helium films.

In one group of experiments, we demonstrate that by using these substrates, high densities of electrons (up to 5.83x10¹¹ cm-²) can be supported on thin films, only a few nanometers thick. We employ a Kelvin probe measurement technique to determine the electron density and show that these surface electrons are mobile at high densities. While not conclusively shown in this work, this is a promising lead toward an observation of quantum melting of the 2D Wigner crystal.

In a second group of experiments, we characterize the transport of electrons across a thin helium film. We are able to move the surface-state electrons between two measurement regions which are separated by an amorphous metal electrode covered with thin helium film. We use these measure­ ments to put a lower bound on the electron mobility.

Adviser:  Stephen Lyon