  Images of electron flow through a two-dimensional electron gas from a quantum
point contact (QPC) can be obtained at liquid He temperatures using scanning
probe microscopy (SPM). A negatively charged SPM tip depletes the electron gas
immediately below it and decreases the conductance by backscattering electrons.
Images of electron flow are obtained by recording the conductance as the tip is
scanned over the sample. These images show angular patterns that are
characteristic of electron flow through individual modes of the QPC, as well as
well-defined branches at longer distances. The addition of a prism formed by a
triangular gate bends electron paths as the electron density is reduced under
the prism by an applied gate voltage. Under the conditions of the experiment,
electron-electron scattering is the dominant inelastic process. By observing
how the amplitude of backscattered electrons in images of electron flow
decreases with added electron energy, we are able to determine the average
length and time necessary for inelastic scattering. A dc voltage Vo applied
across the QPC accelerates electrons so that their energy is greater than the
Fermi energy before inelastic scattering occurs. The signal is observed to
decrease in amplitude and eventually disappear at distances from the QPC that
decrease progressively as Vo is increased.
