  We measure the energy distribution of electrons passing through a
two-dimensional electron gas using a scanning probe microscope. We present
direct spatial images of coherent electron wave flow from a quantum point
contact formed in a GaAs/AlGaAs two-dimensional electron gas using a liquid He
cooled SPM. A negative voltage is placed on the tip, which creates a small
region of depleted electrons that backscatters electron waves. Oscillating the
voltage on the tip and locking into this frequency gives the spatial derivative
of electron flow perpendicular to the direction of current flow. We show images
of electron flow using this method. By measuring the amount of electrons
backscattered as a function of the voltage applied to the tip, the energy
distribution of electrons is measured.
