  We have used the scanning charged tip of an Atomic Force Microscope (AFM) to
produce images of the conductance variation of a quantised 1D ballistic
channel. The channel was formed using electron beam defined 700 nm wide split
gate surface electrodes over a high mobility GaAs/AlGaAs heterostructure with a
two dimensional electron gas (2DEG) 98 nm beneath the surface. We operate the
AFM at 1.5 K and 4.2 K in magnetic fields up to 2 T to observe several
phenomena. With a dc voltage on the AFM tip we have produced conduction images
of the tip potential perturbation, as the channel is a sensitive probe of the
electrostatic potential. We have also performed gate sweeps with the tip at a
series of points across the width of the channel. The observed structure in
transconductance corresponds to the theoretical electron density for the first
three sub-bands. When certain gates were biased near pinch off, stable two
level switching was observed in the images. We were able to control the state
of the switch with the gate bias and tip position, and so roughly locate the
position of the switching source. One of the responsible defect systems was
located beneath the 2DEG, and due to screening of the tip potential, the image
reveals the 1D channel. By asymmetrically biasing the two gate electrodes we
have produced images showing a total channel movement of 102 nm across the
width of the channel, but accompanied by 201 nm of movement along the length of
the channel which is due to imperfections in the surface electrodes and
disorder in the doping layer.
