Scanning gate microscopy (SGM), developed in the late 1990's, has become
a powerful tool to investigate the local electronic properties in
semiconductor nano devices. SGM is based on the AFM technique but the
metallic tip is used as a movable gate capacitively coupled to the
device, and the electron transport property is studied on influence of
this gate, providing spatial information with high resolution. This
thesis presents the SGM measurement results on various nano devices, all
of which are fabricated from InGaAs/InAlAs heterostructures containing a
high mobility 2DEG located a few tens of nanometers below the surface.
In a work on Braess paradox, with the help of numerical simulations, we
discover a Braess paradox effect by modulating a channel width in a
'double-ring' shaped mesoscopic device in analogy with the one that
occurs in a classical network. By a detailed study of the conductance
changes, we discover several charge traps from the SGM map, and propose
a model to interpret the conductance change with the presence of charge
traps. We develop a method to directly image the charge traps by
transconductance measurements with a voltage modulation on the tip.