  We present a theoretical model of split-gate quantum wires that are
fabricated from GaAs-AlGaAs heterostructures. The model is built on the
physical properties of donors and of semiconductor surfaces, and considerations
of equilibrium in such systems. Based on the features of this model, we have
studied different ionization regimes of quantum wires, provided a method to
evaluate the shallow donor density, and calculated the depletion and pinchoff
voltages of quantum wires both before and after illumination. A real split-gate
quantum wire has been taken as an example for the calculations, and the results
calculated for it agree well with experimental measurements. This paper
provides an analytic approach for obtaining much useful information about
quantum wires, as well as a general theoretical tool for other gated
nanostructure systems.
