  In a model of a gate-patterned quantum device it is important to choose the
correct electrostatic boundary conditions (BCs) in order to match experiment.
In this study, we model gated-patterned devices in doped and undoped GaAs
heterostructures for a variety of BCs. The best match is obtained for an
unconstrained surface between the gates, with a dielectric region above it and
a frozen layer of surface charge, together with a very deep back boundary.
Experimentally, we find a 0.2V offset in pinch-off characteristics of
one-dimensional channels in a doped heterostructure before and after etching
off a ZnO overlayer, as predicted by the model. Also, we observe a clear
quantised current driven by a surface acoustic wave through a lateral induced
n-i-n junction in an undoped heterostructure. In the model, the ability to pump
electrons in this type of device is highly sensitive to the back BC. Using the
improved boundary conditions, it is straightforward to model quantum devices
quite accurately using standard software.
