The electron and current density distributions in the close proximity of
quantum point contacts (QPCs) are investigated. A three dimensional Poisson
equation is solved self-consistently to obtain the electron density and
potential profile in the absence of an external magnetic field for gate and
etching defined devices. We observe the surface charges and their apparent
effect on the confinement potential, when considering the (deeply) etched QPCs.
In the presence of an external magnetic field, we investigate the formation of
the incompressible strips and their influence on the current distribution both
in the linear response and out of linear response regime. A spatial asymmetry
of the current carrying incompressible strips, induced by the large source
drain voltages, is reported for such devices in the non-linear regime.