  Quantum point contacts (QPC) are fundamental building blocks of
nanoelectronic circuits. For their emission dynamics as well as for interaction
effects such as the 0.7-anomaly the details of the electrostatic potential are
important, but the precise potential shapes are usually unknown. Here, we
measure the one-dimensional subband spacings of various QPCs as a function of
their conductance and compare our findings with models of lateral parabolic
versus hard wall confinement. We find that a gate-defined QPC near pinch-off is
compatible with the parabolic saddle point scenario. However, as the number of
populated subbands is increased Coulomb screening flattens the potential bottom
and a description in terms of a finite hard wall potential becomes more
realistic.
