Two dimensional electron gases (2DEGs) at surfaces and interfaces of
semiconductors are described straightforwardly with a 1D self-consistent
Poisson-Schr\"{o}dinger scheme. However, their band energies have not been
modeled correctly in this way. Using angle-resolved photoelectron spectroscopy
we study the band structures of 2DEGs formed at sulfur-passivated surfaces of
InAs(001) as a model system. Electronic properties of these surfaces are tuned
by changing the S coverage, while keeping a high-quality interface, free of
defects and with a constant doping density. In contrast to earlier studies we
show that the Poisson-Schr\"{o}dinger scheme predicts the 2DEG bands energies
correctly but it is indispensable to take into account the existence of the
physical surface. The surface substantially influences the band energies beyond
simple electrostatics, by setting nontrivial boundary conditions for 2DEG
wavefunctions.Comment: 9 pages, 7 figures, 2 table
