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[Display omitted] • 2DEG at InAs surfaces is described with the Poisson-Schroedinger model. • Surface is important and it have to be accounted for the model. • IBA treatment may lead to the loss of the 2D character of the surface electron gas. Using angle-resolved photoelectron spectroscopy we study band structures of two dimensional electron gases (2DEGs) formed at surfaces of InAs(001) due to the band bending effect. We find that, for surfaces prepared by nondestructive methods very clear, model 2DEG bands are obtained. In contrast, for ion bombarded surfaces features looking as if 2DEG band contours were uniformly filled with signal are seen. We show that these observations may be explained within the one-electron Poisson-Schrödinger scheme, however, it is necessary to relax the standard boundary conditions with adding a transition zone in which the crystal potential may interpolate between its vacuum and bulk values in nontrivial way. In reality such a zones do exist and correspond to non zero thick surface/interface layers. For ion bombarded surfaces it is also necessary to take into account diffusion and complex reactions of point defects induced with an ion beam. These observations are discussed in the context of electronics devices that often contain similar 2DEGs. [ABSTRACT FROM AUTHOR]