DENSITY OF STATES OF 2D ELECTRON-GAS AND WIDTH OF THE PLATEAU OF IQHE

Density of states of 2DEG in the quantum Hall regime for heterostructures with a thick spacer is studied. It is shown that the spatial distribution of charged impurities should be correlated if a doped region is not entirely depleted. A new mechanism of electron screening is proposed for half-filled Landau levels (LL). At certain values of the filling factor (almost empty or almost occupied LL), the screening becomes non-linear and the width of LL increases very sharply. A localization is supposed to appear at these values. The width of the plateau of IQHE is obtained as a function of the spacer thickness.