The potential, the density of electrons and charged donors, the charge per unit area in the channel and the subband levels are calculated for a high electron mobility transistor (HEMT) under equilibrium conditions. As a new theoretical foundation a modified local density approximation (MLDA) is used which is a convenient and sufficiently exact tool for a quantitative treatment of semiconductor heterostructures. It is shown that a proper consideration of quantum effects and of the influence of charged donors are necessary for obtaining reliable quantitative results. The channel charge is calculated in dependence of important geometrical, material and technological parameters including the temperature and the results are compared with those of other authors. Especially the influence of the thickness of the doped AlxGa1−xAs layer and of an undoped AlxGa1−xAs spacer is discussed carefully.
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