Probing the depletion region of a two-dimensional electron system in high magnetic fields

To investigate a two-dimensional electron system (2DES) in high magnetic fi elds and at temperatures below 0.1 K, a metal single-electron transistor (S ET) was fabricated as a local electrometer on top of a GaAs/AlGaAs heterost ructure containing the 2DES. Probing the bulk of the 2DES, the chemical pot ential variations of the 2DES versus magnetic field were directly measured and relaxation phenomena on a long time scale were observed within quantum Hall plateau regimes of low Landau-level filling factors. To probe the depl etion region of the 2DES, a gate electrode was used to redefine the 2DES ed ge close to the SET by electrostatical depletion. For a 5 mu m distance of the gate electrode's edge to the SET island, the electron concentration und er the SET island is only homogeneously reduced by few percent due to the n egative voltage applied to the gate electrode. But for a 0.9 mu m distance, the SET detects a steep electron concentration gradient, indicating that w ith increasing the depletion voltage, the 2DES edge is indeed shifted towar ds the SET. By this approach we mapped out the screening properties and the electrostatic potential variations within the depletion region of the 2DES for magnetic fields corresponding to Landau-level filling factors between v = 1 and v = 4. Compressible and incompressible strips are resolved. (C) 1 998 Elsevier Science B.V. All rights reserved.