SPATIAL POTENTIAL DISTRIBUTION IN GAAS/ALXGA1-XAS HETEROSTRUCTURES UNDER QUANTUM HALL CONDITIONS STUDIED WITH THE LINEAR ELECTROOPTIC EFFECT

We apply the linear electro-optic effect (Pockels effect) to investigate the spatial potential distribution in GaAs/AlxGa1-xAs heterostructures under quantum Hall conditions. With this method, which avoids electrical contacts and thus does not disturb the potential distribution, we probe the electrostatic potential of the two-dimensional electron gas locally. Scanning across the width of the sample inside a quantized Hall plateau we observe a steep change of the Hall potential at the edges of the two-dimensional electron gas. This steep change occurs over a distance of about 70-mu-m, which is the lateral resolution of the experimental set-up. More than 80% of the total Hall voltage is concentrated near the edges. The remainder of the Hall potential is distributed in the interior of the sample and varies linearly with the position. The results are interpreted in terms of unscreened charge at the edges. If the plateau region is left or if the quantized Hall conditions are violated by increasing the temperature or current level the Hall potential becomes a linear function of position.