Quantum Hall effect in long and in mobility adjusted GaAs/AlxGa1-xAs samples

We study the behaviour of the magnetoresistance in the integer quantum Hall regime in dependence on the sample length and mobility. In Hall-bars with macroscopic lengths of up to 96 cm we find that the longitudinal specific magnetoresistance (rho(xx)) decreases with the distances between voltage probes. The Hall resistance in these samples shows also peculiar features - we measure very deep dips between the quantised values of the plateaus. We give a qualitative explanation for these dependencies, supposing a fully equilibrated electron transport and high back-scattering in the sample with very long dimensions. In order to prove these assumptions, we fabricated samples with. sborter dimensions but with an enhanced inter-edge, channel scattering by focused ion implantation at the sample boundaries. The Hall resistance shows similarities to those of very long samples. Implanting Ga+ ions homogeneously into AlxGa1-xAs/GaAs heterostructures offers the possibility to modify the electron mobility while keeping a constant carrier density. In this way, we vary the electron mobility of the same heterostructure within an order of magnitude whereas the electron density remains constant. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.