An analytic solution of the current distribution in a two-dimensional electron gas (20 EG) near an abrupt variation in the conductance properties is given. This solution is shown to explain the approximate quantization of the two-terminal resistance of a 20 EG at values of h lie . The dilerence between the two-terminal resistance and the Hall resistance is shown to be determined by an interplay of contact and 20 EG properties, and is argued to be of the order of 10~times the Hall resistance or less, for Au-Ge-Ni and Sn contacts. Measurements in agreement with this prediction are presented.
The resistance of metallic point contacts at a temperature of 4.2 K shows oscillations as a function of magnetic field. These oscillations are due to the Landau quantization of the conduction electrons as is proven by their frequencies. The oscillations can originate both in the Maxwell and in the Sharvin part of the point-contact resistance. The oscillations in the Maxwell resistance are a direct result of the oscillations in the bulk resistivity of the material (the Shubnikhovde Haas effect). For a proper understanding of the oscillations in the Sharvin resistance, it is necessary to take diffraction effects of the electron wave functions into account.
%'e experimentally tested a novel method for measuring the resistivity tensor components of a conducting slab in a magnetic field. In this method the conductance properties of an arbitrarily shaped flat conductor are studied with a number of four-terminal resistance measurements. Under the assumption that single values for the resistivity and for the Hall coefficient hold for the entire sample, we use part of the obtained &fata to derive a description of the conductance properties of the sample. Then the remaining independent data are used to check the validity of this assumption. Experimental details of the method are given, and its application to aluminum, germanium, epitaxial gallium arsenide, and a GaAs/(Al, Ga)As heterostructure is discussed. It is found that with the novel method it is possible to observe effects of the contacts, the sample periphery, and material inhomogeneities.
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