Abstract

An analytic solution of the current distribution in a two-dimensional electron gas (2D 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 2D EG at values of h/${\mathrm{ie}}^{2}$. The difference between the two-terminal resistance and the Hall resistance is shown to be determined by an interplay of contact and 2D EG properties, and is argued to be of the order of ${10}^{\mathrm{\ensuremath{-}}6}$ times the Hall resistance or less, for Au-Ge-Ni and Sn contacts. Measurements in agreement with this prediction are presented.

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