A contact limited precision of the quantized Hall resistance

Abstract

A four-terminal Hall resistance is analyzed using the Biittiker formalism of contacts. The possible maximum deviation of a quantized Hall resistance from ideal values ~n a multi terminal device is shown to be limited by the resistances of contacts. A general expressiOn for the possible maximum deviation is derived for a multiterminaI configuration with an arbitrary number of terminals in the condition of an arbitrary (integer) number of filled Landau levels. The influence of an inhomogeneous two-dimensional electron gas on the Hall resistan.ce is also discussed.

The quantum Hall effect as an electrical resistance standard

“…A model based on the Büttiker formalism for contacts [169] allows an estimate to be made on the upper limit for the deviation of the four-terminal resistance as a function of the contact resistance. The magnitude of the effects is similar to the experimental findings of [168].…”

Sources of uncertainty in a DVM-based measurement system for a quantized Hall resistance standard

“…One would think that the resistance of the contacts used to measure the Hall potential are unimportant, for no current flows through them. These contact resistances, however, must also be in the range of a few milliohms, for reasons which arc beyond the scope of this paper [ 7 , 12 ].…”