A higher dimensional theory of electrical contact resistance

The electrical contact resistance is computed for a local constriction of finite length and finite transverse dimension in a conducting current channel. Conformal mapping is used for the case of a rectangular channel. An analytic scaling law is constructed for the contact resistance over a wide range of aspect ratios between the constriction and the main current channel. The classical theory of Holm and Timsit is generalized to include finite length effects of the “a-spot”, defined as a small circular area of zero thickness through which current can flow. Potential applications and extensions of the theory are indicated.