Contact resistance calculations: generalizations of Greenwood's formula including interface films

The calculation of the contact resistance between two rough electrodes is a difficult task, since the contact interface comprises many spots corresponding to more or less conducting paths for the electrons. The present paper starts with an analytical formula derived by J.A. Greenwood (1966) to find the electrical resistance of a cluster of perfect circular microcontacts. It is first shown that Greenwood's formula can be used to derive known and new formulas for the constriction resistance of single spots of various shapes. Then we consider the case where the microcontacts are not perfect, and characterize each microcontact by a film resistance. To generalize Greenwood's formula, we use an intermediate expression derived by this author, and substitute for the constriction resistance term of each spot, a term comprising the constriction resistance and the film resistance. We then test the formulas proposed. In all situations the electrical contact area is modeled by means of a set of square spots. At first, we consider experimental results concerning long rectangular spots. Then, we consider numerical results concerning square ring-shaped spots. And lastly, we consider the ease where two large electrodes communicate through two concentric thin flat rings of variable conductivity. The contact resistance is then calculated using Greenwood's generalized formula and by means of the finite-element method. All tests are passed satisfactorily.