Calculation of the Current Density in the Contacts of a Thin Film Resistor

The two-dimensional boundary value problem appropriate to current flow in a film resistor is examined. A simple closed-form solution for current density into the contact is found to exist for the important case of a thin film resistor with extended lands. The spatial dependence of the current density into the contact is found to be similar to that obtained by Kennedy and Murley for the diffused resistor, with film thickness entering the functional dependence in a role analogous to the diffusion length of the dopant ion in the diffused resistor.