SPREADING RESISTANCE OF AN INHOMOGENEOUS SLAB WITH A DISK ELECTRODE AS A MIXED BOUNDARY-VALUE PROBLEM

This paper presents a treatment of the mixed boundary value problem that arises in determining the spreading resistance of an inhomogeneous slab backed by a perfectly conducting substrate. It is shown that the inhomogeneity enters into the problem through the weight function of a pair of dual integral equations, and that this function is the same as the integration factor that occurs in previous approximate solutions based on assumed source current distributions. Except for the difference in the weight function, the dual integral equations are similar to those for the homogeneous slab. Calculations are performed for structures with exponential resistivity profiles, and the results used to determine the accuracy of three approximate methods currently available for spreading resistance calculations on semiconductor device structures. © 1979.