Spreading resistance calculations for graded structures based on the uniform flux source boundary condition

Abstract

In the approximate calculations of spreading resistance correction factors, two different types of boundary conditions over the source region have hitherto been assumed, viz., a uniform flux distribution, and the specific flux distribution that obtains in the classical solution for the infinitely thick slab. This paper presents results of a theory which has been derived for multilayer structures by using the uniform source flux distribution. The results given include those obtained for a series of exponentially-graded structures of varying steepness in the resistivity profile, whose thickness h 1 ranges from 0.1 to 10 times the circular source contact radius, a. The results show that, as a rule, for an insulating substrate and ( h′ 1/ a) < 0.5, the uniform flux assumption leads to correction factors which differ at most by about 3% from those derived from the infinitely-thick slab flux assumption, while for a conducting substrate and ( h′ 1/ a) = 0.1 to 10, there is a difference of about 8%. Whatever the nature of the resistivity profile studied, it has been found that the difference is never greater than about 8%.