The contact resistance at the interface between a disc electrode and an infinite slab: Mixed-boundary-value solutions

Abstract

We consider the contact-resistance problem that arises when a circular-disc electrode is in imperfect contact with a semiconductor slab, the imperfect contact being modelled by an infinitely thin layer of resistive material at the interface between the disc electrode and the slab. The resulting mixed-boundary-value problem is solved through the use of basis functions that satisfy the boundary conditions outside the source region identically. Calculations of the source current-density and the total slab resistance (including the effect of the contact resistance) are performed for homogeneous slabs of different thicknesses and with different substrate resistivities, for a wide range of values of the contact resistivity of the interface layer. The results obtained show that the presence of a contact resistance tends to make the source current density distribution more uniform. They also confirm the existence of upper and lower bounds for the difference between the total slab resistance and the layer contact-resistance, as predicted by Foxhall and Lewis. Although applied only to slabs of uniform resistivity, the method can be readily extended to slabs of nonuniform resistivity.