Theory for the determination of backside contact resistance of semiconductor wafers from surface potential measurements

Abstract

We present a method for the calculation of the potential on the surface of a homogeneous semiconductor slab with a disc source electrode on part of the front surface and a resistive contact over the backside of the entire slab. The imposed boundary condition of a constant potential over the source region gives rise to a pair of dual integral equations, which is transformed into a Fredholm integral equation of the second kind and subsequently solved using a simple numerical integration. The potential distributions on the surface of the slab are calculated for contact-to-semiconductor resistivity ratio in the range of 0 to 1 and for slab thickness ranging from 0.1 to 5× the radius of the disc contact. The results, which are directly applicable to the microelectronic test pattern NBS-3 [1], show that there is a strong dependence of the surface potential distribution on the backside contact resistivity. A hitherto used two-dimensional model, with a strip source contact and restricted to the special case of a perfectly conducting backside contact, is shown to provide gross overestimates of the corresponding surface potentials when compared to the present method.