A new method to compute the spreading resistance by Tikhonov regularization

The resistance associated with a nonparallel current flow in a substrate is referred to as the spreading resistance of the substrate in question. It has important issues in semiconductor technologies. If the power dissipated as heat energy inside the substrate is denoted by W, while the total current entering into the substrate is I  , then the spreading resistance in question is defined as R=W/I2R=W/I2. On the other hand R   can also be defined as R=V/IR=V/I, where V stands for the potential difference between the back-plate and source. In the present work we consider a canonical structure composed of an infinitely large lossy dielectric slab, backed by a metallic plane and fed by a constant current, and compute R   exactly. We show first of all that both definitions give the same result (i.e. W/I2=V/IW/I2=V/I). Then we reduce the determination of R into solution of a dual integral equation of the first kind whose kernel is weakly singular. To solve this latter numerically, we propose a method that is based on the regularization in the sense of Tikhonov.