A Nondestructive Method for Accurately Extracting Substrate Parameters of Arbitrary Doping Profile in Nanoscale VLSI

In this paper, a new approach is presented for determining the substrate parameters of an arbitrary doping profile. It is general, technology independent, nonintrusive, and relies on simple direct-current measurements. A single measurement is required for uniform substrates, whereas two more measurements are needed for each additional layer in the multilayer case. Two different kernels are introduced for substrate resistance computation. One features a closed-form analytical solution of the Laplace equations defining the problem under study. The other relies on a geometric formulation of the current streamlines in order to compute the substrate resistance. Both simulations and measurements are exploited in order to show the validity of the proposed scheme. For measurements, data from literature are utilized and also data from a fabricated test chip. The results demonstrate that the proposed method succeeds in computing the substrate parameters fast and with high accuracy. In uniform substrates, the error falls to zero, whereas, in epitaxial substrates, the average error is kept bellow 4%.