Quasi-Static Compact Model for Coupling Between Aligned Contacts on Finite Substrates With Insulating or Conducting Backplanes

We derive a closed-form quasi-static model for the coupling impedance between aligned coplanar rectangular contacts on bulk and epitaxial semiconductor substrates by resolving the 3-D field lines into simpler components (vertical, lateral, fringing, 2-D, etc.). Both insulating and conducting (grounded or floating) backplane conditions are considered. Our model reflects all the geometry and process parameters, and its constants are process independent and universal. The model also gives the capacitive coupling via ambient, i.e., via the region outside the substrate, and specifies conditions under which a given thickness or lateral extension of the substrate can be regarded as infinite. Comparisons with technology computer-aided design simulations and measurements validate the model over a wide range of width/length and width/separation ratios of the contacts.