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

Abstract

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.

A Quasi-Static Model for the Coupling Impedance between Coplanar Rectangular Contacts on a Bulk Substrate

“…Thus, one is left to choose between a rigorous (purely analytical) approach with unrealistic assumptions and formulae, and a phenomenological approach with realistic assumptions and formulae. The literature on coupling resistance [6], [7], [10], [12], [15]- [21] has adopted the latter, since, apart from the approach or methodology, utility is an overriding criterion for "goodness" of models in engineering and design. Moreover, a phenomenological approach is based on observations having a physical basis, and so, is consistent with first principles though not derived analytically from these as the starting point.…”

“…The derivation models the misaligned geometry's resistance as a linear combination of resistances of aligned geometries, and the resistance of an aligned non-identical geometry as the average of resistances of aligned identical geometries which have been modeled in [12]. As discussed in [12], if R represents the substrate resistance between two contacts, the coupling capacitance C between the same two contacts is given by…”

“…Recently [11], [12], we presented scalable models for coupling resistance between two contacts. Ref [11] modeled the resistance due to 2D current flow between stripe contacts using an empirical approach.…”

“…Ref [11] modeled the resistance due to 2D current flow between stripe contacts using an empirical approach. On the other hand, [12] considered the realistic case of 3D flow between two aligned and equally sized or identical rectangular contacts, and modeled both the coupling resistance and capacitance using a phenomenological approach. In the present work, we utilize this model to develop a scalable model for coupling between rectangular contacts of arbitrary location and size, i.e.…”

“…that of aligned contacts. Section IV expresses the resistance of non-identical aligned contacts in terms of identical aligned contacts.Section V gives an improved version of our previous resistance model [12] for identical aligned contact geometries; the improvement makes the model applicable for a wider range of contact geometries. Section VI validates the complete model obtained by putting the results of sections III-V together, by comparison with numerical simulations.…”