Exact closed-form expressions for substrate resistance and capacitance extraction in nanoscale VLSI

Authors:
Yiorgos I. Bontzios;Michael G. Dimopoulos;Alexandros I. Dimitriadis;Alkis A. Hatzopoulos
Affiliations:
Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece;TIMA Laboratory (CNRS, Grenoble INP, UJF), 46 Avenue Félix Viallet, 38031 Grenoble Cedex, France;Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece;Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Venue:
Microelectronics Journal
Year:
2013

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Abstract

A new exact formula to determine the substrate resistance and capacitance is presented in this work. It is derived from the solution of the Laplace equations for equivalent problems. It achieves the level of accuracy of standard electromagnetic methods while it is orders of magnitude faster than them. Equations for both rectangular and non-rectangular shapes of interconnect lines which apply to sub-micron technologies are presented. Both data from commercial simulators and measurement data obtained from a fabricated test chip are utilized in order to show the validity of the proposed formula. The results show that the proposed formula succeeds in computing the substrate's resistive and capacitive coupling.