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DISTRIBUTED INDUCTANCE AND RESISTANCE PER-UNIT-LENGTH FORMULAS FOR VLSI INTERCONNECTS ON SILICON SUBSTRATE H. Ymeri, 1 B. Nauwelaers, 1 and Karen Maex 1, 2 1 ( ) Department of Electrical Engineering ESAT Div. ESAT-TELEMIC Katholieke Universiteit Leuven B-3001 Leuven-Heverlee, Belgium 2 IMEC B-3001 Leuven, Belgium Recei  ed 23 March 2001 ( ABSTRACT: A new analytic model is presented the model is based on ) the induced current density distribution inside silicon substrate to calcu- late the frequency-dependent distributed inductance and the associated distributed series resistance of silicon semiconducting VLSI intercon- nects. The  alidity of the proposed model has been checked by a comparison with CAD-oriented modeling methodology in conjunction with a quasi-TEM spectral-domain approach. It is found that the silicon semiconducting substrate skin effect must be considered for the accurate prediction of the high-frequency characteristics of VLSI interconnects.  2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 302304, 2001. Key words: VLSI interconnect; magnetic potential; distributed inductance and resistance; lossy silicon substrate 1. INTRODUCTION As the density, complexity, and speed of VLSI circuits are continuing to increase, the management of the on-chip inter- connects becomes of paramount concern to the IC designer, especially with respect to the internal parasitics parameters’  immunity 1 . In order to accomplish this, it is necessary to   analyze and model the broadband characteristics 2  6, 9 of the silicon VLSI interconnects since the signals tend to exhibit both short rising and falling times. For the case of silicon, the effect of the high-loss substrate on the distributed inductance and resistance of the interconnects has not been modeled well with analytical closed-form expressions. In this Ž letter, we suggest an analytical model based on silicon- . substrate-induced current distribution that can accurately predict the frequency-dependent inductance and resistance of silicon-substrate IC interconnects, with good agreement with the quasi-TEM spectral-domain approach and full-wave numerical simulation over a wide range of dimensions, sub- strate conductivity, and frequency. MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 30, No. 5, September 5 2001 302