In this paper, we present a new approach for capacitance matrix calculation of lossy multilayer VLSI interconnects based on quasi-static analysis and Fourier projection technique. The formulation is ...independent from the position of the interconnect conductors and number of layers in the structure, and is especially adequate to model 2D and 3D layered structures with planar boundaries. Thanks to the quasi-static algorithms considered for the capacitance analysis and the expansions in terms of convergent Fourier series the tool is reliable and very efficient; results can be obtained with relatively little programming effort. The validity of the technique is verified by comparing its results with on-surface MEI method, moment method for total charges in the structure, and CAD-oriented equivalent-circuit methodology, respectively.
A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based on ...a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations needed to obtain the desired expressions. As a result, for the first time, we present a new, simple, yet surprisingly accurate, closed-form expression which yields accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulae describe the mutual line impedance behaviour over the whole frequency range (i.e. also in the transition region between the skin effect, slow-wave and dielectric quasi-TEM modes). The results have been compared with reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.
Simple and accurate closed-form expressions to calculate frequency-dependent distributed inductance and associated distributed series resistance per-unit-length of single on-chip interconnects on a ...lossy silicon substrate are presented. The analytic formulas for the frequency-dependent series impedance parameters are obtained using a closed-form integration method and the vector magnetic potential equation. It is shown that the calculated frequency-dependent inductance
L(
f) and resistance
R(
f) per-unit-length are in good agreement with the results obtained from rigorous full wave solutions and CAD-oriented equivalent-circuit modeling approach.
A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of a lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based ...on a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations which are needed in obtaining the desired expressions. As a result, for the first time, we present a new simple, yet surprisingly accurate closed-form expression which yield accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulas describe the mutual line impedance behaviour over the whole frequency range ( i.e. also in the transition region between the skin effect, slow wave, and dielectric quasi-TEM modes). The results have been compared with the reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.
A new analytic model is presented (the model is based on the induced current density distribution inside silicon substrate) to calculate frequency dependent mutual inductance and resistance per unit ...length of coupled on-chip interconnects in CMOS technology. The validity of the proposed model has been checked by a comparison with a quasi-TEM spectral domain numerical simulation and equivalent-circuit modeling procedure. 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.
In this paper a method for computing the capacitance matrix of a multiconductor interconnect line in a multilayered dielectric region is presented. The number of conductors and dielectric layers are ...arbitrary. The conductors are infinitesimally thin, and can be placed anywhere in the structure. The formulation is obtained by using a semi-analytic Green's function for multilayer structures, which is integrated to a series expansion, valid for uniform charge distribution on the conductors. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. Computed results are given for some cases of the integrated circuit interconnects to show the advantages and simplicity of our procedure as compared to the methods available in the literature.
A new method for analysis of IC interconnects propagation parameters is suggested. A potential integral formalism is employed that enables us to express general solutions for the scalar potential in ...each layer of a multilayer model. These expressions for potential led to the derivation of an equation for calculating the line parameters of interconnect lines in such a multilayer configuration. This approach is verified by two-dimensional examples of the integrated circuit interconnects with errors within 0.5 per cent to 1 per cent.
