Techniques for including dielectrics when extracting passive low-order models of high speed interconnect (original) (raw)
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Microwave and Optical Technology Letters, 2001
In this paper, a method for computing the capacitance and conductance matrices of multiconductor IC interconnects in a multilay-ered dielectric region is presented. The number of conductors and the number of dielectric layers are arbitrary. The conductors are¨ery thick ( ) as usual for on-chip interconnects , and can be placed anywhere in the structure. The formulation is obtained by using a semianalytic Green's function of multilayer structures, which is integrated to a series expansion,¨alid for charge-density distribution on the conductors. In addition, the quasianalytical e¨aluation of the entries of the Galerkin matrix leads to a¨ery efficient and accurate computer code. The accuracy of the suggested method is¨alidated by comparing it with the rigorous simulation data obtained from full-wa¨e sol¨ers and the CAD-oriented equi¨alent-circuit approach. In our research, we ha¨e¨alidated the capacitance and conductance matrices of interconnects on lossy silicon substrate o¨er a wide range of frequencies up to 20 GHz. ᮊ
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Proceedings of the 35th annual conference on Design automation conference - DAC '98, 1998
As VLSI circuit speeds have increased, reliable chip and system design can no longer be performed without accurate threedimensional interconnect models. In this paper, we describe an integral equation approach to modeling the impedance of interconnect structures accounting for both the charge accumulation on the surface of conductors and the current traveling in their interior. Our formulation, based on a combination of nodal and mesh analysis, has the required properties to be combined with Model Order Reduction techniques to generate accurate and guaranteed passive low order interconnect models for efficient inclusion in standard circuit simulators. Furthermore, the formulation is shown to be more flexible and efficient than previously reported methods.
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Abstract A new method is formulated for modeling current distributions inside conductors for a quasi-static or a full-wave electromagnetic field simulator. In our method, we model current distributions inside interconnects using a small number of conduction modes as global basis functions for discretization of the mixed potential integral equation. A very simple example is presented to illustrate the potential of our method
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The paper deals with the inclusion of inhomogeneous dielectrics in a full-wave transmission line model for high-frequency analysis of interconnects. This “enhanced” transmission line model is derived from a full-wave integral formulation of the electromagnetic problem, and the inclusion of dielectrics is performed by an accurate semi-analytical evaluation of the Green functions for layered planar structures. The resulting model has a computational cost typical of a TL model but is able to perform a full-wave analysis in frequency ranges where the standard TL model may no longer be used. Moreover, as shown in the proposed examples, the model gives the possibility to investigate separately several phenomena affecting the high-frequency behavior of interconnects, like losses in dielectrics, unwanted radiation and excitation of parasitic modes.
IEEE Transactions on Microwave Theory and Techniques, 2014
A novel single-source surface-volume-surface integral equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new equation originates in the volume integral equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface integral equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductor's boundary. As no approximation is utilized and all underlying boundary conditions and pertinent equations are satisfied in the reduction, the new integral equation is rigorously equivalent to the solution of the traditional volume electric field integral equation. The rigorous nature of the proposed single-source surface integral equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface integral equation is also presented. Numerical solution of the proposed surface integral equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.