Using conduction modes basis functions for efficient electromagnetic anaysis of on-chip and off-chip interconnect (original) (raw)
Interconnect electromagnetic modeling using conduction modes as global basis functions
2000
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
A surface-based integral-equation formulation for coupled electromagnetic and circuit simulation
Microwave and Optical Technology Letters, 2002
A surface-based integral-equation formulation for coupled electromagnetic and circuit simulation is presented. The approach is sufficiently general to model arbitrarily shaped structures and highfrequency skin effects. The formulation is implemented in both an equivalent circuit form for spice compatibility, and in a more general form as a coupled-matrix system outside spice. The overall approach can be interpreted as either a modified surface-only partial element equivalent circuit approach, or as a circuit-coupled version of the surface-based method of moments.
Strategy for electromagnetic interconnect modeling
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2001
In order to design on-chip interconnect structures in a flexible way, a computer-aided design approach is advocated in three dimensions, describing high-frequency effects such as current redistribution due to the skin effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by a scalar electric potential and a magnetic vector potential. These potentials are not uniquely defined and in order to obtain a consistent discretization scheme, a gauge transformation field is introduced. The displacement current is taken into account to describe current redistribution and a small-signal analysis solution scheme is proposed based upon existing techniques for fields in semiconductors.
Electromagnetic interconnects and passives modeling: software implementation issues
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2002
This is the second paper in a series on the simulation of on-chip high-frequency effects. A computer-aided approach in three dimensions is advocated, describing high-frequency effects such as current redistribution due to the skin-effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by an electric scalar potential and a magnetic vector potential as well as a ghost field. The latter one guarantees a stable numerical implementation. This paper deals with the software implementation, the treatment of interfaces and domain boundaries, scaling considerations, numbering schemes, and solver requirements. Some illustrative examples are shown.
Computational electromagnetic methods for interconnects and small structures
Superlattices and Microstructures, 2000
The continual advances in speed and integration scale of electronic circuits have created enormous demands for high-speed, high-density packages which ensure reduced interconnection delays and improved electrical performance. Such structures usually involve a large number of planar transmission lines at various levels within the package, whereas the geometrical orientation of these lines is not necessarily uniform. Also, the existence of multiple dielectric layers, discontinuities, bends, and wire bounds adds considerable complexity to the package. It is therefore essential that full-wave computational electromagnetic (CEM) techniques, such as the finite element method (FEM) and the finite-difference time-domain (FDTD) method, be developed and used to accurately model the electrical performance of these devices and circuits.
2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157)
Absfract-The adaptive integral method (AIM) is used to accelerate the electromagnetic solution of dense integrated circuits inside metallic enclosures of rectangular cross section. The computational complexity and memory requirements for the proposed AIM-based electromagnetic solver scale as O(N1ogN) and 0 0 , respectively, where N is the number of unknowns in the discrete approximation of the governing integral equation. The accuracy and efficiency of the solver is demonstrated through its application to the modeling of a shielded patch array used for spatial power combining.
IEEE/ACM International Conference on Computer Aided Design. ICCAD - 2000. IEEE/ACM Digest of Technical Papers (Cat. No.00CH37140)
The finite-difference time-domain (FDTD) method of solving the full-wave Maxwell's equations has been recently extended to provide accurate and numerically stable operation for time steps exceeding the Courant limit. The elimination of an upper bound on the size of the time step was achieved using an alternating-implicit direction (ADI) timestepping scheme. This greatly increases the computational efficiency of the FDTD method for classes of problems where the cell size of the three-dimensional space lattice is constrained to be much smaller than the shortest wavelength in the source spectrum. One such class of problems is the analysis of highspeed VLSI interconnects where full-wave methods are often needed for the accurate analysis of parasitic electromagnetic wave phenomena. In this paper, we present an enhanced FDTD-ADI formulation which permits the modeling of realistic lossy materials such as semiconductor substrates and metal conductors as well as artificial lossy materials needed for perfectly matched layer (PML) absorbing boundary conditions. Simulations using our generalized FDTD-ADI formulation are presented to demonstrate the accuracy and extent to which the computational burden is reduced by the ADI scheme.
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.
Mixed-mode circuit simulation with full-wave analysis of interconnections
1997
A simulation technique, which couples full-wave, electromagnetic sim¬ ulation of interconnections and distributed semiconductor device mod¬ eling, is described in this paper. A 3D FDTD scheme is adopted to describe the circuit passive part, whereas conventional device simu¬ lation techniques are employed for the active semiconductor devices. The resulting scheme allows for accurate mixed-mode simulation, inher¬ ently accounting for propagation and radiative effects. An application example is discussed, consisting of the simulation of a Si-MMIC RF switch.
Efficient computation of interconnect capacitances using the domain decomposition approach
IEEE Transactions on Advanced Packaging, 1999
In this paper, we present a novel technique for efficient computation of capacitance matrices of complex interconnect configurations. It applies the finite difference (FD) method in conjunction with the perfectly matched layer (PML) and impedance boundary condition for mesh truncation, and combines these with the overlapping domain decomposition approach to handle complex configurations that are too large to handle in one step. Convergence and efficiency issues of the proposed algorithm are examined and numerical examples are presented to illustrate the usefulness of the proposed scheme.
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.
Design, Automation, and Test in Europe, 1998
As VLSI circuit speeds have increased, the need for accurate three-dimensional interconnect models has become essential to accurate chip and system design. 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 along conductors. Unlike previous methods, our approach
Journal of Electromagnetic Analysis and Applications, 2012
Integral formulations are widely used for full-wave analysis of microstrip interconnects. A weak point of these formulations is the inclusion of the proper planar-layered Green's Functions (GFs), because of their computational cost. To overcome this problem, usually the GFs are decomposed into a quasi-dynamic term and a dynamic one. Under suitable approximations, the first may be given in closed form, whereas the second is approximated. Starting from a general criterion for this decomposition, in this paper we derive some simple criteria for using the closed-form quasi-dynamic GFs instead of the complete GFs, with reference to the problem of evaluating the full-wave current distribution along microstrips. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. The layered GFs have been embedded into a full-wave transmission line model and the results are first benchmarked with respect to a full-wave numerical 3D tool, then used to assess the proposed criteria.
Numerical Analysis of Electromagnetic Fields in Interconnecting Grids
The development of integrated circuits has reached a situation today that the circuit operating speed is not limited by the parameters of the transistors any more, but rather by the electrical parameters of the interconnections inside the integrated circuit (1). For this reason, it is necessary to take in account the properties of interconnecting conductors from the start of the circuit design process. Undesirable parasitic electromagnetic couplings appear between the interconnecting lines, causing the transfer of interfering impulses onto the signal-carrying lines. These interfering impulses then result in random errors and/or disturbances in the integrated circuit. In order to be able to solve the problem of electromagnetic couplings inside integrated circuits, it is imperative to be able to determine the electrical parameters of the interconnecting girds as accurately as possible.