Xiren Wang

Improved Boundary Element Method for Fast 3-D Interconnect Resistance Extraction

SUMMARY Efficient extraction of interconnect parasitic parameters has become very important for present deep submicron designs. In this paper, the improved boundary element method (BEM) is presented for 3D interconnect resistance extraction. The BEM is accelerated by the recently proposed quasi-multiple medium (QMM) technology, which quasicuts the calculated region to enlarge the sparsity of the overall coefficient matrix to solve. An un-average quasi-cutting scheme for QMM, advanced nonuniform element partition and technique of employing the linear element for some special surfaces are proposed. These improvements considerably condense the computational resource of the QMM-based BEM without loss of accuracy. Experiments on actual layout cases show that the presented method is several hundred to several thousand times faster than the well-known commercial software Raphael, while preserving the high accuracy.

A new boundary element method for accurate modeling of lossy substrates with arbitrary doping profiles

It is important to model substrate couplings for SoC/mixed-signal circuit designs. After introducing the continuation equation of full current in lossy substrates, we present a new direct boundary element method (DBEM), which can handle the substrates with arbitrary doping profiles. Three techniques can speed up the DBEM remarkably, which include reusing coefficient matrices for multiple-frequency calculation, condensing the linear system, and sparsifying coefficient matrix. Numerical experiments illustrate that DBEM has high accuracy and high efficiency, and is versatile for arbitrary doping profiles

Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits

Resistance and capacitance (RC) extraction is an essential step in modeling the interconnection wires and substrate coupling effect in nanometer-technology integrated circuits (IC). The field-solver techniques for RC extraction guarantee the accuracy of modeling, and are becoming increasingly important in meeting the demand for accurate modeling and simulation of VLSI designs. Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits presents a systematic introduction to, and treatment of, the key field-solver methods for RC extraction of VLSI interconnects and substrate coupling in mixed-signal ICs. Various field-solver techniques are explained in detail, with real-world examples to illustrate the advantages and disadvantages of each algorithm.This book will benefit graduate students and researchers in the field of electrical and computer engineering as well as engineers working in the IC design and design automation industries.Dr. Wenjian Yu is an Associate Professor at the Department of Computer Science and Technology at Tsinghua University in China; Dr. Xiren Wang is a R&D Engineer at Cadence Design Systems in the USA.

An Incremental Boundary Element Method for the Variation-Aware Library-Building Procedure of Capacitance Extraction

The variation of process parameters makes the number of geometry patterns in capacitance extraction increase for magnitudes, which brings a heavy burden to the library-building procedure. An incremental BEM solver is proposed for the variation-aware library-building. This method reuses the coefficient matrix and solution of the original pattern for the sequent computations for varied patterns. Numerical results show the proposed method is five times faster than the method just repeats the computation for all patterns, while preserving high accuracy

Fast extraction of 3-D interconnect resistance: numerical-analytical coupling method

Fast and accurate parasitic parameter extraction becomes more and more important for VLSI design. In this paper, a fast and accurate method is presented to extract three-dimensional interconnect resistance. In this method, the whole resistance region is firstly cut into regular parts and irregular parts. The resistance extraction of these two kinds of parts is solved using the analytical formula and the numerical method of 3-D boundary element method respectively. Experiments on real layout cases show that, compared with the commercial software Raphael and the method of 3-D BEM without analytical method coupled, the proposed analytical-numerical coupling method has a speedup of more than 2000 and 40 respectively while preserving high accuracy.Fast and accurate parasitic parameter extraction becomes more and more important for VLSI design. In this paper, a fast and accurate method is presented to extract three-dimensional interconnect resistance. In this method, the whole resistance region is firstly cut into regular parts and irregular parts. The resistance extraction of these two kinds of parts is solved using the analytical formula and the numerical method of 3-D boundary element method respectively. Experiments on real layout cases show that, compared with the commercial software Raphael and the method of 3-D BEM without analytical method coupled, the proposed analytical-numerical coupling method has a speedup of more than 2000 and 40 respectively while preserving high accuracy.

Substrate resistance extraction with direct boundary element method

It is important to model the substrate coupling for mixed-signal circuit designs today. This paper presents the direct boundary element method (BEM) for substrate resistance calculation, where only the boundary of substrate region is discretized. Firstly, an efficient scheme for non-uniform element partition is proposed. Secondly, a new technique is presented which can reduce the scale of produced linear system and then accelerate the equation solving, especially for the multiple right-hand sides problem like substrate resistance extraction. Experiments show that the proposed method has shown high efficiency compared with existing methods while preserving high accuracy.

An improved direct boundary element method for substrate coupling resistance extraction

It is important to model the substrate coupling for mixed-signal circuit designs today. This paper presents an improved direct boundary element method (DBEM) for substrate resistance calculation, where only the boundary of substrate volumes is discretized and only the free-space Green function is used. At first, we discard some inessential unknowns to compress the linear system without accuracy loss. Then we make the coefficient matrix sparser. In this way, solving the linear system is greatly accelerated. Experiments on various substrates validate that DBEM is several to tens of times faster than DCT-accelerated Greens function methods and the eigendecomposition method, while preserving high accuracy. Besides, another experiment shows that this method is versatile for irregular substrates.

A New Boundary Element Method for Multiple-Frequency Parameter Extraction of Lossy Substrates

The couplings via realistic lossy substrates can be modeled as frequency-dependent coupling parameters. The fast extraction at multiple frequencies can be accomplished in two sequent steps. The first is to extract the coupling resistance using a direct boundary element method (DBEM). The second is to revise the resistance into the parameter at the frequency in an exact and rapid way. The first step is time-consuming, while it runs only one time; the second repeats at each frequency, but is much easier. For more frequency calculation, this method is more advanced. Numerical experiments illustrate that this method has high accuracy, and it can be hundreds of times faster than an advanced Greens function based method. Substrates with arbitrary doping profiles can also be easily handled, which is partly verified by experiment.

Modeling lossy substrates with direct boundary element method

It is important to model coupling effects of lossy substrates for the designs of RF or mixed-signal circuits. A direct boundary element method using the complex permittivity concept is presented for accurate modeling the lossy couplings. Only the free-space Greens function is used in this method, and then the method is versatile for substrates with arbitrary doping profiles. Numerical experiments illustrate that our method gives accurate results, and it can easily model a more complex than stratified substrate

Boundary element method for substrate resistance calculation

It is important to model the substrate coupling for todays mixed-signal circuit designs. In substrate coupling resistance calculation, the focus is the information about current only on the substrate boundary. This paper presents the boundary element method (BEM) for the calculation, whose meshes are only on the boundary. Moreover, there are few limitations for the structure that BEM is to handle. In realization, BEM has some difficulty. One is the large scale of the coefficient matrix, and another is the ill condition of the matrix. Their solutions are also presented. Experiments show that the improved BEM is able to produce results comparable to existent methods. Besides, BEM is of high efficiency both in running time and memory usage.