Quasi-multiple Medium Research Articles

Efficient Direct Boundary Element Method for Resistance Extraction of Substrate With Arbitrary Doping Profile

It is important to model the substrate coupling for mixed-signal or RF circuit designs. In this paper, a direct boundary element method (DBEM) and related efficient techniques are presented to calculate the coupling resistances for three-dimensional substrate structure. First, a nonuniform meshing scheme is presented to reduce boundary elements while preserving accuracy. Then, the unknowns on top medium surface are removed from the discretized linear system of DBEM with a matrix reduction technique. The third technique is applying the quasi-multiple medium idea (W. Yu, Z. Wang, and J. Gu, "Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM," IEEE Trans. Microwave Theory Tech., vol. 51, no. 1, pp. 109-199, Jan. 2003), which greatly reduces the expense of matrix reduction and makes the final coefficient matrix much sparser. With these proposed techniques, the linear equation system is largely condensed and sparsified and then solved with a preconditioned generalized minimum residual solver for multiple right-hand sides to get the whole resistance matrix. Numerical experiments on typical substrates with various doping profiles show the high accuracy of the DBEM-based method. The authors also compared the DBEM method with the Green's function methods accelerated by discrete cosine transform or eigendecomposition techniques. The results show that the DBEM-based method is several times or tens of times faster than the other two. At the same time, the DBEM method has no difficulty in handling substrates with more complex than stratified doping profiles, which is a large advantage over the existing methods

Efficient 3-D extraction of interconnect capacitance considering floating metal fills with boundary element method

Inserting dummy (area fill) metals is necessary to reduce the pattern-dependent variation of dielectric thickness in the chemical-mechanical polishing (CMP) process. Such floating dummy metals affect interconnect capacitance and, therefore, signal delay and crosstalk significantly. To take the floating dummies into account, an efficient method for three-dimensional (3-D) capacitance extraction based on boundary element method is proposed. By introducing a floating condition into the direct boundary integral equation (BIE) and adopting an efficient preconditioning technique, and the quasi-multiple medium (QMM) acceleration, the method achieves very high computational speed. For some typical structures of area fill, the presented algorithm has shown over 1000/spl times/ speedup over the industry-standard Raphael while preserving high accuracy. Compared with the recently proposed PASCAL in the work of Park et al. (2000), the proposed method also has about ten times speedup. Since the dummies are not regarded as normal electrodes in capacitance extraction, the proposed method is much more efficient than the conventional method, especially in cases with a large number of floating dummies.

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.

Enhanced QMM-BEM Solver for Three-Dimensional Multiple-Dielectric Capacitance Extraction Within the Finite Domain

The computational time and memory of three-dimensional capacitance extraction have been greatly reduced by using a quasi-multiple medium (QMM) technology, because it enlarges the matrix sparsity produced by the direct boundary element method. In this paper, an approach to automatically determining the QMM cutting pair number and a preconditioning technique are proposed to enhance the QMM-based capacitance extraction. With these two enhancements, the capacitance extraction can achieve much higher speed and adaptability. Experimental results examine the efficiency of two enhancements and show over 10/spl times/ speed-up and memory saving over the multipole approach with comparable accuracy.

A fast quasi-multiple medium method for 3-D bem calculation of parasitic capacitance

A quasi-multiple medium (QMM) method is proposed to accelerate the boundary element method (BEM) for the 3-D parasitic capacitance calculation. In the QMM method, a homogeneous dielectric is decomposed into a number of fictitious medium blocks, each with the same permittivity of original medium. By the localization character of BEM, the QMM method makes great sparsity to the coefficient matrix of the overall discretized BEM equations. Then, using storing technique of sparse matrix and iterative equation solvers, the sparsity is explored to greatly reduce CPU time and memory usage of BEM computation. The computational complexity of the QMM accelerated BEM for a single-medium model problem is analyzed, and it is concluded as O( N), if the number of iterations is bounded. Numerical results verify the theoretical analysis and show the accelerating efficiency of the QMM method for calculation of 3-D parasitic capacitance.

Fast capacitance extraction of actual 3-D VLSI interconnects using quasi-multiple medium accelerated BEM

A quasi-multiple medium (QMM) method based on the direct boundary element method (BEM) is presented to extract the capacitance of three-dimensional (3-D) very large scale integration interconnects with multiple dielectrics. QMM decomposes each dielectric layer into a few fictitious medium blocks, and generates an overall coefficient matrix with high sparsity. With the storage technique of a sparse blocked matrix and iterative equation solver generalized minimal residual, the QMM can greatly reduce the CPU time and memory usage of large-scale direct BEM computation. Numerical examples of 3-D multilayered and multiconductor structures cut from actual layout show the efficiency of the QMM method for capacitance extraction. We also compared the QMM accelerated BEM with geometry independent measured equation of invariance (GIMEI) and Zhu's overlapping domain decomposition method (ODDM).