Session 2B: Interconnect Modeling and Simulation Techniques

2B-1 (Time: 13:30 - 13:55)

Title Efficient Numerical Modeling of Random Rough Surface Effects for Interconnect Internal Impedance Extraction
Author *Quan Chen, Ngai Wong (The Univ. of Hong Kong, Hong Kong)
Abstract This paper proposes an efficient model for numerically evaluating the impact of random surface roughness on the internal impedance for large-scale interconnect structures. The effective resistivity (ER) and effective permeability (EP) are numerically formulated to avoid the computationally prohibitive global discretization, while maintaining the model accuracy and flexibility. A modified stochastic integral equation (SIE) method is proposed to significantly speed up the computation for the mean values of ER and EP under the assumption of random surface roughness. Numerical experiments then verify the efficacy of our approach.

2B-2 (Time: 13:55 - 14:20)

Title Efficient Techniques for 3-D Impedance Extraction Using Mixed Boundary Element Method
Author *Fang Gong, Wenjian Yu, Zeyi Wang (Tsinghua Univ., China), Zhiping Yu (Tsinghua Univ., China), Changhao Yan (Fudan Univ., China)
Abstract In this paper, we describe the algorithms implemented in MBEM, a program for wideband impedance extraction of complicated 3-D structures. MBEM is based on a mixed boundary element method (BEM), which reduces the number of unknowns from about 7N in FastImp to 4N, for MQS analysis. Efficient techniques are proposed to handle the extra matrix multiplication, form post-process matrices, and solve the final linear equation system. The inaccuracy of calcu- lation using FastImp at low frequency is also analyzed, which shows the mixed BEM eliminates it completely. Experiments on several typical 3-D structures validate the advantage of MBEM over FastImp, on both accuracy and efficiency.

2B-3 (Time: 14:20 - 14:45)

Title Generating Stable and Sparse Reluctance/Inductance Matrix under Insufficient Conditions
Author *Yuichi Tanji (Kagawa Univ., Japan), Takayuki Watanabe (The Univ. of Shizuoka, Japan), Hideki Asai (Shizuoka Univ., Japan)
Abstract This paper presents generating stable and sparse reluctance/inductance matrix from the inductance matrix which is extracted under insufficient discretization. So far, to generate the sparse reluctance matrix with guaranteed stability, this matrix has to be diagonally dominant M matrix. Hence, the repeated inductance extractions are necessary using a smaller grid size, in order to obtain the well-defined matrix. Alternatively, this paper provides some ideas for generating the sparse reluctance matrix, even if the extracted reluctance matrix is not diagonally dominant M matrix, precisely, the positive off-diagonal elements are even found. This eases the extraction tasks greatly. Furthermore, the sparse inductance matrix is also generated by using the practical and sophisticated double inverse methods, which is useful for the SPICE simulation, since reluctance components are not still supported in SPICE-like simulators.

2B-4 (Time: 14:45 - 15:10)

Title Hierarchical Krylov Subspace Reduced Order Modeling of Large RLC Circuits
Author Duo Li, *Sheldon X.-D. Tan (Univ. of California, Riverside, USA)
Abstract In this paper, we propose a new model order reduction approach for large interconnect circuits using hierarchical decomposition and Krylov subspace projection-based model order reduction. The new approach, called hiePrimor, first partitions a large interconnect circuit into a number of smaller subcircuits and then performs the projection-based model order reduction on each of subcircuits in isolation and on the top level circuit thereafter. The new approach can exploit the parallel computing to speed up the reduction process. Theoretically we show hiePrimor can have the same accuracy as the flat reduction method given the same reduction order and it can also preserves the passivity of the reduced models as well. We also show that partitioning is important for hierarchical projection-based reduction and the minimum-span objective should be required to archive best performance for hierarchical reduction. The proposed method is suitable for reducing large global interconnects like coupled bus, transmission lines, large clock nets in the post layout stage. Experimental results demonstrate that hiePrimor can be significantly faster than flat projection method like PRIMA and be order of magnitude faster than PRIMA with parallel computing without loss of accuracy.

2B-5 (Time: 15:10 - 15:35)

Title Statistical Noise Margin Estimation for Sub-Threshold Combinational Circuits
Author *Yu Pu (Technische Universiteit Eindhoven, The Netherlands), Jose Pineda de Gyvez (NXP Research Eindhoven, The Netherlands), Henk Corporaal (Technische Universiteit Eindhoven, The Netherlands), Yajun Ha (Nat’l Univ. of Singapore, Singapore)
Abstract The increasingly popular sub-threshold design is strongly calling for EDA support to estimate noise margins, minimum functional supply voltage, as well as the functional yield. In this paper, we propose a fast, accurate and statistical approach to accomplish these goals. First, we derive close-form functions based on a new equivalent resistance model which enables the fast estimation of noise margins of individual cells at the gate-level. Second, we propose to calculate and propagate the noise margin information with an affine arithmetic model that takes into account process variations and correspondent inter-cell correlations. Experiments with ISCAS benchmarks have shown that the new approach has an accuracy of 98.5% w.r.t. transistor-level Monte Carlo simulations. The running time per input vector of the new approach only needs a few seconds, in contrast to the many hours required by transistor-level DC Monte-Carlo simulations. To the best of our knowledge, we are the first to provide a fast, accurate and statistical methodology other than Monte-Carlo simulation for the noise margin estimation of sub-threshold combinational circuits.
Last Updated on: January 31, 2008