RWCap: A Floating Random Walk Solver for 3-D Capacitance Extraction of Very-Large-Scale Integration Interconnects

Yu, Wenjian; Zhuang, Hao; Zhang, Chao; Hu, Gang; Li, Zhi

doi:10.1109/tcad.2012.2224346

Cited by 89 publications

(55 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…, n P edge pixels p j := p EDGE Γ k | j are picked on the edge of Γ k according to (24); the command edge can be used for this task. They lead to the footpoint guesses {z 0 j } according to (23) and, by (22), to the footpoints {z j }. Now, χ k can be constructed on them if the footpoints are ordered sequentially (but not necessarily equispaced) along the level set ψ E = −h around Γ k .…”

Section: Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

Bernal¹,

Acebrón²,

Anjam³

2014

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

Abstract. We present an algorithm for two-and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algorithm decreases with better resolution of the input image. Those features render the presented algorithm well suited for fast prototyping while using the most realistic IC geometry data.

show abstract

Section: Algorithmmentioning

confidence: 99%

“…The FRW has been much improved since [10,22], but the efficient handling of nonManhattan designs remains inadequate. It must be stressed that Manhattan geometries are just a useful idealization of the IC, for there may be individual components which are not rectangular.…”

mentioning

confidence: 99%

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

Bernal¹,

Acebrón²,

Anjam³

2014

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

show abstract

“…Recently, a general FRW algorithm [3] and a hierarchical FRW algorithm [4] were proposed to deal with arbitrary dielectric configuration and for a fabric-aware extraction problem, respectively. In 2013, an FRW algorithm [5] was proposed for the interconnect structure with multilayered dielectrics, where the cross-interface transition probability and weight value are precharacterized for a given process technology. The algorithm was further accelerated with a comprehensive variance reduction scheme, and has been developed to a program called RWCap [5].…”

Section: Introductionmentioning

confidence: 99%

“…In 2013, an FRW algorithm [5] was proposed for the interconnect structure with multilayered dielectrics, where the cross-interface transition probability and weight value are precharacterized for a given process technology. The algorithm was further accelerated with a comprehensive variance reduction scheme, and has been developed to a program called RWCap [5]. Although employing an Octree-based space management approach, RWCap is not efficient for handling the large-scale structures with thousands of conductors.…”

Section: Introductionmentioning

confidence: 99%

“…With the Gauss theorem, charge Q i of conductor i becomes [5] (1) ω(r, r (1) )P (1) (r, r (1) )φ(r (1) )dr (1) dr (2) where F(r) is the dielectric permittivity at point r, g is a constant, and function ω(r, r (1) ) is called the weight value [1], [5]. Here, P (1) denotes the surface Green function for S (1) enclosing r. With the Monte Carlo (MC) method, Q i can be estimated as the statistical mean of sampled values on G i , which is further the mean of sampled values on S (1) multiplying the weight value.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Space Management Techniques for Large-Scale Interconnect Capacitance Extraction With Floating Random Walks

Zhang

2013

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

Self Cite

View full text Add to dashboard Cite

In the capacitance extraction with the floating random walk (FRW) algorithm, the space management approach is required to facilitate finding the nearest conductor. The Octree and grid-based spatial structures have been used to decompose the whole domain into cells and to store information of local conductors. In this letter, the techniques with the distance limit of cell and only searching in cell's neighbor region are proposed to accelerate the construction of the spatial structures. A fast inquiry technique is proposed to fasten the nearest conductor query. We also propose a grid-Octree hybrid structure, which has advantages over existing structures. Experiments on large very large scale integration structures with up to 484 441 conductors have validated the efficiency of the proposed techniques. The improved FRW algorithm is faster than RWCap for thousands times while extracting a single net, and several to tens times while extracting 100 nets.Index Terms-Capacitance extraction, floating random walk (FRW), space management, spatial data structure, very large scale integration (VLSI) circuit. I. IntroductionThe floating random walk (FRW) algorithm [1]-[6] is a major field-solver method for capacitance extraction. Compared with the deterministic algorithms (e.g., boundary element method [7]), the FRW algorithm has the advantages of lower memory usage, better scalability, and tunable accuracy.Today, the FRW algorithm has become the kernel of commercial capacitance solvers (such as QuickCap). With parallel computing techniques, they have been applied to the block-or chip-level extraction task in the sign-off verification of very large scale integration (VLSI) circuits. Recently, a general FRW algorithm [3] and a hierarchical FRW algorithm [4] were proposed to deal with arbitrary dielectric configuration and for a fabric-aware extraction problem, respectively. In 2013, an FRW algorithm [5] was proposed for the interconnect structure with multilayered dielectrics, where the cross-interface transition probability and weight value are precharacterized for a given process technology. The algorithm was further accelerated with a comprehensive variance reduction scheme, and has been developed to a program called RWCap [5]. Although employing an Octree-based space management approach, RWCap is not efficient for handling the large-scale structures with thousands of conductors. Another approach based on an array data structure has been used, and achieved remarkable speedup over the K-D tree based technique [6]. However, it is not well compared with other techniques, and its details are not published. In [8], several data structures were discussed to speed up the distance queries in the FRW

show abstract

Improved pre‐characterization method for the random walk based capacitance extraction of multi‐dielectric VLSI interconnects

Zhang

2015

Int J Numerical Modelling

Self Cite

View full text Add to dashboard Cite

Accurately extracting capacitances among the interconnects in modern multi-dielectric technology of integrated circuits is a challenging task. The floating random walk (FRW) algorithm is advantageous for capacitance extraction and has been extended by W. Yu et al. to accurately handle multi-dielectric structures with a precharacterization approach. In this paper, we improve this pre-characterization approach by permitting the cubic transition domains with three or four-dielectric layers. The techniques of pre-characterizing and utilizing these multi-dielectric transition cubes are proposed. Experiments on the test cases under actual manufacture technologies show that the proposed method brings 13× speedup on average, with affordable memory overhead. The experiments also validate the accuracy of the proposed method and reveal the significant error caused by the dielectric homogenization approach in a commercial FRW solver. Finally, on a machine with 12-core CPU, the parallel FRW algorithm equipped with the proposed pre-characterization method demonstrates more than 10× speedup of parallelization.

show abstract

RWCap: A Floating Random Walk Solver for 3-D Capacitance Extraction of Very-Large-Scale Integration Interconnects

Cited by 89 publications

References 20 publications

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

Efficient Space Management Techniques for Large-Scale Interconnect Capacitance Extraction With Floating Random Walks

Improved pre‐characterization method for the random walk based capacitance extraction of multi‐dielectric VLSI interconnects

Contact Info

Product

Resources

About