Fast quasi-static capacitance extraction using CSurf

Parasitic parameter (capacitance and inductance, etc.) extraction and optimization from electrical interconnect and packaging is a critical step toward a successful physical design of high-speed integrated circuits. CSurf is a software tool incorporating the state-of-the-art numerical techniques, that allows users to perform a larger and more complex parasitic capacitance extractions under both homogeneous and inhomogeneous environment than was previously possible. Also it can more accurately analyze electrical performance for improved estimates of noise sources and improved component models. Benchmarks have demonstrated that Csurf can out-perform current tools by over 100 times for via array structures in multilayer dielectrics.

Parasitic parameter extraction demands advanced EDA (Electrical Design Automation) tools to achieve superior performance. Facing dramatically increased complexity of today’s chip and packaging structure, two major obstacles are challenging the extraction tools: problem size capacity and inhomogeneous environment capability. Direct volume or surface solvers cannot handle the huge number of unknowns generated from electromagnetic discretization. Inhomogeneous dielectrics commonly presented together with interconnect and packaging structures make most fast solvers very difficult to implement. Csurf was developed to overcome these two difficulties.

Modeling electromagnetic performance requires dealing with Maxwell’s equations. Solving them numerically means constructing and solving a set of linear algebraic equations. Differential equation and surface integral equation are two primary approaches used to construct the linear system. However, the later one produces significantly fewer unknowns but a dense system matrix. Csurf takes advantage of surface integral equations to have far less unknowns than the volumetric method (differential equation based). But it uses “divide and conquer” strategy to hierarchically solve the dense capacitance matrix efficiently. It partitions the problem into small regions (cells) automatically and each region is analyzed separately. Every cell generates a dense capacitance matrix (BCM) representing its internal and external capacitive coupling physics. An inverse binary-tree browse procedure is employed to combine BCMs from leafy level of the tree to the root. A global capacitance matrix is obtained at the root of the tree without computing the charge distribution. Careful manipulation of the boundary conditions on both real and artificial surfaces allows the inhomogeneous problems to be treated as homogeneous problems.

The keys to the extraction performance are the accuracy of surface integrals and dimension reduction. Because surface integrals are needed in each cell, most coupling effects are within the near-field range. Therefore contributions for dipole and monopole are both evaluated using analytical forms. A novel closed-form double-layer integral for rectangular basis has been developed to accelerate the basic cell construction. To further reduce the computational load, novel dimension reductions based on physical boundary conditions are applied exclusively from the leafy level of the tree to its root. Because of the existence of tremendous amount of ground and power structures in typical package applications, this dimension reduction significantly reduced the computational cost. Benchmarks have demonstrated that Csurf can out-perform available commercial tools by over 100 times for via array structures in multilayer dielectrics. It has been successfully used by the IBM Worldwide Package Development Group in East Fishkill to generate the rules embedded in the EDA developed ERC (Electri Rule Checker) tools. It also has been integrated into on-chip wiring analysis tool AQUAIA for STG clock and wide data-bus design for microprocessor chips.

IBM pioneered the first electromagnetic modeling tools in the early 1970’s and since it has built up an extensive suite of extremely powerful and accurate solvers. These tools have been verified for accuracy with thousands of practical cases, and are continually evolving to encompass new techniques. They provide comprehensive static and full wave electromagnetic modeling functional to both scientific and engineering users. A complete suite has been posted to IBM Alphaworks for both academia and industries.

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