Parameter extraction, or simulation, of electronic elements has a significant role in the design of modern integrated circuits (IC) operating increasingly at frequencies in the range of hundreds of megahertz. Increasing IC operating frequencies, coupled with reduced, submicron size structures, have made accurate simulation critical for components created within an IC.
As described in the parent application, U.S. Ser. No. 08/904,488, incorporated herein by reference in its entirety, historically, capacitive elements were computed from the geometry of an IC by using general purpose field solvers based on finite-difference or finite-element tools. Typical of these tools of the prior art is a requirement for volume or surface discretization. For finite-element tools, solutions are computed for large numbers of points descriptive of the electric field of the volume of an element within a device. Using this approach, as frequencies go up, the number of points required for a simulation also goes up resulting in large computation time and memory use for the completion of one simulation.
Another approach of the prior art is the use of integral equation methods. An example of this approach is FastCap: A multipole accelerated 3-D capacitance extraction program IEEE Transaction on Computer Aided Design 10(10):1447-1459, November 1991, incorporated herein by reference in its entirety.
Integral formulations have certain advantages over finite-difference or finite-element tools. These include good conditioning, reduction in dimensionality and ease in dealing with layered dielectrics. Discretizing an element using integral equations generally leads to a linear system of equations represented conveniently using a "dense" matrix. The inverse of this matrix is required to solve for the parameter being sought. Previous solution methods for this "dense" matrix have discretized the integral equation using a first-order collocation. In these methods, the charge density is assumed to be piecewise constant. With this crude approximation, computing accurate answers mandates large discretizations even for simple problems. That is, the matrix to be solved involves a large number of points thus impacting negatively the time required to arrive at a solution.