Abstract: An effective spacing is calculated for each physical spacing between two or more neighbor nets of a target net. Segment boundaries are determined based on the calculated effective spacing to define segments for the target net and one of the segments is selected. A metal configuration for the selected segment is identified and a table of capacitance per-unit-length is accessed for the identified metal configuration to return an above capacitance value, a below capacitance value, a left-side capacitance value, and a right-side capacitance value for the corresponding segment, the table comprising at least a two-dimensional (2D) table. The capacitance values are scaled based on a corresponding segment length determined from the calculated effective spacing. The selecting, identifying, accessing and scaling operations are repeated for each remaining segment of the target net. Optionally, the above, below, left, and right capacitance values for all segments of the target net are summed.

Abstract: An effective spacing is calculated for each physical spacing between two or more neighbor nets of a target net. Segment boundaries are determined based on the calculated effective spacing to define segments for the target net and one of the segments is selected. A metal configuration for the selected segment is identified and a table of capacitance per-unit-length is accessed for the identified metal configuration to return an above capacitance value, a below capacitance value, a left-side capacitance value, and a right-side capacitance value for the corresponding segment, the table comprising at least a two-dimensional (2D) table. The capacitance values are scaled based on a corresponding segment length determined from the calculated effective spacing. The selecting, identifying, accessing and scaling operations are repeated for each remaining segment of the target net. Optionally, the above, below, left, and right capacitance values for all segments of the target net are summed.

Abstract: An integrated circuit includes a target wiring layer, a first adjacent wiring layer above the target wiring layer, and a second adjacent wiring layer below the target wiring layer. Each adjacent wiring layer including crossing wires orthogonal to the target wiring layer. Modify a putative design of the integrated circuit by selecting a target wire; identifying lateral neighbors of the target wire; defining regions of the target wire where the lateral neighbors are homogeneous in cross-section; for each region of the target wire, calculating a wire pattern for the crossing wires; identifying segments within above and below portions of the wire pattern; for each above and below segment pair, obtaining a per-unit-length capacitance from a reduced pattern database; extracting a total parasitic capacitance from the per-unit-length pattern capacitances; and in response to an assessment of the impact of the total parasitic capacitance on circuit performance, producing a modified design.

Abstract: Computing the gradients of capacitances in an integrated circuit chip layout with respect to design and process parameters is described. Included is a shape processing engine in the form of a variational mapping engine and a capacitance calculation engine that includes a gradient calculation engine. The variational mapping engine translates physical parameter variations into variations on the edges of the elementary patterns to which the layout of the integrated circuit is decomposed. The gradient calculation engine computes capacitance gradients by combining information from two sources. The first source consists of pre-existing gradients in a capacitance lookup table. The second source consists of analytical expressions of capacitance correction factors.

Abstract: A computer system selects a shape included in an integrated circuit's layout file, and then selects a first contact and a second contact located on the shape. Next, the computer system computes a nominal resistance between the first contact and the second contact based upon a nominal boundary of the shape, and then computes an adjoint system vector based upon a perturbed boundary of the shape. Using the adjoint system vector, the computer system computes a resistance sensitivity between the first contact and the second contact. In turn, the computer system simulates the integrated circuit using the computed nominal resistance and the computed resistance sensitivity.

Abstract: The Width Bias Calculator (WBC) calculates electrical values by effectively averaging the electrical values to either side of a target wire shape whereby values are approximated for design validation without a significant impact on performance or memory consumption.

Abstract: A computer system selects a shape included in an integrated circuit's layout file, and then selects a first contact and a second contact located on the shape. Next, the computer system computes a nominal resistance between the first contact and the second contact based upon a nominal boundary of the shape, and then computes an adjoint system vector based upon a perturbed boundary of the shape. Using the adjoint system vector, the computer system computes a resistance sensitivity between the first contact and the second contact. In turn, the computer system simulates the integrated circuit using the computed nominal resistance and the computed resistance sensitivity.

Abstract: Computing the gradients of capacitances in an integrated circuit chip layout with respect to design and process parameters is described. Included is a shape processing engine in the form of a variational mapping engine and a capacitance calculation engine that includes a gradient calculation engine. The variational mapping engine translates physical parameter variations into variations on the edges of the elementary patterns to which the layout of the integrated circuit is decomposed. The gradient calculation engine computes capacitance gradients by combining information from two sources. The first source consists of pre-existing gradients in a capacitance lookup table. The second source consists of analytical expressions of capacitance correction factors.

Abstract: The Width Bias Calculator (WBC) calculates electrical values by effectively averaging the electrical values to either side of a target wire shape whereby values are approximated for design validation without a significant impact on performance or memory consumption.

Abstract: A tetrahedralization and triangulation method used with the proximity based rounding method to satisfy topological consistency of tetrahedralization with the bounded precision of a digital computer is described. Tetrahedralization is applied to a VLSI design, and more specifically for solving Maxwell's equation to extract parasitic capacitances and 3-D optical proximity correction applications. The exactness of solving Maxwell's equation and finite element analysis depends on the correctness of the topological properties of the tetrahedralization. Among the important aspects of the correctness of the topological properties is the absence of spurious intersection of two or more tetrahedra. In a typical digital computer, numbers are represented using finite sized words. Round-off errors occur when a long number is represented using the finite word size. As a result, tetrahedralization loses its topological consistency.

Abstract: A tetrahedralization and triangulation method used with the proximity based rounding method to satisfy topological consistency of tetrahedralization with the bounded precision of a digital computer is described. Tetrahedralization is applied to a VLSI design, and more specifically for solving Maxwell's equation to extract parasitic capacitances and 3-D optical proximity correction applications. The exactness of solving Maxwell's equation and finite element analysis depends on the correctness of the topological properties of the tetrahedralization. Among the important aspects of the correctness of the topological properties is the absence of spurious intersection of two or more tetrahedra. In a typical digital computer, numbers are represented using finite sized words. Round-off errors occur when a long number is represented using the finite word size. As a result, tetrahedralization loses its topological consistency.