Digital integrated circuits contain two basic components: transistors and interconnections. At low integration levels, circuit speed, packing density, and yield are determined by transistors, but this no longer valid for ULSI circuits. Simple scaling of the circuits components assumes a reduction in the capacitive load of the wires. But the increasing number of transistors on the chip requires a wiring structure with more complexity, which increases the total length of the wiring. Therefore a significant part of power is dissipated by reloading the wiring charges. Currently in high-performance CMOS-microprocessors and dynamic memories a good portion of the power is dissipated by the drivers.
The reduction of the simulation problem from three to two dimensions is hardly ever successful, because of the intrinsically three-dimensional layout of the wirings. Therefore the developed package for the numerical capacitance calculation has two- and three-dimensional capabilities. The numerical calculation of the electrostatic field problem is done by the finite element method. The partitioning of the spatial structure, which is the main problem for the numerical calculation of differential equations for arbitrary three-dimensional domains, has been solved by a method which utilizes the layered structure of wirings. As a second choice for grid generation, a mapping method was also implemented.
The mapping method uses a transfinite interpolation which requires a crude prediscretization of the structure into hexahedrons. As a special feature, these hexahedronal elements may have curved edges.
The layered approach is apt to grid moderately nonplanar structures automatically. The possibility to generate a well suited grid from a simple specification of the wiring structures allows an easy handling of the object geometry even to the occasional user of the package.
The partitioning of the geometry specification into a horizontal and vertical part enables an easy parametrization of the geometry, which can be used in optimization problems for instance. Since the preprocessor contains all basic components for the gridding of two-dimensional objects, an additional two-dimensional preprocessor was implemented to grid cross sections of wiring structures.
The package contains the three previously mentioned preprocessors, the field and capacitance extraction program and a visualization tool with various options to check the grid quality and to visualize the calculated potential distributions.
The numerical calculation of the electrostatic field problem requires the solution of a big linear equation system. The calculation can only be performed by methods which utilize the main memory of the computer in an efficient way. For three-dimensional problems a preconditioned conjugate gradient solver gives the best results in terms of memory consumption and speed.
The field and capacitance calculation program is able to assemble triangular elements for two-dimensional problems and tetrahedronal elements for three-dimensional structures.
A shell allows a guided usage of the various programs.