Smart Analysis Programs is a collection of tools for numerical simulations of electric, magnetic, and thermal phenomena occurring in interconnect lines of integrated circuits. It has been developed by Robert Bauer [9], Rainer Sabelka [10], and Christian Harlander [11]. The package contains preprocessing tools, a finite element simulator, and visualization software. The two- and three-dimensional finite element analysis program STAP is utilized for electric and magnetic field calculation and consequent RLC extraction. It can perform transient and static thermal analysis of interconnects under electrical stress. A transient electric or electro-quasistatic mode is supported for the simulation of delay times or crosstalk.
CUTGRID is the preprocessing tool for two-dimensional solid modeling and a mesh generation, well suited for cross-sectional two-dimensional planes. Its output is a triangular mesh which is used by the finite element simulator STAP as input. Another preprocessing software is the three-dimensional geometry specification and mesh generation tool LAYGRID. The interconnect lines in the integrated circuits build a layered structure. This allows the cumbersome problem of three-dimensional geometry description to be reduced to flat mask definitions and planar or non-planar layers. Thereby, the masks can easily be extracted from a layout description and layers can be derived from cross sections. LAYGRID generates a tetrahedral mesh suitable for further investigations with STAP.
For capacitance extraction STAP solves the Laplace equation for the electric potential in the simulation domain. It is assumed that the electrodes of the capacitor are ideal conductors and the dielectric is an ideal insulator. The surfaces of the electrodes represent Dirichlet boundary conditions. The capacitance is extracted from the electric field energy. STAP provides global grid refinement and quadratic shape scalar functions in order to increase the accuracy of the simulation. The finite element discretization leads often to a large linear equation system, which is solved by a preconditioned conjugate gradient method. Thereby a compressed matrix format for the sparsely occupied stiffness matrix is used in order to achieve an efficient utilization of computer memory.
For simulation of periodic structures STAP uses the so-called periodic boundary conditions. In this case the simulation is performed only in the geometrical period, which is usually much smaller than the entire structure. The periodic boundaries capability of the preprocessing tools CUTGRID and LAYGRID were developed and implemented by Wilfried Wessner [12].
The generated mesh and the resulting two- and three-dimensional distributions can be inspected with the visualisation tool SV.