non-Manhattan Geometries Research Articles

Computational rule-based approach for corner correction of non-Manhattan geometries in mask aligner photolithography.

In proximity mask aligner photolithography, diffraction of light at the mask pattern is the predominant source for image shape distortions such as line end shortening and corner rounding. One established method to mitigate the impact of diffraction is optical proximity correction. This method relies on a deliberate sub-resolution modification of photomask features to counteract such shape distortions, with the goal to improve pattern fidelity and uniformity of printed features. While previously considered for masks featuring only rectangular shapes in horizontal or vertical orientation, called Manhatten geometries, we demonstrate here the capabilities of computational mask aligner lithography by extending optical proximity correction to non-Manhattan geometries. We combine a rigorous simulation method for light propagation with a particle-swarm optimization to identify suitable mask patterns adapt to each occurring feature in the mask. The improvement in pattern quality is demonstrated in experimental prints. Our method extends the use of proximity lithography in optical manufacturing, as required in a multitude of micro-optical devices.

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries

We present an algorithm for two- and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algorithm decreases with better resolution of the input image. Those features render the presented algorithm well suited for fast prototyping while using the most realistic IC geometry data.

A Conformal Mesh for Efficient Planar Electromagnetic Analysis

A planar electromagnetic analysis can provide faster analysis by using larger subsections at the cost of reduced accuracy. However, even if both rectangular and triangular subsections are used, large subsections are not practical for complicated curving planar circuits. This paper describes a method for joining small subsections so that the large subsections so formed can follow the arbitrarily curving edges of a complicated circuit while still inherently including the high edge current. Using such conformal subsections, non-Manhattan geometries can be analyzed efficiently and accurately. This is especially important for continuously curving geometries (like circular spiral inductors), which cannot be efficiently meshed using rectangular and triangular subsections. These conformal subsections retain nearly all the accuracy of small subsection size while also realizing the speed of large subsections, even for complicated geometries.

A DRC-based algorithm for extraction of critical areas for opens in large VLSI circuits

This paper describes an algorithm for the extraction of the critical area for opens. The presented algorithm allows for the analysis of industrial size ICs with non-Manhattan geometry. Illustrative examples of the proposed algorithm, implemented by using design rule checker operations, are presented. It is shown that the extraction of the critical area for realistic size VLSI circuits designs can be done in an acceptable time.