Favorable hierarchy detection through Lempel-Ziv coding based algorithm to aid hierarchical fracturing in mask data preparation

Runtime of the Mask Data Preparation (MDP) tool is largely dependent on the hierarchy of the input layout data. In this paper, we present a technique where a hierarchical or flat input design layout or almost flat mask data can be converted into a favorable hierarchical data which can be directly used by MDP tools for fracturing. A favorable hierarchy is a hierarchy of cells where polygons within cells do not overlap with each other even if bounding boxes of cells might overlap with each other. This is an important characteristic which can be intelligently made use of by intra-polygonal operations like fracturing. Otherwise, a mask data preparation (MDP) tool has to take the responsibility for resolving overlaps among polygons, which slows down the processing and increases the data size. MDP on a favorable hierarchy will thus speed up the fracturing or re-fracturing steps and also minimize the output fractured data size, as shown through the experimental results in the paper. In the proposed technique, the favorable hierarchy is generated using a modified version of the Lempel-Ziv (LZ) coding algorithm, which was originally devised for compressing character strings. A hierarchical fracturing algorithm can be employed to work on the favorable hierarchy generated, which will utilize the property of a favorable hierarchy that polygons do not overlap with each other. Apart from the obvious runtime benefits, such a favorable hierarchy allows considerable reduction in fractured data size as most mask data formats allow representation of a hierarchy containing two levels.