Reduced complexity compression algorithms for direct-write maskless lithography systems

Abstract

Achieving the throughput of one wafer layer per minute with a direct-write maskless lithography system, using 22 nm pixels for 45 nm feature sizes, requires data rates of about 12 Tb/s. In our previous work, we developed a novel lossless compression technique specifically tailored to flattened, rasterized, layout data called Context-Copy-Combinatorial-Code (C4) which exceeds the compression efficiency of all other existing techniques including BZIP2, 2D-LZ, and LZ77, especially under limited decoder buffer size, as required for hardware implementation. In this paper, we present two variations of the C4 algorithm. The first variation, Block C4, lowers the encoding time of C4 by several orders of magnitude, concurrently with lowering the decoder complexity. The second variation which involves replacing hierarchical combinatorial coding part of C4 with Golomb run-length coding, significantly reduces the decoder power and area as compared to Block C4. We refer to this algorithm as Block Golomb Context Copy Code (Block GC3). We present the detailed functional block diagrams of Block C4 and Block GC3 decoders along with their hardware performance estimates as the first step of implementing the writer chip for maskless lithography.

Transform-Based Lossless Image Compression Algorithm for Electron Beam Direct Write Lithography Systems

“…The resulting 5-bit gray level image rasterized on a 250nm grid satisfies the minimum edge spacing of 8nm. For this circuit our algorithm CornerGray runs on the entire 107 Transform-Based Lossless Image Compressionlayout image, but Block C4 [Liu et al (2007)] has a memory shortage/failure. We therefore divided the image in a way to enable the successful application of Block C4.…”

“…Their first algorithm C4 attempts to handle the varying characteristics of layout images by using context prediction and finding repeated regions within an image. Liu et al (2007) later proposed Block C4, which significantly reduces the encoding complexity. Based on the framework of Dai & Zakhor (2006) and Liu et al (2007), Yang & Savari (2010) improved the compression algorithm via a corner-based representation of the Manhattan polygons.…”

“…Liu et al (2007) later proposed Block C4, which significantly reduces the encoding complexity. Based on the framework of Dai & Zakhor (2006) and Liu et al (2007), Yang & Savari (2010) improved the compression algorithm via a corner-based representation of the Manhattan polygons. Their initial algorithm Corner achieves higher compression rates than Block C4 on an irregular circuit.…”

Hardware implementation of Block GC3 lossless compression algorithm for direct-write lithography systems

“…To this end, we have proposed a series of lossless layout compression algorithms for flattened, rasterized data. In particular, Block Golomb Context Copy Coding (Block GC3) has been shown to outperform all existing techniques such as BZIP2, 2D-LZ, and LZ77 in terms of compression efficiency, especially under limited decoder buffer size and hardware complexity, as required for hardware implementation [2] [3].…”

Lossless Compression Algorithms for Post-OPC IC Layout

“…There exist compression algorithms to reduce the mask data size in the rasterized domain for direct write lithography systems [2,3]. There are also algorithms which can be adapted to compress hierarchical IC layout data.…”