Abstract A new Open Artwork System Interchange Standard (OASIS) has been recently proposed for replacing the GDSII format. A primary objective of the new OASIS format is to enhance the compressibility of layout data. We compare the data compression capability of the Full OASIS set of operators with those also present in GDSII, which we refer to as the Restricted OASIS format. We measure the compression quality of the OASIS and GDSII operators in two contexts: (1) Compressible fill generation, where the fill amounts are specified and compressible fill is then generated, and (2) Post-fill data compression, when fill has already been generated and is then compressed. Our experimental results confirm the advantages of the OASIS compression operators: compressed file sizes using the Full OASIS format are on average about twice as small as those obtained using the Restricted OASIS format. We propose new OASIS-based compression algorithms which outperform industry physical verification tools. We also evaluate the respective merits of the individual repetition operators in OASIS and suggest possible improvements to the OASIS repetition operators.

Motivation Dummy Fill is added to VLSI layouts to reduce manufacturing variation, but it explodes layout data volume and creates a bottle neck in the design-to-manufacturing handoff. We require dummy fill compression. Filled layout with dummy fill grouped in 9 repetitions Post-CMP ILD thickness Features Dummy featuresPost-CMP ILD thickness Dummy fill equalizes spatial layout density and improves CMP uniformity

Full OASIS Repetition Types Geometry Compression Operators TYPE 4 TYPE 5 TYPE 6 TYPE 7 TYPE 8 The OASIS Format An OASIS file is a sequence of bytes divided into records. A fill feature (rectangle, polygon, trapezoid, circle, etc.) is represented by the corresponding OASIS record format. OASIS defines eight repetition types. A repetition represents an “array” of records, and thus enables compression of fill data. Restricted OASIS = “GDSII AREF” TYPE 1 TYPE 2 TYPE 3

Compression ratio of a repetition: R c = ( M  N  A)/(A+R) M,N = #rows, columns in a fill feature array; A = #integers needed to represent a single fill feature; R = #integers needed to store additional information when using repetitions Compressibility TypeDescription (M, N, P > 1)RcRc Asymptotic R c 1 M  N matrix with uniform orthogonal spacing 7MN/11MN 2N vector with uniform horizontal spacing7N/9N 3M vector with uniform vertical spacing7M/9M 4N vector with non-uniform horizontal spacing7N/(7+N)7 5M vector with non-uniform vertical spacing7M/(7+M)7 6 M  N repetition with uniform and (potentially) diagonal displacements 7MN/11 ~ 7MN/13 MN 7 P repetition with uniform and (potentially) diagonal displacements 7P/9 ~ 7P/10 P 8 P-element repetition with uniform and (potentially) diagonal displacements 7P/(6+2P)3.5

Generic Strategy Generic Strategy for both Compressible Fill Generation and Fill Compression Find a repetition of Type 1, 2, 3, 6, or 7 (types with maximum compression ratio R c ) If R c > limitCR, output (= accept) the repetition and update fill data Repeat Steps 1 and 2 until no repetition exists with R c > limitCR Find a repetition of Type 4, 5 to satisfy the fill requirements (compressible fill generation case) or to cover the remaining fill geometries (fill compression case) Experimentally, limitCR = 5.0 is chosen for all algorithms. Types 1 and 6 appear to be the most powerful operators, followed by Types 2, 3 and 7. Types 4 and 5 appear least powerful.

Problem: Given a design rule-correct layout L consisting of m  n tiles, and fill site arrays for each tile, create a minimum size compressed fill pattern file F using OASIS repetitions, such that the window density variation in the layout L+F is within the given density bounds (L b,U b ). Strict greedy heuristic: iteratively find an available repetition with largest compression ratio O(n 5 ) time complexity: provides good solutions but is impractical Greedy speedup scheme: trade off between time complexity and compression performance by picking an acceptable, rather than best- possible, repetition  time complexity becomes practical. Use Greedy speedup of compressible fill generation algorithm to compare between availability of Repetition Types 1-7 (Full OASIS) and availability of only Repetition Types 1-3 (GDSII = Restricted OASIS) Compressible Fill Generation

Compressible Fill Generation Results FULL OASIS vs. RESTRICTED OASIS RESULT: Full OASIS compression operators yield file sizes approximately one-half those obtained with Restricted OASIS compression operators. This confirms a definite, but limited, advantage of OASIS over GDSII Stream format.

Problem: Given a fill layout, output a minimum-size compressed representation using OASIS repetition types. Exhaustive-Search Based Greedy (ESBG) For each fill geometry, find all repetitions of Types {1, 2, 3, 6, 7} originating at that site, and output (= accept) the repetition with maximum compression ratio R c >limitCR Update list of remaining uncovered fill geometries Use perfect bipartite matching to find minimum cover of remaining fill layout sites using repetition Types {4, 5} Regularity-Search Based Greedy (RSBG) Use spatial regularity-detection algorithm (KahngRobins91) to find maximal sets of regularly spaced collinear sites (1-D lattices), or maximal regularly spaced 2-D lattices of sites Construct instances of repetition Types by chaining together lattices that have same periodicity Use perfect bipartite matching to find minimum cover of remaining fill layout sites using repetition Types {4, 5} Fill Compression

FULL vs. RESTRICTED, ESBG vs. RSBG : Run both ESBG and RSBG using either Full OASIS or Restricted OASIS compression operators RESULT: Full OASIS reduces data volume by 1.4x (2x) over Restricted OASIS when using ESBG (RSBG) compression RESULT: ESBG (RSBG) is superior on Restricted (Full) OASIS RESULT: Repetition Types 6, 7 helpful only in special “tilted fill” context; Types 4, 5 surprisingly valuable for compression We suggest a new Repetition Type = product of Types 4 and 5 to achieve an asymptotically intermediate level of compression. Fill Compression Results