Yen-Ting Yu Iris Hui-Ru Jiang Yumin Zhang Charles Chiang DRC-Based Hotspot Detection Considering Edge Tolerance and Incomplete Specification ICCAD’14

Outline Introduction Preliminaries Hotspot Detection Framework Experimental Result Conclusion

Introduction In modern manufacturing processes, certain layout configurations are susceptible to lithographic process Patterns with similar layouts could become process- hotspots Represent these similar patterns by a representative pattern with edge tolerances and incomplete specified regions

String-matching-based  Each pattern and layout window are encoded by strings

Overview

The key features of this work  Redefine MTCG and the extraction rules to reflect the impacts of don’t care regions and edge tolerances  DRC searching space reduction technique  Longest common subsequence on strings to handle the impact of don’t care regions

Preliminaries Design Rule Checking (DRC)  Design rules are a set of parameters to ensure the manufacturability of a layout  Fundamental rules include the minimum width, minimum spacing, and minimum enclosure rules

Modified Transitive Closure Graph (MTCG)

Problem Formulation Given  Hotspot pattern with edge tolerances and incompletely specified regions (don’t care regions)  A layout Report  All hotspot locations considering eight possible orientations in the layout

Hotspot Detection Framework

Pattern Enumeration Edge tolerances within a given pattern may lead to different pattern topologies Extend the idea of All-Pair Min-Range Path (APMRP) algorithm to form pattern enumeration algorithm

APMRP  m and n denote the minimum and maximum distance between two edges  minimize the (n – m) value  If m 0 (m, n) set contains three subsets: {(m, −1), (0, 0), (1, n)}  If m < 0 and n = 0 (m, n) set contains two subsets: {(m, −1), (0, 0)}  If m = 0 and n > 0 (m, n) set contains two subsets: {(0, 0), (1, n)}  Else only one subset {(m, n)}

MTCG with Don’t Care Regions and Critical DRC Rule Extraction To use the aid of DRC to realize hotspot detection Interpret all edge constraints to design rules Redefine five types of rules in [1] All rules can be extracted only from C h,h and C v,v, C h,v and C v,h are serve for boundary checking

Rule 1(internal rule)–the width and height of a block tile  find the dimension of each block tile that does not touch the window boundary

Rule 2(external rule)–the distance between two adjacent block tiles  find the dimensions of all space tiles that do not touch the window boundary and are located in between block tiles

Rule 3(diagonal rule)–the diagonal relations between two convex corners of block (space) tiles  find the diagonal relations between any two convex corners of block (space) tiles

Rule 4(longedge rule)–the space or block tile with one edge touching the window boundary

Rule 5(segment rule)–the space tile with two or three adjacent edges touching the window boundary or space tiles

The dimensions of each extracted rule can be represented by a rule rectangle The height and width of a rule rectangle are defined by its corresponding edge constraints

Define two types of don’t care regions  Don’t region with two or three adjacent edges fully facing the window boundaries  Don’t region in between two facing edges of polygons

Rule 6––the space tile with one edge or two opposite edges touching the boundary tiles

Searching Space Reduction A pattern may have eight possible orientations Divide these eight orientations into two sets Generate a runset file for each set and run DRC twice to obtain the locations that hit any generated rule

The region AND technique

Rule Ordering Even a simple range pattern may generate tons of different pattern topologies after pattern enumeration With the region AND technique, how to cover the whole pattern topologies during DRC with fewest DRC rules becomes an issue

The topology covering problem is NP-hard  U = {1, 2, 3, 4, 5} four subsets S = {{1, 2, 3}, {2, 4}, {3, 4}, {4, 5}} subsets{1, 2, 3} {4, 5} A greedy heuristic can be applied to this problem

Rules priority  {internal rule, external rule, diagonal rule} v {longedge rule, sixth rule} v {segment rule}

Candidate Identification Each generated pattern topology is represented by a set of DRC rules Encoding rule rectangles to two strings, one in the vertical, one in the horizontal

To identify the potential hotspot locations in the layout, based on DRC results and rule priorities

Finalization Some locations contain extra polygons that are not related to any of our extracted DRC rules and are not within the don’t care regions

Experimental Result Implemented in the C programming language on a Linux platform Hotspot patterns

Integrate a state-of-the-art industrial DRC engine into our framework

Conclusion Proposed an accurate and efficient hotspot detection framework to handle hotspot patterns with edge tolerances and incompletely specified regions Compared with the state-of-the-art work, our approach can reach promising success rate with significant speedups