Closing the Smoothness and Uniformity Gap in Area Fill Synthesis Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s.

Slides:

Advertisements

Similar presentations

On allocations that maximize fairness Uriel Feige Microsoft Research and Weizmann Institute.

Advertisements

Hierarchical Dummy Fill for Process Uniformity Supported by Cadence Design Systems, Inc. NSF, and the Packard Foundation Y. Chen, A. B. Kahng, G. Robins,

New Graph Bipartizations for Double-Exposure, Bright Field Alternating Phase-Shift Mask Layout Andrew B. Kahng (UCSD) Shailesh Vaya (UCLA) Alex Zelikovsky.

1 LP Duality Lecture 13: Feb Min-Max Theorems In bipartite graph, Maximum matching = Minimum Vertex Cover In every graph, Maximum Flow = Minimum.

Solving IPs – Cutting Plane Algorithm General Idea: Begin by solving the LP relaxation of the IP problem. If the LP relaxation results in an integer solution,

Chapter 3 Workforce scheduling.

1 Chapter 11 Here we see cases where the basic LP model can not be used.

Introduction to Sensitivity Analysis Graphical Sensitivity Analysis

Ispd-2007 Repeater Insertion for Concurrent Setup and Hold Time Violations with Power-Delay Trade-Off Salim Chowdhury John Lillis Sun Microsystems University.

Approximation Algorithms Chapter 14: Rounding Applied to Set Cover.

Optimization of thermal processes2007/2008 Optimization of thermal processes Maciej Marek Czestochowa University of Technology Institute of Thermal Machinery.

Dummy Feature Placement for Chemical- mechanical Polishing Uniformity in a Shallow Trench Isolation Process Ruiqi Tian 1,2, Xiaoping Tang 1, D. F. Wong.

Multi-Project Reticle Floorplanning and Wafer Dicing Andrew B. Kahng 1 Ion I. Mandoiu 2 Qinke Wang 1 Xu Xu 1 Alex Zelikovsky 3 (1) CSE Department, University.

Minimum-Buffered Routing of Non- Critical Nets for Slew Rate and Reliability Control Supported by Cadence Design Systems, Inc. and the MARCO Gigascale.

Background: Scan-Based Delay Fault Testing Sequentially apply initialization, launch test vector pairs that differ by 1-bit shift A vector pair induces.

Monte-Carlo Methods for Chemical-Mechanical Planarization on Multiple-Layer and Dual-Material Models Supported by Cadence Design Systems, Inc., NSF, the.

Performance-Impact Limited Area Fill Synthesis

Fill for Shallow Trench Isolation CMP

Design-Manufacturing Interface Formulations and Algorithms Andrew B. Kahng, CSE 291 Spring 2001

Practical Iterated Fill Synthesis for CMP Uniformity Supported by Cadence Design Systems, Inc. Y. Chen, A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UVA.

Computational Methods for Management and Economics Carla Gomes

DPIMM-03 1 Performance-Impact Limited Area Fill Synthesis Yu Chen, Puneet Gupta, Andrew B. Kahng (UCLA, UCSD) Supported by Cadence.

Fill for Shallow Trench Isolation CMP Andrew B. Kahng 1,2 Puneet Sharma 1 Alexander Zelikovsky 3 1 ECE Department, University of California – San Diego.

Foundations for LP Sean Eom. In this course, LP is the foundation of all other quantitative models. Study of LP and related techniques (Integer LP and.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract.

Handling Constraints 報告者 : 王敬育. Many researchers investigated Gas based on floating point representation but the optimization problems they considered.

Integer Programming Difference from linear programming –Variables x i must take on integral values, not real values Lots of interesting problems can be.

UC San Diego Computer Engineering VLSI CAD Laboratory UC San Diego Computer Engineering VLSI CAD Laboratory UC San Diego Computer Engineering VLSI CAD.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract.

Lei He, Andrew B. Kahng*, Kingho Tam, Jinjun Xiong

Approximation Algorithms for MAX-MIN tiling Authors Piotr Berman, Bhaskar DasGupta, S. Muthukrishman S. Muthukrishman Published on Journal of Algorithms,

1 University of Denver Department of Mathematics Department of Computer Science.

Design of Integrated-Circuit Interconnects with Accurate Modeling of Chemical-Mechanical Planarization Lei He, Andrew B. Kahng*, Kingho Tam, Jinjun Xiong.

1 Area Fill Generation With Inherent Data Volume Reduction Yu Chen, Andrew B. Kahng, Gabriel Robins, Alexander Zelikovsky and Yuhong Zheng (UCLA, UCSD,

UC San Diego Computer Engineering. VLSI CAD Laboratory.. UC San Diego Computer EngineeringVLSI CAD Laboratory.. UC San Diego Computer EngineeringVLSI CAD.

Hierarchical Dummy Fill for Process Uniformity Supported by Cadence Design Systems, Inc. Y. Chen, A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA.

RLC Interconnect Modeling and Design Students: Jinjun Xiong, Jun Chen Advisor: Lei He Electrical Engineering Department Design Automation Group (

Abstract A new Open Artwork System Interchange Standard (OASIS) has been recently proposed for replacing the GDSII format. A primary objective of the new.

Hierarchical Dummy Fill for Process Uniformity Supported by Cadence Design Systems, Inc. NSF, and the Packard Foundation Y. Chen, A. B. Kahng, G. Robins,

Linear Programming Operations Research – Engineering and Math Management Sciences – Business Goals for this section  Modeling situations in a linear environment.

Linear Programming Topics General optimization model LP model and assumptions Manufacturing example Characteristics of solutions Sensitivity analysis Excel.

© J. Christopher Beck Lecture 5: Project Planning 2.

ECE 556 Linear Programming Ting-Yuan Wang Electrical and Computer Engineering University of Wisconsin-Madison March

NTUEE 1 Coupling-Constrained Dummy Fill for Density Gradient Minimization Huang-Yu Chen 1, Szu-Jui Chou 2, and Yao-Wen Chang 1 1 National Taiwan University,

3.4 Linear Programming p Optimization - Finding the minimum or maximum value of some quantity. Linear programming is a form of optimization where.

Closing the Smoothness and Uniformity Gap in Area Fill Synthesis Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s.

 Chemical-Mechanical Polishing (CMP)  Rotating pad polishes each layer on wafers to achieve planarized surfaces  Uneven features cause polishing pad.

1 Max 8X 1 + 5X 2 (Weekly profit) subject to 2X 1 + 1X 2  1000 (Plastic) 3X 1 + 4X 2  2400 (Production Time) X 1 + X 2  700 (Total production) X 1.

Branch-and-Cut Valid inequality: an inequality satisfied by all feasible solutions Cut: a valid inequality that is not part of the current formulation.

Integer LP In-class Prob

Non-parametric Methods for Clustering Continuous and Categorical Data Steven X. Wang Dept. of Math. and Stat. York University May 13, 2010.

Character Design and Stamp Algorithms for Character Projection Electron-Beam Lithography P. Du, W. Zhao, S.H. Weng, C.K. Cheng, and R. Graham UC San Diego.

Operations Research.  Operations Research (OR) aims to having the optimization solution for some administrative problems, such as transportation, decision-making,

An Introduction to Linear Programming

Data Driven Resource Allocation for Distributed Learning

Closing the Smoothness and Uniformity Gap in Area Fill Synthesis

Integer Programming (정수계획법)

Linear Programming.

Sensitivity Analysis and

I. Floorplanning with Fixed Modules

Max Z = x1 + x2 2 x1 + 3 x2  6 (1) x2  1.5 (2) x1 - x2  2 (3)

CMPS 3130/6130 Computational Geometry Spring 2017

Chapter 5. The Duality Theorem

Integer Programming (정수계획법)

Constraint satisfaction problems

Flow Feasibility Problems

Operations Research.

Constraint satisfaction problems

Presentation transcript:

Closing the Smoothness and Uniformity Gap in Area Fill Synthesis Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative Y. Chen, A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA and GSU)

overlapping windows Fixed-Dissection Fill Problem Use dummy features to improve layout uniformity for CMP process w w/r tile Fixed-Dissection Fill Problem:  given:  rule-correct layout in n  n region  upper bound U on density  partition layout into nr/w  nr/w fixed dissections  monitor only fixed set of windows consisting of r 2 tiles  fill layout subject to given constraints w.r.t. Min-Var or Min-Fill objective

fixed dissection window with maximum density The Smoothness Gap Fill result will not satisfy the given bounds Despite this gap (observed in 1998), all published filling methods fail to consider this smoothness gap floating window with larger density Fixed-dissection analysis ≠ floating window analysis Gap!

Accurate Layout Density Analysis Optimal extremal-density analysis with complexity inefficient  any arbitrary window contains some shrunk on-grid window  any arbitrary window is contained in some bloated on-grid window  gap between max bloated and max on-grid window accuracy Multi-level density analysis algorithm: Gap between bloated window and on-grid window

Smoothness Gap in Existing Methods Window density variation and violation of max window density in fixed-dissection filling are underestimated Density Variation Testcase Org DenLPGreedyMCIGreedyIMC T/W/rMaxDMinDFDMLFDMLFDMLFDMLFDML Spatial Density Model L1/16/ L1/16/ L2/28/ L2/28/ Effective Density Model L1/16/ L1/16/ L2/28/ L2/28/

Local Density Variations Type I: max density variation of every r neighboring windows in each row of the fixed-dissection Type III: max density variation of every cluster of windows which cover tiles Type II: max density variation of every cluster of windows which cover one tile

Linear Programming Formulations Lipschitz Types: with Combined Objective:  linear summation of Min-Var, Lip-I and Lip-II objectives with specific coefficients:  add Lip-I and Lip-II constraints as well as:

Computational Experience Solutions with best Min-Var objective value do not always have the best value in terms of local smoothness LP with combined objective achieves best comprehensive solutions TestcaseMin-Var LPLipI LPLipII LPLipIII LPComb LP T/W/rDen VLipILipIILipIIILipILipIILipIIIDen VLipILipIILipIII Spatial Density Model L1/16/ L1/16/ L2/28/ L2/28/ Effective Density Model L1/16/ L1/16/ L2/28/ L2/28/

Thank you!