Monte-Carlo Methods for Chemical-Mechanical Planarization on Multiple-Layer and Dual-Material Models Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative Y. Chen Y. Chen , , A. B. Kahng, G. Robins, A. A. B. Kahng, G. Robins, A. Zelikovsky Zelikovsky (UCLA, UCSD, UVA and GSU) (UCLA, UCSD, UVA and GSU) http://vlsicad.ucsd.edu http://vlsicad.ucsd.edu
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Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and
Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative. Monte-Carlo Methods for Chemical-Mechanical Planarization on Multiple-Layer and Dual-Material Models. Y. Chen , A. B. Kahng, G. Robins, A. Zelikovsky - PowerPoint PPT Presentation
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Monte-Carlo Methods for Chemical-Mechanical Planarization on
Multiple-Layer and Dual-Material Models
Monte-Carlo Methods for Chemical-Mechanical Planarization on
Multiple-Layer and Dual-Material Models
Supported by Cadence Design Systems, Inc.,NSF, the Packard Foundation, and
State of Georgia’s Yamacraw Initiative
Y. ChenY. Chen,, A. B. Kahng, G. Robins, A. ZelikovskyA. B. Kahng, G. Robins, A. Zelikovsky
(UCLA, UCSD, UVA and GSU)(UCLA, UCSD, UVA and GSU)
http://vlsicad.ucsd.eduhttp://vlsicad.ucsd.edu
OutlineOutline
Layout Density Control for CMP
Our Contributions
STI Dual-Material Dummy Fill
Multiple-layer Oxide CMP Dummy Fill
Summary and Future Research
CMP and Interlevel Dielectric ThicknessCMP and Interlevel Dielectric Thickness
Interlevel-dielectric (ILD) thickness feature density Insert dummy features to decrease variation
ILD thicknessFeatures
Layout Density ModelLayout Density Model Effective Density Model
window density weighted sum of tiles' feature area
weights decrease from center tile to neighboring tiles
Filling ProblemFilling Problem
Given rule-correct layout in n n region
upper bound U on tile density
Fill layout subject to the given constraints
Min-Var objective
minimize density variation subject to upper bound
Min-Fill objective
minimize total amount of filling subject to fixed density variation
LP and Monte-Carlo MethodsLP and Monte-Carlo Methods
Single-layer fill problem linear programming problem
impractical runtime for large layouts
essential rounding error for small tiles
Monte-Carlo method (accurate and efficient) calculate priority of each tile according to its effective
density higher priority of a tile higher probability to be filled pick the tile for next filling randomly if the tile is overfilled, lock all neighboring tiles update priorities of all neighboring tiles
OutlineOutline
Layout Density Control for CMP
Our Contributions new Monte-Carlo methods for STI Min-Var and Min-Fill
objectives LP formulations for a new multiple-layer fill objective new Monte-Carlo methods for multiple-layer fill problem
STI Dual-Material Dummy Fill
Multiple-layer Oxide CMP Dummy Fill
Summary and Future Research
Our ContributionsOur Contributions
Fill problem in STI dual-material CMP
new Monte-Carlo methods for STI Min-Var objective
new Monte-Carlo/Greedy methods with removal phase
for STI Min-Fill objective
Fill problem in Multiple-layer oxide CMP
a LP formulation for a new multiple-layer fill objective
new Monte-Carlo methods
OutlineOutline
Layout Density Control for CMP
STI Dual-Material Dummy Fill
new Monte-Carlo methods for Min-Varr and Min-Fill
objectives
Multiple-layer Oxide CMP Dummy Fill
Summary and Future Research
Shallow Trench Isolation ProcessShallow Trench Isolation Process
Nitride
Silicon
nitride deposition on silicon
Oxide
oxide deposition
Uniformity requirement on CMP in STI
under polish
over polish
etch shallow trenches through nitride silicon
remove excess oxide and partially nitride by CMP
nitride stripping
height difference height difference HH
STI CMP ModelSTI CMP Model
STI post-CMP variation can be controlled by changing the feature density distribution using dummy features insertion
Compressible pad model polishing occurs on both up and down areas after
some step height
Dual-Material polish model two different materials are for top and bottom
surfaces
STI Fill ProblemSTI Fill Problem
Non-linear programming problem
Min-Var objective: minimize max height variation
Previous method (Motorola) dummy feature is added at the location having the
smallest effective density terminates when there is no feasible fill position left
Min-Fill objective: minimize total number of inserted fill, while keeping the given lower bound
Previous method (Motorola) adds dummy features greedily concludes once the given bound for ΔΗ is satisfied
Drawbacks of previous work can not guarantee to find a global minimum since it
is deterministic for Min-Fill, simple termination when the bound is
first met is not sufficient to yield optimal/sub-optimal solutions.
Monte-Carlo Methods for STI Min-VarMonte-Carlo Methods for STI Min-Var
Monte-Carlo method calculate priority of tile(i,j) as H - H (i, j, i’, j’) pick the tile for next filling randomly if the tile is overfilled, lock all neighboring tiles update tile priority
Iterated Monte-Carlo method repeat forever run Min-Var Monte-Carlo with max height difference H exit if no change in minimum height difference delete as much as possible pre-inserted dummy
features while keeping min height difference M
MC/Greedy methods for STI Min-FillMC/Greedy methods for STI Min-Fill
Find a solution with Min-Var objective to satisfy the given lower bound
Modify the solution with respect to Min-Fill objective
Algorithm
Run Min-Var Monte-Carlo / Greedy algorithm
Compute removal priority of each tile
WHILE there exist an unlocked tile DO Choose unlock tile Tij randomly according to priority Delete a dummy feature from Tij
Update the tile’s priority
STI Fill ResultsSTI Fill Results
Methods (Greedy, MC, IGreedy ad IMC) for STI Fill under Min-Var objective
Methods(GreedyI, MCI, GreedyII and MCII) for STI Fill under Min-Fill objective
testcase Orig H final H Area CPU Area CPU Area CPU Area CPUL1/32/4 695.2 395.1 10336 3.1 12003 3.1 8962 3.2 9141 3.2 L1/32/8 999.6 462.7 22091 3.9 20679 3.4 15615 3.6 14754 3.4 L2/28/4 801.8 526.2 7491 4.8 15164 4.9 7593 5.1 6543 5.1 L2/28/8 1124.6 639.8 16808 5.7 26114 5.5 8367 5.9 7142 5.5 L3/28/4 1095.2 563.2 24274 8.2 27114 8 16628 8.6 16142 8.5
MCIIGreedyI MCI GreedyII
OutlineOutline
Layout Density Control for CMP
Our Contributions
STI Dual-Material Dummy Fill
Multiple-layer Oxide CMP Dummy Fill LP formulations for a new multiple-layer fill objective new Monte-Carlo methods
Summary and Future Research
Multiple-Layer Oxide CMPMultiple-Layer Oxide CMP
Each layer except the bottom one can’t assume a perfect flat starting surface
Layer 0
Layer 1
Multiple-layer density model
^ : fast Fourier transform operator
:effective local density
: step height
: local density for layer k
Multiple-Layer Oxide Fill ObjectivesMultiple-Layer Oxide Fill Objectives
LP formulation Min M Subject to:
(Min-Var objective) minimize
sum of density variations on all layers can not guarantee the Min-Var objective on each layer A bad polishing result on intermediate layer may cause problems on