Hsiu-Yu Lai Ting-Chi Wang A TPL-Friendly Legalizer for Standard Cell Based Design SASIMI ‘15.
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Transcript of Hsiu-Yu Lai Ting-Chi Wang A TPL-Friendly Legalizer for Standard Cell Based Design SASIMI ‘15.
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Hsiu-Yu Lai
Ting-Chi Wang
A TPL-Friendly Legalizer for Standard Cell Based Design
SASIMI ‘15
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Outline
Introduction Problem Formulation The Legalizer Experimental Results Conclusion
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Introduction
As the shrinking of the feature size patterning lithography (DPL) is no longer enough for 14/10nm technology node
Triple patterning lithography (TPL) is a nature extension from DPL
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The TPL decomposition problem in two types of standard cell based design pre-colored design
Foundries
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un-colored design Design houses
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Most of the related work focus on minimal conflicts and stitches for TPL layout decomposition during or after the routing stage
TPL-friendly standard cell legalization problem in order to move the TPL layout decomposition issue to an earlier design stage
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Problem Formulation
No prior work on standard cell legalization considers the possibility of reordering cells and inserting white space to help resolve TPL conflicts
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Given Global placement of standard cells
Do Produce a legal placement
Objective Primary objective is to minimize the total number
of TPL coloring conflicts Secondary objective is to minimize the total
amount of cell displacement
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The Legalizer
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Cell Reordering
Since each standard cell from the cell library has a fixed layout
Pre-construct a table to store the minimum number of sites that has to keep between any two cells such that no pair of polygons cells has a TPL coloring violation
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Cell Reordering by Grouping
Divide a row of cells into small groups and consider all cell permutations in each group
For each cell permutation, a cost measuring the difference between the permutation and the original cell order is calculated
The total amount of white space it needs to reserve between each pair of adjacent cells in the permutation is also calculated
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To consider cell displacement The amount of position change from the original
order as the cost
EX:
Original : ABCDE
A permutation : BADCE
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To consider the amount of white space that needs to be reserved for a permutation
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A reordering graph
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Amplify the amount of white space on each node or edge in the graph
Multiplying it by a constant to minimize the number of sites reserved for avoiding any TPL spacing violation
Find a shortest path from a node in the first group to a node in the last group
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Refinement
After reordering cells in a row, there may still leave room for further reducing required white space by swapping cells
Swapping a cell that has white space reserved to its left or right with another cell
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White Space Insertion
If a row has enough space for all of white spaces we reserve, we will insert all of them in the row
Dynamic programming based linear placement algorithm to place the cells and blank cells
Try to further minimize the total displacement
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When a row is not wide enough, we need to choose which white space should we insert
In order to reduce TPL conflicts as many as possible
First sort the set of white spaces reserved in adjacent cells in a non-decrease order of their amounts
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Experimental Results
Implemented in C++ Linux workstation with an Intel Xeon 2.4
GHz and 12G memory
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Comparisons of Algorithm
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Comparisons of Group Size
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Conclusion
Presented a TPL-friendly legalizer that adopts cell reordering and white space insertion
A possible future work is to combine our legalizer and a TPL-aware detailed placer, to achieve a TPL conflict-free placement