隨著超大型積體電路(VLSI )製程越來越小，要設計一個電路變
得越來越困難且耗時。製程遷徙是指當我們希望可以將電路從當
前的製程轉換到一個比較新穎的製程以提升效能時所做的動作，
而在許多類比電路中設計一個電路並非非常容易的， 因此如果有
一個的製程遷徙工具可以有效率的自動將電路做製程遷徙會是十
分有貢獻的。在將整個電路做縮小時， 可能會有些區塊無法縮小
至目標大小， 導致整個電路中不同區塊的縮放比例不同， 此現象
會導致不同區塊間的連線斷線， 為了解決此一問題我們的方法會
自動的去偵測出在做縮小前與縮小後物件的相連關係， 當發現有
兩個物件在縮小前後的先連關係不同便是我們需要去做繞現的地
方。而做繞線的部分我們會分成兩部分， 第一部分是一個簡單的
迷宮繞線但會產生一些冗贅的轉彎， 因此我們會再做完第二部分
來解決這個問題。實驗結果顯示我們在真實的電路中， 這種問題
可以完全解決， 並且沒有違反製程規定。

With advanced Very-Large-Scale Integration (VLSI) technology, migration method is
more important in analog circuit or some special custom design. Sometimes two blocks in
circuit will be migrated with different scale factor, and result in some connection between
two blocks broken. To solve the problem described before, we propose a scanline base
break point detection method that can construct the connection between polygons efficient.
After compare the connection between non-sizing and sizing, we can obtain all break point
what we need to route. To route the break point, an implicit connection graph base maze
router is proposed, it can fully use the routing resource and get a small bend solution. As
the result, our router use in layout migration method has a DRC clean solution in a real
case.
ii

Acknowledgement i
Abstract ii
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Preliminaries 5
2.1 R*-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Implicit Connection Graph . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Algorithm 7
3.1 Break Point Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.1 Scanline Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.2 Break Polygon Set Detection . . . . . . . . . . . . . . . . . . . . . 13
3.1.3 Angle 45 Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Maze Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Construct Routing Graph . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.2 Pass1:Normal Maze Route . . . . . . . . . . . . . . . . . . . . . . 16
iii
3.2.3 Pass2:Minimal Bend Routing . . . . . . . . . . . . . . . . . . . . 17
4 Experiment Result 19
5 Conclusion 26
Reference 27

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