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研究生:翁琳妮
研究生(外文):Lannie Weng
論文名稱:45度虛擬線路填充降低化學機械研磨平坦化金屬耦合電容
論文名稱(外文):Coupling Capacitance Minimization by 45-Degree Metal Fill Insertion in Chemical-Mechanical Planarization
指導教授:張耀文張耀文引用關係
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:電子工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:97
語文別:英文
論文頁數:52
中文關鍵詞:虛擬填充耦合電容梯度密度違反時序總計值違反序最大延遲
外文關鍵詞:dummy fill insertioncoupling capacitancegradient densitytotal negative slackworst negative slack
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虛擬金屬填充技術主要應用於晶片設計的後繞線階段,在現今晶圓製程相當著名,主要用來確保晶片內金屬線路密度的一致性並且降低晶片在化學機械研磨平坦化過程中所產生的厚度差異性。我們也必須確保虛擬金屬填充過程中的梯度密度,確保密度在一個特定大小的區域中的厚度差異性不能超過一定的值。這個值通常都由晶片製造廠建議。虛擬金屬填充將導致耦合電容的增加,過高的耦合電容將造成時間延遲近而影響整個晶片的效能。在本論文中,我們提出一套虛擬金屬填充設計流程與45度角虛擬金屬填充的貪婪演算法和強度導向演算法,此設計流程包括設計準備階段、虛擬區域抽取階段、以及虛擬線路填充階段。實驗結果顯示,強度導向演算法的45度電容模型擺放,將有效減少1.9%~14.1%的耦合電容。同時我們也用90度和180度虛擬金屬填充,結果顯示影響晶片效能13 到344兆分之一秒。實驗證實我們所提供的方法,有效減少耦合電容並維持晶片運作效能。
Dummy metal insertion is one of the latest methods to be commonly used in
the post-layout step during design implementation. It is used to keep the metal den-
sity within the chip area at a constant value and reduce the variation in thickness
of chemical-mechanical planarization (CMP) [5]. During metal fill insertion, the
gradient of metal density should be also considered to ensure that the density vari-
ation is not above a threshold within a sliding window. This threshold is typically
recommended by foundry [29]. However, the coupling capacitance is significantly
increased by dummy metal insertion, and the increased coupling capacitance may
cause timing failure in the chip''s performance. This thesis proposes one metal fill
insertion design flow and two algorithms, greedy and force-directed, for inserting
the 45-degree metal fills (diagonal fills). The design flow includes three stages: the
design preparation stage, the dummy fill region extraction stage and the dummy fill
insertion stage. The force-directed algorithm which is applied in the dummy fill in-
sertion stage considers the coupling capacitance as a weight and avoids the impact
of the timing slack.
Diagonal metal fills are simulated and it is concluded that they have less
capacitance than 0-degree metal fills (parallel fills) and 90-degree metal fills (per-
pendicular fills). Compared with 0- and 90-degree metal fills, 45-degree metal fills
could reduce capacitance by 1.9%{14.1%. TNS (total negative slack) and WNS
(worst negative slack) [22] are also maintained with 45-degree metal fills, whereas
0- and 90-degree metal fills increase the timing delay from 13 pico-seconds in ex-
perimental test case of design3 [9] to 344 pico-seconds in experimental test case
of design6. Design3 is the design with clock cycle of 2000 pico-seconds, whereas
design6 is the design with clock cycle of 14000 pico-seconds. Experimental results
based on commercial tools demonstrate that our proposed force-directed methods
can decrease the coupling capacitance and improve timing performance.
Acknowledgements i
Abstract (Chinese) ii
Abstract iii
List of Tables vii
List of Figures viii
Chapter 1. Introduction 1
1.1 Chemical-Mechanical Planarization . . . . . . . . . . . . . . . . . . . . . 2
1.2 Coupling Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Dummy Metal Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Diagonal Dummy Metal Pattern . . . . . . . . . . . . . . . . . . . 6
1.3.2 Different Dummy Patterns of Coupling Comparison . . . . . . . . 7
1.4 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1 Different Patterns of Dummy Fills . . . . . . . . . . . . . . . . . . 12
1.4.2 Coupling Threshold for Dummy Insertion . . . . . . . . . . . . . . 12
1.4.3 Multilevel Analysis of Gradient Constraint . . . . . . . . . . . . . 13
1.5 Our Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Chapter 2. Problem Definition 17
2.1 Gradient Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Dummy Region Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Slack Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Elmore Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Dummy Metal Insertion Problem . . . . . . . . . . . . . . . . . . . . . . 20
Chapter 3. Algorithm 22
3.1 Design Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.1 Partition Database . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.2 Density Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 Multilevel Analysis of Gradient Density Constraint . . . . . . . . . 24
3.1.4 Timing Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Dummy Fill Region Generation . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Dummy Region Extraction . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Dummy Region Density Assignment . . . . . . . . . . . . . . . . . 30
3.3 Dummy Fill Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 Greedy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Force-Directed Algorithm . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Chapter 4. Experimental Results 37
Chapter 5. Conclusions and Future Works 46
Bibliography 48
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