Kappa:加上漏電流與浮接導體的金屬導線模擬軟體

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研究生：	林明青
論文名稱：	Kappa:加上漏電流與浮接導體的金屬導線模擬軟體 Kappa: An Interconnect Simulator with Tunneling Current and Floating Conductor
指導教授：	張彌彰
口試委員:	張彌彰張克正郭治群
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電子工程研究所 Institute of Electronics Engineering
論文出版年：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	103
中文關鍵詞：	interconnect
相關次數：	點閱：3 下載：0
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隨著半導體技術持續的進步，最小線寬越來越小，元件尺寸及元件間的連結都縮小了。當元件間的導線越來越靠近時，寄生電容、寄生電阻就變得很重要。為了降低寄生電容，研發出低介電質材料以及超低介電質材料。這些材料可以讓由尺寸縮小造成導線間電容值增加的曲線變得平緩一點，這項優點讓這先進技術很快的被採用。然而縮小的導線線間距也會使得漏電流增加，當漏電流增強到一定程度之後就會對介電層造成永久性的破壞。所以如果能將漏電流納入模擬範疇，則可讓導線的模擬技術更上層樓，因此造就了Kappa的誕生。
Kappa 是用以模擬二維導線的軟體。目前市面上已經有可供使用的導線模擬軟體，像是 Raphael。但與元件模擬，例如Medici，相比之下，導線軟體又顯得缺乏一些功能性，例如沒有包含漏電流。針對此缺失，我們在Kappa內裝有三種漏電流模型，分別為：傅勒-諾德翰穿隧電流模型(Fowler-Nordheim tunneling current model)、普爾-夫倫克爾穿隧電流模型(Poole-Frenkel current model)、熱離子發射模型(thermionic emission model)。半導體領域的研究員們可藉由這些漏電流模型分析不同結構下它們的漏電流成份，了解基礎漏電流路徑以及在未來的半導體科技上發展出更完善的導線技術。
對於在介電質中的電場來說這些漏電流模型是屬於非線型方程式。可以使用自洽(self-consistent)方式來求解電場(Poisson’s equation)以及漏電流，也就是得到的解會同時符合泊松方程式(Poisson’s equation)以及漏電流方程式。或者是分開求解，先解出電場，再用電場算出漏電流，稱之為後製作處理(post processing) 。這兩種方法在Kappa都可使用，本論文也包含了這兩種方式的分析與比較。Kappa還包含了多種功能，例如:多種有效率的格點方式以及內建材料標準資料庫等等。總體來說，Kappa是一個為了推進技術發展而生的，有效率且強健的導線模擬軟體。

Contents 
摘要    i
Abstract    ii
誌謝    iv
Contents    v
List of Figures    viii
List of Tables    xi
Chapter 1 Introduction    1
1 Motivation and Purpose    1
2 Thesis Organization    2
Chapter 2 Program Design    4
1 Targeted Structures and Simulations    4
2 Input Format of Kappa    6
3 Program Structure    8
4 Summary    15
Chapter 3 Algorithm    16
1 Matrix Equation    16
1.1 Poisson’s equation    17
1.2 Kirchhoff’s Current Law    19
2 Boundary Condition    20
2.1 Mirror Boundary Condition    20
2.2 Nodes Touching Metal Conductors    22
3 Solution Methods    23
3.1 Conjugate Gradient (CG) Algorithm    23
3.2 Bi-Conjugate Gradient (bi-CG) Method    24
3.3 Gaussian Elimination (GE) Method    24
3.4 Comparison of CG and GE Methods    26
3.5 Newton’s Method    28
Chapter 4 Models, Calculation Methods and Functions    31
1 Models    31
1.1 Linear Models – Basic Electrical Models    31
1.2 Nonlinear Models – Leakage Current Models    32
1.3 Summary    42
2 Calculation Methods    42
2.1 Self-consistent    42
2.2 Post Processing    44
2.3 Summary    48
3 Functions    49
3.1 Creation of Objects    49
3.2 Options    51
3.3 Calculations    57
Chapter 5 Results    62
1 Simulation with Tunneling Current    62
1.1 Application of Three Leakage Current Models Simultaneously with Self-consistent Mechanism    63
1.2 Application of Leakage Current Models Separately with Self-consistent Mechanism    65
1.3 Application of Three Leakage Current Models Simultaneously with Post Processing Mechanism    67
1.4 Summary    69
2 Simulation with Floating Conductor and Dielectric    71
2.1 Simulation of Floating Conductors and Dielectrics Separately    71
2.2 Simulation with Floating Conductors and Dielectrics    75
2.3 Summary    77
3 Comparison between Kappa and Raphael    78
3.1 The Shapes of Items    78
3.2 Simulation Results, Number of Grid Points, and Processing Times    82
3.3 Summary    84
Chapter 6 Summary and Future Work    86
1 Summary    86
2 Future work    87
References    88
Appendix    89

                                

References
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