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研究生:徐國展
研究生(外文):Kuo-Chan Hsu
論文名稱:多物理仿真應用於靜電吸盤之晶圓熱傳分析
論文名稱(外文):Multiphysics Modeling and Analysis of Heat Transfer of Wafer on Electrostatic Chuck
指導教授:楊照彥
指導教授(外文):Jaw-Yen Yang
口試委員:黃俊誠湯國樑黃美嬌
口試委員(外文):Juan-Chen HuangGwo-Liang TangMei-Jiau Huang
口試日期:2015-06-24
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:103
語文別:英文
論文頁數:81
中文關鍵詞:靜電吸盤晶圓溫度熱傳遞路徑氮化鋁氧化鋁
外文關鍵詞:Electrostatic Chuck (ESCE-Chuck)Wafer temperatureHeat transfer pathAluminium Nitride (AlN)Aluminium oxide (Al_2 O_3)
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本文為了改善12吋晶圓上的溫度均勻度,氮化鋁及氧化鋁靜電吸盤中的熱傳遞路徑在不同運作參數下被研究,並比較兩種吸盤尺寸(293mm及299mm)的特性。一個等效熱電路的模型及其關係式被本文中所觀察的參數所建構,以便觀察各參數對靜電吸盤熱傳特性的影響。藉由過去文獻的相關實驗及數值模擬結果與本文作比較,並驗證此模型的可靠性。
本文分為兩部分做討論:靜電吸力及晶圓溫度。首先,為了找出最佳的吸附力及避免反覆實驗,一系列與電極相關的參數被個別探討,例如:電極位置、材料性質、粗糙度及所施加電壓。靜電吸盤上的背部冷卻於晶圓溫度及均勻度上扮演著關鍵的角色。本文並顯示出氦氣相較於其它鈍性氣體展現出一最佳的熱傳遞效果,與壓力呈線性關係且在製程中易受環境的變動,有利於控制其特性。統計上的長條圖及標準差被用來判斷晶圓上溫度分佈及其均勻度。其結果顯示氮化鋁吸盤(293mm)於晶圓邊緣處有良好的冷卻效果,但隨著壓力升高卻不利於改善溫度均勻度;然而,由於氧化鋁吸盤(293mm)於晶圓上的溫度震盪效果不顯著,因此均勻度會隨壓力升高而改善。再者,隨著背部氦氣壓力升高,兩種陶瓷材料的靜電吸盤,其熱傳特性的差異會逐漸縮小。本文並探討一大尺寸的靜電吸盤(299mm),相較於氧化鋁吸盤(299mm),其不利於利用氣壓控制溫度均勻度及高溫的特性,指出其氮化鋁吸盤(299mm)具有ㄧ最佳的熱傳效果,並能有效地降低其晶圓溫度並改善其均勻度。


The complete heat transfer path on the AlN and Al2O3 electrostatic chuck (ESC), which were utilized under the various operational conditions, is studied for the potential improvement on the temperature uniformity of the 12-inch wafer. In addition, an identical study on the expanded chuck (299mm) is also carried out for a comparison of the original chuck (293mm). An equivalent thermal circuit analogical to an electrical circuit was illustrated and formulated in terms of variables observed to offer a simple calculation toward a potential optimization. In addition, a good agreement with previous work was achieved and examined the reliability in this model system.
The content of this study is divided in two parts: electrostatic force and wafer temperature. First, in order to optimize the functionality of the attractive force and in avoiding excessive “trial and error” chuck designs, a set of simulations were obtained under various conditions pertaining to the position of the electrode, material, finish and voltage, individually. Second, the ability of backside cooling plays a critical role in the need to control the wafer temperature and its uniformity. It demonstrates that helium exhibited the best performance among He, Ne and Ar, which shows a controllable function with a linear dependence on the pressure and insensitive to the environmental variation during the process. The histogram with a standard deviation (SD), as an indicator of the temperature uniformity, are used to illustrate a fraction of discrete values of the wafer temperature. It discovered the characteristics of the AlN chuck (293mm) exhibited an excellent ability for the wafer cooling on the edge, but unfavorable to the temperature uniformity which Al2O3 chuck (293mm) is capable without temperature oscillations while the backside pressure increases. In addition, it suggested that the characteristics of the different chucks (AlN and Al2O3 ) become more comparable with the increase of the level of the backside pressure. The AlN chuck (299mm) with a linearly dependent on SD and superior in the mean, is regarded as the best one among other chucks, one of which is the Al2O3 chuck (299mm) which SD becomes independent on the pressure and high mean.


ACKNOWLEDGE i
摘要 ii
ABSTRACT iii
CONTENTS v
LIST OF FIGURES vii
NOMENCLATURE xii
Chapter 1 Introduction 1
1.1 Background and Overview 1
1.2 Literature Review 4
1.2.1 Wafer temperature issues 4
1.2.2 Electrostatic chucking issues 7
1.3 Objectives and Scopes 9
1.4 Organization of Thesis 11
Chapter 2 Theory and Governing Equations 14
2.1 Heat Transfer Physics 15
2.1.1 Method of Heat Transfer 15
2.1.2 Principle Dependencies of Temperature 18
2.1.3 Cooper-Mikic-Yovanovich Correlation 21
2.1.4 Equivalent Thermal Resistance Circuits 25
2.2 Navier-Stokes Equations 30
2.3 Electrostatic field 33
2.3.1 Maxwell stress tensor 34
2.3.2 Equivalent electric circuit 36
2.4 Conjugate Interface 38
Chapter 3 Numerical Results and Discussions 42
3.1 Electrostatic Field on the Wafer 42
3.1.1 Electrostatic distribution and electric field 43
3.1.2 Electrostatic pressure 45
3.2 Wafer Temperature Distribution 51
3.2.1 Coefficient of thermal convection 51
3.2.2 Temperature distribution of the wafer 53
3.2.3 Heat transfer path 68
3.2.4 Validation with literature works 71
Chapter 4 Conclusions and Limitations 72
4.1 Conclusions Remarks 72
4.2 Limitations 75
BIBLIOGRAPHY 77


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