統計方法在次100 奈米電晶體製程最佳化及敏感度分析之研究

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國立交通大學

統計學研究所

碩士論文

統計方法在次 100 奈米電晶體製程最佳化及敏感度分析之研究

A Novel Statistical Methodology for Sub-100nm MOSFET

Fabrication Optimization and Sensitivity Analysis

研究生：周穎劭

指導教授：周幼珍博士

李義明博士

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統計方法在次 100 奈米電晶體製程最佳化及敏感度分析之研究

A Novel Statistical Methodology for Sub-100nm MOSFET Fabrication

Optimization and Sensitivity Analysis

研究生：周穎劭 Student:

Ying

Shao

Chou

指導教授：周幼珍博士

Advisor:

Dr.

Yow-Jen

Jou

李義明博士

Advisor:

Dr.

Yiming

Li

國立交通大學

統計學研究所

碩士論文

A Thesis

Submitted to the Department of Statistics

National Chiao Tung University

in partial Fulfillment of the Requirements

for the Degree of

Master

in

Statistics

July 2005

Hsinchu, Taiwan

中華民國九十四年七月

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c

° Copyright by Ying Shao Chou 2005

All Rights Reserved

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統計方法在次 100 奈米電晶體製程最佳化及敏感度分析之研究

指導教授：周幼珍博士

學生：周穎劭

李義明博士

國立交通大學統計研究所碩士班

摘

要

本文提出一個系統化之統計方法用來研究次 100 奈米金屬氧化物半

導體場效應電晶體製程參數最佳化以及特性敏感度之問題。經過一系

列的篩選實驗、實驗設計、工程用製程元件模擬器、二次反應曲面模

型以及用願望函數(Desirability Function)，吾人可取得製程最佳解，

使得五種重要的元件特性在製程最佳化之後皆能達到所限定的規格

與範圍。這五種元件特性與規格限制分別為：一、臨界電壓望目。二、

次臨界電壓斜率望小。三、漏電流望小。四、飽和電流望目。五、汲

極偏壓導致通道能障降低效應望小。

針對 90 奈米金屬氧化物半導體場效應電晶體之製程，吾人首先透過

篩選實驗，七個顯著的製程因子被挑選出做進一步的中央合成設計，

v

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進而成功地導出各特性的相對應二次反應曲面模型。在模型建構過程

中，所需用到的實驗設計矩陣，有別於傳統常用的中央合成設計需要

七十九個實驗，吾人同時提出其他兩種小型合成設計：一為需四十七

個實驗之較小合成設計，另一為需三十七個實驗的最小合成設計。在

不失工程準確性的要求下，此方法有效地提供了快速的模型建構與製

程最佳化之應用。接著吾人運用所建構的模型，提出最佳的製程參

數，分析了參數及元件特性的敏感度。針對準確性校正後結果再調整

之需求，吾人亦提出一個校正的步驟，讓最佳化後的結果更符合需求。

本研究所使用的方法，在時間、成本、效率的考量上，顯得很有經濟

效益；例如傳統中央合成設計需要花費 316 小時的 TCAD 模擬時間

來取得完整的製程與元件特性資料，吾人使用之最小合成設計只需

148 小時，比傳統中央合成設計減少一半以上的模擬時間，即可獲得

完整的資料。在實際的半導體製程與量測上，此方法亦具有相同的效

益。總之，透過嚴密的統計分析以及實驗驗證之過程，本論文不僅成

功地提供一有系統化的統計方法，來探討製程參數最佳化及特性敏感

度之問題，同時亦可達成工程上所預想的結果。

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A Novel Statistical Methodology for Sub-100nm MOSFET Fabrication

Optimization and Sensitivity Analysis

Student: Ying Shao Chou Advisor: Dr. Yow-Jen Jou

Dr. Yiming Li

Department of Statistics

National Chiao Tung University

Abstract

In this thesis, a fabrication optimization problem of sub-100nm NMOSFET devices is investigated by a systematically statistical method. Based on the screening design, the design of experiment, a well-known industrial used TCAD simulation tool, the response surface methodology, and the optimization using desirability function, the device performances after fabrication have been statistically optimized with respect to five specified physical constraints. They are 1) shifting the value of threshold voltage to the specific target; 2) minimizing the subthreshold slope; 3) minimizing the off-state current; 4) moving the value of on-state current to a specific target; 5) and minimizing the drain-induced barrier lowing.

In the 90nm NMOSFET fabrication, seven significant factors are selected from the screen design and then used to perform a central composite design with seventy-nine experiments. They are: 1) gate length; 2) threshold voltage implant dose; 3) threshold voltage implant energy; 4) punch-through implant dose; 5) punch-through implant energy; 6) oxide growth temperature; and 7) oxide growth time. These results of experiments are then used for building response surface models and applied for the

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optimization and the process sensitivity analysis. Then we perform a verification experiment to verify that the optimal conditions which are suggested by this work indeed give the projected improvement. For the requirement of the adjustment after the accuracy verification, we further provide an empirical procedure to meet this goal. Besides the traditional central composite design, two smaller composite designs; one is a smaller composite design with forty-seven experiments and the other is a smallest composite design with thirty-seven experiments are investigated in this work. These two designs are more computationally economical then the traditional design in terms of accuracy and computing-time.

In this work we use the face central cube design, a special form of the central composite design, to build the response surface models. About 316 hours computing-time is required to perform this design. Two smaller designs could be used instead of this traditional one; a smaller composite design spend about 188 hours to get all of the information, the other smallest composite design only need about 148 hours. More than 50% time is saved in this design, and we find that the device performances which are fabricated by these three optimal recipes are close to each other and also acceptable in our physical constrains. Thus we suggest that engineers could use these economical designs to analyze the fabrication optimization problems rather than the central composite design.

Finally, the purpose of this study is to provide a systematically statistical method to analysis the problems of the parameter optimization and the process sensitivity for the 90nm MOSFET. Through several sequential statistical experiments and simulation verifications, the achieved results are good in terms of several fabrication specifications and accuracy of the targets. We believe that the proposed statistical methodology will benefit the design and fabrication of nanoscale MOSFET devices.

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致

謝

這份論文終於算是可以告一個段落了。沒想到真要寫這最後一段感言的時候竟然腦袋一片空白，不知道應該寫些什麼。我的人生因為自己不停的轉換跑道，從管理轉到統計再轉到半導體製程，雖然豐富，但也搞的自己的生活充滿了兵荒馬亂和不適應。不可否認，因為這些經歷讓自己成長了不少，一路走來，歡笑的印象總是比淚水多，我很感謝在這段時期有非常多的師長幫助和朋友相挺，才能讓我現在可以有一個美好的結束，沒有大家的幫助，就沒有現在的成果。感謝我的指導老師周幼珍老師總是像媽媽一樣的關心我，給我很多精神上的自由和實質上的幫助；也感謝我另一個指導老師李義明老師，感謝老師總是包容我所有的任意妄為，總是很仔細很有邏輯性的在指導著我論文的方向脈絡，我想如果沒有老師在幫我層層把關，這份論文沒有辦法完成；另外感謝彭松村老師、趙天生老師、陳志榮老師來當我的口試委員，因為他們的指導與建議，讓我的論文可以更加完備，更符合統計和工程雙方面的觀點。我還要感謝交通大學諮商中心的閔肖蔓老師，感謝他在我人生迷惘的時候，用他的理智與同理心，讓我學會如何冷靜的看待問題並且解決問題，使我在無助且慌亂的時候，找出方向並且成長。研究室方面，我要感謝李介文學長特意每天撥空教我很多製程上面的觀念，真的讓我獲益匪淺；感謝陳璞學長幫了我很多忙，學長總是可以一眼看出這篇論文還有什麼地方有不足或瑕疵，並且替我想辦法解決我所遭遇的困難。感謝陳穎峙學長把我教會如何使用模擬器。還有感謝紹銘學長、宏穆、緯昕學弟，總是無條件的當我論文問題的求救對象。傳盛學長、建松學弟、宏榮學弟，也幫了我很多，加上柏賢學弟，在此一並感謝。統研所方面，感謝景嵐、豐洋，以及育仕、玉均、如美、秀仁；因為你們的關心，帶給我歡笑，鼓勵我，替我加油打氣，以及平時貼心的舉動與由衷的關懷，讓我可以在遇到苦悶的研究瓶頸時，還可以擁有瘋狂大笑的發洩管道。統研所真 ix

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的是一個溫暖的好地方，認識你們我實在是非常的幸運與開心，也讓我有可以撐下去的動力，讓我擁有高興的好情緒。還有很多統研所的學弟妹，婉文、沛君、清峰、奕倫、國偉，大家都很認真的在博感情，互相幫忙，互相砥礪，讓我很感動，不知道要怎麼說，總之很感謝你們大家。我還要感謝我最親愛的室友蘭綺和我的前室友怡君，我的苦我的淚我的笑我的瘋，因為你們的陪伴，讓這些情感都成為了美好且有意義的回憶。另外感謝我的摯友瑞萍，謝謝你在我苦悶的那一陣子，每天都講一件開心的事情給我聽讓我開心。尤其是最後待在交大那段慌亂且忙碌的時光中，因為有你們逗我陪我，讓我得以平心靜氣，一步一步的走向目標。我更應該要感謝的，是我的男朋友承文，一路走來風風雨雨，不論發生什麼事情，就像是個中流砥柱一樣的矗立在那裡，給我依靠，平撫我的情緒，一起幫我解決我的問題，給我歡樂，陪我吃苦。當我情緒的支撐點，讓我從崩潰中站起來，從不開心中平靜，從困難挫折中成長，繼而能夠順利的解決問題，通過一道道的關卡。沒有你，不會有現在。也感謝我男朋友的爸爸媽媽，他們就像照顧親生女兒一般的照顧我，讓我在身心疲累之餘又多了一個避風港可以休息。最後我最應該感謝的，是我的媽媽，爸爸，和我的姊姊，沒有你們無私的付出和關懷，我早就放棄了，不可能完成這篇論文。出外這兩年讓你們擔心很多事情，爸爸媽媽從來不讓我煩惱家裡的任何事，也都毫無保留的供應我任何的需要，因為這份愛與支持，讓我能夠毫無顧慮的勇敢的任性的在外面闖蕩，現在我終於可以完成論文畢業了，真的很感謝你們。感謝這段期間大家對我的包容、關懷與愛護。這篇論文，這個工作，以及我在交大的一切成長，沒有你們，是完全沒有辦法達成的，一切的功勞都歸因於全部的人。謝謝大家一直挺我鼓勵我，使我順順利利的度過這段非凡且精采的日子。在此將這篇論文獻給所有關心我以及我所愛的人，謝謝你們。周穎劭謹誌中華民國九十四年七月于風城交大 x

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List of Figures

1.1 Procedure flow chart in this work. . . 4

1.2 The flowchart of the device manufacturing process. . . 8

1.3 The flowchart of the TCAD simulation and the circuit simulation. . . 9

1.4 Close-up of the gate-drain corner of an nMOSFET with finite element grid. TCAD simulators solve physical partial differential equations on a finite element grid representing a discretized model of the physical device. . . 10

2.1 Systematic scheme for sub-100nm MOSFET fabrication optimization and applications. . . 18

2.2 Central composite design for 3 factors. . . 23

2.3 Comparison of the CCC design and the CCF design. . . 24

2.4 Comparison of the three types of central composite designs. . . 25 2.5 The contour plots of the threshold voltage and the subthreshold slope. Two

factors are the threshold implant dose and the punch-through implant energy. 41 xvi

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2.6 Region of the optimum found by overlaying threshold voltage and sub-threshold slope response surface. The deep gray part means the optimal region through the contour overlap. . . 42 2.7 Individual desirability functions for simultaneous optimization. . . 44 3.1 90nm NMOSFET device structure obtained from nominal process

parame-ter setting. . . 53 3.2 Id-Vg curves of the 90nm NMOSFET device structure obtained from the

nominal case process parameter setting. . . 54 4.1 A plot of the half-normal effect plot for the threshold voltage. . . 60 4.2 A plot of the half-normal effect plot for the subthreshold slope. . . 61 4.3 A plot of the half-normal effect plot for the off-state current using log

trans-formation. . . 62 4.4 A plot of the half-normal effect plot for the on-state current. . . 63 4.5 A plot of the half-normal effect plot for the drain-induced barrier lowing

using log transformation. . . 64 5.1 The scatter plot matrix of the five physical quantities. . . 72 6.1 Residual normal probability plot of the 90nm NMOSFET Vth’s response

surface model using CCF design. . . 75 xvii

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6.2 Residual normal probability plot of the 90nm NMOSFET SS’ response surface model using CCF design. . . 76 6.3 Residual normal probability plot of the 90nm NMOSFET log(Ioff)’s

re-sponse surface model using CCF design. . . 77 6.4 Residual normal probability plot of the 90nm NMOSFET Idsat’s response

surface model using CCF design. . . 78 6.5 Residual normal probability plot of the 90nm NMOSFET log(DIBL)’s

re-sponse surface model using CCF design. . . 79 6.6 Residual normal probability plot of the 90nm NMOSFET Vth’s response

surface model using SCD1 design. . . 82 6.7 Residual normal probability plot of the 90nm NMOSFET SS’ response

surface model using SCD1 design. . . 83 6.8 Residual normal probability plot of the 90nm NMOSFET log(Ioff)’s

re-sponse surface model using SCD1 design. . . 84 6.9 Residual normal probability plot of the 90nm NMOSFET Idsat’s response

surface model using SCD1 design. . . 85 6.10 Residual normal probability plot of the 90nm NMOSFET log(DIBL)’s

re-sponse surface model using SCD1 design. . . 86 xviii

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6.11 Residual normal probability plot of the 90nm NMOSFET Vth’s response surface model using SCD2 design. . . 89 6.12 Residual normal probability plot of the 90nm NMOSFET SS’ response

surface model using SCD2 design. . . 90 6.13 Residual normal probability plot of the 90nm NMOSFET log(Ioff)’s

re-sponse surface model using SCD2 design. . . 91 6.14 Residual normal probability plot of the 90nm NMOSFET Idsat’s response

surface model using SCD2 design. . . 92 6.15 Residual normal probability plot of the 90nm NMOSFET log(DIBL)’s

re-sponse surface model using SCD2 design. . . 93

8.1 The Vth’s contour plot of the optimal solution for the CCF design using the full 2nd_{order response surface models. . . 111}

8.2 The SS’ contour plot of the optimal solution for the CCF design using the full 2nd_{order response surface models. . . 112}

8.3 The log(Ioff)’s contour plot of the optimal solution for the CCF design using the full 2nd _{order response surface models. . . 113}

8.4 The Idsat’s contour plot of the optimal solution for the CCF design using the full 2nd_{order response surface models. . . 114}

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8.5 The log(DIBL)’s contour plot of the optimal solution for the CCF design using the full 2nd_{order response surface models. . . 115}

8.6 The Vth’s contour plot of the optimal solution for the SCD1 design using the full 2nd_{order response surface models. . . 116}

8.7 The SS’ contour plot of the optimal solution for the SCD1 design using the full 2nd _{order response surface models. . . 117}

8.8 The log(Ioff)’s contour plot of the optimal solution for the SCD1 design using the full 2nd_{order response surface models. . . 118}

8.9 The Idsat’s contour plot of the optimal solution for the SCD1 design using the full 2nd_{order response surface models. . . 119}

8.10 The log(DIBL)’s contour plot of the optimal solution for the SCD1 design using the full 2nd_{order response surface models. . . 120}

8.11 The Vth’s contour plot of the optimal solution for the SCD2 design using the full 2nd_{order response surface models. . . 121}

8.12 The SS’ contour plot of the optimal solution for the SCD2 design using the full 2nd _{order response surface models. . . 122}

8.13 The log(Ioff)’s contour plot of the optimal solution for the SCD2 design using the full 2nd_{order response surface models. . . 123}

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8.14 The Idsat’s contour plot of the optimal solution for the SCD2 design using the full 2nd_{order response surface models. . . 124}

8.15 The log(DIBL)’s contour plot of the optimal solution for the SCD2 design using the full 2nd _{order response surface models. . . 125}

8.16 The Vth’s contour plot of the optimal solution for the CCF design using the stepwise regression models. . . 128 8.17 The SS’ contour plot of the optimal solution for the CCF design using the

stepwise regression models. . . 129 8.18 The log(Ioff)’s contour plot of the optimal solution for the CCF design

using the stepwise regression models. . . 130 8.19 The Idsat’s contour plot of the optimal solution for the CCF design using

the stepwise regression models. . . 131 8.20 The log(DIBL)’s contour plot of the optimal solution for the CCF design

using the stepwise regression models. . . 132 8.21 The Vth’s contour plot of the optimal solution for the SCD1 design using

the stepwise regression models. . . 133 8.22 The SS’ contour plot of the optimal solution for the SCD1 design using the

stepwise regression models. . . 134 xxi

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8.23 The log(Ioff)’s contour plot of the optimal solution for the SCD1 design using the stepwise regression models. . . 135 8.24 The Idsat’s contour plot of the optimal solution for the SCD1 design using

the stepwise regression models. . . 136 8.25 The log(DIBL)’s contour plot of the optimal solution for the SCD1 design

using the stepwise regression models. . . 137 8.26 The Vth’s contour plot of the optimal solution for the SCD2 design using

the stepwise regression models. . . 138 8.27 The SS’ contour plot of the optimal solution for the SCD2 design using the

stepwise regression models. . . 139 8.28 The log(Ioff)’s contour plot of the optimal solution for the SCD2 design

using the stepwise regression models. . . 140 8.29 The Idsat’s contour plot of the optimal solution for the SCD2 design using

the stepwise regression models. . . 141 8.30 The log(DIBL)’s contour plot of the optimal solution for the SCD2 design

using the stepwise regression models. . . 142 9.1 Statistical distribution of the model for the threshold voltage in the SCD1

design, which are calculated by the sensitivity analysis and using the full 2nd_{order response surface models, where the unit of Vth is V. . . 148}

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9.2 Statistical distribution of the model for the subthreshold slope in the SCD1 design, which are calculated by the sensitivity analysis and using the full 2nd _{order response surface models, where the unit of SS is V/dec. . . 149}

9.3 Statistical distribution of the model for the log off-state current in the SCD1 design, which are calculated by the sensitivity analysis and using the full 2nd _{order response surface models, where the unit of log(Ioff) is A/µm. . . 150}

9.4 Statistical distribution of the model for the on-state current in the SCD1 design, which are calculated by the sensitivity analysis and using the full 2nd _{order response surface models, where the unit of Idsat is A/µm. . . 151}

9.5 Statistical distribution of the model for the log drain-induced barrier lowing in the SCD1 design, which are calculated by the sensitivity analysis and us-ing the full 2nd_{order response surface models, where the unit of log(DIBL)}

is V. . . 152 10.1 The log Id-Vg curves of the 90nm NMOSFET device structure obtained

from the nominal case and all desings parameter settings. . . 157 10.2 The Id-Vg curves of the 90nm NMOSFET device structure obtained from

the nominal case and all designs parameter settings. . . 158 11.1 Flow diagram of TCAD driven process design to circuit analysis. . . 168 11.2 Procedure flow chart for the future work. . . 169

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A.1 The operability region and the square (solid line) and circular (dashed curve) regions of interest in two dimensions. The capital word O means the operability region, and the capital word R means the experimental region.184 C.1 Residual normal plots of the CCC design. . . 199 C.2 Residual normal plots of the CCF design. . . 200 C.3 Residual normal plots of the CCI design. . . 201

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List of Tables

2.1 A list of the central composite designs for 2 ≤ k ≤ 10 factors . . . 27 3.1 The physical quantities in the nominal case. . . 54 3.2 Simulation steps and initial parameter settings of the 90nm NMOSFET

process flows for the nominal case. . . 55 4.1 A list of the computed results of the screening design. . . 65 4.2 Experiment levels for all factors. . . 66 5.1 Identified process conditions displaying a significant effect on the 90nm

NMOSFET device characteristics. . . 68 5.2 Comparison among the CCF design, SCD1 design, and SCD2 design. . . . 69 5.3 Response surface design space for the studied 90nm NMOSFET process. . 70 6.1 A list of the 5 calculated response surface models for the 90nm NMOSFET

process using CCF design. . . 74 xxv

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6.2 The 36 coefficients of the response surface models with coded factors using the CCF design. . . 80 6.3 A list of the 5 calculated response surface models for the 90nm NMOSFET

process using the SCD1 design. . . 81 6.4 The 36 coefficients of the response surface models with the coded factors

using the SCD1 design. . . 87 6.5 A list of the 5 calculated response surface models for the 90nm NMOSFET

process using the SCD2 design. . . 88 6.6 The 36 coefficients of the response surface models with coded factors using

the SCD2 design. . . 94

7.1 The final equations of the reduced response models for CCF design in terms of the actual factors for 90nm NMOSFET . . . 98 7.2 Variable selection results of response surface models using the stepwise

regression in the CCF design. . . 100 7.3 A list of the calculated information in the 5 response surface models for the

90nm NMOSFET process after the stepwise regression in the CCF design. . 101 7.4 A list of the calculated information in the 5 response surface models for the

90nm NMOSFET process after the stepwise regression in the SCD1 design. 102 xxvi

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7.5 Variable selection results of response surface models using the stepwise regression in the SCD1 design. . . 103 7.6 A list of the calculated information in the 5 response surface models for the

90nm NMOSFET process after the stepwise regression in the SCD2 design. 104 7.7 Variable selection results of response surface models using the stepwise

regression in the SCD2 design. . . 105

8.1 The constraints of the process parameters. . . 107 8.2 The targets of the responses. . . 107 8.3 Comparison of the recipe between the nominal case and three optimal cases

using the full 2nd _{order response surface models. . . 109}

8.4 Optimal values calculated by the full 2nd_{order response surface models. . . 109}

8.5 Optimal recipes calculated by the full 2nd _{order response surface models.}

The first row in each design is the priority solution in our models, number 2 means the second priority. The first priority recipe is performed to our proposal. . . 110 8.6 The comparison of the recipe between nominal case and three optimal cases

using stepwise regression models. . . 126 8.7 Optimal values calculated by the stepwise regression models. . . 127

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8.8 Optimal recipes calculated by the stepwise regression models. The first row in each design is the priority solution in our models, number 2 means the second priority. The first priority recipe is performed to our proposal. . . 127

9.1 Sensitivity analysis for the studied the 90nm NMOSFET process in the SCD1 design using the full 2nd _{order response surface models, displaying}

calculated mean and standard deviation for resulting physical quantities. . . 145 9.2 Sensitivity analysis for the 90nm NMOSFET process in the CCF design

us-ing the full 2nd _{order response surface models, displaying calculated mean}

and standard deviation for resulting physical quantities. . . 145 9.3 Sensitivity analysis for the 90nm NMOSFET process in the CCF design

us-ing the stepwise regression response surface models, displayus-ing calculated mean and standard deviation for resulting physical quantities. . . 146 9.4 Sensitivity analysis for the 90nm NMOSFET process in the SCD1 design

using the stepwise regression response surface models, displaying calcu-lated mean and standard deviation for resulting physical quantities. . . 146 9.5 Sensitivity analysis for 90nm NMOSFET process in the SCD2 design

us-ing the stepwise regression response surface models, displayus-ing calculated mean and standard deviation for resulting physical quantities. . . 147

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10.1 The comparison of the TCAD results between the nominal case and three

optimal cases using the full 2nd_{order response surface models. . . 154}

10.2 The comparison of the TCAD results between the nominal case and three optimal cases using the stepwise regression models. . . 155

10.3 Desirability values between the nominal case and three optimal cases using the full 2nd_{order response surface models. . . 155}

10.4 Desirability values between the nominal case and three optimal cases using the stepwise regression models. . . 156

10.5 The targets of the responses. . . 161

10.6 The results of the estimated values from the RSM and the verified values from the TCAD. . . 161

10.7 The new adjusted targets of the responses. . . 162

10.8 Comparison of the optimal recipe between the original SCD1 case and the new case through adjustment using the full 2nd_{order response surface models.162} 10.9 The original results and the adjusted results of the verified values from the TCAD. . . 163

C.1 The CCC design space. . . 196

C.2 The CCF design space. . . 196

C.3 The CCI design space. . . 197 xxix

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xxx

C.4 The estimated R2 _{and MSE of the responses in the CCC design. . . 198}

C.5 The estimated R2 _{and MSE of the responses in the CCF design. . . 199}

統計方法在次100 奈米電晶體製程最佳化及敏感度分析之研究

國立交通大學

統計學研究所

碩 士 論 文

統計方法在次 100 奈米電晶體製程最佳化及敏感度分析之研究

A Novel Statistical Methodology for Sub-100nm MOSFET

Fabrication Optimization and Sensitivity Analysis

研 究 生：周穎劭

指導教授：周幼珍 博士

李義明 博士

統計方法在次 100 奈米電晶體製程最佳化及敏感度分析之研究

A Novel Statistical Methodology for Sub-100nm MOSFET Fabrication

Optimization and Sensitivity Analysis

研 究 生：周穎劭 Student:

Ying

Shao

Chou

指導教授：周幼珍 博士

Advisor:

Dr.

Yow-Jen

Jou

李義明 博士

Advisor:

Dr.

Yiming

Li

國立交通大學

統計學研究所

碩 士 論 文

A Thesis

Submitted to the Department of Statistics

National Chiao Tung University

in partial Fulfillment of the Requirements

for the Degree of

Master

in

Statistics

July 2005

Hsinchu, Taiwan

中華民國九十四年七月

c

° Copyright by Ying Shao Chou 2005

All Rights Reserved

統計方法在次 100 奈米電晶體製程最佳化及敏感度分析之研究

指導教授：周幼珍 博士

學生：周穎劭

李義明 博士

國立交通大學 統計研究所 碩士班

摘

要

本文提出一個系統化之統計方法用來研究次 100 奈米金屬氧化物半

導體場效應電晶體製程參數最佳化以及特性敏感度之問題。經過一系

列的篩選實驗、實驗設計、工程用製程元件模擬器、二次反應曲面模

型以及用願望函數(Desirability Function)，吾人可取得製程最佳解，

使得五種重要的元件特性在製程最佳化之後皆能達到所限定的規格

與範圍。這五種元件特性與規格限制分別為：一、臨界電壓望目。二、

次臨界電壓斜率望小。三、漏電流望小。四、飽和電流望目。五、汲

極偏壓導致通道能障降低效應望小。

針對 90 奈米金屬氧化物半導體場效應電晶體之製程，吾人首先透過

篩選實驗，七個顯著的製程因子被挑選出做進一步的中央合成設計，

進而成功地導出各特性的相對應二次反應曲面模型。在模型建構過程

中，所需用到的實驗設計矩陣，有別於傳統常用的中央合成設計需要

七十九個實驗，吾人同時提出其他兩種小型合成設計：一為需四十七

個實驗之較小合成設計，另一為需三十七個實驗的最小合成設計。在

不失工程準確性的要求下，此方法有效地提供了快速的模型建構與製

程最佳化之應用。接著吾人運用所建構的模型，提出最佳的製程參

數，分析了參數及元件特性的敏感度。針對準確性校正後結果再調整

之需求，吾人亦提出一個校正的步驟，讓最佳化後的結果更符合需求。

本研究所使用的方法，在時間、成本、效率的考量上，顯得很有經濟

效益；例如傳統中央合成設計需要花費 316 小時的 TCAD 模擬時間

來取得完整的製程與元件特性資料，吾人使用之最小合成設計只需

148 小時，比傳統中央合成設計減少一半以上的模擬時間，即可獲得

完整的資料。在實際的半導體製程與量測上，此方法亦具有相同的效

益。總之，透過嚴密的統計分析以及實驗驗證之過程，本論文不僅成

功地提供一有系統化的統計方法，來探討製程參數最佳化及特性敏感

度之問題，同時亦可達成工程上所預想的結果。

A Novel Statistical Methodology for Sub-100nm MOSFET Fabrication

Optimization and Sensitivity Analysis

Student: Ying Shao Chou Advisor: Dr. Yow-Jen Jou

碩士論文

研究生：周穎劭

指導教授：周幼珍博士

李義明博士

研究生：周穎劭 Student:

指導教授：周幼珍博士

李義明博士

碩士論文

指導教授：周幼珍博士

李義明博士

國立交通大學統計研究所碩士班