多变量控制图的理论分析与实际应用
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摘要
随着超大规模集成电路的发展,集成电路的集成度已达到10 9的量级,而失效率则已经降到10FET,从而对微电路生产的工艺质量和可靠性评价技术提出了新的要求。采用先进的质量保证和评价技术应用在我国的微电路生产方面显得尤为紧迫。本文针对微电路生产的实际特点,在微电路生产工艺质量控制的SPC系统中引入了多变量控制图技术,解决了微电路生产中的多变量受控分析问题,实现了微电路制造中具有多元特性工艺的控制。针对多变量控制图的失控因素的诊断问题,通过同时绘制Hotelling T~2控制图以及控制椭圆,从数据变化以及图形直观等两个方面来判断过程是否受控。另外采用分解多变量统计量方法,确定和解释多变量控制图中出现失控时的失控原因,并结合微电路工艺控制实例分析了单变量和多变量失控之间的关系。结合控制椭圆的扁平程度与变量的相关性,判断过程失控时,是单变量单独作用对统计值T~2的贡献大还是由于变量之间的相关性的作用对统计值T~2的贡献大。
With the development of the VLSI(VLSI: Very Large-scale Integration), a ICs chip could hold more than 10 9transistors, and the failure rate has been reduced to 10 FET level. The requirement has emerged for the new process quality and reliability evaluative technique in the microcircuit manufacture. A multivariate control module is introduced in this paper. Frequently the pattern of points on the multivariate control charts will contain information, about whether the process is under control. It is shown in this paper that with drawing the Hotelling T~2 control charts and the control ellipse at the same time, we can judge whether the process is under control in these two different ways: variable data and the intuitive graphic way. It is also shown in this paper that the interpretation of an out-of-control signal from a T~2 statistic is greatly aided if the corresponding value is partitioned into independent parts.The result from this decomposition could give the information for further analyzing the out-of-control signal. Using the method of decomposition of statistic T~2, with the data analysis of the out-of-control signals, we can finally find out which made the process out of control, univariate variable or the correlation between variables.
With the development of the VLSI(VLSI: Very Large-scale Integration), a ICs chip could hold more than 10 9transistors, and the failure rate has been reduced to 10 FET level. The requirement has emerged for the new process quality and reliability evaluative technique in the microcircuit manufacture. A multivariate control module is introduced in this paper. Frequently the pattern of points on the multivariate control charts will contain information, about whether the process is under control. It is shown in this paper that with drawing the Hotelling T~2 control charts and the control ellipse at the same time, we can judge whether the process is under control in these two different ways: variable data and the intuitive graphic way. It is also shown in this paper that the interpretation of an out-of-control signal from a T~2 statistic is greatly aided if the corresponding value is partitioned into independent parts.The result from this decomposition could give the information for further analyzing the out-of-control signal. Using the method of decomposition of statistic T~2, with the data analysis of the out-of-control signals, we can finally find out which made the process out of control, univariate variable or the correlation between variables.
引文
[1] Robert W. Hoyer and Wayne C. Ellis,“A Graphical Exploration of SPC”, Quality Progress May 1996 & June 1996
[2] Robert L.Mason, A Practical Approach for Interpreting Multivariate T 2 Control Chart Signals, Southwest Research Institute, San Antonio,Oct 1997
[3] Costas J. Spanos, Raymond L. Chen,“Using Qualitative Observations for Process Tuning and Control”, IEEE Trans on Semiconductor Manufacturing, Vol. 10, No. 2, May 1997
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[16] Hayter. A. J, Tsui. K. L,“Identification and Quantification in Multivariate QualityControl”, Journal of Quality Technology, Vol. 26, No. 4, 1994
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[19] William A. Levinson,“Statistical Process Control in Microelectronics Manufacturing”, Semiconductor International, 1995
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[22] Jackson. J. E, Multivariate Quality Control. Communications in Statistical-Theory and Methods, Vol. 14, 1985
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[24] Nola D. Tracy, John C. Young, Robert L. Mason,“Multivariate Control Chart for Individual Observations”, Journal of Quality Technology, Vol. 24, No. 2, April 1992
[25] James Hunter,“In-situ Particle Monitoring Reduces Wafer Defects”, Semiconductor International, Novermber 1993
[26] Douglas W. Cooper, Jan V. Babcock, Frances Dipietro,“Initiating Six Sigma Statistical Quality Control Techniques for Cleanroom Settling Monitor”, Solid State Technology, February 1993
[27] Gary S. May, Jiahua Huang and Costas J. Spanos,“Statistical Experimental Design in Plasma Etch Modeling”, IEEE Trans. on Semiconductor Manufacturing, Vol. 7, No. 1, Feb. 1994
[28] Purnendu K. Mozumder and Gabriel G. Bama,“Statistical Feedback Control of a Plasma Etch Process”, IEEE Trans. On Semiconductor Manufacturing, Vol. 7, No. 1, Feb. 1994
[29] Gregg Bartlett, Jon Dahm, Karen Mappin,“Using‘Six Sigma’to Gauge PECVD”, Semiconductor International, June 1992
[30] Costas J. Spanos,“Statistical Process Control in Semiconductor Manufacturing”, Proceedings of the IEEE, Vol. 80, No. 6, June 1992
[31]吴少雄,多元质量控制的MATLAB实现,福建工程学院学报,第4卷,第1期,2006
[32]王沫然,MATLAB6.0与科学计算,北京:电子工业出版社,2001
[33]盛骤、谢式千、潘承毅,概率论与数理统计,第3版,北京:高等教育出版社,2001
[34]史保华、贾新章、张德胜,微电子器件可靠性,西安:西安电子科技大学,1999
[35]曹定华、罗汉,多元分析基础,北京:科学出版社,2001
[36]陈建国、周六辉,SPC技术及应用,微电子技术,第6期,2003
[37]滕丽、夏志勇、欧昌银,SPC技术在键合工艺中的应用,微电子学,第1期,2007
[38]贾新章、李京苑,统计过程控制与评价——Cpk、S PC、PPM技术和6σ设计,北京:电子工业出版社,2004
[39]宋景涛、方明霞,统计过程控制(SPC)及MATLAB实现,电子质量,第6期,2007
[40]张维铭、施雪忠、楼龙翔,小批量生产的单值多变量控制图,浙江工程学院学报,第17卷,第4期,2000
[41]张皓东,SPC技术在电子元器件生产中的应用,信息技术与标准化,第8期,2005
[42]张公绪、孙静,两种质量多元诊断理论应用实例,中国质量,第8期,2002
[43]司马锡生,多变量统计过程控制图及其判别,化工质量,第1期,1999
[44]司马锡生,多变量统计过程诊断技术的进展,南京化工大学学报,第6期,2000
[45]万长兴,IC SPC分析中的缺陷成团效应和多变量模型研究,西安电子科技大学硕士论文,1999
[46]龚自立,PPM,水平下微电路工艺质量分析和可靠性评价关键技术研究,西安电子科技大学硕士论文,2001
[47]刘长宏,高健,陈新,郑德涛,引线键合工艺参数对封装质量的影响因素分析,《半导体技术》,2007
[2] Robert L.Mason, A Practical Approach for Interpreting Multivariate T 2 Control Chart Signals, Southwest Research Institute, San Antonio,Oct 1997
[3] Costas J. Spanos, Raymond L. Chen,“Using Qualitative Observations for Process Tuning and Control”, IEEE Trans on Semiconductor Manufacturing, Vol. 10, No. 2, May 1997
[4] Sam. Kash. Kachigan, Statistical Analysis, New York, Radius Press, 1986
[5] Jay. Devore, Roxy Peck, Statistics-The Exploration and Analysis of Data, 2th, Wadsworth, Duxbury Press, 1993
[6] Champ. C. W, W. H. Woodall,“Exact Results for Shewhart Control Charts with Supplementary Runs Rules”, Techno metrics, Vol. 29, 1987
[7] Alt. L. W, Multivariate Quality Control, New York, John Wiley & Sons, 1984
[8] Eugene L. Grant, Richard S. Leavenworth, Statistical Quality Control, 6th, McGraw-Hill, 1976
[9] Douglas C. Montgomery, Introduction to Statistical Quality Control, 3th, New York, John Wiley & Sons, 1997
[10] P. H. Singer,“New SPC Standard Set by JEDEC”, Semiconductor International, pp46-48, April 1988, pp56-58, May 1988
[11] P. K. Mozumder and A. J. Strojwas,“Statistical Control of VLSI Fabrication Process”, Proceedings of the IEEE, Vol. 78, No. 2 Feb. 1990
[12] Cynthia. A. Lowry, Douglas C. Montgomery,“A Review of Multivariate Control Charts”, IIE Transactions (1995)27,800-810
[13] James T. McClave, P. George Benson, Terry Sincich, A First Course in Business Statistics, 6th, New Jersey, Prentice Hall, 1995
[14] Kolakowski. D, Bock. R. D,“Multivariate Quality Control”, Biometrics, 37. 541-551
[15] Robert L. Mason, Nola D. Tracy, John C. Young,“Decomposition of T 2 for Multivariate Control Chart Interpretation”, Journal of Quality Technology, Vol. 27, No. 2, April 1995
[16] Hayter. A. J, Tsui. K. L,“Identification and Quantification in Multivariate QualityControl”, Journal of Quality Technology, Vol. 26, No. 4, 1994
[17] Douglas M. Hawkins,“Regression Adjustment for Variables in Multivariate Quality Control”, Journal of Quality Technology, Vol. 25, No.3, July 1993
[18] Nola D. Tracy, John C. Young, Robert L. Mason,“Multivariate Control Charts for Individual Observations”, Journal of Quality Technology, Vol. 24, No. 2, 1992
[19] William A. Levinson,“Statistical Process Control in Microelectronics Manufacturing”, Semiconductor International, 1995
[20] Susan Billat,“Process Control: Covering All of The Bases”, Semiconductor International, September 1993
[21] Murphy. B. J,“Selecting Out-of-control-variables with T 2 Multivariate Quality Control Procedure”, The Statistician, Vol. 36, 1987
[22] Jackson. J. E, Multivariate Quality Control. Communications in Statistical-Theory and Methods, Vol. 14, 1985
[23] Joe H. Sullivan, William H. Woodall,“A Comparison of Multivariate Control Chart for Individual Observations”, Journal of Quality Technology, Vol. 28, No.4, October 1996
[24] Nola D. Tracy, John C. Young, Robert L. Mason,“Multivariate Control Chart for Individual Observations”, Journal of Quality Technology, Vol. 24, No. 2, April 1992
[25] James Hunter,“In-situ Particle Monitoring Reduces Wafer Defects”, Semiconductor International, Novermber 1993
[26] Douglas W. Cooper, Jan V. Babcock, Frances Dipietro,“Initiating Six Sigma Statistical Quality Control Techniques for Cleanroom Settling Monitor”, Solid State Technology, February 1993
[27] Gary S. May, Jiahua Huang and Costas J. Spanos,“Statistical Experimental Design in Plasma Etch Modeling”, IEEE Trans. on Semiconductor Manufacturing, Vol. 7, No. 1, Feb. 1994
[28] Purnendu K. Mozumder and Gabriel G. Bama,“Statistical Feedback Control of a Plasma Etch Process”, IEEE Trans. On Semiconductor Manufacturing, Vol. 7, No. 1, Feb. 1994
[29] Gregg Bartlett, Jon Dahm, Karen Mappin,“Using‘Six Sigma’to Gauge PECVD”, Semiconductor International, June 1992
[30] Costas J. Spanos,“Statistical Process Control in Semiconductor Manufacturing”, Proceedings of the IEEE, Vol. 80, No. 6, June 1992
[31]吴少雄,多元质量控制的MATLAB实现,福建工程学院学报,第4卷,第1期,2006
[32]王沫然,MATLAB6.0与科学计算,北京:电子工业出版社,2001
[33]盛骤、谢式千、潘承毅,概率论与数理统计,第3版,北京:高等教育出版社,2001
[34]史保华、贾新章、张德胜,微电子器件可靠性,西安:西安电子科技大学,1999
[35]曹定华、罗汉,多元分析基础,北京:科学出版社,2001
[36]陈建国、周六辉,SPC技术及应用,微电子技术,第6期,2003
[37]滕丽、夏志勇、欧昌银,SPC技术在键合工艺中的应用,微电子学,第1期,2007
[38]贾新章、李京苑,统计过程控制与评价——Cpk、S PC、PPM技术和6σ设计,北京:电子工业出版社,2004
[39]宋景涛、方明霞,统计过程控制(SPC)及MATLAB实现,电子质量,第6期,2007
[40]张维铭、施雪忠、楼龙翔,小批量生产的单值多变量控制图,浙江工程学院学报,第17卷,第4期,2000
[41]张皓东,SPC技术在电子元器件生产中的应用,信息技术与标准化,第8期,2005
[42]张公绪、孙静,两种质量多元诊断理论应用实例,中国质量,第8期,2002
[43]司马锡生,多变量统计过程控制图及其判别,化工质量,第1期,1999
[44]司马锡生,多变量统计过程诊断技术的进展,南京化工大学学报,第6期,2000
[45]万长兴,IC SPC分析中的缺陷成团效应和多变量模型研究,西安电子科技大学硕士论文,1999
[46]龚自立,PPM,水平下微电路工艺质量分析和可靠性评价关键技术研究,西安电子科技大学硕士论文,2001
[47]刘长宏,高健,陈新,郑德涛,引线键合工艺参数对封装质量的影响因素分析,《半导体技术》,2007