LSAWs技术检测ULSI互连布线low-k介质薄膜杨氏模量的算法研究
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摘要
LSAWs技术是利用声表面波在多层薄膜介质中传播时产生色散的原理来进行样品测量的。
本文研究声表面波在分层媒质中传播模型及色散理论,着重对LSAWs实验系统优化,数据采集及处理等的研究进展进行阐述。
在理论方面,建立了各向同性薄膜/硅衬底的计算模型,通过理论推导,得到了声表面波频散曲线和各参数之间的关系。本文以薄膜的硬度为主要切入点,重点研究了薄膜的杨氏模量同声表面波频散曲线之间的关系,并通过一定的仿真,获得了理论频散曲线的特性。
在实验中,分析各个因素对实验信号的影响,深入研究了信号的屏蔽处理方法,完成了对实验系统的优化,实现了实验微弱信号的采集,并获得了具有可观信噪比的声表面波信号。考虑到匹配的精确性,对实验信号进行了进一步的滤波处理,本文通过对数字滤波器的研究和比较,设计了以凯瑟窗为基础的滤波器,并通过实验数据对窗函数参数进行调试,防止了频谱的泄漏,通过一定的仿真获得了很好的实验信号。为获得实验的频散曲线,研究了快速傅立叶变换的相关理论并随后进行了频谱分析,就DFT变换容易出现的问题,通过末尾增零的方法来减弱频谱的栅栏效应,最终得到了符合要求的实验频散曲线。
本文采用了基于最小二乘原理的曲线平滑算法对实验频散曲线进行处理,并基于实验研究中发现的频散曲线的特殊规律提出了一种基于二分法的快速查找算法,大大提高了查找速度和匹配精度,完成对实验曲线和理论曲线的匹配,自动得到被测样品的杨氏模量。
LSAWs (Laser-generated Surface Acoustic Waves) technology measures samples based on the dispersion of surface acoustic waves when propagating along thin multilayer film media.
This article studies the dissemination models and dispersion theory of surface acoustic waves progating along layered media, focusing on system optimization of LSAWs experiment and research of data acquisition and processing.
In theoretical aspect, the "isotropic thin film / silicon substrate" calculation model was established, the SAW dispersion curve and the relationship between each parameter were obtained. In this paper, taking the hardness of thin films as the main entry point, the relationship between Young's modulus of thin film and the surface wave dispersion curve was investigated, the theoretical dispersion curve characteristics was obtained through simulation.
During experimental procedural, influence of various factors on the experimental signal was analyzed, the shielding and processing methods of the signal were studied, the optimization of the experimental system was completed, the experimental weak signal was acquired, and surface acoustic wave signal with a substantial signal to noise ratio was obtained. Through research and comparison of digital filter, Kaiser window-based filter was designed, and the experimental data were taken to debug window function parameters, thus preventing the leakage of the spectrum. good experimental signal was obtained through simulation. In order to obtain the experimental dispersion curve, relevant theory on the fast Fourier transform was studied and a frequency spectral analysis was carried out. In view of common problems in DFT transform, the fence effect of spectrum was weaken by adding zero at the end of the signal, and ultimately the experimental dispersion curve was obtained in accordance with the requirements.
In this paper, based on the principle of least squares curve smoothing algorithm, the experimental dispersion curve was handled. According to the special law of dispersion curves found during experimental study, a dichotomy-based fast search algorithm was proposed which greatly improved the search speed and matching accuracy. This method can complete the match of experimental curve and theoretical curve and acquire the Young's modulus of measured sample automatically.
本文研究声表面波在分层媒质中传播模型及色散理论,着重对LSAWs实验系统优化,数据采集及处理等的研究进展进行阐述。
在理论方面,建立了各向同性薄膜/硅衬底的计算模型,通过理论推导,得到了声表面波频散曲线和各参数之间的关系。本文以薄膜的硬度为主要切入点,重点研究了薄膜的杨氏模量同声表面波频散曲线之间的关系,并通过一定的仿真,获得了理论频散曲线的特性。
在实验中,分析各个因素对实验信号的影响,深入研究了信号的屏蔽处理方法,完成了对实验系统的优化,实现了实验微弱信号的采集,并获得了具有可观信噪比的声表面波信号。考虑到匹配的精确性,对实验信号进行了进一步的滤波处理,本文通过对数字滤波器的研究和比较,设计了以凯瑟窗为基础的滤波器,并通过实验数据对窗函数参数进行调试,防止了频谱的泄漏,通过一定的仿真获得了很好的实验信号。为获得实验的频散曲线,研究了快速傅立叶变换的相关理论并随后进行了频谱分析,就DFT变换容易出现的问题,通过末尾增零的方法来减弱频谱的栅栏效应,最终得到了符合要求的实验频散曲线。
本文采用了基于最小二乘原理的曲线平滑算法对实验频散曲线进行处理,并基于实验研究中发现的频散曲线的特殊规律提出了一种基于二分法的快速查找算法,大大提高了查找速度和匹配精度,完成对实验曲线和理论曲线的匹配,自动得到被测样品的杨氏模量。
LSAWs (Laser-generated Surface Acoustic Waves) technology measures samples based on the dispersion of surface acoustic waves when propagating along thin multilayer film media.
This article studies the dissemination models and dispersion theory of surface acoustic waves progating along layered media, focusing on system optimization of LSAWs experiment and research of data acquisition and processing.
In theoretical aspect, the "isotropic thin film / silicon substrate" calculation model was established, the SAW dispersion curve and the relationship between each parameter were obtained. In this paper, taking the hardness of thin films as the main entry point, the relationship between Young's modulus of thin film and the surface wave dispersion curve was investigated, the theoretical dispersion curve characteristics was obtained through simulation.
During experimental procedural, influence of various factors on the experimental signal was analyzed, the shielding and processing methods of the signal were studied, the optimization of the experimental system was completed, the experimental weak signal was acquired, and surface acoustic wave signal with a substantial signal to noise ratio was obtained. Through research and comparison of digital filter, Kaiser window-based filter was designed, and the experimental data were taken to debug window function parameters, thus preventing the leakage of the spectrum. good experimental signal was obtained through simulation. In order to obtain the experimental dispersion curve, relevant theory on the fast Fourier transform was studied and a frequency spectral analysis was carried out. In view of common problems in DFT transform, the fence effect of spectrum was weaken by adding zero at the end of the signal, and ultimately the experimental dispersion curve was obtained in accordance with the requirements.
In this paper, based on the principle of least squares curve smoothing algorithm, the experimental dispersion curve was handled. According to the special law of dispersion curves found during experimental study, a dichotomy-based fast search algorithm was proposed which greatly improved the search speed and matching accuracy. This method can complete the match of experimental curve and theoretical curve and acquire the Young's modulus of measured sample automatically.
引文
[1]苏祥林,吴振宇,汪家友等,低k层间介质研究进展,微纳电子技术,2005,42(10):463-468.
[2]蒋昱,吴振宇,汪家友,低k氟化非晶碳层间介质对芯片性能的影响,微纳电子技术,2005,42(8):365-368.
[3]The National Technology Roadmap for Semiconductors, Semiconductor Industry Association, san Joes,CA,1997.
[4]陈倩栎,Konrad Herrmann, Febo Menelao,纳米压痕仪和激光超声技术检测薄膜弹性模量,中国测试技术,2007,33(1):77-81.
[5]Oliver W C,Pharr G M, An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments, Materials Research, 1992, 7(6):1564-1583.
[6]陈隆庆,张统一,薄膜的力学测试技术,机械强度,2001,23(4):413-429.
[7]郑伟涛,薄膜材料与薄膜技术,北京:化工工业出版社,2004.
[8]Schneider D, Schwarz T, Laser-acoustic Thin Film Analyzer Handbook.
[9]黎明,温诗铸,纳米压痕技术及其应用,中国机械工程,2002,13(16):1437-1439.
[10]Hainsworth S V, Chandler H W, Page T F, Analysis of Nanoindentation Load-Displacement Loading Curves. J. Mater. Res., 1996, 11(8):1987-1995.
[11]Nix W D. Elastic and plastic properties of thin films on substrates: nanoindentation techniques, J. Mater. Sci. & Eng, 1997, A234-236:37-44.
[12]武以立,声表面波原理及其在电子技术中的应用,北京:国防工业出版社,1983,8.
[13]Dieter Schneider, Thomas Schwarz, Hans-Joachim Scheibe, et al. Non-destructive Evaluation of diamond and diamond-like carbon films by laser induced surface acoustic waves, Thin Solid Films, 1997,295:107-116.
[14]J.W.Tucker, V.W.Pampton, microwave ultrasonics in Solid State Physics, Amsterdam:North-Holland Publishing Company, 1972,358.
[15]A.A.Oliner, Acoustic Surface Waves, New York : Springer-Verlag Berlin Heidelberg, 1978, 21.
[16]C.M.Flannery,H.Von Kiedrowski, Roughness-caused dispersion of high frequency surface acoustic waves on crystal materials, AIP Conference Proceedings, New York:AIP,2003,1056-1063.
[17]严刚,沈中华,陆建等,利用PVDF检测激光声表面波的实验方法,2007,21(3):261-265.
[18]严刚,徐晓东,陆建等,激光激发源对声表面波的影响,激光技术,2006,30(3):317-319.
[19]ZHANG Sh, Laser ultrasound and nondestructive evaluation in materials. Applied Acoustics,1992,11(4):1-6.
[20]陈佳圭,微弱信号检测,北京:中央广播电视大学出版社,1987.
[21]张伦[译],传感器和信号调节(第二版),北京:清华大学出版社,2003.
[22]于爱民,弱电回路屏蔽信号线屏蔽层接地方式,电力自动化设备,2001(11):61-63.
[23]温世仁,微弱信号检测系统中的接地与屏蔽技术分析,宇航计测技术,2005,25(2):46-49.
[24]张洪涛,数字信号处理,电子工业出版社,2007,36-44.
[25]奥本海姆,数字信号处理(中文版),西安交通大学出版社,210-224.
[26]唐向宏,数字信号处理原理、实现与仿真,电子工业出版社,2006,133-139.
[27]M.H.海因斯,数字信号处理(全美经典),科学出版社,284-285.
[28]胡广书,数字信号处理理论、算法及实现,北京:清华大学出版社,1997,235-245.
[29]奥本海姆,数字信号处理(中文版),西安交通大学出版社,174-181.
[30]唐向宏,数字信号处理原理、实现与仿真,电子工业出版社,2006,275-281.
[31]张登奇,李望移,基于MATLAB的FIR数字滤波器设计,计算机时代,2007,11:47-48.
[32]刘顺至,数字信号处理,电子工业出版社,2004.
[33]柴政,关于数字滤波器设计方式的探讨,通信电源技术,2007, 1:33-35.
[34]关治,陈景良,数值计算方法,北京:清华大学出版社,1990,50-163.
[35]王海涛,朱洪,改进的二分法查找,计算机工程,2006,32(10):60-63.
[36]Cruz R L, A Calculus for Network Delay, Part 1: Network Elements in Isolation. IEEE Transaction on Information Theory, 1991, 37(1):114-131.
[2]蒋昱,吴振宇,汪家友,低k氟化非晶碳层间介质对芯片性能的影响,微纳电子技术,2005,42(8):365-368.
[3]The National Technology Roadmap for Semiconductors, Semiconductor Industry Association, san Joes,CA,1997.
[4]陈倩栎,Konrad Herrmann, Febo Menelao,纳米压痕仪和激光超声技术检测薄膜弹性模量,中国测试技术,2007,33(1):77-81.
[5]Oliver W C,Pharr G M, An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments, Materials Research, 1992, 7(6):1564-1583.
[6]陈隆庆,张统一,薄膜的力学测试技术,机械强度,2001,23(4):413-429.
[7]郑伟涛,薄膜材料与薄膜技术,北京:化工工业出版社,2004.
[8]Schneider D, Schwarz T, Laser-acoustic Thin Film Analyzer Handbook.
[9]黎明,温诗铸,纳米压痕技术及其应用,中国机械工程,2002,13(16):1437-1439.
[10]Hainsworth S V, Chandler H W, Page T F, Analysis of Nanoindentation Load-Displacement Loading Curves. J. Mater. Res., 1996, 11(8):1987-1995.
[11]Nix W D. Elastic and plastic properties of thin films on substrates: nanoindentation techniques, J. Mater. Sci. & Eng, 1997, A234-236:37-44.
[12]武以立,声表面波原理及其在电子技术中的应用,北京:国防工业出版社,1983,8.
[13]Dieter Schneider, Thomas Schwarz, Hans-Joachim Scheibe, et al. Non-destructive Evaluation of diamond and diamond-like carbon films by laser induced surface acoustic waves, Thin Solid Films, 1997,295:107-116.
[14]J.W.Tucker, V.W.Pampton, microwave ultrasonics in Solid State Physics, Amsterdam:North-Holland Publishing Company, 1972,358.
[15]A.A.Oliner, Acoustic Surface Waves, New York : Springer-Verlag Berlin Heidelberg, 1978, 21.
[16]C.M.Flannery,H.Von Kiedrowski, Roughness-caused dispersion of high frequency surface acoustic waves on crystal materials, AIP Conference Proceedings, New York:AIP,2003,1056-1063.
[17]严刚,沈中华,陆建等,利用PVDF检测激光声表面波的实验方法,2007,21(3):261-265.
[18]严刚,徐晓东,陆建等,激光激发源对声表面波的影响,激光技术,2006,30(3):317-319.
[19]ZHANG Sh, Laser ultrasound and nondestructive evaluation in materials. Applied Acoustics,1992,11(4):1-6.
[20]陈佳圭,微弱信号检测,北京:中央广播电视大学出版社,1987.
[21]张伦[译],传感器和信号调节(第二版),北京:清华大学出版社,2003.
[22]于爱民,弱电回路屏蔽信号线屏蔽层接地方式,电力自动化设备,2001(11):61-63.
[23]温世仁,微弱信号检测系统中的接地与屏蔽技术分析,宇航计测技术,2005,25(2):46-49.
[24]张洪涛,数字信号处理,电子工业出版社,2007,36-44.
[25]奥本海姆,数字信号处理(中文版),西安交通大学出版社,210-224.
[26]唐向宏,数字信号处理原理、实现与仿真,电子工业出版社,2006,133-139.
[27]M.H.海因斯,数字信号处理(全美经典),科学出版社,284-285.
[28]胡广书,数字信号处理理论、算法及实现,北京:清华大学出版社,1997,235-245.
[29]奥本海姆,数字信号处理(中文版),西安交通大学出版社,174-181.
[30]唐向宏,数字信号处理原理、实现与仿真,电子工业出版社,2006,275-281.
[31]张登奇,李望移,基于MATLAB的FIR数字滤波器设计,计算机时代,2007,11:47-48.
[32]刘顺至,数字信号处理,电子工业出版社,2004.
[33]柴政,关于数字滤波器设计方式的探讨,通信电源技术,2007, 1:33-35.
[34]关治,陈景良,数值计算方法,北京:清华大学出版社,1990,50-163.
[35]王海涛,朱洪,改进的二分法查找,计算机工程,2006,32(10):60-63.
[36]Cruz R L, A Calculus for Network Delay, Part 1: Network Elements in Isolation. IEEE Transaction on Information Theory, 1991, 37(1):114-131.