金属互连电迁移可靠性的新表征参量研究
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摘要
随着现代电子技术的飞速发展，集成电路的小型化趋势越来越明显，器件特征尺寸向着亚微米甚至超深亚微米量级发展，金属互连在电路中所占的比例越来越大，互连线单位面积上承载的电流密度也越来越大，金属互连电迁移已成为超大规模集成电路的主要失效机理之一。
本文在电迁移失效机理及电迁移传统表征参量探讨的基础上，将时间序列分析方法引入电迁移噪声序列的分析。电迁移噪声序列是一种分形信号，具有分形维数及自相似性。相关积分方法是一种时域分析方法。电迁移噪声的相关积分分析结果表明，随着电迁移的进行，噪声信号主要成分发生变化，即由随机成分占主导变化为确定性成分占主导。通过噪声信号产生的物理机制分析可以推断金属薄膜中的电子运动状态由动态平衡转变为非平衡状态。另外，利用相关积分结果估算的电迁移噪声信号分形维数可为探索金属薄膜材料中电迁移动力学提供信息。
本文还应用高阶统计量分析方法分析了信号的非高斯性强弱。对电迁移实验数据分析结果表明，信号的非高斯性随电迁移过程不断增强。这两种方法对于鉴定电迁移损伤程度，预测电迁移失效都是比较灵敏的，可以作为新的互连电迁移可靠性分析方法。
With the development of modern electronic technology, the miniaturization trend of the integrated circuit is more and more obvious, the characteristic measurement of the device is becoming the sub-micrometer and even deep, the volume proportion of metallic interconnection in circuit and the current density dropped on interconnection are more and more greater, electromigration has become one of the major failure mechanisms in VLSI.
Based on a brief description to the damage mechanism for electromigration and traditional token parameter, the time series analysis methods are taken into electromigration noise analysis. The noise series of electromigration is one kind of fractal signals, fractal dimension and self-similarity of the system can be obtained through it. Correlation integral is a method of fractal theory, using it in electromigration analysis, we find that through electromigration process, the primary component of noise signal is changed, the dominant component is changed from random component to certainty component, and electrons movement is changed from equilibrium to non-equilibrium, it shows the generation mechanism of noise has changed. And through the estimate of correlation dimension, we can evaluate the fractal dimension of signal which brings us some useful information in system modeling and simplification. High order statistics reflects the non-gauss of signal, our analysis shows that the non-gauss is more and more obviously though electromigration process. These two methods are valid in characterizing electromigration process and predicting interconnection invalidation, they can be used as news analysis methods in electromigration research.
本文在电迁移失效机理及电迁移传统表征参量探讨的基础上，将时间序列分析方法引入电迁移噪声序列的分析。电迁移噪声序列是一种分形信号，具有分形维数及自相似性。相关积分方法是一种时域分析方法。电迁移噪声的相关积分分析结果表明，随着电迁移的进行，噪声信号主要成分发生变化，即由随机成分占主导变化为确定性成分占主导。通过噪声信号产生的物理机制分析可以推断金属薄膜中的电子运动状态由动态平衡转变为非平衡状态。另外，利用相关积分结果估算的电迁移噪声信号分形维数可为探索金属薄膜材料中电迁移动力学提供信息。
本文还应用高阶统计量分析方法分析了信号的非高斯性强弱。对电迁移实验数据分析结果表明，信号的非高斯性随电迁移过程不断增强。这两种方法对于鉴定电迁移损伤程度，预测电迁移失效都是比较灵敏的，可以作为新的互连电迁移可靠性分析方法。
With the development of modern electronic technology, the miniaturization trend of the integrated circuit is more and more obvious, the characteristic measurement of the device is becoming the sub-micrometer and even deep, the volume proportion of metallic interconnection in circuit and the current density dropped on interconnection are more and more greater, electromigration has become one of the major failure mechanisms in VLSI.
Based on a brief description to the damage mechanism for electromigration and traditional token parameter, the time series analysis methods are taken into electromigration noise analysis. The noise series of electromigration is one kind of fractal signals, fractal dimension and self-similarity of the system can be obtained through it. Correlation integral is a method of fractal theory, using it in electromigration analysis, we find that through electromigration process, the primary component of noise signal is changed, the dominant component is changed from random component to certainty component, and electrons movement is changed from equilibrium to non-equilibrium, it shows the generation mechanism of noise has changed. And through the estimate of correlation dimension, we can evaluate the fractal dimension of signal which brings us some useful information in system modeling and simplification. High order statistics reflects the non-gauss of signal, our analysis shows that the non-gauss is more and more obviously though electromigration process. These two methods are valid in characterizing electromigration process and predicting interconnection invalidation, they can be used as news analysis methods in electromigration research.
引文
[1] International Technology Roadmap for Semiconductors. Austin, TX: SEMATECH, 1999.
[2] A. S. Oates, "Electromigration failure of contacts and vias in sub-micron integrated circuit metallization", Microelectronics Reliability, Vol. 36, No. 7/8, 925-953, 1996.
[3] R. Rosenberg, L. Berenbaum, "Resistance monitoring and effects of nonadhesion during electromigration in aluminum films," Applied Physics Letters, Vol. 12(5), 201-204, 1968.
[4] J. L. Vossen, Applied Physics Letters, Vol. 2, 287; 1973.
[5] Birkelund Y, Johansen J A, Hanssen A, et al. Time series analysis of low-frequency noise in SiGe HBTs[J]. proceedings of the 2003 Norwegian Symposium on Signal Processing, 2003,1-6.
[6] Cher M T, Shin Y L. Application of Wigner-Ville Distribution in Electromigration Noise Analysis[J]. IEEE Transaction on Device and Materials Reliability, 2002, 2(2): 30-35.
[7] 张贤达，保铮．非平稳信号分析与处理[M]．北京：国防工业出版社，1999．
[8] Qian S, Chen D P. Joint time-frequency analysis[J]. IEEE Signal Processing Mag., 1999, 16(2): 52-67.
[9] J. P. Dekker and A. Lodder. Calculated electromigration wind force in face-centered-cubic and body-centered-cubic metals. Journal of applied physics. 1998, 84(4): 1958-1962.
[10] D. G. Pierce, P. G. Brusiusi, "Electromigration: A review", Microelectronics Reliability, Vol. 37, No. 7, 1053-1072, 1997.
[11] P. Waltz, L. Amaud, G. Yartavel, G. Lormand, "Infulence of thermal heating effect on pulsed DC electromigration result analysis", ESSDERC'97 Conference
[12] B. Greenebaum, A.I. Sauter, P. A. Flinn, and W. D. Nix, "Stress in metal lines under passivation; comparison of experiment with finite element calculations," Appl. Phys. Lett., vol. 58(17), pp. 1845-1847, 1991.
[13] H. M. Hunt, "Comparison of electromigration failure rates and grain boundary kinetics in Aluminum lines and films", Ph. D dissertation, The university of Rochester, New York, 2000.
[14] K. N. Tu, "Recent advances on electromigration-in very-large-scale-integration of interconnects", Journal of applied physics, Vol. 94, No. 9, 2003.
[15] J. Clement, "Electromigration modeling for integrated circuit interconnect reliability analysis", IEEE Transactions on Device and Materials Reliability, 1(1): 33-42, March 2001.
[16] Q. F. Duan. On the prediction of electromigration voiding using Stress-based modeling. Journal of Applied Physics. 2000, 87(8): 4039-4041.
[17] E. Simoen, C. Claeys, "Reliability aspects of the low-frequency noise behaviour of submicron CMOS technologies", Semicond. Sci. Technol. 14, No 8: 61-71.
[18] J. R. Lloyd and R. H. Koch, "Study of Electromigration-induced resistance and resistance decay in Al thin-film conductors, "Applied Physics Letters, Vol. 52(3), pp. 194-196, 1988.
[19] A. H. Verbruggen, M. J. C. Van den Homberg, L. C. Jacobs, A. J. Kalkman, J. R. Kraayveld, and S. Radelaar, "Resistance changes induced by the formation of a single void/hillock during electromigration, "AIP Coference Procedings 418. 135-146, 1998.
[20] J. R. Kraayeveld, A. H. Verbruggen, A. W. Willemsen and S. Radelaar, "Critical current-length product for electromigration induced resistance changes in short Al lines, "Applied Physics Letters, Vol. 67(9), 1995.
[21] Celasce M, "Thermal equilibrium properties of vacancies in metal through current-noise measurement", Phys. Rev. Lett, 1976, 36(1): 38-42.
[22] Simoen E, Claeys C. Reliability aspects of the low-frequency noise behaviour of submicron CMOS technologies[J]. Semicond Sci Technol, 1999, 14: R61-R70.
[23] Feng S, Lee P A, Store A D. Sensitivity of the conductance of a disordered metal to the motion of a single atom: implications for 1/f noise[J]. Phys Rev Lett, 1986, 56: 1960-1963.
[24] Satoshi H. A study of 1/f noise in Aluminum, Al alloys and Copper films[D]. New York: city university of New York, 1999.
[25] Cottle J G, Chen M T. Activation Energies Associated With Current Noise of Thin Metal Films[J]. J Electron Mater, 1988, 17(5): 467-471.
[26] Birkelund Y, Johansen J A, Hanssen A, et al. Time series analysis of low-frequency noise in SiGe HBTs[J]. proceedings of the 2003 Norwegian Symposium on Signal Processing, 2003, 1-6.
[27] 刘华杰，分形艺术，湖南：湖南电子音像出版社，1997．
[28] 杨冬云，王司，1／f分形噪声理论及其在信号处理中的应用研究综述，黑龙江工程学院学报，18(3)，2004．
[29] Yazici B, Kashyap R L, "Second order stationary models for 1/f processes" Information Theory. IEEE International Symposium on, 1994:302.
[30] Grassberger P, Procaccia I. Characterization of Strange Attractors[J]. Physical Review Letters, 1983, 31(1): 346-349.
[31] Ivan O, Mary A F H, Ying C L, et al. Observation on the application of the correlation dimension and correlation integral to the prediction of seizures[J]. Journal of Clinical Neurophysiology, 2001,18(3): 269-274.
[32] Ying C L, Ivan O, Mary A F H, et al. correlation-dimension and autocorrelation fluctuations in epileptic seizure dynamics[J]. Physical Review E, 2002.
[33] Caroline B, Frank B, Dirk R, et al. Analysis of heart rate variability with correlation dimension method in a normal population and in heart transplant patients [J]. Autonomic Neuroscience Basic and Clinical, 2001, 90: 142-147.
[34] Naoto B, Germaine C, Franz H, et al. Relationship between correlation dimension and indices of linear analysis in both respiratory movement and electron cephalogram[J]. Clinical Neurophysiology, 2001, 112: 1147-1153.
[35] James T. Spurious dimension from correlation algorithms applied to limited time-series data[J]. Physical Review A, 1986, 34: 2427-2432.
[36] Bloom I, Balberg I. Nonlinear 1/f noise characteristics in luminescent porous silicon[J]. Applied Physics Letters, 1999.
[37] Milotti E.1/f noise: a pedagogical review[/OL]. www.nslii-genetics.org/wli/lfnoise
[38] Birkelund Y, Johansen J A. Time Series Analysis of Low-Frequency Noise in SiGe HBTs[A]. proceedings of the 2003 Norwegian Symposium on signal processing, 2003.
[39] Antal T, Droz M, Gyorgyi G, et al. Roughness distributions for 1/f~α signals. arXiv:cond-mat 2001.
[40] Takagi k, Excess Low Frequency Noise in Some Electronic Materials and Components [A]. EMT/IMC Symposium ,1998.
[41] Doron Kletter, Hagit Messer, Suboptimal Detection of Non-Gaussian Signals by Third-order Spectral Analysis [J]. IEEE transactions on acoustics, speech, and signal processing 1990.
[42] Hinich M J, Clay C S . Testing for Gaussianity and linearity of a stationary time series[J]. Time Series Analysis, 1982.
[43] Garth L M, Bresler Y. A Comparison of Optimized Higher Order Spectral Detection Techniques for Non-Gaussian Signals[J]. IEEE transactions on signal processing, 1996.
[44] 周越，杨杰．水声信号的非高斯特性分析与检测方法的研究[J]．信号处理，2001，17(5)．
[45] Sanna P, Pedro J, Heikki H. Signal processing of vibrations for condition Monitoring of an induction motor[J]. First international symposium on control communications and signal processing, 2004, 499-502.
[46] 杜宁平，史军，朱红涛．高阶统计量分析在油气预测中的应用[J]．海洋地质动态，2004，20(8)．
[47] Ismail G. In situ approach to characterization of nanoscale electromigration [D]. USA: university of Nebraska, 2002.
[2] A. S. Oates, "Electromigration failure of contacts and vias in sub-micron integrated circuit metallization", Microelectronics Reliability, Vol. 36, No. 7/8, 925-953, 1996.
[3] R. Rosenberg, L. Berenbaum, "Resistance monitoring and effects of nonadhesion during electromigration in aluminum films," Applied Physics Letters, Vol. 12(5), 201-204, 1968.
[4] J. L. Vossen, Applied Physics Letters, Vol. 2, 287; 1973.
[5] Birkelund Y, Johansen J A, Hanssen A, et al. Time series analysis of low-frequency noise in SiGe HBTs[J]. proceedings of the 2003 Norwegian Symposium on Signal Processing, 2003,1-6.
[6] Cher M T, Shin Y L. Application of Wigner-Ville Distribution in Electromigration Noise Analysis[J]. IEEE Transaction on Device and Materials Reliability, 2002, 2(2): 30-35.
[7] 张贤达，保铮．非平稳信号分析与处理[M]．北京：国防工业出版社，1999．
[8] Qian S, Chen D P. Joint time-frequency analysis[J]. IEEE Signal Processing Mag., 1999, 16(2): 52-67.
[9] J. P. Dekker and A. Lodder. Calculated electromigration wind force in face-centered-cubic and body-centered-cubic metals. Journal of applied physics. 1998, 84(4): 1958-1962.
[10] D. G. Pierce, P. G. Brusiusi, "Electromigration: A review", Microelectronics Reliability, Vol. 37, No. 7, 1053-1072, 1997.
[11] P. Waltz, L. Amaud, G. Yartavel, G. Lormand, "Infulence of thermal heating effect on pulsed DC electromigration result analysis", ESSDERC'97 Conference
[12] B. Greenebaum, A.I. Sauter, P. A. Flinn, and W. D. Nix, "Stress in metal lines under passivation; comparison of experiment with finite element calculations," Appl. Phys. Lett., vol. 58(17), pp. 1845-1847, 1991.
[13] H. M. Hunt, "Comparison of electromigration failure rates and grain boundary kinetics in Aluminum lines and films", Ph. D dissertation, The university of Rochester, New York, 2000.
[14] K. N. Tu, "Recent advances on electromigration-in very-large-scale-integration of interconnects", Journal of applied physics, Vol. 94, No. 9, 2003.
[15] J. Clement, "Electromigration modeling for integrated circuit interconnect reliability analysis", IEEE Transactions on Device and Materials Reliability, 1(1): 33-42, March 2001.
[16] Q. F. Duan. On the prediction of electromigration voiding using Stress-based modeling. Journal of Applied Physics. 2000, 87(8): 4039-4041.
[17] E. Simoen, C. Claeys, "Reliability aspects of the low-frequency noise behaviour of submicron CMOS technologies", Semicond. Sci. Technol. 14, No 8: 61-71.
[18] J. R. Lloyd and R. H. Koch, "Study of Electromigration-induced resistance and resistance decay in Al thin-film conductors, "Applied Physics Letters, Vol. 52(3), pp. 194-196, 1988.
[19] A. H. Verbruggen, M. J. C. Van den Homberg, L. C. Jacobs, A. J. Kalkman, J. R. Kraayveld, and S. Radelaar, "Resistance changes induced by the formation of a single void/hillock during electromigration, "AIP Coference Procedings 418. 135-146, 1998.
[20] J. R. Kraayeveld, A. H. Verbruggen, A. W. Willemsen and S. Radelaar, "Critical current-length product for electromigration induced resistance changes in short Al lines, "Applied Physics Letters, Vol. 67(9), 1995.
[21] Celasce M, "Thermal equilibrium properties of vacancies in metal through current-noise measurement", Phys. Rev. Lett, 1976, 36(1): 38-42.
[22] Simoen E, Claeys C. Reliability aspects of the low-frequency noise behaviour of submicron CMOS technologies[J]. Semicond Sci Technol, 1999, 14: R61-R70.
[23] Feng S, Lee P A, Store A D. Sensitivity of the conductance of a disordered metal to the motion of a single atom: implications for 1/f noise[J]. Phys Rev Lett, 1986, 56: 1960-1963.
[24] Satoshi H. A study of 1/f noise in Aluminum, Al alloys and Copper films[D]. New York: city university of New York, 1999.
[25] Cottle J G, Chen M T. Activation Energies Associated With Current Noise of Thin Metal Films[J]. J Electron Mater, 1988, 17(5): 467-471.
[26] Birkelund Y, Johansen J A, Hanssen A, et al. Time series analysis of low-frequency noise in SiGe HBTs[J]. proceedings of the 2003 Norwegian Symposium on Signal Processing, 2003, 1-6.
[27] 刘华杰，分形艺术，湖南：湖南电子音像出版社，1997．
[28] 杨冬云，王司，1／f分形噪声理论及其在信号处理中的应用研究综述，黑龙江工程学院学报，18(3)，2004．
[29] Yazici B, Kashyap R L, "Second order stationary models for 1/f processes" Information Theory. IEEE International Symposium on, 1994:302.
[30] Grassberger P, Procaccia I. Characterization of Strange Attractors[J]. Physical Review Letters, 1983, 31(1): 346-349.
[31] Ivan O, Mary A F H, Ying C L, et al. Observation on the application of the correlation dimension and correlation integral to the prediction of seizures[J]. Journal of Clinical Neurophysiology, 2001,18(3): 269-274.
[32] Ying C L, Ivan O, Mary A F H, et al. correlation-dimension and autocorrelation fluctuations in epileptic seizure dynamics[J]. Physical Review E, 2002.
[33] Caroline B, Frank B, Dirk R, et al. Analysis of heart rate variability with correlation dimension method in a normal population and in heart transplant patients [J]. Autonomic Neuroscience Basic and Clinical, 2001, 90: 142-147.
[34] Naoto B, Germaine C, Franz H, et al. Relationship between correlation dimension and indices of linear analysis in both respiratory movement and electron cephalogram[J]. Clinical Neurophysiology, 2001, 112: 1147-1153.
[35] James T. Spurious dimension from correlation algorithms applied to limited time-series data[J]. Physical Review A, 1986, 34: 2427-2432.
[36] Bloom I, Balberg I. Nonlinear 1/f noise characteristics in luminescent porous silicon[J]. Applied Physics Letters, 1999.
[37] Milotti E.1/f noise: a pedagogical review[/OL]. www.nslii-genetics.org/wli/lfnoise
[38] Birkelund Y, Johansen J A. Time Series Analysis of Low-Frequency Noise in SiGe HBTs[A]. proceedings of the 2003 Norwegian Symposium on signal processing, 2003.
[39] Antal T, Droz M, Gyorgyi G, et al. Roughness distributions for 1/f~α signals. arXiv:cond-mat 2001.
[40] Takagi k, Excess Low Frequency Noise in Some Electronic Materials and Components [A]. EMT/IMC Symposium ,1998.
[41] Doron Kletter, Hagit Messer, Suboptimal Detection of Non-Gaussian Signals by Third-order Spectral Analysis [J]. IEEE transactions on acoustics, speech, and signal processing 1990.
[42] Hinich M J, Clay C S . Testing for Gaussianity and linearity of a stationary time series[J]. Time Series Analysis, 1982.
[43] Garth L M, Bresler Y. A Comparison of Optimized Higher Order Spectral Detection Techniques for Non-Gaussian Signals[J]. IEEE transactions on signal processing, 1996.
[44] 周越，杨杰．水声信号的非高斯特性分析与检测方法的研究[J]．信号处理，2001，17(5)．
[45] Sanna P, Pedro J, Heikki H. Signal processing of vibrations for condition Monitoring of an induction motor[J]. First international symposium on control communications and signal processing, 2004, 499-502.
[46] 杜宁平，史军，朱红涛．高阶统计量分析在油气预测中的应用[J]．海洋地质动态，2004，20(8)．
[47] Ismail G. In situ approach to characterization of nanoscale electromigration [D]. USA: university of Nebraska, 2002.
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