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相同线性能量传输值(linear energy transfer, LET)、不同能量和种类的离子在径迹特征方面存在差异, 导致这些离子在组合逻辑电路中产生的单粒子瞬态(single event transients, SET)有所不同, 这种现象随着电路特征工艺尺寸的缩减逐渐凸显. 开展离子径迹特征与纳米组合逻辑电路SET的关联性研究对准确预估纳米器件在轨单粒子效应软错误率具有重要意义. 本文以65 nm互补金属氧化物半导体工艺的体硅反相器链为研究载体, 建立了反相器链的三维器件物理模型, 开发了体硅中离子径迹的粒子输运计算程序, 基于器件物理和粒子输运的耦合仿真, 研究了相同LET值的高低能离子(低能离子能量小于10 MeV·n–1, 高能离子能量介于几十MeV·n–1和几百MeV·n–1之间)在反相器链中所产生的SET脉宽差异. 研究结果表明: 增加高低能离子每核子能量比率, 或者在该比率相近时提高LET值, 会使得具有相同LET值的高低能离子的径迹差异变大, 进而导致两者产生的SET脉宽差异更明显; 离子径迹特征对SET的影响与离子入射角度存在一定的依赖关系, 但与反相器链偏置电压的关联性不强.Ions with the same linear energy transfer (LET) value, but different energies and species have various ion track characteristics, and thus induce different single event transient (SET) responses in combinational logics. As the technology feature size shrinks, this issue continues to be serious. The research of the relationship between ion track characteristics and SETs in the nanometer combinational logic circuits is of great significance for accurately predicting the soft error rates of nanometer devices used in spacecraft. The combinational logic circuit investigated in this paper is a 65 nm bulk silicon complementary metal oxide semiconductor (CMOS) technology inverter chain. The three-dimensional TCAD model of the inverter chain is established, and the particle transport program for the ion track in bulk silicon is developed by Geant4. The track characteristics of high- and low-energy ions (the energy of low-energy ions is less than 10 MeV·n–1, the energy of high-energy ions ranges from tens of MeV·n–1 to hundreds of MeV·n–1) which have the same LET value are compared with each other. Based on the coupled simulation of TCAD and Geant4, the difference in SET pulse widths, induced by ions with the same LET value but different energies, are investigated. It is found that when the energy per nucleon ratio of high-energy ion to low-energy ion increases, the difference in electron-hole pair densities near the center axis of the ion track is more significant, and thus the difference in SET pulse widths is larger. If the energy per nucleon ratio is similar, raising the LET value of ions can increase the difference in electron-hole pair densities on the same radial scale of the ion tracks, and make the SET pulse width difference more obvious. For the high- and low-energy ions with the same LET value, the single event charge generations are different. On the other hand, the change of the ion incident angle results in different charge collections. The coupling of these two factors makes the difference in SET pulse widths dependent on the incident angle of ions. In addition, the influence of ion track characteristics on SET has a weak correlation with the bias voltage of the inverter chain.
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Keywords:
- single event transients /
- ion track /
- combinational logic circuit /
- linear energy transfer
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图 1 四级反相器链的(a)电路原理图和(b)三维TCAD模型
Fig. 1. (a) Schematic and (b) three-dimensional TCAD model of the 4-stage inverter chain.
图 2 NMOS晶体管的I-V特性校准 (a) Ids-Vds曲线; (b) Ids-Vgs曲线
Fig. 2. Calibration of I-V characteristics of the NMOS transistor: (a) Ids-Vds curves; (b) Ids-Vgs curves.
图 3 PMOS晶体管的I-V特性校准 (a) Ids-Vds曲线; (b) Ids-Vgs曲线
Fig. 3. Calibration of I-V characteristics of the PMOS transistor: (a) Ids-Vds curves; (b) Ids-Vgs curves.
图 5 Geant4计算得到的三组离子入射硅材料生成的电子-空穴对密度随离子径迹径向尺度的变化 (a) 第一组高低能离子; (b)第二组高低能离子; (c)第三组高低能离子
Fig. 5. Density of electron-hole pairs generated by ion incidence into silicon vs. the radial scale of ion track: (a) The first group of ions; (b) the second group of ions; (c) the third group of ions.
图 6 离子入射位置示意图(*表示入射位置)
Fig. 6. Schematic diagram of ion strike locations, where * indicates the ion strike locations.
图 7 第二组高低能离子导致的瞬态脉宽差异在不同入射位置上的分布 (a)第二组离子Ti和Xe的比较; (b)第二组离子Ti和Ta的比较
Fig. 7. Distribution of the transient pulse width differences at various strike locations for the second group of ions: (a) Low- and high-energy ions are Ti and Xe respectively; (b) low- and high-energy ions are Ti and Ta respectively.
图 8 三组高低能离子导致的瞬态脉宽差异在不同入射位置上的分布 (a)第一组离子Si和Kr的比较; (b)第二组离子Ti和Xe的比较; (c)第三组离子Br和Ta的比较
Fig. 8. Distribution of the transient pulse width differences at various strike locations: (a) Comparison of Si and Kr ions in the first group; (b) comparison of Ti and Xe ions in the second group; (c) comparison of Br and Ta ions in the third group.
图 9 每核子能量比率接近的三组高低能离子入射硅材料生成的电子-空穴对密度随离子径迹径向尺度的变化
Fig. 9. Density of electron-hole pairs generated by ion incidence into silicon vs. the radial scale of ion track. The energy per nucleon ratios of high-energy ion to low-energy ion are similar for the three groups.
图 10 第三组的 Br和Ta离子在不同入射角度下导致的瞬态脉宽差异随入射位置的变化 (a)沿阱方向30º入射; (b)沿阱方向60º入射; (c)垂直阱方向30º入射; (d)垂直阱方向60º入射
Fig. 10. Distribution of the transient pulse width differences at various strike locations for the Br and Ta ions in the third group at different ion incidence angles: (a) 30º along the well; (b) 60º along the well; (c) 30º across the well; (d) 60º across the well.
图 11 第三组的Br和Ta离子沿阱方向30º入射(0.51 μm, 0.77 μm)时, 反相器链各级输出端的SET波形
Fig. 11. Transient waveforms for N+-drains of the inverter chain, which are induced by Br and Ta ions in the third group. The ion incidence angle is 30º along the well. The strike location is with the coordinate of (0.51 µm, 0.77 µm).
图 12 第三组的Br和Ta离子沿阱方向60º入射(0.51 μm, 0.77 μm)时, 反相器链各级输出端的SET波形
Fig. 12. Transient waveforms for N+-drains of the inverter chain, which are induced by Br and Ta ions in the third group. The ion incidence angle is 60º along the well. The strike location is with the coordinate of (0.51 µm, 0.77 µm).
图 13 不同偏置电压下, 第二组的Ti和Xe离子导致的瞬态脉宽差异随入射位置的变化
Fig. 13. Transient pulse width differences under different supply voltages vs. the strike location for the Ti and Xe ions in the second group.
表 1 重离子的详细信息
Table 1. Detail information of the heavy ions.
离子
分组离子
种类每核子能量 /(MeV·n–1) 硅表面的LET值/(MeV·cm2·mg–1) 射程/μm 第一组 Si 5.3 8.8 58 Kr 83.3 8.8 1940 第二组 Ti 3.8 21.3 38 Xe 66.7 21.3 1150 Ta 150.3 21.3 3520 第三组 Br 3.4 41.4 36 Ta 50.3 41.4 684 
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表 2 第三组的Br和Ta离子在不同入射角度下导致的瞬态脉宽差异平方和
Table 2. Square sum of the transient pulse width differences at various strike locations for the Br and Ta ions in the third group at different ion incidence angles.
入射角度 Σ 值 沿阱方向30º 93602 沿阱方向60º 161159 垂直阱方向30º 13765 垂直阱方向60º 14131
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[1] Stassinopoulos E G, Raymond J P 1988 Proc. IEEE 76 1423
Google Scholar
[2] Stapor W J, McDonald P T, Knudson A R 1988 IEEE Trans. Nucl. Sci. 35 1585
Google Scholar
[3] Dodd P E, Schwank J R, Shaneyfelt M R 2007 IEEE Trans. Nucl. Sci. 54 889
Google Scholar
[4] 高丽娟, 郭刚, 蔡莉 2014 原子能科学技术 48 1496
Google Scholar
Gao L J, Guo G, Cai L 2014 Atomic Energy Sci. Technol. 48 1496
Google Scholar
[5] Raine M, Gaillardin M, Sauvestre J E 2010 IEEE Trans. Nucl. Sci. 57 1892
Google Scholar
[6] MA Xapsos 1992 IEEE Trans. Nucl. Sci. 39 1613
Google Scholar
[7] Connell L W, Sexton F W, McDaniel P J 1996 IEEE Trans. Nucl. Sci. 43 2814
Google Scholar
[8] Campbell A B, Musseau O, Cavrois V F 1998 IEEE Trans. Nucl. Sci. 45 1603
Google Scholar
[9] Raine M, Hubert G, Gaillardin M 2011 IEEE Trans. Nucl. Sci. 58 840
Google Scholar
[10] King M P 2011 Ph. D. Dissertation (Nashville: Vanderbilt University)
[11] 韩建伟 2000 空间科学学报 20 333
Google Scholar
Han J W 2000 Chin. J. Space Sci. 20 333
Google Scholar
[12] 刘建德, 孙友梅, 刘杰 2012 原子核物理评论 29 419
Google Scholar
Liu J D, Sun Y M, Liu J 2012 Nucl. Phys. Rev. 29 419
Google Scholar
[13] 王斌 2017 博士学位论文 (兰州: 中国科学院近代物理研究所)
Wang B 2017 Ph. D. Dissertation (Lanzhou: Institute of Modern Physics, Chinese Academy of Sciences) (in Chinese)
[14] Geng C, Liu J, Xi K 2013 Chin. Phys. B 22 109501
Google Scholar
[15] 张战刚, 雷志锋, 岳龙 2017 物理学报 66 246102
Google Scholar
Zhang Z G, Lei Z F, Yue L 2017 Acta Phys. Sin. 66 246102
Google Scholar
[16] Shivakumar P, Kistlery M, Keckler S W 2000 Proceedings of the International Conference on Dependable Systems and Networks Washington, USA, June 23–26, 2002 p389
[17] Mavis D G, Eaton P H 2000 Proceedings of the Military and Aerospace Applications of Programmable Devices and Technologies Conference Laurel, USA, September 10–12, 2000 p1
[18] Dodd P E, Shaneyfelt M R, Felix J A 2004 IEEE Trans. Nucl. Sci. 51 3278
Google Scholar
[19] Ferlet-Cavrois V, Paillet P, Gaillardin M 2006 IEEE Trans. Nucl. Sci. 53 3242
Google Scholar
[20] Benedetto J M, Eaton P H, Mavis D G 2006 IEEE Trans. Nucl. Sci. 53 3462
Google Scholar
[21] Gadlage M J, Eaton P H, Benedetto J M 2005 IEEE Trans. Nucl. Sci. 52 2120
Google Scholar
[22] Gola D, Singh B, Tiwari P K 2017 IEEE Trans. Electron Devices 64 3534
Google Scholar
[23] Gola D, Singh B, Tiwari P K 2018 IEEE Trans. Electron Devices 65 1663
Google Scholar
[24] Liu L, Yue S, Lu S 2015 J. Semicond. 36 115007
Google Scholar
[25] Tiny XML Library, Michael R S http://www.minixml.org [2021-2-20]
[26] GDML, Pokorski W http://gdml.web.cern.ch/GDML/ [2021-2-20]
[27] Geant4, Geant4 Working Groups & Coordinators http://www.cern.ch/geant4 [2021-2-20]
[28] Wei Y, Xie H G, Gong D 2012 Proceedings of Spring World Congress on Engineering and Technology Xi’an, China, May 27–30, 2012 p978
[29] Kobayashi A S, Sternberg A L, Massengill L W 2004 IEEE Trans. Nucl. Sci. 51 3312
Google Scholar
[30] Raine M, Valentin A, Gaillardin M 2012 IEEE Trans. Nucl. Sci. 59 2697
Google Scholar
[31] Michael M, Avraham A, Joseph B 2008 IEEE Trans. Nucl. Sci. 55 3046
Google Scholar
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