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Electromagnetic–Thermo–Mechanical Coupling Behavior of Cu/Si Layered Thin Plate Under Pulsed Magnetic Field

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Abstract

Semiconductor-based electronic devices usually work under multiphysics fields rendering complex electromagnetic–thermo–mechanical coupling. In this work, we develop a penalty function method based on a finite element analysis to tackle this coupling behavior in a metal/semiconductor bilayer plate—the representative unit of semiconductor antenna, which receives strong and pulsed electromagnetic signals. Under these pulses, eddy current is generated, of which the magnitude varies remarkably from one plate to another due to the difference in electrical conductivity. In the concerned system, the metal layer generates much larger current, resulting in the large temperature rise and the nonnegligible Lorentz force, which could lead to delamination and failure of the semiconductor-based electronic device. This study provides theoretical guidance for the design and protection of semiconductor-based electronic devices in complex environments.

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References

  1. Klyuchnik AV, Pirogov YA, Solodov AV. Investigation of the IC resistance to pulsed electromagnetic radiation. J Commun Technol Electron. 2011;56(3):342–6.

    Article  Google Scholar 

  2. Giles JC, Prather WD. Worldwide high-altitude nuclear electromagnetic pulse simulators. IEEE Trans Electromagn Compatibil. 2013;55(3):475–83.

    Article  Google Scholar 

  3. Chakarothai J, Watanabe S, Wake K. Numerical dosimetry of electro- magnetic pulse exposures using FDTD method. IEEE Trans Antennas Propag. 2018;66(9):5397–408.

    Article  Google Scholar 

  4. Li GJ, Amer N, Hafez HA, Huang SH, Turchinovich D, Mochain VN, Hegmann FA, Titova LV. Dynamical control over terahertz electromagnetic interference shielding with 2D Ti3C2Ty mxene by ultrafast optical pulses. Nano Lett. 2020;20(1):636–43.

    Article  Google Scholar 

  5. Yeong-Kook O, Kim WC, Park KR, et al. Commissioning and initial operation of KSTAR superconducting tokamak. Fusion Eng Design. 2009;84:344–50.

    Article  Google Scholar 

  6. Shimomura Y. Overview of International Thermonuclear Experimental Reactor (ITER) engineering design activities. Phys Plasmas. 1994;1:1612–8.

    Article  Google Scholar 

  7. Radasky WA, Baum CE, Wik MW. Introduction to the special issue on high-power electromagnetics and intentional electromagnetic interference. IEEE Trans Electromagn Compatibil. 2004;46(3):314–21.

    Article  Google Scholar 

  8. Shurenkov VV, Pershenkov VS. Electromagnetic pulse effects and damage mechanism on the semiconductor electronics. FACTA Univ Ser Electron Energet. 2016;29(4):621–9.

    Article  Google Scholar 

  9. Baek JE, Cho YM, Ko KC. Analysis of design parameters reducing the damage rate of low-noise amplifiers affected by high-power electromagnetic pulses. IEEE Trans Plasma Sci. 2018;46(3):524–9.

    Article  Google Scholar 

  10. Lee K, Ko K. Propagation model of high-power electromagnetic pulse by using a serial-parallel resistors circuit. IEEE Trans Plasma Sci. 2014;42(9):3309–12.

    Article  Google Scholar 

  11. Deng FX, Cao QL, Han XT, Chen Q, Li L. Principle and realization of an electromagnetic pulse welding system with a dual-stage coil. Int J Appl Electromagn Mech. 2018;57(4):389–98.

    Article  Google Scholar 

  12. Jin JM, Yan S. Multiphysics modeling in electromagnetics. IEEE Antennas Propag Magaz. 2019;61(2):14–26.

    Article  Google Scholar 

  13. Tavakoli MH, Karbaschi H, Samavat F. Computational study of electromagnetic fields, eddy currents and induction heating in thin and thick work pieces. Commun Comput Phys. 2010;8(1):211–25.

    Article  MATH  Google Scholar 

  14. Karimi M, Shahidi AR. Bending and buckling analyses of BiTiO3-CoFe2O4 nanoplates based on nonlocal strain gradient and modified couple stress hypotheses: rate of surface layers variations. Appl Phys A. 2019;125:530.

    Article  Google Scholar 

  15. Stampfli R, Youssef G. Multiphysics computational analysis of multiferroic composite ring structures. Int J Mech Sci. 2020;177:105573.

    Article  Google Scholar 

  16. Horie T, Niho T. Electromagnetic and structural coupled analysis with the effect of large deflection. IEEE Trans Magn. 1997;33(2):1658–61.

    Article  Google Scholar 

  17. Tanaka Y, Horie T, Niho T. Simplified analysis method for vibration of fusion reactor components with magnetic damping. Fusion Eng Design. 2000;51:263–71.

    Article  Google Scholar 

  18. Hu YD, Li J. Magneto-elastic combination resonances analysis of current- conducting thin plate. Appl Math Mech-Engl Ed. 2008;29(7):1053–66.

    Article  MATH  Google Scholar 

  19. Zhang JP, Yan ZJ, Ding QF, Wu H, Pan WG. Analysis of magnetoelastic interaction of cantilever conductive thin plate with nonlinear dynamic response. Eur J Mech A Solids. 2013;37:132–8.

    Article  MathSciNet  MATH  Google Scholar 

  20. Ghayesh MH, Farokhi H, Alici G. Size-dependent electro-elasto-mechanics of MEMS with initially curved deformable electrodes. Int J Mech Sci. 2015;103:247–64.

    Article  Google Scholar 

  21. Liu Y, Chai CC, Yang YT, et al. Damage effect and mechanism of the GaAs high electron mobility transistor induced by high power microwave. Chin Phys B. 2016;25(4):048503.

    Article  Google Scholar 

  22. Lu TJ, Jin JM. Coupled electrical-thermal-mechanical simulation for the reliability analysis of large-scale 3-D interconnects. IEEE Trans Compon Pack Manuf Technol. 2017;7(2):229–37.

    Google Scholar 

  23. Lu TJ, Jin JM. Electrical-thermal co-simulation for analysis of high-power RF/microwave components. IEEE Transa Electromagn Compatibil. 2017;59(1):93–102.

    Article  Google Scholar 

  24. Dobykin VD. Dependence of the criterial levels of damage in semiconductor structures under the action of high-power electromagnetic pulse on the pulse rise rate. J Commun Technol Electron. 2011;56(2):214–9.

    Article  Google Scholar 

  25. Musii RS. Thermal stressed state of conducting cylinders subjected to the electromagnetic action in the mode with pulsed modulating signals. Mater Sci. 2015;50(4):496–506.

    Article  Google Scholar 

  26. Liu Y, Chai C, Yu X, Fang Q, Yang Y, Xi X, Liu S. Damage effects and mechanism of the GaN high electron mobility transistor caused by high electromagnetic pulse. Acta Phys Sin. 2016;65(3):038402.

    Article  Google Scholar 

  27. Dobykin V, Kharchenko V. Electromagnetic-pulse functional damage of semiconductor devices modeled using temperature gradients as boundary conditions. J Commun Technol Electron. 2006;51(2):231–9.

    Article  Google Scholar 

  28. Ren Z, Yin WY, Shi YB, Liu QH. Thermal accumulation effects on the transient temperature responses in LDMOSFETs under the impact of a periodic electromagnetic pulse. IEEE Trans Electron Devices. 2010;57(1):345–52.

    Article  Google Scholar 

  29. Zhou WF, Zhou L, Lin L, Yin WY, Mao JF. Electrothermal-stress interactions of LDMOS FET induced by DCI RF-pulses. IEEE Trans Electromagn Compatibil. 2014;56(5):1178–84.

    Article  Google Scholar 

  30. Zhou L, Yin WY, Zhou WF, Lin L. Experimental investigation and analysis of the LDMOS FET breakdown under HPM pulses. IEEE Trans Electromagn Compatibil. 2013;55(5):909–16.

    Article  Google Scholar 

  31. Zhou L, San ZW, Hua YJ, Lin L, Zhang S, Zhao ZG, Zhou HJ, Yin WY. Investigation on failure mechanisms of GaN HEMT caused by high-power microwave (HPM) pulses. IEEE Trans Electromagn Compatibil. 2017;59(3):902–9.

    Article  Google Scholar 

  32. Zhang C, Zhang R, Yan T, Yang Z, Ren W, Zhu Z. A 3D theoretical model for EMP thermal runaway in semiconductor devices. Int Conf Electromagn Adv Appl. 2019;2019:1156–9.

    Google Scholar 

  33. Li Y, Xie H, Yan H, Wang J, Yang Z. A thermal failure model for MOSFETs under repetitive electromagnetic pulses. IEEE Access. 2020;8:228245–54.

    Article  Google Scholar 

  34. Camp M, Gerth H, Garbe H, Haase H. Predicting the breakdown behavior of microcontrollers under EMP/UWB impact using a statistical analysis. IEEE Trans Electromagn Compatibil. 2004;46(3):368–79.

    Article  Google Scholar 

  35. Xi XW, Chai CC, Ren XR, Yang YT, Zhang B, Hong X. EMP injection damage effects of a bipolar transistor and its relationship between the injecting voltage and energy. J Semiconduct. 2010;31(4):044005.

    Article  Google Scholar 

  36. Ma ZY, Chai CC, Ren XR, Yang YT, Chen B, Song K, Zhao YB. Microwave damage susceptibility trend of a bipolar transistor as a function of frequency. Chin Phys B. 2012;21(8):098502.

    Article  Google Scholar 

  37. Genender E, Garbe H, Sabath F. Probabilistic risk analysis technique of intentional electromagnetic interference at system level. IEEE Trans Electromagn Compatibil. 2014;56(1):200–7.

    Article  Google Scholar 

  38. Shurenkov VV, Pershenkov VS. Electromagnetic pulse effects and damage mechanism on the semiconductor electronics. Facta Univ Ser Electron Energet. 2016;29(4):621–9.

    Article  Google Scholar 

  39. Baek J, Cho Y, Ko K. Analysis of design parameters reducing the damage rate of low-noise amplifiers affected by high-power electromagnetic pulses. IEEE Trans Plasma Sci. 2018;46(3):524–9.

    Article  Google Scholar 

  40. Gao Y, Xu B, Huh H. Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields. Acta Mech. 2010;210(1–2):99–116.

    Article  MATH  Google Scholar 

  41. Grilli F, Pardo E, Stenvall A, Nguyen DN, Yuan W, Gomory F. Computation of losses in HTS under the action of varying magnetic fields and currents. IEEE Trans Appl Superconduct. 2014;24(1):78–110.

    Article  Google Scholar 

  42. Takagi T, Hashimoto M, Arita S, Norimatsu S, Sugiura T, Miya K. Experimental verification of 3D eddy current analysis code using T-method. IEEE Trans Magn. 1990;26(2):474477.

    Article  Google Scholar 

  43. Zheng XJ, Zhang JP, Zhou YH. Dynamic stability of a cantilever conductive plate in transverse impulsive magnetic field. Int J Solids Struct. 2005;42:24172430.

    Article  Google Scholar 

  44. Rybicki EF, Kanninen MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech. 1977;9(4):931–8.

    Article  Google Scholar 

  45. Shivakumar K, Tan P, Newman J. A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies. Int J Fract. 1988;36(3):R43-50.

    Article  Google Scholar 

  46. Bagchi A, Evans AG. The mechanics and physics of thin film decohesion and its measurement. Interface Sci. 1996;3(3):169–93.

    Article  Google Scholar 

  47. Chang-Chun L. Overview of interfacial fracture energy predictions for stacked thin films using a four-point bending framework. Surf Coat Technol. 2013;237:333–40.

    Article  Google Scholar 

  48. Guotao Wang C, Zhao MJ-H, Groothuis SK, Ho PS. Packaging effects on reliability of Cu/low-k interconnects. IEEE Trans Device Mater Reliabil. 2003;3(4):119–28.

    Article  Google Scholar 

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant nos. 11772294, 11621062), and the Fundamental Research Funds for the Central Universities (Grant no. 2017QNA4031).

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Authors and Affiliations

  1. Department of Engineering Mechanics, and Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China

    Qicong Li & Linli Zhu

  2. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong, China

    Haihui Ruan

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  1. Qicong Li
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  2. Linli Zhu
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Correspondence to Linli Zhu or Haihui Ruan.

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Li, Q., Zhu, L. & Ruan, H. Electromagnetic–Thermo–Mechanical Coupling Behavior of Cu/Si Layered Thin Plate Under Pulsed Magnetic Field. Acta Mech. Solida Sin. 35, 90–100 (2022). https://doi.org/10.1007/s10338-021-00250-y

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  • DOI: https://doi.org/10.1007/s10338-021-00250-y

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