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Nano- and micrometer-scale thin-film-interconnection failure theory and simulation and metallization lifetime prediction, Part 1: A general theory of vacancy transport, mechanical-stress generation, and void nucleation under electromigration in relation to multilevel-metallization degeneration and failure

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Abstract

The physical principles are considered of on-chip interconnection degeneration and failure in sub-1-µm technologies from the viewpoint of multilevel-metallization reliability. A general theory and simulation results are presented that deal with electromigration-induced failure of thin-film conducting tracks on the micro- and nanometer scales. They provide a detailed treatment of micro-, meso-, and nanoscopic mechanisms underlying the deformation and breaking of actual interconnection configurations. Parts 1 and 2 contain (i) the derivation and analysis of basic kinetic equations; (ii) the formulation and solution of three-dimensional boundary-value problems representing the transport of vacancies (both in the bulk and along grain boundaries) and the development of deformation and stress; (iii) models of void nucleation and development; (iv) an analysis of a multilevel-metallization lifetime; and (v) the identification of potential break locations in a multilevel metallization in relation to current density, metallization structure and layout, temperature, and the grain structure of the conducting material. Part 3 deals with electromigration in doped on-chip polycrystalline interconnections in terms of lengthening their lifetime. To predict electromigration resistance, models are constructed that represent the influence of texture and other grain-boundary properties on the effective charges of native and dopant ions.

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References

  1. Grigor’ev, I.S. and Meilikhova, E.Z., Fizicheskie velichiny. Spravochnik (Physical Quantities: A Handbook), Moscow: Energoatomizdat, 1991.

    Google Scholar 

  2. Kaur, I., Mishin, Y., and Gust, W., Fundamentals of Grain and Interphase Boundary Diffusion, Chichester: Wiley, 1995, 3rd ed.

    Google Scholar 

  3. d’Heurle, F.M. and Rosenberg, R., Electromigration in Thin Films, in Physics of Thin Films: Advances in Research and Development, New York: Academic, 1973, vol. 7, pp. 257–310.

    Google Scholar 

  4. Black, J.R., Electromigration Failure Modes in Aluminum Metallization for Semiconductor Devices, in IEEE Int. Reliability Physics Symp. Proc., 1969, vol. 57, pp. 1587–1593.

    Google Scholar 

  5. Makhviladze, T.M., Sarychev, M.E., and Valiev, K.A., Modeling of Ion Electromigration Process in Microelectronic Structure, in Proc. 6th Int. Conf. on the Numerical Analysis of Semiconductor Devices and Integrated Circuits (NACE-CODE), Dublin: Boole, 1989, pp. 521–525.

    Google Scholar 

  6. Valiev, K.A., Makhviladze, T.M., and Sarychev, M.E., Ion-Electromigration Mechanism in Metals and Dielectrics, Dokl. Akad. Nauk SSSR, 1989, vol. 306, no. 1, pp. 91–94.

    Google Scholar 

  7. Valiev, K.A., Makhviladze, T.M., and Sarychev, M.E., Ion-Electromigration Kinetics in Solids, Mikroelektronika, 1990, vol. 19, no. 5, pp. 419–429.

    Google Scholar 

  8. Valiev, K.A., Makhviladze, T.M., and Sarychev, M.E., Migration Model for the Kinetics of Failures Caused by an Electric Field and Mechanical Stress, in Tr. FTIAN, 1991, vol. 2, pp. 73–83.

    Google Scholar 

  9. Blech, I.A., Electromigration in Thin Aluminum Films on Titanium Nitride, J. Appl. Phys., 1976, vol. 47, pp. 1203–1208.

    Article  Google Scholar 

  10. Kirchheim, R. and Kaeber, U., Atomistic and Computer Modeling of Metallization Failure of Integrated Circuits by Electromigration, J. Appl. Phys., 1991, vol. 70, pp. 172–181.

    Article  Google Scholar 

  11. Kirchheim, R., Stress and Electromigration in Al-Lines of Integrated Circuits, Acta Metal Mater, 1992, vol. 40, pp. 309–323.

    Article  Google Scholar 

  12. Korhonen, M.A., Borgesen, P., Tu, K.N., and Li, C.Y., Stress Evolution Due To Electromigration in Confined Metal Lines, J. Appl. Phys., 1993, vol. 73, pp. 3790–3799.

    Article  Google Scholar 

  13. Thompson, C.V., Microstructure Based Modelling of Stress Migration and Electromigration Induced Failure Distributions, in Proc. 1993 SEMICON/Korea Tech. Symp., Seoul, 1993, pp. 1–12.

  14. Knowlton, B.D., Clements, P.C., Thompson, C.V., and Walton, D.T., Simulation of the Effects of Grain Structure and Grain Growth on Electromigration and Reliability of Interconnects, J. Appl. Phys., 1997, vol. 81, pp. 6073–6080.

    Article  Google Scholar 

  15. Clement, J.J. and Thompson, C.V., Modeling Electromigration Induced Stress Evolution in Confined Metal Lines, J. Appl. Phys., 1995, vol. 78, pp. 900–904.

    Article  Google Scholar 

  16. Kirchheim, R., Modeling Electromigration and Induced Stresses in Aluminum Lines, in Mat. Res. Soc. Symp. Proc., 1993, vol. 309, pp. 101–110.

    Google Scholar 

  17. Sasagava, K., Nakamura, N., Saka, M., and Abe, H., A New Approach to Calculate Atomic Flux Divergence by Electromigration, Trans. ASME, 1998, vol. 120, no. 12, pp. 360–366.

    Google Scholar 

  18. Abe, H., Sasagava, K., and Saka, M., Electromigration Failure of Metal Lines, Int. Fracture, 2006, vol. 138, no. 1, pp. 219–240.

    Article  MATH  Google Scholar 

  19. Makhviladze, T.M., Sarychev, M.E., and Zhitnikov, Yu.V., Modeling of Electromigration and Void Nucleation Kinetics in Polycrystalline Metal Lines, in Proc. IPT RAS: Modeling and Simulation of Submicron Technology and Devices, 1997, vol. 13, pp. 98–114.

    Google Scholar 

  20. Goldstein, R.V., Makhviladze, T.M., Sarychev, M.E., Zhitnikov, Yu.V., et al., Modeling of Electromigration and Void Nucleation Kinetics in Via Structures, in Proc. IPT RAS: Modeling and Simulation of Submicron Technology and Devices, 1996, vol. 11, pp. 61–76.

    Google Scholar 

  21. Sarychev, M.E., Zhitnikov, Yu.V., Makhviladze, T.M., Borucki, L., and Liu, C.-L., General Model for Mechanical Stress Evolution during Electromigration, J. Appl. Phys., 1999, vol. 86, no. 6, pp. 3068–3075.

    Article  Google Scholar 

  22. Makhviladze, T.M., Sarychev, M.E., Zhitnikov, Yu.V., Borucki, L., and Liu, C.-L., A New, General Model for Mechanical Stress Evolution during Electromigration, Thin Solid Films, 2000, vol. 365, pp. 211–218.

    Article  Google Scholar 

  23. Goldstein, R.V., Makhviladze, M.E., and Sarychev, M.E., Modeling Reliability and Mechanisms of Destruction of Metallization and Interconnects in Micro- and Nanoelectronic Structures, in Nanotechnology International Forum, Abstracts, Scientific and Technological Sections, Moscow, 2008, vol. 2, pp. 140–142.

    Google Scholar 

  24. Makhviladze, T.M., Sarychev, M.E., and Zhitnikov, Yu.V., A Model for Calculations of Effective Ion Charges in Microcircuit Interconnects, in Proc. Int. Conf. on IC Design and Technology (ICICDT), Grenoble, 2008, pp. G17–G20.

  25. Makhviladze, T. and Sarychev, M., New Results of Modeling in Micro- and Nanoelectronics, in Int. Conf. on IC Micro- and Nanoelectronics (ICMNE-2007), Book of Abstracts, Moscow, 2007, p. L1–06.

  26. Shatzkes, M. and Lloyd, J.R., A Model for Conductor Failure Considering Diffusion Concurrently with Electromigration Resulting in a Current Exponent of 2, J. Appl. Phys., 1986, vol. 59, pp. 3890–3893.

    Article  Google Scholar 

  27. Clement, J.J., Vacancy Supersaturation Model for Electromigration Failure under DC and Pulced DC Stress, J. Appl. Phys., 1992, vol. 71, pp. 4264–4268.

    Article  Google Scholar 

  28. Nix, W.D. and Arzt, E., On Void Nucleation and Growth in Metal Interconnect Lines under Electromigration Conditions, Metall. Trans. A, 1992, vol. 23, pp. 2007–2013.

    Article  Google Scholar 

  29. Cheremskoi, P.G., Slezov, V.V., and Betekhtin, V.I., Pory v tverdom tele (Pores in a Solid-State Body), Moscow: Energoatomizdat, 1990.

    Google Scholar 

  30. Kristensen, Dzh.U., Phase Transformations, in Fizicheskoe metallovedenie (Physical Metallurgy), 1968, issue 2, pp. 227–346.

  31. Rosenberg, R. and Ohring, M.J., Void Formation and Growth during Electromigration in Thin Films, J. Appl. Phys., 1971, vol. 42, pp. 5671–5679.

    Article  Google Scholar 

  32. Raj, R. and Ashby, M.F., Intergranular Fracture at Elevated Temperature, Acta Metall., 1975, vol. 23, pp. 653–666.

    Article  Google Scholar 

  33. Russell, K.C., Nucleation of Voids in Irradiated Metals, Acta Metall., 1971, vol. 19, pp. 753–758.

    Article  Google Scholar 

  34. Russell, K.C., The Theory of Void Nucleation in Metals, Acta Metall., 1978, vol. 26, pp. 1615–1630.

    Article  Google Scholar 

  35. Bokshtein, B.S., Diffuziya v metallakh (Diffusion in Metals), Moscow: Metallurgiya, 1978.

    Google Scholar 

  36. Sorbello, R.S., A Pseudopotential Based Theory of the Driving Forces for Electromigration in Metals, J. Phys. Chem. Solids, 1973, vol. 34, no. 3, pp. 937–950.

    Article  Google Scholar 

  37. Zhitnikov, Yu.V. and Sarychev, M.E., Modeling of Effective Ion Charges on Metal Grain Boundaries, in Tr. FTIAN, 2001, vol. 17, pp. 83–96.

    Google Scholar 

  38. Landau, L.D. and Lifshitz, E.M., Teoriya uprugosti (Theory of Elasticity), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  39. Zeldovich, Ya.B., On Phase Nucleation: Cavitation, Zh. Eksp. Teor. Fiz., 1942, vol. 12, pp. 525–538.

    Google Scholar 

  40. Feder, J., Russell, K.C., Lothe, J., and Pound, G.M., Homogeneous Nucleation and Growth of Droplets in Vapours, Adv. Phys., 1966, vol. 15, pp. 111–178.

    Article  Google Scholar 

  41. Regel’, V.R., Slutsker, A.I., and Tomashevskii, E.E., Kineticheskaya priroda prochnosti tverdykh tel (The Kinetic Nature of the Strength of Solids), Moscow: Nauka, 1974.

    Google Scholar 

  42. Kawasaki, H., Lee, C., Yu, T.K., Realistic Electromigration Lifetime Projection of VLSI Interconnects, Thin Solid Films, 1994, vol. 253, pp. 508–512.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia

    K. A. Valiev, R. V. Goldstein, Yu. V. Zhitnikov, T. M. Makhviladze & M. E. Sarychev

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  1. K. A. Valiev
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  2. R. V. Goldstein
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  3. Yu. V. Zhitnikov
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  4. T. M. Makhviladze
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  5. M. E. Sarychev
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Correspondence to T. M. Makhviladze.

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Original Russian Text © K.A. Valiev, R.V. Goldstein, Yu.V. Zhitnikov, T.M. Makhviladze, M.E. Sarychev, 2009, published in Mikroelektronika, 2009, Vol. 38, No. 6, pp. 404–427.

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Valiev, K.A., Goldstein, R.V., Zhitnikov, Y.V. et al. Nano- and micrometer-scale thin-film-interconnection failure theory and simulation and metallization lifetime prediction, Part 1: A general theory of vacancy transport, mechanical-stress generation, and void nucleation under electromigration in relation to multilevel-metallization degeneration and failure. Russ Microelectron 38, 364–384 (2009). https://doi.org/10.1134/S106373970906002X

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