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2 - Fundamentals of Electromigration

Published online by Cambridge University Press:  05 May 2022

Paul S. Ho ,
Chao-Kun Hu ,
Martin Gall  and
Valeriy Sukharev
Paul S. Ho
Affiliation:
University of Texas, Austin
Chao-Kun Hu
Affiliation:
IBM T J Watson Research Center, New York
Martin Gall
Affiliation:
GlobalFoundries
Valeriy Sukharev
Affiliation:
Siemens Business
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Summary

In this chapter, electromigration is formulated as a phenomenon of mass transport in metals under an electrical current driving force within the framework of irreversible thermodynamics. Based on this approach, the solute effect on electromigration is analyzed by considering the correlation in atomic jumping processes, a problem that is of interest to understand how solute addition can affect electromigration in metals. This is followed by a review of the theory of the electromigration driving force and a discussion of the controversy of the electron screening effect. This chapter is concluded by reviewing the results on substitutional and interstitial electromigration in bulk metals.

Keywords

electromigrationfundamentalsirreversible thermodynamicstheorysubstitutional systemsinterstitial systems
Type
Chapter
Information
Electromigration in Metals
Fundamentals to Nano-Interconnects
 , pp. 8 - 33
Publisher: Cambridge University Press
Print publication year: 2022

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References

Adda, Y. and Philibert, J., La Difusion dans les Solides, vol. 1 (Paris: Presses Universitaires de France, 1966).Google Scholar
Huntington, H. B., Diffusion in Solids: Recent Developments, ed. Nowick, A. S. and Burton, J. J. (New York: Academic Press, 1974), pp. 303–352.Google Scholar
Balluffi, R. W., Allen, S. M. and Carter, W. C., Kinetics of Materials (Wiley Pub., 2005).CrossRefGoogle Scholar
Ho, P. S. and Kwok, T., Electromigration in metals, Reports on Progress in Physics 52 (1989), 301–348.Google Scholar
Ho, P. S., Solute effects on electromigration, Physical Review B8 (1973), 4534: https://doi.org/10.1103/PhysRevB.8.4534.CrossRefGoogle Scholar
d’Heurle, F. M. and Rosenberg, R., Physics of Thin Films, vol. 7 (New York: Academic Press, 1973) p. 257.Google Scholar
Doan, N. V., Effet de valence en electromigration dans l’argent, Journal of Physics and Chemistry of Solids 31 (1970), 2079–2085.Google Scholar
Manning, J. R., Diffusion Kinetics for Atoms in Crystals (Princeton: Van Nostrand-Reinhold, 1968).Google Scholar
Bocquet, J. L., Correlation factor for diffusion in cubic crystals with solute–vacancy interactions of arbitrary range, Philosophical Magazine 94 (2014), 3603–3631.Google Scholar
Howard, R. E. and Manning, J. R., Kinetics of solute-enhanced diffusion in dilute face-centered-cubic alloys, Physical Review 154 (1967): https://doi.org/10.1103/PhysRev.154.561.Google Scholar
Doan, N. V., A new method of determination of the vacancy jump frequency ratios by electromigration in dilute alloy, Journal of Physics and Chemistry of Solids 33 (1972), 2161–2166.Google Scholar
Ames, I., d’Heurle, F. M., and Horstmann, R. E., Reduction of electromigration in aluminum films by copper doping, IBM Journal of Research and Development 44 (1970): 89–91.Google Scholar
Hu, C. K., Ohm, J., Gignac, L. M. et al., Electromigration in Cu(Al) and Cu(Mn) damascene lines, Journal of Applied Physics 111 (2012), 093722.Google Scholar
Fiks, V. B., Forces produced by conduction electrons in metals located in external fields, Soviet Physics of the Solid State 1 (1959), 14.Google Scholar
Huntington, H. B. and Grone, A. R., Current-induced marker motion in gold wires, Journal of Physics and Chemistry of Solids 20 (1961), 76–81.CrossRefGoogle Scholar
Bosvieux, C. and Friedel, J., Sur l’electrolyse des alliages metalliques, Journal of Physics and Chemistry of Solids 23 (1962), 123–136.Google Scholar
Sorbello, R. S., Electro- and Thermo-Transport in Metals and Alloys, ed. Hummel, R. E. and Huntington, H. B. (New York: AIME, 1977), ch.1.Google Scholar
Sorbello, R. S., Theory of the direct force in electromigration, Physical Review B 31 (1985), 798. https://doi.org/10.1103/PhysRevB.31.798.Google Scholar
Verbruggen, A. H., Unpublished PhD Thesis, Free University of Amsterdam (1985).Google Scholar
Guilmin, P., Turban, L., and Gerl, M., Electrotransport d’impuretes dans Cu et Ni, Journal of Physics and Chemistry of Solids 34 (1973), 951–959.CrossRefGoogle Scholar
Ho, P. S. and Huntington, H. B., Electromigration and void observation in silver, Journal of Physics and Chemistry of Solids 27 (1966), 1319–1329.Google Scholar
Das, A. K. and Peierls, R., The force of electromigration, Journal of Physics C: Solid State Physics 8 (1975), 3348.Google Scholar
Sorbello, R. S. and Dasgupta, B., Local fields in electron transport: Application to electromigration, Physical Review B 16 (1977), 5193; https://doi.org/10.1103/PhysRevB16.5193.Google Scholar
Schaich, W. L., Theory of the driving force of electromigration: Weak-charge solutions, Physical Review B 19 (1979), 620; doi.org/10.1103/PhysRevB.19.620.Google Scholar
Kumar, P. and Sorbello, R. S., Linear response theory of the driving forces for electromigration, Thin Solid Films 25 (1975), 25–35.Google Scholar
Sham, L. J., Microscopic theory of the driving force in electromigration, Physical Review B 12 (1975), 3142; https://doi.org/10.1103/PhysRevB.12.3142.CrossRefGoogle Scholar
Schaich, W. L., Theory of the driving force for electromigration, Physical Review B 13 (1976), 3350: https://doi.org/10.1103/PhysRevB.13.3350.Google Scholar
Rimbey, P. R. and Sorbello, R. S., Strong-coupling theory for the driving force in electromigration, Physical Review B 21 (1980), 2150: https://doi.org/10.1103/PhysRevB.21.215.Google Scholar
Landauer, R. and Woo, J. W., Driving force in electromigration, Physical Review B 10 (1974), 1266: https://doi.org/10.1103/PhysRevB.10.1266.Google Scholar
Landauer, R., Spatial carrier density modulation effects in metallic conductivity, Physical Review B 14 (1976),1474: https://doi.org/10.1103/PhysRevB.14.1474.CrossRefGoogle Scholar
Verbruggen, A. H., Griessen, R., and de Groot, D. G., Electromigration of hydrogen in vanadium, niobium and tantalum, Journal of Physics F: Metal Physics 16 (1986), 557.Google Scholar
Hsieh, M. Y., Huntington, H. B. and Jeffrey, R. N., Electromigration of Au and Ag in lead. Crystal Lattice Defects 7 (1977), 9–22.Google Scholar
Gangulee, A. and d’Heurle, F. M., Electromigration and transport reversal in copper–silver thin films, Journal of Physics and Chemistry of Solids 35 (1974), 293–299.Google Scholar
Sorbello, R. S., A pseudopotential based theory of the driving forces for electromigration in metals, Journal of Physics and Chemistry of Solids 34 (1973), 937–950.Google Scholar
Feit, M. D. and Huntington, H. B., Transport in nearly-free-electron-model metals. I. Point-defect scattering, Physical Review B5 (1972), 1416; https://doi.org/10.1103/PhysRevB.5.1416.Google Scholar
Huntington, H. B., Alexander, W. B., Feit, W. B., and Routbout, J. L., Atomic Transport in Solids and Liquids, ed. Lodding, A. and Lagerwall, T. (Tubingen: Z. Naturf: 1971), p. 91.Google Scholar
Genoni, T. C. and Huntington, H. B., Transport in nearly-free-electron metals. IV. Electromigration in zinc, Physical Review 16 (1977), 1344. https://doi.org/10.1103/PhysRevB.16.Google Scholar
Jones, W. and Dunleavy, H. N., The calculation of electromigration forces and resistivities for liquid binary alloys, Journal of Physics F: Metal Physics 9 (1979), 1541.Google Scholar
Gupta, R. P., Serruys, Y., Brebec, G. and Adda, Y., Calculation of the effective valence for electromigration in niobium, Physical Review B 27 (1983), 672. https://doi.org/10.1103/PhysRevB.27.672.CrossRefGoogle Scholar
d’Heurle, F. M. and Ho, P. S., Thin Films: Interdiffusion and Reactions, ed. Poate, J M et al. (New York: Wiley-Interscience, 1978), p. 183.Google Scholar
Penney, R. V., Current-induced mass transport in aluminum, Journal of Physics and Chemistry of Solids 25 (1964), 335–345.Google Scholar
Ho, P. S. and Howard, J. K., Grain‐boundary solute electromigration in polycrystalline films, Journal of Applied Physics 45 (1974), 3229. https://doi.org/10.1063/1.1663763.CrossRefGoogle Scholar
Tai, K. L. and Ohring, M., Grain‐boundary electromigration in thin films. I. Low‐temperature theory, Journal of Applied Physics 48 (1977), 28; https://doi.org/10.1063/1.323375.Google Scholar
Tai, K. L. and Ohring, M., Grain‐boundary electromigration in thin films. II. Tracer measurements in pure Au, Journal of Applied Physics 48 (1977), 28; https://doi.org/10.1063/1.323336.Google Scholar
Ho, P. S., Analysis of grain boundary electromigration, Journal of Applied Physics 49 (1978), 2735; https://doi.org/10.1063/1.325196.Google Scholar
Ho, P. S., Lewis, J. E., and Howard, J. K., Kirkendall study of electromigration in thin films, Thin Solid Films 25 (1975), 301–315.Google Scholar
Blech, I. A. and Kinsbron, E., Electromigration in thin gold films on molybdenum surfaces Thin Solid Films 25 (1975), 327–334.Google Scholar
1. Coehn, A. and Specht, W., Über die Beteiligung von Protonen an der Elektrizitätsleitung in Metallen. Z. Physik 62 , 1–31 (1930). https://doi.org/10.1007/BF01340398.CrossRefGoogle Scholar
Seith, W. and Kubaschewski, O., Die elektrolytische Überführung von Kohlenstoff in festen Stahl, Zeitschrift für Elektrochemie 41 (1935), 551. https://doi.org/10.1002/bbpc.19350410755.Google Scholar
Carson, O. N., Schmidt, F. A., and Pederson, D. T., Electrotransport of interstitial atoms in yttrium, Journal of Less-Common Metals 10 (1966), 1–11.Google Scholar
Pederson, D. T. and Schmidt, F.A., Electrotransport of carbon, nitrogen and oxygen in lutetium, Journal of Less-Common Metals 18 (1969), 111–116.Google Scholar
Pederson, D. T. and Schmidt, F. A., Electrotransport of carbon, nitrogen and oxygen in gadolinium, Journal of Less-Common Metals 29 (1972), 321–327.Google Scholar
Flynn, C. P. and Stoneham, A. M., Quantum theory of diffusion with application to light interstitials in metals, Physical Review B 1 (1970), 3966. https://doi.org/10.1103/PhysRevB.1.3966.Google Scholar
Stoneham, A. M. and Flynn, C. P., Journal of Physics F: Metal Physics 3 (1973), 503.CrossRefGoogle Scholar
Wever, H., Elecktro und thermotransport in metals. Electro- and Thermo-Transport in Metals and Alloys, ed. Hummel, R. E. and Huntington, H. B. (New York: AIME, 1977) Ch. 8, 140–159.Google Scholar
Erckmann, V. and Wipf, H., Electrotransport of Interstitial H and D in V, Nb, and Ta as Experimental Evidence for the Direct Field Force, Physical Review Letters 37 (1976), 341. https://doi.org/10.1103/PhysRevLett.37.341.Google Scholar
Verbruggen, A. H., Griessen, R., and de Groot, D. G., Electromigration of hydrogen in vanadium, niobium and tantalum, Journal of Physics F: Metal Physics 16 (1986), 557. https://doi.org/10.1088/0305-4608/16/5/006.Google Scholar
Hu, C. K. and Huntington, H. B., Diffusion and electromigration of impurities in lead solders, Diffusion Phenomena in Thin Films and Microelectronic Materials, ed. Gupta, D. and Ho, P. S. (Park Ridge: Noyes Publications, 1988), 2546–581.Google Scholar
Oriani, R. A. and Gonzales, O. D., Electromigration of hydrogen isotopes dissolved in alpha iron and in nickel, Transactions of the Metallurgical Society of AIME 239 (1967), 1041.Google Scholar
Einzinger, R. E. and Huntington, H. B., Electromigration and permeation of hydrogen and deuterium in silver, Journal of Physics and Chemistry of Solids 35 (1974), 1563–1573.Google Scholar
Herold, A., Mareche, J. F., and Rat, J. C., Electromigration des isotopes de l’hydrogene dans le vanadium, le niobium et le tantale, Academy of Science, Paris 273 (1971), 1736–1739.Google Scholar
Seith, W. and Wever, H., A new effect in the electrolytic transfer in solid alloys, Z. Elektrochem 57 891 (1953), 61.Google Scholar
Verhoeven, J., Electrotransport in metals, Metall. Rev. 8 (1963), 311–368.Google Scholar
Pai, S. T. and Marton, J. P., Electromigration in metals, Canadian Journal of Physics 55 (1977), 103. https://doi.org/10.1139/p77–013.CrossRefGoogle Scholar
Gilder, H. M. and Lazarus, D., Effect of high electronic current density on the motion of Au 195 and Sb 125 in gold, Physical Review 145 (1966), 507–511.Google Scholar
Doan, N. V., Vacancy flow effect on electromigration in silver, Journal of Physics and Chemistry of Solids 32 (1971), 2135–2143.CrossRefGoogle Scholar
Patil, H. R. and Huntington, H. B., Electromigration and associated void formation in silver, Journal of Physics and Chemistry of Solids 31 (1970), 463–474.CrossRefGoogle Scholar
Sullivan, G. A., Search for reversal in copper electromigration, Journal of Physics and Chemistry of Solids 28 (1967a), 347–350.CrossRefGoogle Scholar
Grimme, D., Atomic Transport in Solids and Liquids, ed. Lodding, A. and Lagerwall, T. (Tübingen: Z. Naturf. 1971), 178.Google Scholar
Thernquist, P. and Lodding, A., Electrotransport of lattice defects in lithium metal, Z. Naturforsch. 23a (1968), 627–628.Google Scholar
Sullivan, G. A., Electromigration and thermal transport in sodium metal, Physical Review 154 (1967b), 605.Google Scholar
Routbort, J. L., Electromigration in zinc single crystals, Physical Review 176 (1968), 796.Google Scholar
Alexander, W. B., Electromigration in single crystal cadmium 1, Zeitschrift für Naturforschung A 26 (1971), 18–20.Google Scholar
Wohlgemuth, J., Electromigration in polycrystalline and single crystal magnesium. Journal of Physics and Chemistry of Solids 36 (1975), 1025–1031.Google Scholar
Heumann, T. and Meiners, H., Electrotransport in aluminium, Z. Phys. 57 (1966), 571.Google Scholar
Lodding, A., Current induced motion of lattice defects in indium metal, Journal of Physics and Chemistry of Solids 26 (1965), 143–151.Google Scholar
Lodding, A., Electrotransport and effective self-diffusion in pure liquid gallium metal, Journal of Physics and Chemistry of Solids 28 (1967), 557–568.Google Scholar
Lundan, A., Christofferson, S., and Lodding, A., Electrotransport in molten indium-thallium alloys, Z. Naturf A 27 (1972), 156.Google Scholar
Hering, H. and Wever, H., Electro- and thermotransport in nickel, Z. Phys. Chem.1 (1967), 310–325.Google Scholar
Ho, P. S., Electromigration and Soret effect in cobalt, Journal of Physics and Chemistry of Solids 27 (1966), 1331–1338.Google Scholar
van Gurp, G. J., Electromigration in cobalt films, Thin Solid Films 38 (1976), 295–311.Google Scholar
van Gurp, G. J., Electromigration and Hall effect in cobalt films, Journal of Physics and Chemistry of Solids 38 (1977), 627–633.Google Scholar
Huntington, H. B. and Ho, P. S., Journal of the Physical Society of Japan Supplement I1 18 (1963), 202.Google Scholar
Campbell, D. R. and Huntington, H. B., Thermomigration and electromigration in zirconium, Physical Review 179 (1969), 601.Google Scholar
D'Amico, J. F. and Huntington, H. B., Electromigration and thermomigration in gamma-uranium, Journal of Physics and Chemistry of Solids 30 (1969), 2607–2621.Google Scholar
Kuz’menko, P. P., Ukrain. Fig. Zhur. 7 (1962), 117.Google Scholar
Khar’kov, E. I. and Kuz’menko, P. P., Ukrain. Fig. Zhur. 5 (1960), 428.Google Scholar
Khosla, A. and Huntington, H. B., Electromigration in tin single crystals, Journal of Physics and Chemistry of Solids 36 (1975), 395–399.Google Scholar
Doan, N. V., Effet de valence en electromigration dans l’argent, Journal of Physics and Chemistry of Solids 31 (1970), 2079–2085.Google Scholar
Blech, I. A. and Sello, H., The failure of thin aluminum current carrying strips on oxidized Silicon, Fifth Annual Symposium on the Physics of Failure in Electronics, (1966), 496–505.Google Scholar

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