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Exploring effective charge in electromigration using machine learning

  • Yu-chen Liu (a1) (a2), Benjamin Afflerbach (a2), Ryan Jacobs (a2), Shih-kang Lin (a1) (a3) (a4) and Dane Morgan (a2)...

Abstract

The effective charge of an element is a parameter characterizing the electromigration effect, which can determine the reliability of interconnection in electronic technologies. In this work, machine learning approaches were employed to model the effective charge (z*) as a linear function of physically meaningful elemental properties. Average fivefold (leave-out-alloy-group) cross-validation yielded root-mean-square-error divided by whole data set standard deviation (RMSE/σ) values of 0.37 ± 0.01 (0.22 ± 0.18), respectively, and R2 values of 0.86. Extrapolation to z* of totally new alloys showed limited but potentially useful predictive ability. The model was used in predicting z* for technologically relevant host–impurity pairs.

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Corresponding author

Address all correspondence to Dane Morgan at ddmorgan@wisc.edu

References

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1.Tu, K.N., Liu, Y., and Li, M.: Effect of Joule heating and current crowding on electromigration in mobile technology. Appl. Phys. Rev. 4, 011101 (2017).10.1063/1.4974168
2.Huntington, H.B. and Grone, A.R.: Current-induced marker motion in gold wires. J. Phys. Chem. Solids 20, 76 (1961).10.1016/0022-3697(61)90138-X
3.Bosvieux, C. and Friedel, J.: Sur l'electrolyse des alliages metalliques. J. Phys. Chem. Solids 23, 123 (1962).
4.Blech, I.A.: Electromigration in thin aluminum films on titanium nitride. J. Appl. Phys. 47, 1203 (1976).
5.Lin, S.-k, Liu, Y.-c., Chiu, S.-J., Liu, Y.-T., and Lee, H.-Y.: The electromigration effect revisited: non-uniform local tensile stress-driven diffusion. Sci. Rep. 7, 3082 (2017).10.1038/s41598-017-03324-5
6.Sorbello, R.S.: Theory of electromigration. Solid State Phys. 51, 159 (1997).
7.Ho, P.S. and Kwok, T.: Electromigration in metals. Rep. Prog. Phys. 52, 301 (1989).10.1088/0034-4885/52/3/002
8.Shi, J. and Huntington, H.B.: Electromigration of gold and silver in single crystal tin. J. Phys. Chem. Solids 48, 693 (1987).10.1016/0022-3697(87)90060-6
9.van Ek, J., Dekker, J.P., and Lodder, A.: Electromigration of substitutional impurities in metals: theory and application in Al and Cu. Phys. Rev. B: Condens. Matter 52, 8794 (1995).10.1103/PhysRevB.52.8794
10.Dekker, J.P., Lodder, A., and van Ek, J.: Theory for the electromigration wind force in dilute alloys. Phys. Rev. B: Condens. Matter 56, 12167 (1997).
11.Dekker, J.P. and Lodder, A.: Calculated electromigration wind force in face-centered-cubic and body-centered-cubic metals. J. Appl. Phys. 84, 1958 (1998).10.1063/1.368327
12.Dekker, J.P., Gumbsch, P., Arzt, E., and Lodder, A.: Calculation of the electromigration wind force in Al alloys. Phys. Rev. B: Condens. Matter 59, 7451 (1999).10.1103/PhysRevB.59.7451
13.Lodder, A.: Direct force controversy in electromigration exit. Defect Diffus. Forum 261–262, 77 (2007).
14.Agrawal, A. and Choudhary, A.: Perspective: materials informatics and big data: realization of the “fourth paradigm” of science in materials science. APL Mater. 4, 053208 (2016).
15.Ramprasad, R., Batra, R., Pilania, G., Mannodi-Kanakkithodi, A., and Kim, C.: Machine learning in materials informatics: recent applications and prospects. NPJ Comput. Mater. 3, 54 (2017).10.1038/s41524-017-0056-5
16.Ward, L., Agrawal, A., Choudhary, A., and Wolverton, C.: A general-purpose machine learning framework for predicting properties of inorganic materials. NPJ Comput. Mater. 2, 16028 (2016).
17.Li, W., Jacobs, R., and Morgan, D.: Predicting the thermodynamic stability of perovskite oxides using machine learning models. Comput. Mater. Sci. 150, 454 (2018).10.1016/j.commatsci.2018.04.033
18.Dimiduk, D.M., Holm, E.A., and Niezgoda, S.R.: Perspectives on the impact of machine learning, deep learning, and artificial intelligence on materials, processes, and structures engineering. Integr. Mater. Manuf. Innovation 7, 157 (2018).10.1007/s40192-018-0117-8
19.Wu, H., Lorenson, A., Anderson, B., Witteman, L., Wu, H., Meredig, B., and Morgan, D.: Robust FCC solute diffusion predictions from ab-initio machine learning methods. Comput. Mater. Sci. 134, 160 (2017).10.1016/j.commatsci.2017.03.052
20.Tanaka, I., Rajan, K., and Wolverton, C.: Data-centric science for materials innovation. MRS Bull. 43, 659 (2018).10.1557/mrs.2018.205
21.De Jong, M., Chen, W., Notestine, R., Persson, K., Ceder, G., Jain, A., Asta, M., and Gamst, A.: A statistical learning framework for materials science: application to elastic moduli of k-nary inorganic polycrystalline compounds. Sci. Rep. 6, 34256 (2016).10.1038/srep34256
22.Mueller, T., Kusne, A.G., and Ramprasad, R.: Machine learning in materials science: recent progress and emerging applications. Rev. Comput. Chem. 29, 186 (2016).
23.Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, É.: Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12, 2825 (2011).
24.Morgan, D., Afflerbach, B., Jacobs, R., Mayeshiba, T., and Wu, H.: MAterials Simulation Toolkit – Machine Learning (MAST-ML) (GitHub, GitHub repository, Madison, WI, USA, 2017).
25.Raschka, S.: MLxtend: providing machine learning and data science utilities and extensions to Python's scientific computing stack. J. Open Source Softw. 3, 638 (2018).
26.DiGiacomo, G., Peressini, P., and Rutledge, R.: Diffusion coefficient and electromigration velocity of copper in thin silver films. J. Appl. Phys. 45, 1626 (1974).
27.Park, C.W. and Vook, R.W.: Electromigration-resistant Cu–Pd alloy films. Thin Solid Films 226, 238 (1993).
28.Lee, K.L., Hu, C.K., and Tu, K.N.: In situ scanning electron microscope comparison studies on electromigration of Cu and Cu(Sn) alloys for advanced chip interconnects. J. Appl. Phys. 78, 4428 (1995).
29.Gilder, H.M. and Lazarus, D.: Effect of high electronic current density on the motion of Au195 and Sb125 in gold. Phys. Rev. 145, 507 (1966).10.1103/PhysRev.145.507
30.Bekiaris, N., Wu, Z., Ren, H., Naik, M., Park, J.H., Lee, M., Ha, T.H., Hou, W., Bakke, J.R., Gage, M., Wang, Y., and Tang, J.: Cobalt fill for advanced interconnects. In 2017 IEEE International Interconnect Technology Conference (IITC) (2017), pp. 1.10.1109/IITC-AMC.2017.7968981
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