Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T13:55:46.583Z Has data issue: false hasContentIssue false
  • English
  • Français

Exploring effective charge in electromigration using machine learning

Published online by Cambridge University Press:  27 May 2019

Yu-chen Liu ,
Benjamin Afflerbach ,
Ryan Jacobs ,
Shih-kang Lin  and
Dane Morgan
Yu-chen Liu
Affiliation:
Department of Materials Science and Engineering, National Cheng Kung University, Tainan city 70101, Taiwan Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, USA
Benjamin Afflerbach
Affiliation:
Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, USA
Ryan Jacobs
Affiliation:
Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, USA
Shih-kang Lin
Affiliation:
Department of Materials Science and Engineering, National Cheng Kung University, Tainan city 70101, Taiwan Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan city 70101, Taiwan Hierarchical Green-Energy Materials (Hi-GEM) Research Center, National Cheng Kung University, Tainan 70101, Taiwan
Dane Morgan*
Affiliation:
Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, USA
*
Address all correspondence to Dane Morgan at ddmorgan@wisc.edu
Get access

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.

Type
Artificial Intelligence Research Letters
Information
MRS Communications , Volume 9 , Issue 2 , June 2019 , pp. 567 - 575
Copyright
Copyright © Materials Research Society 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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).10.1063/1.4974168Google Scholar
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-XGoogle Scholar
3.Bosvieux, C. and Friedel, J.: Sur l'electrolyse des alliages metalliques. J. Phys. Chem. Solids 23, 123 (1962).Google Scholar
4.Blech, I.A.: Electromigration in thin aluminum films on titanium nitride. J. Appl. Phys. 47, 1203 (1976).Google Scholar
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/s41598-017-03324-5Google Scholar
6.Sorbello, R.S.: Theory of electromigration. Solid State Phys. 51, 159 (1997).Google Scholar
7.Ho, P.S. and Kwok, T.: Electromigration in metals. Rep. Prog. Phys. 52, 301 (1989).10.1088/0034-4885/52/3/002Google Scholar
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)90060-6Google Scholar
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.52.8794Google Scholar
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).Google Scholar
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).10.1063/1.368327Google Scholar
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.59.7451Google Scholar
13.Lodder, A.: Direct force controversy in electromigration exit. Defect Diffus. Forum 261–262, 77 (2007).Google Scholar
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).Google Scholar
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/s41524-017-0056-5Google Scholar
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).Google Scholar
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.2018.04.033Google Scholar
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/s40192-018-0117-8Google Scholar
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.2017.03.052Google Scholar
20.Tanaka, I., Rajan, K., and Wolverton, C.: Data-centric science for materials innovation. MRS Bull. 43, 659 (2018).10.1557/mrs.2018.205Google Scholar
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/srep34256Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
27.Park, C.W. and Vook, R.W.: Electromigration-resistant Cu–Pd alloy films. Thin Solid Films 226, 238 (1993).Google Scholar
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).Google Scholar
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.145.507Google Scholar
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.2017.7968981Google Scholar
Supplementary material: File

Liu et al. supplementary material

Liu et al. supplementary material 1

Download Liu et al. supplementary material(File)
File 783.5 KB