Determination of electric current induced motion of a symmetrically tilt Σ5 grain boundary in aluminum using quantum transport calculations

Abstract

Electric current induced structural change is a critical reliability issue in nanoelectronics. So far, microstructure evolution models have considered the electromigration (EM) force caused by high current density to be uniform everywhere in the conductor. In this work, the EM force acting on atoms near Σ5 grain boundaries (GBs) of aluminum is calculated for the first time using a quantum transport method. Although the EM forces exhibit a complex distribution near the GB, the regional averaged EM force from GB atoms points toward the opposite direction of the bulk EM force. This striking result leads to GB motion in the direction of the electron current, whereas previous structural evolution models considering uniform EM forces predict GB motion in the opposite direction. This result highlights the necessity to consider the current-induced grain structure evolution at quantum mechanical level since the local EM force on atoms depends on the electron scattering behavior of the GB structure.

Keywords

Grain boundary / electromigration / multiscale modelling

References

[1] Kim M.,Bui-thi T.,Kang S.,Hong S.,Nam Han H.. Electric current-induced phenomena in metallic materials Curr. Opin. Solid State Mater. Sci. 2024 32 101190

[2] Sorbello R.. A pseudopotential based theory of the driving forces for electromigration in metals J. Phys. Chem. Solids 1973 34 937 50

[3] Dekker J. P.,Lodder A.,Van Ek J.. Theory for the electromigration wind force in dilute alloys Phys. Rev. B. 1997 56 12167 77

[4] Lodder A.,Dekker J. P.. The electromigration force in metallic bulk. In AIP Conference Proceedings; American Institute of Physics, 1998, 418, 315-28

[5] Tu K. N.. Recent advances on electromigration in very-large-scale-integration of interconnects J. Appl. Phys. 2003 94 5451 73

[6] De Orio R.,Ceric H.,Selberherr S.. Physically based models of electromigration: from black’s equation to modern TCAD models Microelectron. Reliab. 2010 50 775 89

[7] Liu J.,Jia D.,Fu Y..et al. Electroplasticity effects: from mechanism to application Int. J. Adv. Manuf. Technol. 2023 131 3267 86

[8] Li X.,Zhu Q.,Hong Y..et al. Revealing the pulse-induced electroplasticity by decoupling electron wind force Nat. Commun. 2022 13 6503 PMC9622885

[9] Gu S.,Kimura Y.,Yan X..et al. Micromachined structures decoupling Joule heating and electron wind force Nat. Commun. 2024 15 6044 PMC11258259

[10] Xiang Z.,Li H.,Zhang X.,Gao P.,Zhan M.. Grain growth kinetics of a nickel-based superalloy under electric pulse treatment Materials. 2025 18 2019 PMC12072762

[11] Ceric H.,Selberherr S.. Electromigration in submicron interconnect features of integrated circuits Mater. Sci. Eng. R Rep. 2011 71 53 86

[12] Bhate D. N.,Kumar A.,Bower A. F.. Diffuse interface model for electromigration and stress voiding J. Appl. Phys. 2000 87 1712 21

[13] Chakraborty S.,Kumar P.,Choudhury A.. Phase-field modeling of grain-boundary grooving and migration under electric current and thermal gradient Acta Mater. 2018 153 377 90

[14] Liang S. B.,Ke C. B.,Wei C.,Zhou M. B.,Zhang X. P.. Phase field modeling of grain boundary migration and preferential grain growth driven by electric current stressing J. Appl. Phys. 2018 124 175109

[15] Farmer W.,Ankit K.. Phase-field simulations of electromigration-induced defects in interconnects with non-columnar grain microstructure J. Appl. Phys. 2020 127 175301

[16] Clark K. W.,Zhang X. G.,Vlassiouk I. V.,He G.,Feenstra R. M.,Li A. P.. Spatially resolved mapping of electrical conductivity across individual domain (grain) boundaries in graphene ACS Nano 2013 7 7956 66

[17] Bevan K. H.,Guo H.,Williams E. D.,Zhang Z.. First-principles quantum transport theory of the enhanced wind force driving electromigration on Ag(111) Phys. Rev. B. 2010 81 235416

[18] Bevan K. H.,Zhu W.,Stocks G. M.,Guo H.,Zhang Z.. Local fields in conductor surface electromigration: a first-principles study in the low-bias ballistic limit Phys. Rev. B. 2012 85 235421

[19] Zhu Q.,Cao G.,Wang J..et al. In situ atomistic observation of disconnection-mediated grain boundary migration Nat. Commun. 2019 10 156 PMC6329749

[20] Schratt A. A.,Mohles V.. Efficient calculation of the ECO driving force for atomistic simulations of grain boundary motion Comput. Mater. Sci. 2020 182 109774

[21] Wang N.,Ji Y.,Wang Y.,Wen Y.,Chen L.. Two modes of grain boundary pinning by coherent precipitates Acta Mater. 2017 135 226 32

[22] Datta S.. Quantum Transport: Atom to Transistor; Cambridge University Press, 2005

[23] Taylor J.,Guo H.,Wang J.. Ab initio modeling of quantum transport properties of molecular electronic devices Phys. Rev. B. 2001 63 245407

[24] Feldman B.,Park S.,Haverty M.,Shankar S.,Dunham S. T.. Simulation of grain boundary effects on electronic transport in metals, and detailed causes of scattering phys. stat. sol. (b) 2010 247 1791 6

[25] César M.,Liu D.,Gall D.,Guo H.. Calculated resistances of single grain boundaries in copper Phys. Rev. Appl. 2014 2 044007

[26] Hirel P.. Atomsk: A tool for manipulating and converting atomic data files Comput. Phys. Commun. 2015 197 212 9

[27] Plimpton S.. Fast parallel algorithms for short-range molecular dynamics J. Comput. Phys. 1995 117 1 19 12669780

[28] Mishin Y.,Farkas D.,Mehl M. J.,Papaconstantopoulos D. A.. Interatomic potentials for monoatomic metals from experimental data andab initiocalculations Phys. Rev. B. 1999 59 3393 407

[29] Blöchl P. E.. Projector augmented-wave method Phys. Rev. B. 1994 50 17953 6873586

[30] Tourret D.,Liu H.,Llorca J.. Phase-field modeling of microstructure evolution: recent applications, perspectives and challenges Prog. Mater. Sci. 2022 123 100810

[31] Zhao Y.,Xing H.,Zhang L..et al. Development of phase-field modeling in materials science in China: a review Acta Metall. Sin. 2023 36 1749 75

[32] Mukherjee A.,Ankit K.,Mukherjee R.,Nestler B.. Phase-field modeling of grain-boundary grooving under electromigration J. Electron. Mater. 2016 45 6233 46

[33] Wang N.,Guo H.,Provatas N.. Connecting the phase-field-crystal model of electromigration with electronic and continuum theories Phys. Rev. Materials 2021 5 115002

[34] Perdew J. P.,Wang Y.. Accurate and simple analytic representation of the electron-gas correlation energy Phys. Rev. B. 1992 45 13244

[35] Olmsted D. L.,Foiles S. M.,Holm E. A.. Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy Acta Mater. 2009 57 3694 703

[36] Zhang Y.,Hong Z.,Ye Z.,Pan X.. Theoretical understanding of electromigration-related surface diffusion and current-induced force in Ag-Pd systems ACS Omega 2024 9 29576 84

[37] Crampin S.,Vvedensky D. D.,MacLaren J. M.,Eberhart M. E.. Electronic structure near (210) tilt boundaries in nickel Phys. Rev. B. 1989 40 3413

[38] Xiao Z.,Su X.,Mordehai D.,Wang N.. Controlling grain boundary mobility in phase-field-crystal model Computational Materials Science 2025 253 113869

[39] Fallah V.,Korinek A.,Ofori-opoku N.,Provatas N.,Esmaeili S.. Atomistic investigation of clustering phenomenon in the Al-Cu system: three-dimensional phase-field crystal simulation and HRTEM/HRSTEM characterization Acta Mater. 2013 61 6372 86

[40] Rohrer G. S.,Chesser I.,Krause A. R..et al. Grain boundary migration in polycrystals Annu. Rev. Mater. Res. 2023 53 347 69

[41] Bhattacharya A.,Shen Y. F.,Hefferan C. M..et al. Grain boundary velocity and curvature are not correlated in Ni polycrystals Science 2021 374 189 93

[42] Zhang J.,Ludwig W.,Zhang Y..et al. Grain boundary mobilities in polycrystals Acta Mater. 2020 191 211 20

[43] Kocher G.,Provatas N.. Thermodensity coupling in phase-field-crystal-type models for the study of rapid crystallization Phys. Rev. Mater. 2019 3 053804