Exploring effective charge in electromigration using machine learning
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rtificial Intelligence Research Letter
Exploring effective charge in electromigration using machine learning Yu-chen Liu, 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 and Ryan Jacobs, Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, USA Shih-kang Lin, 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, Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, USA Address all correspondence to Dane Morgan at [email protected] (Received 22 December 2018; accepted 7 May 2019)
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-squareerror divided by whole data set standard deviation (RMSE/σ) values of 0.37 ± 0.01 (0.22 ± 0.18), respectively, and R 2 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.
Introduction Electromigration (EM) is the biased diffusion of certain species under electric current, and causes significant reliability problems in modern electronic products, e.g., the EM-induced formation of voids/hillocks, which can lead to device malfunction via short circuit and open circuit.[1] Theoretical explanations for the EM effect have included, in chronological order, the semiballistic model,[2] polarization model,[3] back stress model,[4] and lattice strain model.[5] Today the driving force of EM is typically considered as a combination of the electron wind force, which is due to electron-ion scattering, and the direct force, which originates from the external electric field. The overall driving force for the EM effect is often formulated as shown in Eq. (1): ∗
F = (zd + zw )erj = z erj
(1)
where zd is the valence charge associated with the direct force contribution, zw is the effective charge associated with the electron wind force contribution, z* is the effective charge sum of the previous two terms of a given species, e is the elementary charge, ρ is the resistivity, and j is the current density. The value of z* is often approximately formulated as shown in Eq. (2): ∗
z = zd + zw ≈ zd +
K r(T)
(2)
where ρ(T ) is the resistivity of the host and K is a host- and
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