Visualizing the Electron Wind Force in the Elastic Regime

Abstract

With continued scaling toward higher component densities, integrated circuits (ICs) contain ever greater lengths of nanowire that are vulnerable to failure via electromigration. Previously, plastic electromigration driven by the “electron wind” has been observed, but not the elastic response to the wind force itself. Here we describe mapping, via electron energy-loss spectroscopy, the density of a lithographically defined aluminum nanowire with sufficient precision to determine both its temperature and its internal pressure. An electrical current density of 108 A/cm2 produces Joule heating, tension upwind, and compression downwind. Surprisingly, the pressure returns to its ambient value well inside the wire, where the current density is still high. This spatial discrepancy points to physics that are not captured by a classical “wind force” model and to new opportunities for optimizing electromigration-resistant IC design.

Room temperature control of grain orientation via directionally modulated current pulses

“…The former can be neglected in most cases as it nullifies itself due to the opposite polarity of positive ions surrounded by negative electrons. The electron wind force, generated by the momentum transfer between the electron and lattice, acts in the direction of current flow [27]. In electromigration literature, such directionality creates a convective diffusion mode of atomic mass transfer.…”

“…In electromigration literature, such directionality creates a convective diffusion mode of atomic mass transfer. The high current density also generates Joule heating, which facilitates void growth and creates a positive feedback loop to accelerate the thermal force [26][27][28]. Xu et al [21] reported that the high-density current could increase the material temperature to 600 °C, and the associated thermal force can essentially overcome the activation energy for the grain-boundary diffusion, resulting in grain growth.…”

Revealing the pulse-induced electroplasticity by decoupling electron wind force

“…However, the occurrence of electromigration needs dozens of hours and the resultant back-stress needs enough time to build up (for the accumulation of vacancy gradient) 40 ; while, with the nanosecond pulse in our experiments, the contribution of electromigration and resultant back-stress should be negligible. It is also noticed that the transient second density-changing effect created by the electron wind can induce a pressure gradient that increases linearly with the distance along the axial direction of sample 43 . But in our experiments, the non-directional migration of ITB mainly proceeded along the radial direction of our samples, and thus the pressure resulted from the electron wind force should be constant or have very limit variation during the ITB migration, which should not influence the conclusion of our experiments.…”

Materials Quest for Advanced Interconnect Metallization in Integrated Circuits

“…In an electric field, the conductor is affected by the direct electrostatic force (F e ) generated in the same direction as the electric field, and the electron wind or ion wind force (F w ), generated in the opposite direction as the electric field under the influence of momentum exchange with other charge carriers. [116,117] Therefore, the total driving force F tot that the activated ion inside the electric field receives is…”

“…In an electric field, the conductor is affected by the direct electrostatic force ( F e ) generated in the same direction as the electric field, and the electron wind or ion wind force ( F w ), generated in the opposite direction as the electric field under the influence of momentum exchange with other charge carriers. [ 116,117 ] Therefore, the total driving force F tot that the activated ion inside the electric field receives is $$$$\begin{equation} {\stackrel{\to}{F}}_{\mathrm{tot}}={\stackrel{\rightarrow}{F}}_{\mathrm{e}}\ +\ {\stackrel{\rightarrow}{F}}_{\mathrm{w}}=\ q\cdot \left({Z}_{\mathrm{e}}-{Z}_{\mathrm{w}}\right)\cdot \stackrel{\rightarrow}{E} \ =\ q \cdot {Z}^{\ast}\cdot {\stackrel{\rightarrow}{E}}\ =\ q\cdot {Z}^{\ast}\cdot \rho \cdot {\stackrel{\rightarrow}{J}} \end{equation}$$$$where q is the electric charge of the ions, Z e and Z w are the valences corresponding to the electrostatic and wind forces, respectively, Z* is the effective valence of the material, J is the current density of the conductor, and ρ is the resistivity of the material. Each material for a specific technology node requires a discrete calibration to manage any effects during manufacturing and operation.…”