Upwind electromigration of sub-10-nm metallic nano-interconnects

Abstract

Nanoscale electronic devices face critical reliability challenges under extreme operating conditions, where electromigration—atomic motion driven by high density current—progressively degrades metallic components. Conventional wisdom maintains that electron wind force drives atomic migration along electron flow direction in metallic interconnects. However, using an integrated in situ nanofabrication-electropulsing approach, we reveal an anomalous electromigration phenomenon in next-generation transition metal nano-interconnects at atomic scale, where surface atoms migrate against the direction of electron flow. This upwind migration demonstrates universality across different refractory nano-interconnects including tungsten and molybdenum. First-principles calculations attribute this reversal to the predominance of direct forces over electron wind forces in materials with complex electronic structures. Our findings challenge the existing paradigm of electromigration and hold great implications for optimizing the reliability of next-generation electronic interconnections toward extreme process.

By tracking atomic motion pulse-by-pulse, this work reveals “upwind” electromigration against electron flow in next-generation interconnects. This paradigm diverges from common electromigration, guiding reliability design for future electronics.

Introduction

Aggressive integration and miniaturization of nanoelectronics face fundamental challenges in keeping the stability of nanocomponents at atomic scales^1–4, as extreme operational conditions greatly accelerate the degradation of nanomaterials^5–7. A central issue arises from electromigration⁸, where the biased diffusion of atoms driven by high-density currents progressively damages the nanosized metallic interconnects and leads to the failure of the entire device^9–11. In conventional interconnect materials, electromigration typically drives mass transport in the direction of electron flow (Fig. S1), as momentum transfer from electrons pushes atoms toward the anode^12–15. This phenomenon has long guided strategies for mitigating reliability risks in electronics based on current interconnect materials like copper (Cu) and gold (Au).

While widely deployed, Cu and Au are particularly vulnerable to electromigration on the sub-10 nm scale due to the long electron mean free path¹⁶ (leading to increased resistivity with the size reduction) and low activation energy for diffusion¹⁷. Transition metals such as tungsten (W) and molybdenum (Mo) possess shorter electron mean free paths, which can largely mitigate the resistivity size effects and possess high resistance to electromigration at sub-10 nm dimensions¹⁸. Thus, they have emerged as promising alternatives for next-generation nano-interconnects in advanced integrated circuit^19,20, especially in nanodevices toward extreme applications. Unfortunately, elucidating the electromigration behavior in those refractory nano-interconnects with complex electronic structures presents substantial challenges to conventional experimental approaches, where the atomistic feature structures of nano-interconnects impose great difficulties for the fabrication, testing and visualization. This gap greatly hinders the reliability design of nanocomponents for extreme operating conditions. Although in situ transmission electron microscopy (TEM) has become a powerful tool in directly visualizing electromigration dynamics (e.g., Cu^13,21, Ag^22,23, Al²⁴, Pt²⁵ and Pd-Pt alloys²⁶), its application has still been limited to conventional interconnect metals and relatively large structures (tens to hundreds of nanometers) due to the technological challenges in sample fabrication and testing, leaving the atomic-scale mechanism largely obscure. We devise an integrated in situ nanofabrication and electropulsing approach in TEM tailored for different metallic nanomaterials, enabling the efficient visualization of atomistic surface dynamics during electromigration. Surface atoms on nanosized W and Mo exhibit migration against the electron flux upon electropulsing, opposite to the conventional electromigration along the direction of electron flow¹⁵.

Results

Atomic observation of upwind electromigration

In our experiments, W and Mo nanowires with different structures and diameters all exhibited upwind surface electromigration, under pulses with distinct parameters (summarized in Table S1). Figure 1a–f show a typical set of atomistic surface dynamics of a W nanowire under the sequentially-applied pulses of 1 V (Supplementary Movie 1). Before electropulsing series, the bicrystal W nanostructure with a single grain boundary (GB, on the left) was fabricated by in situ nanowelding (see Methods; Fig. S2 presents the overall morphology of the whole nanowire). The interested grain has a growth direction of [01$\overline{1}$] and contains six-layers of (110) mono-atomic surface facets on the top surface (Fig. 1a). During the electropulsing, significant migration of surface atoms occurred upon the application of each pulse, mainly at the surface facet sites (the maximum current density passing this nanowire is estimated to be 5 × 10⁹ A/cm²). Figure 1b-f track the evolution of surface configuration at each surface facet, while the direction of pulse current (opposite to the direction of electron flux) is marked by the arrow below Fig. 1f. With the successive applications of individual pulse, atom fluctuations were observed on the step edges of the primitive surface island (Fig. 1b-f). In particular, the step edges located at the left region of the nanowire demonstrated growth, see the gradual accumulation of extra columns of adatoms at steps 1’ to 6’ (Fig. 1b-f); while, the step edges on the right generally experienced corresponding shrinkage, as marked out by the missing atoms in Fig. 1f. Generation of new adatom columns (left) and disappearance of initial atomic columns (right) on the intensity profiles of the outermost (110) plane after 3 pulses (Figs. 1g, S3), as well as the morphology changes in Fig. S4, further evidence that the surface atomic layers undergo mass transport in the direction of current. This means that the electromigration of surface atoms of W is in opposite to the direction of electron flow (denoted as the upwind electromigration hereafter), in contrast to the conventional electromigration driven by the electron wind^13,14,27,28. A series of pulse applications in Fig. S5 consistently demonstrated the upwind electromigration behavior even when the current direction was reversed. We noticed that a surface dislocation (confirmed by the strain field maps on nanowire surface in Fig. 1h, see Methods for details) also underwent a sequential evolution of annihilation (Fig. 1b), reproduction (Fig. 1c), migration (Fig. 1d), and annihilation again (Fig. 1e) under pulses. This suggests that the dislocation core is another atomic defect site sensitive to the electromigration driven force. Figure 1i (the perspective view) and Fig. 1j (the front view) schematically illustrate the process of pulse-induced upwind electromigration of surface atoms on three W(110) layers. Surface electromigration should involve two pathways: migrating along the edges of the terrace (rose arrows), or jumping from one terrace to a neighboring terrace (red arrows). Both processes proceed along the upwind direction of electron flux and are accompanied by the annihilation and/or generation of atomic columns, either on the same terrace or the neighboring terrace, as schematically shown in Fig. 1i, j.

Fig. 1. Pulse-induced atom migration on the surface of a W nanowire.

a–f Atomically-resolved surface electromigration of a [100]-viewed W nanowire under pulsing. Circles in (b–f) represent the columns of adatom (red) and missing atoms (blue), while the numbers marked out each surface step edge. The directions of current flow and electron migration are labelled by the arrows at bottom. Surface dislocations are marked by “⊥”. g Intensity profiles for the outermost (110) plane at the initial state and after 3 pulses. h In-plane (ε_xx) and out-of-plane (ε_yy) strain field maps on nanowire surface. The shaded areas represent vacuum regions. i Schematic in perspective view showing the mass transport of three W(110) surface layers under pulsing. The light yellow and cyan balls represent atoms that move from the outermost layer and atoms moving from the secondary-outer layer, respectively. j Front view of the schematic along the [100] direction. Source data are provided as a Source Data file.

Atomic surface dynamics

Accumulation of pulse-induced surface electromigration can contribute significant mass transport, greatly changing the surface morphology and shape of the nanosized W interconnect. Figure 2 presents the geometrical variations of a W nanowire under the sequentially applied pulses of 0.45 V, with a bottom-to-top current flow along the nanowire. This nanowire has a growth direction of [11$\overline{2}$] (Fig. 2a), differing from the one presented in Fig. 1. However, upon the axially applied pulse, this nanowire showed the same pulse-induced surface electromigration. Specifically, the surface atoms exhibited an upwind migration behavior against the direction of electron flux, and as this biased mass transport accumulated with the pulsing, the top part of the nanowire thickened gradually while the bottom became progressively thinner (Fig. 2a–d). Evolution of corresponding strain field maps (ε_xx) in Fig. 2e–h illustrates that no evident strain gradient existed in the direction of mass transport. This demonstrates again that the stress gradient is not the cause of electromigration. Additionally, shrinkage of island-like fringes (probably representing the step edges of top surface) in Fig. 2e–g also shows the atoms at step edges were moving upward. We further quantified the diameter variations at fixed positions of the anode side (D₁ beneath the necking zone, on the downwind side of electron motion) and the cathode side (D₂ above the necking zone, on the upwind side of electron motion), respectively (marked by the red and blue arrows in Fig. 2a, the reference details can be seen in Fig. S6). Notably, the diameter D₂ increased continuously with the pulsing, while the diameter D₁ decreased firstly and then increased slightly (Fig. 2i). This suggests net mass transport from the anode side (downwind) to the cathode side (upwind) under pulsing, opposite to the observations in conventional electromigration¹⁵. The slight increase of D₁ at late stage of pulsing can be ascribed to the downward shift of the necking zone (see Fig. 2c, d), where the continuous upwind mass transport induced the thickening of the initial necking zone. Atomic image (Fig. 2j) and fast Fourier transform (FFT) patterns (Fig. 2k) show that the W nanowire remained a perfect [111] body-centered cubic (BCC) lattice after pulsing. This indicates that the morphological changes of the nanowire are unrelated to its internal defect. In classic theory, the size variation of a nanowire can be estimated by a diffusion-based theoretical model (i.e. Gibbs-Thomson effect¹⁴), where the reduction in curvature radius will result in an increase in surface chemical potential, thereby creating a tendency for surface atoms to migrate toward the larger diameter during the growth of nanomaterials. However, the driving force of electromigration induces a new chemical potential gradient, resulting in a biased mass transport differing from that of simple thermal diffusion. This directional surface diffusion could ultimately lead to anode-side fracture of the nanowire (Supplementary Movie 2).

Fig. 2. Structural evolution of a W nanowire via surface electromigration.

a–d Surface electromigration induced-morphological changes of a nanowire with the growth direction of [11$\overline{2}$]. The dashed lines marked indicate two reference positions D₁ and D₂. e–h Corresponding strain field maps (ε_xx) of (a–d). The shaded areas represent vacuum regions. i Variation of D₁ and D₂ during the pulsing sequence. The yellow dashed line indicates the transition points of the diameter evolution of D₂. The error bars represent the average deviation of three measurements. j, k Lattice structure and corresponding Fast Fourier Transformation pattern at the center of the nanowire after electropulsing. Source data are provided as a Source Data file.

To further reveal the mechanisms of the pulse-induced surface atomic migration, we examined the atomic dynamics of surface terraces in Fig. 3. Surface terraces consisting of mono-atomic steps, on both the left and right surfaces, were tracked, respectively, and the local diameters of the nanowire were controlled to be identical for uniform current density across terraces (Fig. 3a). Under successive pulse applications, a consistent and steady growth of these mono-atomic steps was observed on both sides, though morphological evolution differences emerged. On the right side (Fig. 3b), the curved surface (necking zone of the initial nanowire, indicated by the yellow profile) was gradually filled, as demonstrated by the migration of marked surface steps and surface profile variations after 12 pulses. During this process, the atoms on the right surface moved in the upward direction (schematically shown by the arrows in Fig. 3b), inducing the gradual growth of each surface layer (i.e. 1 to 7 in Fig. 3b). In contrast to the formation of a clean (1$\overline{1}$0) plane on the right surface (Fig. 3b), the left surface tended to develop a stepped surface aligned with the current direction, and these surface steps showed a downward growth behavior (Fig. 3c).

Fig. 3. Atom-step dynamics during the surface electromigration.

a Magnified image of Fig. 2a. The cyan and pink arrows indicate 7 consecutive mono-atomic steps on the left and right surfaces, respectively. b, c Atomic step evolutions on the right and left surfaces, respectively. d Schematic potential diagrams for a W atom moving toward a step. Top: In the absence of pulse. Middle: Pulse applied along the step-down direction. Bottom: Pulse applied along the step-up direction. The adjacent narrow terrace and wide terrace are highlighted in red and blue, respectively. e Average moving distances (in the vertical direction) of mono-atomic steps in (b, c), with respect to the pulse sequence. Insert shows the current direction (indicated by yellow arrows) relative to the surface steps. The cyan and pink arrows show the growth direction of surface steps. The error bars represent the variation of moving distance of the seven steps to their arithmetic mean. f Schematic illustrating the surface electromigration of vicinal (110) W surfaces under pulsing. Source data are provided as a Source Data file.

Figure 3d schematically depicts a series of hypothetical potential energy for moving atoms on the W surface. Step A (the descending step of a narrow terrace) has a higher energy barrier than step B (the descending step of the vicinal wide terrace) owing to its smaller terrace scale²⁹. When a pulse current is applied, intermediate positions between steps become nonequivalent³⁰ (Fig. 3d). For the step-down case, moving atoms on the wide terrace tend to jump into the descending step. However, on the step-up side, the wide terrace facilitates moving atoms incorporating into the ascending step (but hard to jump into the ascending terrace due to a high energy barrier), thus preventing further widening of the wide terrace. The growth rate of steps on the step-down side increased rapidly and nonuniformly until step-bunching formed at the top of the nanowire, see the plot of average moving distance (in the vertical direction) of (1$\overline{1}$0) facet as a function of the pulse sequence (Fig. 3e). This is due to the runaway step-down diffusion and gradual attachment of atoms at the steps. Besides, the moving rate of the marked steps on the step-up side remained relatively stable with minor fluctuation (Fig. 3e). Note that on both surfaces, the directions of atom diffusion were all along the current directions, as illustrated by the changes of surface profiles in Fig. S7. Such evolution of surface configuration observed above is schematically demonstrated in Fig. 3f. When pulse current flows along the step-down direction, the step train (i.e., the succession of atomic steps travelling collectively) on W(110) is unstable and electromigration induces the formation of step bunching. The step-up current, however, transforms the step train into stable equidistant growing. These findings also highlight the significant influence of surface morphology on step dynamics, thereby reinforcing the crucial role of electrical pulses in regulating nanostructure surfaces at the atomic scale.

Electromigration in different metals

Above experiments clearly demonstrate exceptional upwind electromigration in metallic nanowires under pulsing, in contrast to the conventional electromigration in literatures^6,14. This behavior is independent of sample features (including growth direction, geometry, structure and diameter of nanowires), pulse parameters and current directions (see Figs. 1, 2, Figs. S5, S8, and Table S1), and such upwind electromigration can also occur in BCC Mo nanowires (Fig. 4a–d). Surface atom migration, fundamentally a self-diffusion process, depends on temperature, diffusion barrier, atomic species, and external kinetic conditions etc. The biased migration of surface atoms under the direct current (DC) was thought to be a combination of the current-induced wind force³¹ and the Soret effect³², which refers to the mass transport caused by the temperature gradient. In our experiments, the nanowire served as a nanobridge connecting the two metallic matrices; the local heat was rapidly dissipated by the bulk metal at both ends, creating a symmetrical temperature field in the nanowire, without obvious directivity; furthermore, the reversal of current direction has no bearing on the temperature distribution, yet the atomic migration direction reverses (Fig. S5), further eliminating the temperature gradient effect (Supplementary Discussion 1). Having established the athermal, electric-field-driven nature of the migration, we investigated its persistence under DC condition. The upwind electromigration persisted after prolonged continuous current flow of ~10⁹ A cm⁻² in W nanowires (Fig. S9). We further used a Mo nanowire to examine the surface response under staircase DC condition, where surface atoms on the Mo nanowires also conducted a sign of upwind electromigration during the time interval of tens of seconds under a current density of ~10⁸ A cm⁻² (Fig. S10). However, under a current density of ~10⁴–10⁶ A cm⁻² of DC condition, noble metals have demonstrated significant electromigration along the electron flow¹³. On one hand, refractory metals like W and Mo with higher diffusion barriers demand higher activation energies to stimulate the electromigration. On the other hand, differences in electron-atom interaction of metals result in distinct electromigration direction.

Fig. 4. Pulsing-induced surface electromigration in different metals.

a–d Surface electromigration of a Mo nanowire with the growth direction of [01$\overline{1}$]. The directions of the current and electron flow are indicated by the arrows in (a). The white circles mark out initial surface atom columns. The dashed lines represent a pre-existing grain boundary that remains essentially unchanged during pulsing. The red, yellow, and cyan circles mark the adatom columns after one, three, five pulses, respectively. The white and red dotted circles mark the missing atoms. The orange arrow in (c) indicates the migration direction of surface atoms. e Schematic showing the driving force for surface electromigration in different metals. The effective driving force of electromigration is a result of the competition between the direct force and the wind force.

In theory, the driving force on atoms in a metal under an electric field can be described by:

$$\mathbf{F}={\mathbf{F}}_{\mathrm{direct}}+{\mathbf{F}}_{\mathrm{wind}}=\left(Z_{\mathrm{direct}}+Z_{\mathrm{wind}}\right)e\mathbf{E}=Z^{*}e\mathbf{E}$$ 1

where the direct force F_direct (i.e. Z_direct eE) is induced by a net charge of the moving metal-ion, the wind force F_wind (i.e. Z_wind eE) is caused by the scattering of current-carrying electrons off the atom, e is the absolute value of the electronic charge and E is the electric field. The effective valence Z^* consists of direct force valence Z_direct and wind force valence Z_wind. In metals such as Au and Cu, the wind force is generally about 5 to 10 times greater than the direct force³³, acting as the dominant driving force in their electromigration. However, the difference of electron band structure leads to the obvious variation of resistivity and electron scattering behaviors in transition metals, where the balance of the direct force and wind force can be completely changed³⁴. Specifically, Z_wind can be calculated by Huntington’s formulation:

$$Z_{\mathrm{wind}}=K/\rho \left(T\right)$$ 2

where K is a temperature-independent quantity, ρ is the resistivity that can be influenced by temperature T. This formulation gives a simple qualitative relationship that the higher the resistivity of the metal itself, the less it is affected by the electron wind force.

To ascertain the disparity in surface electromigration between different transition metallic nanowires under electric pulse, responses of surface atoms on Mo (Fig. 4) and Au (Fig. S11) nanowires under pulsing were evaluated. In both cases, the nanowire surfaces manifested similar fluctuations via the motion of atomic step edges. However, the direction of surface electromigration on Au {111} step edge largely aligned with the direction of electron flow (Fig. S11), whereas that on Mo {110} step edge was opposite (Fig. 4). Specifically, in Mo nanowire with a GB (as a reference here), a new terrace was generated on the left side of GB after one pulse, accompanied by the missing of some atomic columns from the right surface, validating the upwind electromigration (Fig. 4b). Upon subsequent pulses, some atoms located at the step edge of the new terrace further moved along the current direction toward the opposite step due to the upwind surface electromigration (marked by the orange arrow in Fig. 4c), and eventually formed a new atomic layer after the fifth pulse (Fig. 4d). Throughout this process (Supplementary Movie 3), the overall profile of the GB remained essentially unchanged.

To theoretically clarify the competition of effective electromigration driving force, here we calculated the wind force valence Z_wind of W, Mo, Au and Cu using the density functional theory calculations. Slab models containing 5 or more atomic layers were constructed to model the surface steps, as shown in Fig. S12, and the surface structures were optimized while fixing the bottom layers with experimental lattice constants to mimic the bulk behavior. The distance between step edges and the vacuum spacings are larger than 10 Å to avoid artificial interactions between periodic images. Using the computational approached described in Methods section, Z_wind can be evaluated using electron-phonon interaction matrix, electron scattering time, and the Fermi velocity. The electron-phonon interaction matrix was calculated for step edge atoms using the above slab models, while the electron scattering time and Fermi velocity were extracted using experimental data in the literature¹⁹ (see “Methods” and Fig. S12 for details). The associated values are shown in Table S2.

The calculated |Z_wind| on W(110), Mo(110) and Au(111) atoms at step edges are 5.066, 3.669 and 40.116, respectively. This indicates the wind forces on W and Mo atoms are much weaker than that on Au atoms. The large wind force for Au and Cu originates from stronger electron-phonon coupling, longer electron scattering time and Fermi velocity. As shown in Table S2, the electron-phonon coupling of Au(111) step edge atom is 1.58 eV/Å, which is almost twice those of W(110) (0.74 eV/Å) and Mo(110) (0.80 eV/Å). The electron scattering time τ are 27.3 fs for Au and 36 fs for Cu, which are much longer than those of W (16 fs) and Mo (12 fs). The Fermi velocities of Au and Cu are also slightly greater. For the direct force Z_direct, we estimate from the charge of bare ion without free electron, giving the values of around 6 for W and Mo, 1 for Au and Cu (Supplementary Discussion 2). This leads to a |Z_direct | /|Z_wind| ratio of 1.2 for W surface and 1.6 for Mo surface. For Au and Cu surfaces, on the contrary, all |Z_direct | /|Z_wind| ratios are less than 0.05. Therefore, the electromigration driving force for surface electromigration in W and Mo nanowires is dominated by the direct force, opposite to the well-known electromigration behaviors in Au, Cu and Al³³, as schematically shown in Fig. 4e. Note that the transient effect of pulses is not considered in this work because the transition time of electropulse (2–10 ns) used in our study are approximately 5 orders of magnitude longer than the electron relaxation times in W and Mo (tens of fs, Table S2). This ensures that the electron system reaches a quasi-steady state during the pulse.

Discussion

Notably, the wind force can be impacted by the local characteristics of metal surface^12,14,27. In particular, the wind force experienced by an adatom at a step edge varies significantly owing to multiple backscattering of charge carriers²⁷. In accord with reported experiments^14,35, the electromigration driving force was enhanced on atomic defect sites at the island edge or surface dislocation under pulse conditions, and electromigration is characterized by the growth and contraction of surface step-edges. However, for certain transition metals, enhanced interaction between atoms and current (electron wind) unexpectedly results in an upwind electromigration force. A naive physical picture would require hole carriers to be dominant for the upwind electromigration³² (Hall potential measurements show that for a few transition metals, such as W and Mo, the majority of charge carriers are positive). Given that electrical conduction in metals is primarily governed by the response of electrons near the Fermi surface³⁶, a more appropriate picture should be that an incident non-equilibrium distribution of conduction electrons conducts a redistribution of local surface potential. At the step-edges where electrons are scattered over large angles, an enhanced electron density would form at the upwind side, resulting in an enhanced direct force impelling an upwind electromigration.

The upwind electromigration represents a new regime of electro-induced structural variation and electro-degradation in metallic nano-interconnects. Z * is an important parameter in controlling the electromigration behavior of interconnect metals and alloys^33,37, providing criterion for high-throughput screening of interconnect materials with superior electromigration resistance. Engineering the upwind electromigration may bring a new degree of freedom for mitigating the void formation at critical cathode interfaces or even enabling self-healing of anode-side damage. The electropulsing-induced electromigration and structural evolutions are also meaningful for the modern computing and memory devices operated under high-frequency pulsed signals and harsh conditions³³. However, lifetime prediction under such an upwind regime cannot be extrapolated from conventional electromigration models, and a new framework of reliability design needs to be further developed for nanodevices toward harsh applications. Besides, the protocol of in situ nanofabrication-electropulsing testing, as well as electromigration-assisted surface morphology variation (Fig. 3), holds potential implications for atomic-level manufacturing.

Our findings directly visualize the step-edge mediated surface electromigration in sub-10 nm refractory metallic nanowires, where the surface atoms always migrate in the direction opposite to the momentum of electrons. Such upwind electromigration of surface atoms originates from the suppressed electron wind force in W and Mo, where the electron wind is approximately an order of smaller than that in systems like Au and Cu. This surface electromigration can reshape the morphology and thereby induce the functional loss of nanosized interconnects. These findings not only pave the way for more precise theoretical frameworks to forecast electromigration across materials but also inspire engineers to explore novel alloys and composites, such as multilayer designs counteracting electromigration effects, thus holding great promise for enhancing the reliability of advanced electronics.

Methods

Integrated in situ nanofabrication and electropulsing testing

An integrated in situ method of nanofabrication and electropulsing was employed in this study. Take W nanowires as example, two 0.25 mm diameter bulk W rods (99.95 wt.%) were cut using diagonal cutting pliers to create fresh fracture edges with numerous triangular nano-tips. The rods were supplied by Alfa Aesar Inc. To reduce the risk of contamination before cutting, the rods were stored in a glove box filled with helium (with O₂ and H₂O levels both below 1 ppm). Prior to this, they were ultrasonically cleaned in absolute ethyl alcohol and dried overnight under vacuum at 120 °C. Two fractured W rods were mounted onto the fixed end and to the probe side of a PicoFemto® TEM-STM specimen holder (Zeptools Co., Fig. S13). The W nanocontacts were fabricated in situ inside a Cs-corrected FEI Titan G2 60–300 transmission electron microscope (TEM equipped with an image-side aberration corrector, a hot field emission gun, and a monochromator) operating at 300 kV, and then subjected to the electrical pulses with different parameters (typical measured waveforms are shown in Fig. S14). The in situ TEM experiments were conducted with spot size 3, magnification 670 k/850 k, controlled low beam dose rate of approximately 1 × 10⁴ e⁻ nm⁻² s⁻¹. In the process of nanofabrication, the W rod on the probe side was moved using a built-in piezo-manipulator. This was done to bring the rod into contact with the fixed end of the holder, allowing the two selected nano-tips to come into contact. The W nanocontacts without lattice defects were fabricated by nano-welding the tips by pre-applied voltage potential before contact or application of high single electric pulse after contact (with the typical voltage of 3.0–4.0 V or higher)^38–41. Then, individual pulses were sequentially applied on the as-fabricated nanocrystal, to investigate the electromigration. During experiments, a Gatan OneView camera was used to record the process in real time at an exposure time of 0.3–0.5 s (per frame). To quantitatively analyze the local strain distributions in the W nanowires, the geometrical phase analysis (GPA) was performed using open-source program stain++ to quantify different strain components (reference areas are marked in Fig. S15). This technique enables the mapping of two-dimensional local displacement fields by analyzing the phase shift between non-collinear Fourier components of the lattice vectors g₁ and g₂. Uncertainty estimation of GPA is defined by the strain standard deviation of reference region, which are 0.014 for Fig.1h and 0.016 for Fig. 2e–h, respectively.

This integrated in situ nanofabrication and electropulsing method is applicable for different metallic materials, including W, Mo and Au studied in this paper. This method enables the efficient fabrication of nanosized samples (down to few nanometers) with controlled orientation and atomically-resolved lattice structure, but without any surface contaminations, greatly facilitating the investigation of surface electromigration on metallic nanoconductors. The dynamic evolutions of surface structure of Mo and Au nanowires under electropulsing were conducted using the same method detailed above. Quantitative details of the electropulsing parameters are summarized in Table S1. Individual electropulses were applied manually in a triggered mode, with an inter-pulse interval of approximately 1–3 s. To firmly validate the robustness of electromigration phenomenon in W and Mo nanowires under varying pulse conditions, dozens of repeat experiments were conducted within the same re-welded nanowire by switching the pulse current direction and modulating the pulse parameters. Additionally, we performed beam-blank experiments and observed similar electromigration processes (Fig. S16).

Density functional theory modeling

In this work, we compute the wind force from density functional theory (DFT) following the approach of Sorbello et al.⁴² and Dekker et al.⁴³. In this approach, the wind force is evaluated as:

$$F_{\mathrm{wind}}^{\alpha }=-\int \delta n\left(\mathbf{r}\right){\nabla }_{{\mathbf{R}}_{\kappa }}^{\alpha }{v}_{\mathrm{\kappa }}\left(\mathbf{r}-{\mathbf{R}}_{\kappa }\right)dr={\sum }_{\mathbf{k}}{w}_{\mathbf{k}}\delta f_{\mathbf{k}}⟨{\psi }_{\mathbf{k}}\mid -{\nabla }_{{\mathbf{R}}_{\kappa }}^{\alpha }{v}_{\kappa }\mid {\psi }_{\mathbf{k}}⟩$$ 3

This can be understood as the Hellmann-Feynman force⁴⁴ in the presence of electric-field induced electron density perturbation. Here, $\delta n\left(\mathbf{r}\right)={\sum }_{\mathbf{k}}{w}_{\mathbf{k}}\delta f_{\mathbf{k}}{\psi }_{\mathbf{k}}\left(\mathbf{r}\right){\psi }_{\mathbf{k}}^{*}\left(\mathbf{r}\right)$ is the electron density perturbation in the presence of a driving electric field, $w_{\mathbf{k}}$ is the k-point weight, $\delta f_{\mathbf{k}}$ is the electric field-induced Fermi distribution perturbation, ${\psi }_{\mathbf{k}}$ is the Kohn-Sham wave function, and $v_{\kappa }\left(\mathbf{r}-{\mathbf{R}}_{\kappa }\right)$ is the ionic potential around the ion of interest located at ${\mathbf{R}}_{\kappa }$. And the electron-phonon interactions $⟨{\psi }_{\mathbf{k}}\mid -{\nabla }_{{\mathbf{R}}_{\kappa }}^{\alpha }{v}_{\kappa }\mid {\psi }_{\mathbf{k}}⟩$ are directly evaluated from DFT.

In the relaxation time approximation⁴⁵, the Fermi distribution perturbation induced by an electric field E_α along the α direction is:

$$\delta f_{\mathbf{k}}=e{v}_{\mathbf{k}}^{\alpha }{E}_{\alpha }\frac{\partial f_{\mathbf{k}}}{\partial {ϵ}_{\mathbf{k}}}{\tau }_{\mathbf{k}}$$ 4

where e is the elementary charge, $v_{\mathbf{k}}^{\alpha }$ is the group velocity, ϵ_k is the Kohn-Sham energy, and ${\tau }_{\mathbf{k}}$ is the relaxation time. For practical calculation, we make a further isotropic parabolic band approximation and only consider the average value on the Fermi surface such that $v_{\mathbf{k}}^{\alpha }=v_{\mathrm{F}}\cos {\theta }_{\mathbf{k}}$ and ${\tau }_{\mathbf{k}}={\tau }_{\mathrm{F}}$. Finally, we arrive at the wind force effective charge $Z_{\mathrm{wind}}=\frac{F_{\mathrm{wind}}^{\alpha }}{e{E}_{\alpha }}$. The Fermi velocity $v_{\mathrm{F}}$ and relaxation time ${\tau }_{\mathrm{F}}$ are taken from the literature¹⁹.

The DFT calculations are performed on a surface step structure model, where the electron-phonon interactions are evaluated for the highlighted atoms located at the step edges on (110) and (111) surfaces corresponding to our experiments as shown in Fig. S12. The DFT calculations are performed using QUANTUM ESPRESSO^46,47 and the electron-phonon interactions are calculated using our in-house code. Norm-conserving pseudopotentials from Pseudo-Dojo project⁴⁸ and their recommended cutoff energies are used. A vacuum spacing larger than 10 Angstrom and a 2D truncation scheme are used to avoid image interaction.

Author contributions

J.W.W. proposed the idea, directed the project and designed the experiments. Y.H. conducted the experiments and analyzed the data. T.D. performed the DFT calculations. Y.H. and J.W.W. wrote and revised the paper. X.L., Z.H., J.W., K.S. and Z.Z. contributed to the discussion and paper revision.

Peer review

Peer review information

Nature Communications thanks Meng Li and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data that support the findings of this study are available within this article and its Supporting Information. Additional data is available from the corresponding authors upon request. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-70283-9.