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

Domain: physics
Published: 2026-03-06
Editorial outcome: major_revision

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 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.

Introduction
Aggressive integration and miniaturization of nanoelectronics face fundamental challenges in keeping the stability of nanocomponents at atomic scales1-4, as extreme operational conditions greatly accelerate the degradation of nanomaterials5-7. 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 entire device9-11. 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 anode12-15. 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 circuit19,20, 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., Cu13,21, Ag22,23, Al24, Pt25 and Pd-Pt alloys26), yet 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). Fig. 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 [011̅] 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). Fig. 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 (Fig. 1g and Fig. 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 wind13,14,27,28. 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. Fig. 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 and j.

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. Fig. 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 [112̅] (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 (εxx) 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 show 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).

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 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 (11̅0) 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).

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 nanowire, see the plot of average moving distance (in the vertical direction) of (11̅0) 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). Noted 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 literatures6,14. This behavior is independent of sample features (including growth direction, geometry, structure and diameter of nanowires), pulse parameters and current directions (see Figs. 1 and 2, Figs. S5 and 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.

In theory, the driving force on atoms in a metal under an electric field can be described by:
𝐅 = 𝐅 +𝐅 = (𝑍 +𝑍 )𝑒𝐄 = 𝑍∗𝑒𝐄 (1)
direct wind direct wind
where the direct force F (i.e. Z eE) is induced by a net charge of the moving metal-ion, the wind direct direct
force F (i.e. Z eE) is caused by the scattering of current-carrying electrons off the atom, e is the wind wind
absolute value of the electronic charge and E is the electric field. The effective valence Z* consists of direct force valence Z and wind force valence Z . In metals such as Au and Cu, the wind force is direct wind
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 can be calculated by Huntington’s formulation: wind
𝑍 = 𝐾/𝜌(𝑇) (2)
wind
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. S8), 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 of W, Mo, Au and Cu using the density functional theory calculations. Slab wind
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 can be evaluated using electron-phonon interaction matrix, electron wind
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 | on W(110), Mo(110) and Au(111) atoms at step edges are 5.066, 3.669 and wind
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 , we estimate from the charge of bare ion without free electron, giving the values of direct
around 6 for W and Mo, 1 for Au and Cu (Supplementary Discussion 2). This leads to a |Z |/|Z | ratio direct wind
of 1.2 for W surface and 1.6 for Mo surface. For Au and Cu surfaces, on the contrary, all |Z |/|Z | direct 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, in 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.

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 ℃. 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 used by 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 g and g . Uncertainty estimation of GPA is defined by the strain 1 2
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, providing great facilitates for 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 seconds. 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 al42 and Dekker et al43. In this approach, the wind force is evaluated as:
𝐹𝛼 = −∫𝛿𝑛(𝐫)∇𝛼 𝑣 (𝐫−𝐑 )𝑑𝑟 = ∑ I 𝑤 𝛿𝑓 ⟨𝜓 |−∇𝛼 𝑣 |𝜓 ⟩ (3)
wind 𝐑𝜅 𝜅 𝜅 𝐤 𝐤 𝐤 𝐑𝜅 𝜅 𝐤
E𝐤
This can be understood as the Hellmann-Feynman force44 in the presence of electric-field induced electron density perturbation. Here, 𝛿𝑛(𝒓) = ∑ 𝑤 𝛿𝑓 𝜓 (𝒓)𝜓∗(𝒓) is the electron density perturbation in the 𝐤 𝐤 𝐤 𝐤 𝐤
presence of driving electric field, 𝑤 is the k-point weight, 𝛿𝑓 is the electric field-induced Fermi 𝐤 𝐤
distribution perturbation, 𝜓 is the Kohn-Sham wave function, and 𝑣 (𝒓−𝑹 ) is the ionic potential 𝐤R 𝜅 𝜅
around the ion of interest located at 𝑹 . And the electron-phonon interactions ⟨𝜓 |−𝛻𝛼 𝑣 |𝜓 ⟩ are 𝜅 𝐤 𝑹𝜅 𝜅 𝐤
directly evaluated from DFT.

In the relaxation time approximation45, the Fermi distribution perturbation induced by an electric field 𝐸 along 𝛼 direction is:
𝛼
𝜕𝑓
𝛿𝑓 = 𝑒𝑣𝛼𝐸 𝐤 𝜏 (4)
𝐤 𝐤 𝛼𝜕𝜖 𝐤
𝐤
where 𝑒 is the elementary charge, 𝑣𝛼 is the group velocity, 𝜖 is the Kohn-Sham energy, and 𝜏 is 𝐤 𝐤 𝐤
the relaxation time. For practical calculation, we make further isotropic parabolic band approximation and only consider the average value on the Fermi surface such that 𝑣𝛼 = 𝑣 cos𝜃 and 𝜏 = 𝜏 . Finally, we 𝐤 F 𝐤 𝐤 F
𝐹𝛼
arrive at the wind force effective charge 𝑍 = wind. The Fermi velocity 𝑣 and relaxation time 𝜏 wind F F
𝑒𝐸𝛼
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 ESPRESSO46,47 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.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper reports a phenomena about the upwind migration of atoms in metal wires under electrical pulse. The finding is novel controversial to previous findings with enough evidences. The anomality is explained as the results of the suppressed electron wind force in the metal wires of W and Mo. The finding enriches our knowledge about atom migration in the failure of electrical connects in the electronic industry.\nIn Lines 167 and 169 the word of \"Train\" needs explanation.", "reviewer_2": "Comments to NCOMMS-25-73924\nIn the manuscript entitled “Upwind electromigration of sub-10-nm metallic nano-interconnects”, the authors used in situ Transmission electron microscopy to investigate the electromigration of W and Mo nano structures under pulsed electric biasing. Migration of W and Mo against the electron flux is observed, opposite to the conventional understanding of electromigration that the metal atoms move along the direction of electron flow due to electron wind force.\nThe manuscript is well organized, the figures and TEM images are of high quality, the scientific narrative is coherent, the story is convincing supported by elegant in situ TEM evidence and complementary DFT simulations. The findings – upwind electromigration in refractory nano-interconnects – is timely and relevant for next-generation electronic reliability studies.\nHowever, there are some issues that should be addressed before publication.\n1. The methods section is too condensed relative to the complexity of the experiments, making it difficult to assess reproducibility:\na. The TEM parameters (e.g., image- or probe- corrected, hot or cold FEG, monochromated) are not specified.\nb. The in situ experiment settings, such as electron dose rate, is not provided. The authors mentioned beam-blank experiments, but the result is not provided in the supplemental material.\nc. Quantitative details of the electropulsing parameters (pulse width, duration, current density range, number of pulses) for each material are missing.\nd. Clarify how the temperature rise during pulsing was estimated or controlled. The discussion dismisses the Soret effect, but no supporting temperature data are shown.\ne. The description of strain mapping using GPA could include details on reference region selection and uncertainty estimation.\n2. Figures 1–3 beautifully capture atomic motion, but it is not always clear how many independent experiments were conducted for each condition (e.g., W vs. Mo, same vs. different orientations, pulse configurations). The paper would benefit from a short statement on reproducibility or statistical sampling.\n3. The authors present results using applied voltage, whereas current density is the conventional metric in electromigration research. Providing estimated current densities would facilitate direct comparison with previous literature.\n4. Please specify whether the observed “upwind” migration persisted after prolonged continuous current flow, not only during discrete pulses.\n5. The authors should clarify why a pulsed bias was chosen instead of a continuous DC current. While the “electropulsing” approach is mentioned throughout and likely minimizes heating and enables time-resolved atomic tracking, an explicit explanation of its rationale and potential influence on electromigration mechanisms (e.g., transient electron wind vs. steady-state diffusion) would strengthen the methodological transparency.\n6. The DFT section is well executed but very brief. Including a short paragraph in the main text summarizing the computational cell size, surface model, and validation against experimental data would improve transparency. Table S2 (mentioned in the text) should be more prominently referenced or partially reproduced in the main paper.\n7. The discussion on the competition between direct and wind forces is interesting but could use a more quantitative comparison. For instance, showing the ratio of |Z_direct| to |Z_wind| for each metal would help illustrate the argument more clearly. In this discussion, the effect of the pulses is not considered. How would the transient pulses change the results?\n8. Consider briefly discussing the potential implications of this “upwind” mechanism for device-scale interconnect design (e.g., how it might influence lifetime modeling or materials selection).\n9. Minor Points\na. Ensure consistent notation for crystallographic directions ([011̅], [111], etc.).\nb. A short schematic summarizing the entire experimental setup (TEM holder, pulse configuration, current direction) would be very helpful.\nc. Some recent references on in situ electromigration in refractory metals could be cited for context.\nSummary Recommendation\nThis is a strong and visually impressive paper presenting an intriguing and potentially paradigm-shifting observation. The results are convincing, but the experimental and methodological details should be expanded for reproducibility and clarity. Minor revision is recommended.", "reviewer_3": "\"Upwind electromigration of sub-10-nm metallic nano-interconnects\" presents some beautiful data from a few in situ TEM experiments. However, in the presentation important context is either misleading or absent. I include suggestions for improvements below.\nThe statement \"Conventional understanding holds that electromigration follows the direction of electron flow\" is misleading. While Z*<0 is more common, the other case has been calculated and observed (see Ho&Kwok 1989 for example). The references given (12-15) do not seem to support this claim about the \"conventional understanding\". The authors seem to be positioning upwind migration as if it were in defiance of all expectations. They are more circumspect later when they write, \"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 changed.\" In the introduction they should either change their claim or support it more effectively.\nFig.1g I do not understand the phrase \"Intensity profiles for the outermost plane\". Outermost and plane seem contradictory for the irregular wire shape shown. How was this figure generated? Where are its x- and y-origins?\nFig.2 How are the reference positions D1 and D2 located? The problem of fiducials seems challenging when atoms throughout the field of view are relocating.\n\"no holes are present in metals\" is an oversimplification at best - see Kittel's textbook, for example. The reference cited is referring to a specific model and does not support the statement made.\nIn the sup info: \"Joule heating is un-avoided\". I think the authors mean to say \"Joule heating is unavoidable\".\nThe authors have convinced me that the migration observed is driven by the electric fields and not by thermal gradients. However, I think that the paper would still benefit from the inclusion of some estimates of the temperature achieved in the thin parts of the wire during pulsing. The current densities, geometries, electrical conductivity, and thermal conductivity are all known well enough for an estimate.\n\"In situ\" is not sufficiently descriptive of the methods employed. The authors do not mention \"TEM\" or \"transmission electron microscopy\" until page 18 in the manuscript. To place their work in context, they might consider adding a paragraph to the introduction that discusses what has previously been done on electromigration with in situ TEM (e.g. Mecklenburg 2021, Hsueh 2021, Kozlova 2013, and Gao 2011)."}, "author_response": "Point-to-point Response to the Reviewers’ comments\nTitle: Upwind electromigration of sub-10-nm metallic nano-interconnects\nWe sincerely thank the reviewers for their valuable comments and constructive\nsuggestions, which help us to improve the quality of our manuscript a lot. In the\nfollowing, the reviewers’ comments are laid out in italicized font and our response to\neach comment is given in blue text. The manuscript has been revised accordingly and\nthe changes have been highlighted in red color.\nResponse to Reviewer #1\nThe paper reports a phenomena about the upwind migration of atoms in metal wires\nunder electrical pulse. The finding is novel controversial to previous findings with\nenough evidences. The anomality is explained as the results of the suppressed electron\nwind force in the metal wires of W and Mo. The finding enriches our knowledge about\natom migration in the failure of electrical connects in the electronic industry.\nResponse: We sincerely appreciate the reviewer for the positive comments on the\nscientific significance of our work. We hope our response below and the revised\nmanuscript have addressed your concern.\n#1. In Lines 167 and 169 the word of \"Train\" needs explanation.\nResponse:Thank you for this comment. The “train” here means a succession of atomic\nsteps travelling collectively, following the description of S. Stoyanov, Jpn. J. Appl. Phys.\n30, 1 (1991). To avoid any ambiguity, we have provided a parenthetical explanation for\nthis word. The text (Lines 172-175 in Page 9 of the revised manuscript) now reads:\nWhen pulse current flows along the step-down direction, the step train (i.e., the\nsuccession of atomic steps travelling collectively) on W (110) is unstable and\nelectromigration induces the formation of step bunching.\nIn the manuscript entitled “Upwind electromigration of sub-10-nm metallic nano-\ninterconnects”, the authors used in situ Transmission electron microscopy to\ninvestigate the electromigration of W and Mo nano structures under pulsed electric\nbiasing. Migration of W and Mo against the electron flux is observed, opposite to the\nconventional understanding of electromigration that the metal atoms move along the\ndirection of electron flow due to electron wind force.\nThe manuscript is well organized, the figures and TEM images are of high quality, the\nscientific narrative is coherent, the story is convincing supported by elegant in situ TEM\nevidence and complementary DFT simulations. The findings – upwind electromigration\nin refractory nano-interconnects – is timely and relevant for next-generation electronic\nreliability studies.\nHowever, there are some issues that should be addressed before publication.\nResponse: We sincerely appreciate the reviewer for the positive comments on the\nscientific significance of our work. We hope our response below and the revised\nmanuscript have addressed your concerns.\n#1. The methods section is too condensed relative to the complexity of the experiments,\nmaking it difficult to assess reproducibility:\na. The TEM parameters (e.g., image- or probe- corrected, hot or cold FEG,\nmonochromated) are not specified.\nb. The in situ experiment settings, such as electron dose rate, is not provided. The\nauthors mentioned beam-blank experiments, but the result is not provided in the\nsupplemental material.\nc. Quantitative details of the electropulsing parameters (pulse width, duration, current\ndensity range, number of pulses) for each material are missing.\nd. Clarify how the temperature rise during pulsing was estimated or controlled. The\ndiscussion dismisses the Soret effect, but no supporting temperature data are shown.\ne. The description of strain mapping using GPA could include details on reference\nregion selection and uncertainty estimation.\nResponse: We are grateful for the necessary experiment details proposed by the\nreviewer. We have revised the Methods section and Supplementary Information (SI) to\ninclude additional experimental and methodological details:\na. The in situ TEM characterization was performed in a Cs-corrected FEI Titan G2\n60-300 TEM, equipped with an image-side aberration corrector, a hot FEG, and a\nmonochromator.The operating acceleration voltage was 300 kV.\nb. All in situ TEM experiments were conducted with spot size 3, magnification 670\nk/850 k, controlled low beam dose rate of approximately 1×104 e- nm-2 s-1. Beam-\nblank experiment of W nanowire shows similar upwind electromigration, as shown\n2\nin Figure R1, which has been added in SI (Figure S16) for further demonstration.\nc. We have set up the Supplementary Table S1 titled “Samples and pulse parameters\ntested in this study”, where the necessary electropulsing parameters have been\nsummarized. The typical current density was estimated in Supplementary\nDiscussion 3.\nd. A theoretical calculation has been conducted to evaluate the Joule heating effect in\nSupplementary Discussion 4. Taking the W nanowire in main text Fig. 1 for\nexample, a steady-state one-dimensional heat conduction model is adopted to\nestimate the temperature rise, which is estimated to be 40 K and thus can be\nnegligible in our studies. Regarding the Soret effect, firstly the temperature rise in\nour experiments is relatively low, such that the thermal-induced diffusion can be\nlargely neglected; secondly, there should be a symmetrical temperature distribution\nalong the axial direction of nanowires, with the highest temperature rise in the\nregion with smallest diameter. With this symmetrical temperature distribution, the\nthermal-induced atom diffusion should proceed oppositely along the nanowire axis,\nfrom the region with smallest diameter to both ends, in contrast to the directional\nelectromigration observed in current experiments (i.e. atomic migration is always\nconsistent with the current direction, see Fig. S4). Thus, the contribution of Soret\neffect to our observations can be largely excluded.\ne. The reference area of W chosen for GPA is marked by the rectangle in each map in\nFigure R2, which has been added in SI (Figure S15). Uncertainty estimation of GPA\nis defined by the strain standard deviation of reference region, which are 0.014 for\nFig.1h and 0.016 for Fig. 2e-h, respectively. Also, we have expanded the description\nof the GPA analysis in the revised manuscript (Lines 346-348, Page 16).\nFigure R1 Beam-blank experiment of surface electromigration in W nanowire.\n(a) Initial state of the W nanowire, outlined by yellow dotted lines. Fixed reference\npoints on the substrate for image drift correction are marked by white arrows. (b)\nSequence of three electrical pulses (1.2 V, 10 ns) applied under beam-blank\ncondition. (c) Subsequent contour evolution of the nanowire reveals pronounced\nmass transport following the direction of current, as indicated by the curved arrows.\nregions used for strain mapping in (a) Fig. 1h and (b) Fig. 2e of the main text are marked\nby the rectangles.\n#2. Figures 1–3 beautifully capture atomic motion, but it is not always clear how many\nindependent experiments were conducted for each condition (e.g., W vs. Mo, same vs.\ndifferent orientations, pulse configurations). The paper would benefit from a short\nstatement on reproducibility or statistical sampling.\nResponse:We thank the reviewer for this critical and constructive comment. We fully\nagree that stating the reproducibility of the observations is essential for establishing the\nrobustness of our findings. We have performed a systematic review of our experimental\nrecords and have added clear statements regarding the number of independent\nexperiments and the reproducibility of the key phenomena in the manuscript (Line 356,\nPage 16).\nTo firmly validate the robustness of this phenomenon under varying pulse conditions,\nwe performed dozens of repeat experiments within the same re-welded W nanowire by\nswitching the pulse current direction (reversing the voltage) and modulating the pulse\nparameters (varying the pulse width and the lead time). Meanwhile, we have conducted\nrepeat experiments on W and Mo with different orientations (see Table S1).\nSpecifically, the directional electromigration in W and Mo was consistently observed\nin all experiments listed in Table S1.\n#3. The authors present results using applied voltage, whereas current density is the\nconventional metric in electromigration research. Providing estimated current densities\nwould facilitate direct comparison with previous literature.\nResponse:We thank the reviewer for this critical suggestion. We completely agree that\ncurrent density is essential for comparison with the established electromigration\nliterature. The typical current densities for our in situ experiments can be calculated as\nfollow: the maximum current density j is estimated using the equation j=I/A, where I is\nthe maximum current during electropulsing, and A is the cross-section area of the\nnanowire, which could be estimated from the HRTEM images. Based on the pulse\nparameters applied in our experiments, the maximum current density passing the\n4\nnanowires are estimated to be in the range of 2×109 to 9×109A/cm2. The current\ninformation has been added in the revised manuscript.\n#4. Please specify whether the observed “upwind” migration persisted after prolonged\ncontinuous current flow, not only during discrete pulses.\nResponse: We thank the reviewer for raising this important question. We must first\nclarify a technical constraint: due to hardware limitations in our in situ TEM setup\n(specifically, the risk of damaging the sensitive chips under sustained high current),\nthe\nmaximum allowable continuous DC current is capped at ~1.2 mA. This level seems\ninsufficient to drive the pronounced electromigration in our study. Therefore, a direct\nexperimental comparison using true continuous DC at the requisite current density is\ndifficult with our current platform.\nTo solve this point in an alternative way, we have conducted additional experiments by\nfabricating ultra-narrow W nanocontacts (~3.4 nm in diameter) to achieve the high\ncurrent density for pronounce electromigration under DC condition. As shown in Figure\nR2, when 0.4 V bias was applied, it generated a measured current of ~500 μA\n(corresponding to an estimated current density of ~1.4×109 A cm-2). The same “upwind”\natomic migration on the W surface occurs after 11 seconds exposing under this\ncontinuous DC condition. However, at this extreme scale, the nanocontact exhibited\nsevere drift (see the inset of Fig. R3d), which prevented us from extending the\nprolonged duration observation.\nFigure R3 Upwind electromigration under continuous DC current using an\nultrathin W nanocontact. (a-c) Sequential frames showing surface atom migration\n(indicated by red and blue arrows) under a bias of 0.4 V. (d) The measured current-time\ncurve. Inset shows drift of the nanocontact. The blue arrows on the bottom right of (a-\nc) points out a surface step as reference.\nthis point, see Page 10.\n#5. The authors should clarify why a pulsed bias was chosen instead of a continuous\nDC current. While the “electropulsing” approach is mentioned throughout and likely\nminimizes heating and enables time-resolved atomic tracking, an explicit explanation\nof its rationale and potential influence on electromigration mechanisms (e.g., transient\nelectron wind vs. steady-state diffusion) would strengthen the methodological\ntransparency.\nResponse: We thank the reviewer for this insight comment. We have expanded our\nexplanation in the main text and SI to clarify the strategic reasons for choice of\nelectropulsing, which extend beyond mitigating Joule heating (as estimates in the\nSupplementary discussion 4) and enabling atomic tracking.\nThe pulsed approach is particularly relevant because:\na. Technological significance: High-frequency pulsed signals are central to modern\ncomputing and memory devices, yet electromigration under such conditions is\npoorly understood. Our work addresses this gap.\nb. Decoupling fundamental mechanisms: Previous reports on the direction of DC-\ndriven electromigration in W seem conflicting (D. O'Boyle, J. Appl. Phys., 1965 vs.\nH. Cao, Journal of Chinese Electron Microscopy Society, 2024), likely due to\nunresolved thermo-electric coupling. Our pulsed method decouples the electric\neffects from cumulative thermal effects.\nc. Clarifying the dominant mechanism: The nanosecond-scale pulse width far exceeds\nthe electron relaxation time in W/Mo (Table S2), ensuring a stable electron wind\nforce is established. We estimated that the characteristic length for steady-state\ndiffusion (Blech effect) during a single 10 ns pulse is much less than an atomic\nspacing (see the following text), confirming that direct electromigration dominates\nover long-range diffusion in our observations.\nTo quantitatively assess whether the observed long-range, directional atomic migration\nduring a single electropulse could be attributed to steady-state diffusion driven by a\nconcentration gradient, we estimate the characteristic diffusion length within the pulse\nduration. Atomic transport via steady-state diffusion is described by the characteristic\nlength ,where D is the diffusion coefficient, and t is the diffusion time, taken\nhere as 𝐿th=e p√u𝐷lse⋅ w𝑡idth t=1×10-8 s. The diffusion coefficient follows the Arrhenius law\n. To obtain an upper-bound estimate for L, we adopt parameters\n𝐸𝑎\n𝐷fav=or𝐷ab0lee xtpo d(i−ffu\nk\ns\nB\n𝑇\no)n (Grazyna Antczak and Gert Ehrlich, Surface Diffusion : metals,\nmetal atoms, and clusters, 2010): the preexponential factor D =1×10-7 m2 s-1, activation\n0\nenergy E =0.8 eV, temperature T=400 K. Substituting these values, we get L≈0.3 pm,\na\n6\nwhich is much less than an atomic spacing. This result demonstrates that within the 10\nns timescale of a single electropulse, atomic transport via steady-state diffusion is\nnegligible.\nWe are grateful for this constructive suggestion, which helped us clarify how pulsed\nbiasing enables the direct observation of the intrinsic “upwind” electromigration by\neffectively decoupling it from competing thermal and steady-state diffusion effects.\n#6. The DFT section is well executed but very brief. Including a short paragraph in the\nmain text summarizing the computational cell size, surface model, and validation\nagainst experimental data would improve transparency. Table S2 (mentioned in the text)\nshould be more prominently referenced or partially reproduced in the main paper.\nResponse: We have revised the DFT section in the main text following the Referee’s\nsuggestion. While there is currently no direct experimental data for the electron-phonon\ninteractions on the surface, other parameters including the lattice constants used in the\nDFT calculations, the electron relaxation times and the carrier concentrations used in\nwind force calculations were directly extracted from experimental data.\nThe following details have been added in the revised manuscript:\n“To theoretically clarify the competition of effective electromigration driving force, here\nwe evaluate the wind force valence of W, Mo, Au and Cu surface atoms using\nthe density functional theory calculations. Slab models containing 5 or more atomic\n𝑍𝑤𝑖𝑛𝑑\nlayers were constructed to model the surface steps, as shown in Fig. S9, and the surface\nstructures were optimized while fixing the bottom layers with experimental lattice\nconstants to mimic the bulk behavior. The distance between step edges and the vacuum\nspacings are larger than 10 Ang to avoid artificial interactions between periodic images.\nUsing the computational approached described in Methods section, can be\nevaluated using electron-phonon interaction matrix, electron scattering time, and the\n𝑍𝑤𝑖𝑛𝑑\nFermi velocity. The electron-phonon interaction matrix was calculated for step edge\natoms using the above slab models, while the electron scattering time and Fermi\nvelocity were extracted using experimental data in the literature [Ref. 19]. The\nassociated values are shown in Table S2.\nThe calculated on W(110), Mo(110) and Au(111) atoms at step edges are 5.066,\n3.669 and 40.116, respectively. This indicates the wind forces on W and Mo atoms are\n|𝑍𝑤𝑖𝑛𝑑|\nmuch weaker than that on Au atoms. The large wind force for Au and Cu originates\nfrom stronger electron-phonon coupling, longer electron scattering time and Fermi\nvelocity. As shown in Table S2, the electron-phonon coupling of Au(111) step edge atom\nis 1.58 eV/Ang, which is almost twice those of W(110) (0.74 eV/Ang) and Mo(110) (0.80\neV/Ang). The electron scattering time τ are 27.3 fs for Au and 36 fs for Cu, which are\nmuch longer than those of W (16 fs) and Mo (12 fs). The Fermi velocities of Au and Cu\nare also slightly greater. For the direct force , we estimate from the charge of\nbare ion without free electron, giving the values of around 6 for W and Mo, 1 for Au\n𝑍𝑑𝑖𝑟𝑒𝑐𝑡\nand Cu (Supplementary Discussion 2). This leads to a ratio of 1.2\nfor W surface and 1.6 for Mo surface. For Au and Cu surfaces, on the contrary, all\n|𝑍𝑑𝑖𝑟𝑒𝑐𝑡|/|𝑍𝑤𝑖𝑛𝑑|\nratios are less than 0.05. Therefore, the electromigration driving\nforce for surface electromigration in W and Mo nanowires is dominated by the direct\n|𝑍𝑑𝑖𝑟𝑒𝑐𝑡|/|𝑍𝑤𝑖𝑛𝑑|\nforce, in opposite to the well-known electromigration behaviors in Au, Cu and Al, as\nschematically shown in Fig. 4e.”\n#7. The discussion on the competition between direct and wind forces is interesting but\ncould use a more quantitative comparison. For instance, showing the ratio of |Z_direct|\nto |Z_wind| for each metal would help illustrate the argument more clearly. In this\ndiscussion, the effect of the pulses is not considered. How would the transient pulses\nchange the results?\nResponse: Many thanks for this suggestion. We have revised the corresponding\nparagraph in main text as follows:\n“This leads to a ratio of 1.2 for W surface and 1.6 for Mo surface.\nFor Au and Cu surfaces, on the contrary, all ratios are less than\n|𝑍𝑑𝑖𝑟𝑒𝑐𝑡|/|𝑍𝑤𝑖𝑛𝑑|\n0.05.”\n|𝑍𝑑𝑖𝑟𝑒𝑐𝑡|/|𝑍𝑤𝑖𝑛𝑑|\nRegarding the effect of pulses, the transient effect is not considered in this work. This\nis because of the fact that the rise time and fall time of the pulse are around 2 to 10 ns.\nThey are 5 orders of magnitudes longer than the electron relaxation times in these\nmetals which are around tens of femtoseconds, as shown in Table S2. Due to the time-\nscale difference, the electrons are expected to fully relax during the pulse rise and fall,\nand can be treated as in a quasi-steady state. Therefore, the transient pulse effect is\nexpected to be negligible.\n#8. Consider briefly discussing the potential implications of this “upwind” mechanism\nfor device-scale interconnect design (e.g., how it might influence lifetime modeling or\nmaterials selection).\nResponse:We thank the reviewer for this suggestion. Connecting our observed atomic-\nscale “upwind” mechanism to device-scale design considerations will greatly enhance\nthe impact of our work. Following the reviewer’s advice, we have added a brief prospect\nto the Discussion section (Page 14-15) that how our findings offer new insights into the\noptimization of nano-interconnect reliability toward extreme applications.\nFrom a device-scale perspective, structural designs that promote uniform current\ndistribution and minimize the non-uniform distribution of deformation and temperature\nare critical, especially at interfaces involved of different metals (e.g., contacts, gate\nelectrodes, and interconnects). Upwind electromigration mechanism suggests that\nsurface and interface engineering should be strategically used to guide atomic flux away\nfrom sensitive failure sites.\nFor materials selection, our work implies that metals or alloys where the “direct force”\ndominates (Z*>0) may exhibit fundamentally different, and potentially superior\nelectromigration resistance. This may provide a new criterion for high-throughput\nscreening for candidate interconnect materials. Besides, the “upwind” electromigration\nprovides a new degree of freedom for utilizing electromigration. Selecting metals with\na propensity for “upwind” migration could be strategically used to engineer material\ntransport, potentially suppressing void formation at critical cathode interfaces or even\nenabling self-healing of anode-side damage, thereby enhancing overall reliability.\nFor practical applications, the observation of upwind electromigration in W and Mo\nnano-interconnects represents a new regime of electromigration that was not reported\nin conventional metallic nano-interconnects; and the application of electropulses are\nsimilar close to the real working conditions of unidirectional high-frequency pulsing in\nnanodevices. However, the characteristic time is too short for establishing a\ncounteracting concentration gradient, such that the Blech effect, relying on steady-state\nback-stress diffusion, becomes ineffective. Above facts suggest that lifetime prediction\nunder such an upwind regime cannot be extrapolated from conventional DC/AC models\nand requires new framework for nanodevices toward harsh conditions.\n#9. Minor Points\na. Ensure consistent notation for crystallographic directions ([011̅], [111], etc.).\nb. A short schematic summarizing the entire experimental setup (TEM holder, pulse\nconfiguration, current direction) would be very helpful.\nc. Some recent references on in situ electromigration in refractory metals could be cited\nfor context.\nResponse: Many thanks for these minor comments. We have double-checked all the\nnotation and labels in the manuscript, to ensure that they are consistent and correct. A\nschematic illustrating the experimental setup has been added as Fig. S13 in the revised\nSI. Recent references on in situ electromigration have been further cited.\nFigure R4. Experimental setup of the in situ electropulsing test. The real picture is\nthe TEM-STM platform.\n\"Upwind electromigration of sub-10-nm metallic nano-interconnects\" presents some\nbeautiful data from a few in situ TEM experiments. However, in the presentation\nimportant context is either misleading or absent. I include suggestions for\nimprovements below.\nResponse: We sincerely appreciate the reviewer for the constructive comments. We\nhope our response below and the revised manuscript have addressed your concerns.\n#1. The statement \"Conventional understanding holds that electromigration follows the\ndirection of electron flow\" is misleading. While Z*<0 is more common, the other case\nhas been calculated and observed (see Ho&Kwok 1989 for example). The references\ngiven (12-15) do not seem to support this claim about the \"conventional understanding\".\nThe authors seem to be positioning upwind migration as if it were in defiance of all\nexpectations. They are more circumspect later when they write, \"However, the\ndifference of electron band structure leads to the obvious variation of resistivity and\nelectron scattering behaviors in transition metals, where the balance of the direct force\nand wind force can be completely changed.\" In the introduction they should either\nchange their claim or support it more effectively.\nResponse: We sincerely thank you for this insightful comment regarding the lack of\nprecision in our introduction. We have revised the introduction according your\nsuggestion. In fact, our original intention was to frame the “conventional understanding\non electromigration” within the conventional materials for interconnects made of Al,\nCu and Au. In these systems, mass transport does follow electron flow (Z*<0). However,\nas you pointed out, claiming electromigration always follows electron flow is\ninaccurate, as positive effective charge (Z*) have indeed been reported in specific\nsystems (P.S. Ho 1966, D.R. Cambell and H.B. Huntington 1969). We have revised the\nintroduction to correct this misleading claim and to provide a more accurate background.\n#2. Fig.1g I do not understand the phrase \"Intensity profiles for the outermost plane\".\nOutermost and plane seem contradictory for the irregular wire shape shown. How was\nthis figure generated? Where are its x- and y-origins?\nResponse: In Figure 1g (presented here as Figure R5a), the term “outermost plane”\nactually refers to the outermost atom array (just the outmost layer on the center surface\nof the nanowire, not the entire outer contour of the nanowire). To avoid overcrowding\nthe main figure, we have clearly marked the region for intensity analysis in Figure S3.\nTo further address the Referee’s concerns, we show how Fig. 1g generated in Fig. R5b.\nAfter carefully aligning HRTEM image sequence, we selected a same area from two\nimages, i.e., the region containing outmost atom layers, and used Line Profiles in\nDigital Micrograph to acquire the intensity of sampled regions. So, in Fig. 1g, the x-\naxis is the distance traveled along white dashed rectangles, and y-axis is the raw\nintensity (in arbitrary unit) from the HRTEM signal. These details have been further\nclarified in the revised manuscript.\nDiagram showing how intensity profiles were generated along defined regions\n(outermost atom arrays marked by white rectangles) from aligned HRTEM images.\n#3. Fig.2 How are the reference positions D1 and D2 located? The problem of fiducials\nseems challenging when atoms throughout the field of view are relocating.\nResponse:Indeed, finding reliable references during atomic migration is important for\nquantitative analysis. In our experiment, we selected two nanotips on the metallic\nmatrix as reference points to determine positions of D and D , shown in Figure R6a, a\n1 2\nTEM image with a larger view field (marked by red and blue arrows, respectively). Fig.\n2a-d were cropped to highlight the atomic motion, which unfortunately cropping off\nthese reference points. We have now included uncropped image sequence shown in\nFigure R6b as a new supplementary figure (Fig. S6), which clearly shows that the\npositions of D and D remained unchanged throughout the pulsing experiments,\n1 2\nconfirming the reliability of our displacement measurements.\nmeasurement. (a) Wider-field TEM images showing the two stable nanotips on the\nmetallic matrix (marked by red and blue arrows) that serve as the reference points for\ndefining positions D and D . (b) Uncropped image sequence corresponding to the pulse\n1 2\nseries in Fig. 2a-d of the main text. The constant positions of the two reference nanotips\nthroughout the pulsing experiment confirm the reliability of the drift correction and the\nmeasured atomic displacements.\n#4. \"no holes are present in metals\" is an oversimplification at best - see Kittel's\ntextbook, for example. The reference cited is referring to a specific model and does not\nsupport the statement made.\nResponse: Many thanks for pointing out this issue. We have revised the manuscript to\nremove the absolute statement about holes in metals and updated the citation\naccordingly.\nGiven that electrical conduction in metals is primarily governed by the response of\nelectrons near the Fermi surface, a more accurate description of the process is that an\nincident non-equilibrium distribution of these conduction electrons drives the\nredistribution of the local surface potential.\n#5. In the sup info: \"Joule heating is un-avoided\". I think the authors mean to say \"Joule\nheating is unavoidable\".\nResponse: We thank the reviewer for pointing out this typographical error. The\nsentence has been corrected in the revised Supplementary Information.\n#6. The authors have convinced me that the migration observed is driven by the electric\nfields and not by thermal gradients. However, I think that the paper would still benefit\n12\nfrom the inclusion of some estimates of the temperature achieved in the thin parts of the\nwire during pulsing. The current densities, geometries, electrical conductivity, and\nthermal conductivity are all known well enough for an estimate.\nResponse: We thank the reviewer for this constructive suggestion. We agree that\nproviding an estimate of the temperature rise would further strengthen our discussion.\nFollowing the reviewer’s suggestion, we have performed a theoretical calculation to\nevaluate the Joule heating effect. Taking the W nanowire in Fig. S2 as example, a\nsteady-state one-dimensional heat conduction model is adopted to estimate the\ntemperature rise. This model assumes that the generated Joule heat is fully dissipated\nto the substrates through axial heat conduction, achieving a dynamic balance between\nheat generation and heat loss. Given the estimated current density ~5×109 A/cm2 in our\nexperiment, geometry, and temperature-dependent electrical/thermal conductivity, the\nsteady-state temperature distribution during electropulsing is calculated.\nThe results, now included as Supplementary Discussion 4, suggest that the maximum\ntemperature rise in the W nanowire is approximately 40 K. This weak heating effect\nsupports our conclusion that the observed directed atomic migration is primarily driven\nby the electric field rather than a significant thermal effect.\n#7. \"In situ\" is not sufficiently descriptive of the methods employed. The authors do not\nmention \"TEM\" or \"transmission electron microscopy\" until page 18 in the manuscript.\nTo place their work in context, they might consider adding a paragraph to the\nintroduction that discusses what has previously been done on electromigration with in\nsitu TEM (e.g. Mecklenburg 2021, Hsueh 2021, Kozlova 2013, and Gao 2011).\nResponse:We have added new description to the introduction (Lines 53-59 on Page 4)\nthat specifically discusses the progress and challenges in in situ TEM electromigration\nstudies. This section cites the key literature mentioned by the reviewer and highlight\nhow our work provides the direct atomic-scale observation of the “upwind”\nelectromigration behavior in transition metals, a phenomenon that had not been clearly\nresolved in previous findings.\nAdditionally, we have ensured that the term “in situ TEM” is explicitly introduced early\nin the manuscript (Page 4) to emphasize our methods.\n13"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The concerns of the reviewers are addressed properly.", "reviewer_2": "I thank the authors for their thorough and thoughtful responses. The rebuttal adequately addresses all my major and minor concerns, with substantial improvements to the Methods, supplementary data, and discussion that significantly strengthen the rigor, clarity, and reproducibility of the work. The additional experiments and quantitative analyses are convincing, and the conclusions are well supported.\nI am satisfied with the revisions and recommend acceptance of the manuscript in its current form.", "reviewer_3": "The authors have addressed the issues that I raised previously to my satisfaction. I congratulate them on their accomplishment.\nI do have one last minor observation: Ang is not a standard abbreviation for angstrom. It should be replaced with the internationally recognized symbol (the Swedish letter \"A\" with a ring above it)."}, "author_response": "Point-to-point Response to the Reviewers’ comments\nTitle: Upwind electromigration of sub-10-nm metallic nano-interconnects\nWe sincerely thank the reviewers for their positive assessment of our revisions. In the\nfollowing, the reviewers’ comments are typeset in italic and our response to each\ncomment is given in blue text. The manuscript has been revised accordingly and the\nchanges have been highlighted in red.\nResponse to Reviewer #1\nThe concerns of the reviewers are addressed properly.\nResponse: We sincerely appreciate you for your time and the positive comments. We\nare pleased that the revisions meet with your approval.\nResponse to Reviewer #2\nI thank the authors for their thorough and thoughtful responses. The rebuttal adequately\naddresses all my major and minor concerns, with substantial improvements to the\nMethods, supplementary data, and discussion that significantly strengthen the rigor,\nclarity, and reproducibility of the work. The additional experiments and quantitative\nanalyses are convincing, and the conclusions are well supported.\nI am satisfied with the revisions and recommend acceptance of the manuscript in its\ncurrent form.\nResponse: We are grateful for your positive assessment and are pleased that the\nadditional experiments and quantitative analyses addressed your concerns. Thank you\nfor your comprehensive review, which has significantly strengthened our manuscript.\nResponse to Reviewer #3\nThe authors have addressed the issues that I raised previously to my satisfaction. I\ncongratulate them on their accomplishment.\nResponse: We sincerely thank you for your insightful comments and congratulations.\nI do have one last minor observation: Ang is not a standard abbreviation for angstrom.\nIt should be replaced with the internationally recognized symbol (the Swedish letter \"A\"\nwith a ring above it).\nResponse: We have checked all the symbols throughout the manuscript and the\nSupplementary Information, replacing all instances of “Ang” with the standard symbol\n“Å”."}]

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