Abstract
The relentless pursuit of smaller, faster nanoelectronics concentrates intense heat at nanometer scales, threatening performance and reliability. Yet directly mapping this heat from nonequilibrium hot electrons has remained elusive. Here we introduce the non-contact force technique that directly images hot-electron temperature distributions in operando devices. Using a bimodal atomic force microscope with sideband modulation, we harness frequency mixing to greatly boost sensitivity to hot-electron forces while suppressing parasitic electrostatic signals. This enables a thermal force microscope that visualizes hot electrons in the nanoconstriction of a silicon channel. Quantitative analysis reveals that thermal-fluctuation-induced force from hot electrons (\(\Delta {T}_{e} \sim 700\,{{{\rm{K}}}}\)) significantly exceed indirect effects from lattice heating (\(\Delta {T}_{L} \sim 3\,{{{\rm{K}}}}\)) or permittivity changes. At a 5 nm tip–sample gap, this pressure reaches ~3 bar, sufficient to drive substantial electro-thermo-mechanical effects. These results open a powerful route to probing hot-electron dynamics in working nanodevices and inform electro–thermal co-design strategies for post-Moore nanoelectronics.
Data availability
Source data underlying the main figures are provided as Supplementary Data accompanying this article. Additional data supporting the findings of this study are available from the corresponding author without restriction. Source data are provided with this paper.
Code availability
The code used for calculating force and the Hamaker function of this study is available from the corresponding authors upon request.
References
Salahuddin, S., Ni, K. & Datta, S. The era of hyper-scaling in electronics. Nat. Electron. 1, 442–450 (2018).
Lundstrom, M. S. & Alam, M. A. Moore’s law: the journey ahead. Science 378, 722–723 (2022).
Lian, Y. et al. Downscaling micro- and nano-perovskite LEDs. Nature 640, 62–68 (2025).
Datta, S., Chakraborty, W. & Radosavljevic, M. Toward attojoule switching energy in logic transistors. Science 378, 733–740 (2022).
Liu, C. et al. A hot-emitter transistor based on stimulated emission of heated carriers. Nature 632, 782–787 (2024).
Balkan, N. (ed.). Hot Electrons in Semiconductors: Physics and Devices. (Oxford University Press, 1997). https://doi.org/10.1093/oso/9780198500582.001.0001.
Xiang, Y. et al. Subnanosecond flash memory enabled by 2D-enhanced hot-carrier injection. Nature 641, 90–97 (2025).
Brongersma, M. L., Halas, N. J. & Nordlander, P. Plasmon-induced hot carrier science and technology. Nat. Nanotechnol. 10, 25–34 (2015).
Freitag, M. et al. Energy dissipation in graphene field-effect transistors. Nano Lett. 9, 1883–1888 (2009).
Kaasbjerg, K., Thygesen, K. S. & Jauho, A.-P. Acoustic phonon limited mobility in two-dimensional semiconductors: deformation potential and piezoelectric scattering in monolayer MoS${}_{2}$ from first principles. Phys. Rev. B 87, 235312 (2013).
Quan, Y. & Liao, B. Coupled electron-phonon hydrodynamics in two-dimensional semiconductors. Phys. Rev. Lett. 134, 226301 (2025).
Hanks, D. F. et al. Nanoporous membrane device for ultra high heat flux thermal management. Microsyst. Nanoeng. 4, 1 (2018).
Kang, J. S. et al. Integration of boron arsenide cooling substrates into gallium nitride devices. Nat. Electron. 4, 416–423 (2021).
Esmaeilzadeh, H., Blem, E., St. Amant, R., Sankaralingam, K. & Burger, D. Dark silicon and the end of multicore scaling. IEEE Micro 32, 122–134 (2012).
Waldrop, M. M. The chips are down for Moore’s law. Nature 530, 144 (2016).
Cao, W. et al. The future transistors. Nature 620, 501–515 (2023).
Allen, P. B. Theory of thermal relaxation of electrons in metals. Phys. Rev. Lett. 59, 1460–1463 (1987).
Caruso, F. & Novko, D. Ultrafast dynamics of electrons and phonons: from the two-temperature model to the time-dependent Boltzmann equation. Adv. Phys. X 7, 2095925 (2022).
Yang, L., Qian, R. J., An, Z. H., Komiyama, S. & Lu, W. Simulation of temperature profile for the electron and the lattice systems in laterally structured layered conductors. Europhys. Lett. 128, 17001 (2019).
Lin, Z., Zhigilei, L. V. & Celli, V. Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium. Phys. Rev. B 77, 075133 (2008).
Block, A. et al. Tracking ultrafast hot-electron diffusion in space and time by ultrafast thermomodulation microscopy. Sci. Adv. 5, eaav8965 (2019).
Tagliabue, G. et al. Ultrafast hot-hole injection modifies hot-electron dynamics in Au/p-GaN heterostructures. Nat. Mater. 19, 1312–1318 (2020).
Xue, H. et al. Direct observation of hot-electron-enhanced thermoelectric effects in silicon nanodevices. Nat. Commun. 14, 3731 (2023).
Menges, F. et al. Temperature mapping of operating nanoscale devices by scanning probe thermometry. Nat. Commun. 7, 10874 (2016).
Goodwill, J. M. et al. Spontaneous current constriction in threshold switching devices. Nat. Commun. 10, 1628 (2019).
Xie, X. et al. Quantitative thermal imaging of single-walled carbon nanotube devices by scanning joule expansion microscopy. ACS Nano 6, 10267–10275 (2012).
Ward, D. R., Corley, D. A., Tour, J. M. & Natelson, D. Vibrational and electronic heating in nanoscale junctions. Nat. Nanotechnol. 6, 33–38 (2011).
Deshpande, V. V., Hsieh, S., Bushmaker, A. W., Bockrath, M. & Cronin, S. B. Spatially resolved temperature measurements of electrically heated carbon nanotubes. Phys. Rev. Lett. 102, 105501 (2009).
Hillenbrand, R., Abate, Y., Liu, M., Chen, X. & Basov, D. N. Visible-to-THz near-field nanoscopy. Nat. Rev. Mater. 10, 285–310 (2025).
Lu, F., Jin, M. & Belkin, M. A. Tip-enhanced infrared nanospectroscopy via molecular expansion force detection. Nat. Photonics 8, 307–312 (2014).
Weng, Q. et al. Imaging of nonlocal hot-electron energy dissipation via shot noise. Science 360, 775–778 (2018).
Weng, Q. et al. Quasiadiabatic electron transport in room temperature nanoelectronic devices induced by hot-phonon bottleneck. Nat. Commun. 12, 4752 (2021).
Yang, L. et al. Anisotropic hot-electron kinetics revealed by terahertz fluctuation. ACS Photonics 8, 2674–2682 (2021).
Lee, H., Song, K., Lee, M. & Park, J. Y. In situ visualization of localized surface plasmon resonance-driven hot hole flux. Adv. Sci. 7, 2001148 (2020).
Bian, K. et al. Scanning probe microscopy. Nat. Rev. Methods Prim. 1, 36 (2021).
Garcia, R. & Herruzo, E. T. The emergence of multifrequency force microscopy. Nat. Nanotechnol. 7, 217–226 (2012).
Gisbert, V. G. & Garcia, R. Fast and high-resolution mapping of van der Waals forces of 2D materials interfaces with bimodal AFM. Nanoscale 15, 19196–19202 (2023).
Kort-Kamp, W. J. M., Murdick, R. A., Htoon, H. & Jones, A. C. Utilization of coupled eigenmodes in Akiyama atomic force microscopy probes for bimodal multifrequency sensing. Nanotechnology 33, 455501 (2022).
Gisbert, V. G., Amo, C. A., Jaafar, M., Asenjo, A. & Garcia, R. Quantitative mapping of magnetic properties at the nanoscale with bimodal AFM. Nanoscale 13, 2026–2033 (2021).
Nowak, D. et al. Nanoscale chemical imaging by photoinduced force microscopy. Sci. Adv. 2, e1501571 (2016).
Almajhadi, M. A., Uddin, S. M. A. & Wickramasinghe, H. K. Observation of nanoscale opto-mechanical molecular damping as the origin of spectroscopic contrast in photo induced force microscopy. Nat. Commun. 11, 5691 (2020).
Bonaccurso, E., Schönfeld, F. & Butt, H.-J. Electrostatic forces acting on tip and cantilever in atomic force microscopy. Phys. Rev. B 74, 085413 (2006).
Lai, K. et al. Photocatalytic CO2-to-CH4 conversion with ultrahigh selectivity of 95.93% on S-vacancy modulated spatial In2S3/In2O3 heterojunction. Adv. Funct. Mater. 34, 2409031 (2024).
Kim, Y. C. et al. Beneficial effects of PbI2 incorporated in organo-lead halide perovskite solar cells. Adv. Energy Mater. 6, 1502104 (2016).
Strelcov, E. et al. Space- and time-resolved mapping of ionic dynamic and electroresistive phenomena in lateral devices. ACS Nano 7, 6806–6815 (2013).
Cappella, B. & Dietler, G. Force-distance curves by atomic force microscopy. Surf. Sci. Rep. 34, 1–104 (1999).
Joulain, K., Mulet, J.-P., Marquier, F., Carminati, R. & Greffet, J.-J. Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field. Surf. Sci. Rep. 57, 59–112 (2005).
Chan, H. B., Aksyuk, V. A., Kleiman, R. N., Bishop, D. J. & Capasso, F. Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science 291, 1941–1944 (2001).
Klimchitskaya, G. L., Mohideen, U. & Mostepanenko, V. M. The Casimir force between real materials: experiment and theory. Rev. Mod. Phys. 81, 1827–1885 (2009).
Bouillard, J.-S. G., Dickson, W., O’Connor, D. P., Wurtz, G. A. & Zayats, A. V. Low-temperature plasmonics of metallic nanostructures. Nano Lett. 12, 1561–1565 (2012).
Weng, Q. et al. Comparison of active and passive methods for the infrared scanning near-field microscopy. Appl. Phys. Lett. 114, 153101 (2019).
Sushkov, A. O., Kim, W. J., Dalvit, D.aR. & Lamoreaux, S. K. Observation of the thermal Casimir force. Nat. Phys. 7, 230–233 (2011).
Bimonte, G. Observing the Casimir-Lifshitz force out of thermal equilibrium. Phys. Rev. A 92, 032116 (2015).
Robertson, J. & Wallace, R. M. High-K materials and metal gates for CMOS applications. Mater. Sci. Eng. R. Rep. 88, 1–41 (2015).
Li, W. et al. Uniform and ultrathin high-κ gate dielectrics for two-dimensional electronic devices. Nat. Electron. 2, 563–571 (2019).
Yang, H. U. & Raschke, M. B. Resonant optical gradient force interaction for nano-imaging and -spectroscopy. N. J. Phys. 18, 053042 (2016).
Ranjit, G., Atherton, D. P., Stutz, J. H., Cunningham, M. & Geraci, A. A. Attonewton force detection using microspheres in a dual-beam optical trap in high vacuum. Phys. Rev. A 91, 051805 (2015).
Acknowledgements
Z.A. acknowledges the financial support from the National Key Research and Development Program of China (Grant No. 2024YFA1409800), Innovation Program for Quantum Science and Technology (Grant No. 2024ZD0300103), and the National Natural Science Foundation of China under Grant Nos. 11991060/12027805/12474042, Shanghai Science and Technology Committee under Grant No. 23DZ2260100, and the Sino-German Center for Research Promotion (No. M-0174). Y.S. acknowledges the financial support from the National Natural Science Foundation of China (NSFC) (Nos. 12403096), the Explorers Program of Shanghai (Basic Research Funding) (No. 24TS1400800). W.K.L. acknowledges the technological help from Molecular Vista Inc. Part of the experimental work was conducted in the Fudan Nanofabrication Lab.
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Z.A. and W.K.L. conceived the idea and designed the experiments. W.K.L. carried out all experiments with help from Z.X., L.Q., X.G., H.X., H.Z., S.A.B., A.K., K.D., and S.C. contributed to the theoretical analysis. Y.S. assisted with sample fabrication, and Z.Z. provided the wafer growth. Z.A. and W.K.L co-wrote the paper with comments from all authors. Z.A. and W.L. co-supervised the research project.
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Lu, W., Xu, Z., Zhang, H. et al. Thermal Force Imaging of Hot Electrons in Operando Nanodevices. Nat Commun (2026). https://doi.org/10.1038/s41467-026-71712-5
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DOI: https://doi.org/10.1038/s41467-026-71712-5
