Abstract
In nanoscale semiconductor devices, not only do electron–electron interactions require proper treatment but heat transport must also be integrated coherently. In this Perspective, we propose a paradigm shift: to treat electron transport using a three-part phase diagram that includes diffusive, ballistic and viscous electron-fluid regimes and to adopt a statistical-field approach to extend the tools for analysis, including the drift–diffusion model. The statistical-field approach posits that semiconductor devices — as open quantum systems characterized by fluctuating energy and particle numbers — can achieve local equilibrium through frequent microscopic collisions of electrons. The corresponding statistical fields emerge — specifically, spatial and temporal variations in temperature and chemical potential, which dictate the flows of energy and particles. The quantum nature of these statistical fields enables a seamless integration of quantum complexities, and the approach naturally incorporates heat dissipation in a self-consistent theoretical framework (although the proper modelling of boundary conditions requires further attention). We highlight the critical need to identify the transport regime in which short-channel nanodevices operate, to be able to build accurate simulators that will drive device design and optimization.
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Acknowledgements
The authors acknowledge fruitful discussions with I.F. Hu, W.-Y. Woon, L. Yang and W.-X. You. H.-H.L. acknowledges supports from National Science and Technology Council (Taiwan) through grant NSTC-113-2112-M-007-017 and from Taiwan Semiconductor Manufacturing Company through University Joint Development Project TUP-20231011-3510.
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H.-H.L. and S.S.L. proposed and supervised the project. Y.-C.Y. and H.-H.L. performed the theoretical calculations. All authors contributed to discussions and the writing of the manuscript.
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Yang, YC., Lin, HH. & Liao, S.S. A statistical-field approach to electron transport in semiconductor nanodevices. Nat Rev Electr Eng 2, 614–620 (2025). https://doi.org/10.1038/s44287-025-00192-4
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DOI: https://doi.org/10.1038/s44287-025-00192-4
