A statistical-field approach to electron transport in semiconductor nanodevices

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. This Perspective sets out an approach to electron transport in nanoscale devices based on statistical fields — specifically the spatial and temporal variations in temperature and chemical potential that drive energy and particle flow — and highlights the importance of identifying the transport regime, which might be diffusive, ballistic or viscous.