A study of nano-scale electron transport using the McKelvey-Shockley transport framework

Nano-scale electron transport plays an important role in electronic applications, including ultra- scaled and emerging nano-devices. While there are several approaches that can treat nano-scale transport, here we revisit the McKelvey-Shockley (McK-S) flux method, which is a computational efficient and physically transparent framework. This study focuses on reformulating the electron McK-S equations to resolve energy-dependent fluxes, capture the effect of electric field, and include a more rigorous treatment of electron-phonon scattering. This updated McK-S formalism is used to simulate electron transport across a finite-length semiconductor under the influence of constant electric field under varying conditions from ballistic to diffusive and from near-equilibrium to non-equilibrium and are benchmarked against solutions of the Boltzmann transport equation (BTE). The McK-S results display a good agreement with those of the BTE, with some notable differences that will be discussed. Looking forward, the McK-S flux method may enable the treatment of new problems of more complex systems that span multiple length scales.