The past decade has highlighted the importance of semi-classical models while also indicating the need for more rigorous quantum transport methods to explain charge carrier behavior. The emergence of nano-objects from bottom-up nanotechnology and ultra-scaled top-down nano-transistors has introduced new physics that traditional models cannot adequately address. For instance, ultra-thin body (UTB) MOSFETs, like FD-SOI-FETs and Fin-FETs, with silicon channel thicknesses under 1 nm, will soon require attention.

This leads to significant quantization of the electron gas perpendicular to the gate stack, affecting particle distributions and device characteristics. In sub-10 nm gate lengths, electron wave properties may enable tunneling and quantum reflections within the channel.

The Boltzmann or Wigner transport equation, which accounts for rapid potential variations and quantum effects, is useful for studying quantum transport in nanodevices, addressing scenarios like Gaussian wave packet interactions with tunneling barriers. However, the non-equilibrium Green's function (NEGF) approach struggles with carrier scattering and contact modeling. Thus, the Wigner function method may be more effective in intermediate regimes between quantum coherent and semi-classical situations.