Equilibrium to non-equilibrium carrier statistics for a nanolayer

Fermi-Dirac carrier statistics for randomly oriented velocity moments is shown to transform to highly anisotropic non-equilibrium statistics yielding carrier velocity saturation comparable to 2-dimensional (2D) intrinsic velocity. The onset of quantum emission by a boson limits the saturation velocity. The ballistic nature of carriers injected from contacts in scaled-down channels is shown to degrade the mobility in agreement with experimental observations. Saturation velocity is shown to be independent of scattering parameters that control mobility.