Effective Mobility in Nanowire FETs Under Quasi-Ballistic Conditions

In this paper, we investigate the electron mobility in nanowire (NW) FETs operating under quasi-ballistic conditions. Starting from a general expression of the current-voltage characteristics worked out in a previous work, we determine the limiting current at low drain voltage and find the functional dependence of the carrier mobility versus device and gate lengths, barrier height, and momentum-relaxation length. The expression resulting from this procedure is nonlocal and is proved to be given by the Matthiessen's combination of ballistic and scattering-limited mobilities in NW-FETs, thus accommodating the transition between these two limiting transport conditions. Moreover, the relationship between mobility and backscattering coefficient is highlighted, showing that the former is simply proportional to the latter. One of the main results of this paper is that the combined effect of acoustic-phonon and surface-roughness scattering leads to a weakly varying mean-free path versus effective field, at least for NW-FETs with a diameter around 5 nm. Thus, mobility degradation at large gate voltages is predominantly due to carrier degeneracy, which is particularly severe in 1-D structures, rather than an enhanced scattering rate. Finally, we propose a methodology for the extraction of the average momentum-relaxation length from experimental measurements of the drain conductance, which does not require a separate measurement of the carrier density.