Quantum-Transport Study on the Impact of Channel Length and Cross Sections on Variability Induced by Random Discrete Dopants in Narrow Gate-All-Around Silicon Nanowire Transistors

摘要

In this paper, we review and extend recent work on the effect of random discrete dopants on the statistical variability in gate-all-around silicon nanowire transistors. The electron transport is described using the nonequilibrium Green's function formalism. Full 3-D real-space and coupled-mode-space representations are used. Two different cross sections (i.e., $hbox{2.2} times hbox{2.2}$ and $hbox{4.2} times hbox{4.2} hbox{nm}^{2}$) and two different channel lengths (i.e., 6 and 12 nm) have been considered. The resistivity associated with discrete dopants can be estimated from the averaged current–voltage characteristics. The threshold-voltage variability and the subthreshold-slope variability are reduced greatly in the transistors with longer channel length. Both are smaller at equivalent channel lengths in the $hbox{2.2} times hbox{2.2} hbox{nm}^{2}$ device due to better electrostatic integrity. At the same time, the on-state-current variability associated with the varying resistance of the access regions is virtually independent of the channel length. However, it is reduced greatly in the $hbox{4.2} times hbox{4.2} hbox{nm}^{2}$ transistor due to a fourfold increase in the number of dopants in the access regions and corresponding self-averaging effects. Finally, we present results for the smallest transistor combining two sources of variability (i.e., discrete random dopants and surface roughness) and phonon scattering.