Critical Backscattering Length in Nanotransistors

A rigorous expression for the critical length of backscattering ( $\text{L}_{\textbf {Crit}}$ ) is reported. In the new model, $\text{L}_{\textbf {Crit}}$ is obtained from a weighted sum over the transport domain. It is shown that anisotropy of mean free path (MFP) tunes the profile of weight function. Under equilibrium condition with isotropic MFP, the weight is a uniform distribution. As the field grows, it builds up the anisotropy and confines the weight function around the injection boundary. This process quantifies the transition of $\text{L}_{\textbf {Crit}}$ from low to high field regime. We implemented this model in the non-equilibrium Green’s function (NEGF) solver and investigate the compact model form. Contrary to standard model, it is found that MFP of backscattering ( $\boldsymbol {\lambda } $ ) elongates in high drain-source (Vds) bias. Based on these findings, an update of compact model is proposed and verified.