Understanding LER-Induced MOSFET $V_{T}$ Variability—Part II: Reconstructing the Distribution

In this paper, we examine, in more detail, the strong correlation between the distribution of threshold voltage (
VT
) and the average channel length (
L̅
_C
̅) discovered in Part I of this paper. Based on the results of statistical analysis, we investigate an approach whereby the line-edge-roughness (LER)-induced distribution of
VT
can be reconstructed based on the convolution of the distribution of (
L̅
_C
̅) and the subdistributions of
VT
at particular values of (
L̅
_C
̅). Further analysis demonstrates that the actual shape of the subdistributions has little impact on the accuracy of the reconstruction. This result allows a fast and economical semianalytical approach for the simulation of LER-induced
VT
variability, based on the nonlinear transformation of the distribution of (
L̅
_C
̅) into the distribution of
VT
using the channel length dependence of the threshold voltage as a mapping function. The accuracy of the semianalytical approach has been confirmed by comparison with the distributions of
VT
obtained for a broad range of conventional and novel MOSFETs using comprehensive 3-D simulations.