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_C̅) 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_C̅) and the subdistributions of VT at particular values of (L̅_C̅). 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_C̅) 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.