A general approach for multivariate statistical MOSFET compact modeling preserving correlations

Abstract

As feature sizes shrink, random fluctuations gain importance in semiconductor manufacturing and integrated circuit design. Therefore, statistical device variability has to be considered in circuit design and analysis to properly estimate their impact and avoid expensive over-design. Statistical MOSFET compact modeling is required to accurately capture marginal distributions of varying device parameters and to preserve their statistical correlations. Due to limited simulator capabilities, variables are often assumed to be normally distributed. Although correlations may be captured using Principal Component Analysis, such an assumption may be inaccurate. As an alternative, Nonlinear Power Models have been proposed. Since we see some limitations in this approach, we analyze whether the multivariate Generalized Lambda Distribution is an alternative for statistical device modeling. Applying both approaches to extracted statistical device parameters, we conclude that both methods do not differ significantly in accuracy, but the multivariate Generalized Lambda Distribution is more general and less computationally expensive.