Noise Propagation and Statistic Variability in MOSFETs Using Probability Density Functions

Probability density functions using stochastic methods [A. Papoulis and S. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 2002); S. A. Maas, Noise in Linear and Nonlinear Circuits (Artech House, Boston London, 2005)] are shown to be an effective tool in the context of MOSFET noise and variability modeling. These methods are employed here in the context of the charge-based EKV MOSFET model [J.-M. Sallese et al., Inversion charge linearization in MOSFET modeling and rigorous derivation of the EKV compact model, Solid-State Electron. 47 (2003) 677–683, https://doi.org/10.1016/S0038-1101(02)00336-2; C. Enz and E. Vittoz, Charge-based MOS Transistor Modeling: The EKV Model for Low-Power and RF IC Design (John Wiley and Sons, Chichester, 2006)]. As an example, a Gaussian noise density function applied at the gate or the source of a MOSFET causes a corresponding drain current noise density function, which may be expressed analytically as a function of inversion coefficient only. The same expression may be used to model drain current variability due to MOSFET parameters such as threshold voltage. Furthermore, the method is extended to variations of quantities such as transconductance and transconductance-to-current ratio. The method shows promise in variability modeling of MOSFETs and may complement traditional approaches [C. C. McAndrew, Efficient statistical modeling for circuit simulation, in Design of System on a Chip, eds. R. Reis and J. Jess (Kluwer Academic Publishers, New York, 2004), pp. 97–122; L. Yu et al., Statistical modeling with the virtual source MOSFET model, in Design, Automation & Test in Europe Conf. & Exhibition (IEEE, 2013), pp. 1454–1457, https://doi.org/10.7873/DATE.2013.296; R. Laviéville et al., Statistical characterization of drain current local and global variability in sub 15nm Si/SiGe trigate pMOSFETs, in European Solid-State Device Research Conf. (IEEE, 2016), pp. 142–145, https://doi.org/10.1109/ESSDERC.2016.7599607].