Large deviations theory for noisy nonlinear electronics: CMOS inverter as a case study

The latest generations of transistors are nanoscale devices whose performance and reliability are limited by thermal noise in low-power applications. Therefore, developing efficient methods to compute the voltage and current fluctuations in such nonlinear electronic circuits is essential. Traditional approaches commonly rely on adding Gaussian white noise to the macroscopic dynamical circuit laws, but do not capture rare fluctuations and lead to thermodynamic inconsistencies. A correct and thermodynamically consistent approach can be achieved by describing single-electron transfers as Poisson jump processes accounting for charging effects. But such descriptions can be computationally demanding. To address this issue, we consider the macroscopic limit, which corresponds to scaling up the physical dimensions of the transistor and resulting in an increase of the number of electrons on the conductors. In this limit, the thermal fluctuations satisfy a large deviations principle , which we show is also remarkably precise in settings involving only a few tens of electrons, by comparing our results with Gillespie simulations and spectral methods. Traditional approaches are recovered by resorting to an ad hoc diffusive approximation introducing inconsistencies. To illustrate these findings, we consider a low-power CMOS inverter, or NOT gate, which is a basic primitive in electronic design. Voltage (resp. current) fluctuations are obtained analytically (semi-analytically) and reveal interesting features.

Automated summary

This study develops efficient methods to compute voltage and current fluctuations in nanoscale transistors for low-power applications. Traditional approaches fail to capture rare fluctuations, but a correct and thermodynamically consistent method is achieved by describing single-electron transfers as Poisson jump processes. In the macroscopic limit, thermal fluctuations satisfy a large deviations principle, which is remarkably precise even for settings involving only a few tens of electrons. The findings are illustrated through a low-power CMOS inverter, revealing interesting features.