Large deviations theory for noisy non-linear electronics: CMOS inverter as a case study

TL;DR

This paper applies large deviations theory to model thermal noise in nanoscale CMOS inverters, providing a thermodynamically consistent framework that accurately predicts voltage and current fluctuations even with few electrons, surpassing traditional Gaussian noise models.

Contribution

It introduces a large deviations approach for analyzing thermal noise in non-linear electronics, improving accuracy over Gaussian approximations and demonstrating its effectiveness on CMOS inverters.

Findings

Large deviations principle accurately predicts fluctuations with few electrons.

Traditional Gaussian models are inconsistent for small-scale fluctuations.

Analytical and semi-analytical results match simulations for CMOS inverter noise.

Abstract

The latest generation 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 non-linear 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.