Statistical theory of shot noise in quasi-1D Field Effect Transistors in the presence of electron-electron interaction

TL;DR

This paper develops a comprehensive theoretical model for shot noise in quasi-1D FETs that accounts for Coulomb interactions and Pauli exclusion, extending existing formulas and highlighting the importance of Coulomb effects.

Contribution

It introduces a new expression for shot noise in quasi-1D FETs that includes Coulomb interactions via a statistical and many-body approach, extending the Landauer-Buttiker formula.

Findings

Ignoring Coulomb interactions overestimates noise spectrum

Monte Carlo simulations reveal significant Coulomb effects on noise

The model accurately predicts noise behavior in quasi-1D devices

Abstract

We present an expression for the shot noise power spectral density in quasi-one dimensional conductors electrostatically controlled by a gate electrode, that includes the effects of Coulomb interaction and of Pauli exclusion among charge carriers. In this sense, our expression extends the well known Landauer-Buttiker noise formula to include the effect of Coulomb interaction through induced fluctuations in the device potential. Our approach is based on the introduction of statistical properties of the scattering matrix and on a second-quantization many-body description. From a quantitative point of view, statistical properties are obtained by means of Monte Carlo simulations on a ensemble of different configurations of injected states, requiring the solution of the Poisson-Schrodinger equation on a three-dimensional grid, with the non-equilibrium Green functions formalism. In a series of example, we show that failure to consider the effects of Coulomb interaction on noise leads to a gross overestimation of the noise spectrum of quasi-one dimensional devices.