Kinetic theory of shot noise in non-degenerate diffusive conductors

TL;DR

This paper provides an exact kinetic theory analysis of shot noise in non-degenerate diffusive conductors, showing Coulomb interactions suppress noise below Poisson levels and aligning with Monte Carlo simulations.

Contribution

It offers an exact solution to kinetic equations in space-charge limited conduction, including finite voltage and contact effects, advancing understanding beyond previous drift approximations.

Findings

Shot noise is suppressed below Poisson level due to Coulomb repulsion.

Suppression factor is approximately 1/3 in 3D systems, consistent with simulations.

Energy dependence of scattering has minor effects on noise suppression.

Abstract

We investigate current fluctuations in non-degenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the non-linear kinetic equations in the regime of space-charge limited conduction, without resorting to the drift approximation of previous work. By including the effects of a finite voltage and carrier density in the contact region, a quantitative agreement is obtained with Monte Carlo simulations by Gonz{\'a}lez et al., for a model of an energy-independent elastic scattering rate. The shot-noise power $P$ is suppressed below the Poisson value $P_{Poisson}=2e\bar I$ (at mean current $\bar I$) by the Coulomb repulsion of the carriers. The exact suppression factor is close to 1/3 in a three-dimensional system, in agreement with the simulations and with the drift approximation. Including an energy dependence of the scattering rate has a small effect on the suppression factor for the case of short-range scattering by uncharged impurities or quasi-elastic scattering by acoustic phonons. Long-range scattering by charged impurities remains an open problem.