Distribution of transmitted charge through a double-barrier junction

TL;DR

This paper compares semiclassical and quantum models to analyze the charge distribution transmitted through a double-barrier junction at zero temperature, revealing conditions under which the distribution is Gaussian, Poissonian, or intermediate.

Contribution

It introduces a comparative analysis of semiclassical and quantum models for charge transmission, showing their agreement at large times and characterizing the resulting charge distributions.

Findings

Logarithm of the characteristic function matches in both models at large times.

Charge distribution varies from Gaussian to Poissonian depending on barrier heights.

Distribution is intermediate between Gaussian and Poissonian when barriers have equal height.

Abstract

The distribution function of transmitted charge through a double-barrier junction is studied at zero temperature and at small applied voltage. Both a semiclassical model, in which the transport is described by jump rates, and a quantum mechanical model, which averages over resonant and non-resonant states, are used to determine the characteristic function of the transmitted electrons. It is demonstrated that for large times the logarithm of the characteristic function is equal within the two approaches. The charge distribution is in between a Gaussian and a Poissonian distribution if both barriers have equal height and reduces to a Poissonian if one barrier is much higher than the other.