Stochastic approach and fluctuation theorem for charge transport in diodes

TL;DR

This paper develops a stochastic model for charge transport in diodes, incorporating diffusion-reaction equations and the Poisson equation, and demonstrates the fluctuation theorem's validity for current statistics.

Contribution

It introduces a consistent stochastic framework for diode charge transport and verifies the fluctuation theorem for both carrier and total currents.

Findings

Stochastic equations accurately model charge densities and electric fields.

Numerical simulations match expected current-voltage characteristics.

Fluctuation theorem holds for both carrier and total currents.

Abstract

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.