Electronic Transport in Electron-Phonon Gas of Two-Dimensional Holstein's Organic Molecular-Crystal: Non-equilibrium Green's Function Formalism & Boltzmann Transport Framework (A Generalized Mathematical Solution)

TL;DR

This paper develops a comprehensive quantum-mechanical and semi-classical framework for electronic transport in two-dimensional organic molecular crystals, incorporating electron-phonon interactions via NEGF and Boltzmann theories.

Contribution

It introduces a unified approach combining NEGF and Boltzmann transport to analyze electron-phonon interactions in organic semiconductors, adaptable for multi-phonon processes.

Findings

Formulated electron-phonon self-energy interactions using Feynman diagrams.

Established a consistent quantum and semi-classical transport framework.

Potential to extend to multi-phonon interactions for various organic materials.

Abstract

We have presented a consistent electronic transport framework for the two-dimensional extended Holstein's organic molecular-crystal based upon complete quantum-mechanical treatment through the non-equilibrium Green's function (NEGF) formalism and corresponding one-to-one semi-classical framework based upon Boltzmann transport theory for the narrow-bandwidth electronic energy organic semiconductor crystal material and device. In this process, we have formulated electronic self-energy interaction with acoustic and polar optical phonon mode with one phonon and two phonon interactions through Feynman's diagrammatic techniques to investigate combined electronic transport. Furthermore, the aforementioned can readily expand for the three and four phonon interactions on choice based upon the particular class of organic semiconductor crystal and organic polymers for the modern organic device industry.