Statistical mechanics for organic mixed conductors: phase transitions in a lattice gas

TL;DR

This paper models organic mixed conductors using statistical mechanics, revealing phase transitions and metastability that explain experimental phenomena and differ from traditional semiconductor behavior.

Contribution

It introduces a lattice gas model for OMCs analyzed via statistical mechanics, highlighting phase transitions and metastability unique to these materials.

Findings

Identification of a vapor–liquid-like phase transition in OMCs

Explanation of history-dependent device characteristics

Observation of distinct low- and high-density carrier phases

Abstract

Organic mixed conductors (OMCs) represent a promising class of materials for applications in bioelectronics, physical computing, and thermoelectrics. Rather unparalleled, OMCs feature dynamics spanning multiple length and time scales, involving an intricate coupling between electronic, ionic, and mass transport. These characteristics set them notably apart from traditional semiconductors and hinder the description by conventional semiconductor theory. In this work, we approach the charge carrier modulation of OMCs using statistical mechanics. We discuss OMCs from a first-principles perspective and contrast them with established semiconductor materials, highlighting key differences in their collective charge carrier dynamics. This motivates our toy model describing OMCs as a lattice gas, which we analyze within the grand canonical ensemble. The model exhibits a first-order phase transition analogous to a classical vapor$\unicode{x2013}$liquid transition, governed by temperature and chemical potential. In doing so, it explains the formation of distinct low- and high-density carrier phases $\unicode{x2013}$ a mesoscale phenomenon recently observed experimentally. It also demonstrates how metastability near the phase boundary can give rise to history-dependent characteristics in device operation, a similarly well-reported effect in OMC transistors. This work is intended as a simple motivation for studying OMCs through the lens of statistical mechanics, offering a more natural description than traditional semiconductor models developed for materials of fundamentally distinct character.