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

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 timescales, 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 thermodynamic perspective and contrast them with established semiconductor materials, highlighting key differences in their collective charge carrier dynamics. This motivates our description of 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-liquid transition, governed by temperature and chemical potential. In doing so, it captures the formation of distinct low- and high-density carrier phases, consistent with recently reported experimental observations. It also illustrates 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.