A Comprehensive Comparison among Capacitive, Thermodynamic, and Drift–Diffusion Models for Steady-State Responses of Nanostructured Organic Electrochemical Transistors

Abstract

Organic electrochemical transistors (OECTs) have garnered significant interest in organic electronics due to their fast response, high transconductance, low operating voltage, and versatile fabrication processes. Despite their successful application in various devices, the theoretical understanding of OECTs remains incomplete, particularly regarding the nanoscale interaction between ionic and electronic transport within the organic mixed ionic–electronic conductors (OMIECs) used in these devices. This work introduces a drift–diffusion model that addresses the limitations of existing theoretical frameworks. An analytical expression for the steady-state current in the OECTs is derived, which accounts for both electrical parameters (e.g., gate and drain voltages) and material properties (e.g., salt concentration in the electrolyte). The applicability of our model is validated through comparison with experimental data, revealing new insights into the interplay of various factors affecting the OECT performance. Additionally, we revisit and extend the well-established Bernards–Malliaras (BM) model to cover a broader range of operating conditions, as well as a thermodynamic model. We show that correct usage of the theoretical formulas yields agreement with experimental curves for all presented models, rendering the match itself an insufficient proof of the underlying theory. We set up interconversion formulas between the parameters of the different model approaches and analyze what this implies for their meaning, especially because all show good agreement with the experiment, although based on quite different fundamentals. This comparative analysis provides a deeper understanding of how different components contribute to device operation, offering guidance for the targeted optimization of OECT materials and design with a focus on the exploiting nanoscale phenomena.