Transient current responses of organic electrochemical transistors by vertical ionic diffusion and electrolyte resistance

For the successful implementation of organic electrochemical transistors in neuromorphic computing, bioelectronics, and real-time sensing applications it is essential to understand the factors that influence device switching times. Here we describe a physical-electrochemical model of the transient response to a step of the gate voltage. The model incorporates (1) ion diffusion inside the channel that governs the electronic conductivity, (2) horizontal electron transport, and (3) the external elements (capacitance, ionic resistance) of the ion dynamics in the electrolyte. We find a general expression of two different time constants that determine the vertical insertion process in terms of the kinetic parameters, in addition to the electronic transit time. We thus obtain a generalization of Bernards-Malliaras model for the exponential transient, as well as a more general set of nonlinear equations that explain the large perturbation effects. The basic model is confirmed by detailed simulations that enable to visualize the different ions distributions and dynamics.