  The transient behaviour of organic electrochemical transistors (OECT) is
complex due to mixed ionic-electronic properties that play a central role in
bioelectronics, sensing and neuromorphic applications. We investigate the
impedance response of ion-controlled transistors using a model that combines
electronic motion along the channel and vertical ion diffusion by insertion
from the electrolyte, depending on the chemical capacitance, the diffusion
coefficient of ions, the electronic transit time, and the series impedance
components due to the electrolyte and its interfaces. Based on transport and
charge conservation equations, we show that the vertical impedance produces a
standard result of diffusion in intercalation systems, while the transversal
impedance (drain current vs gate voltage) contains the electronic parameters of
hole accumulation and transport along the channel. We establish the spectral
shapes of drain and gate currents and the complex admittance spectra by
reference to equivalent circuit models for the vertical and transversal
impedances, that describe well the measurements of a PEDOT:PSS OECT. We obtain
new insights to the determination of mobility by the relationship between drain
and gate currents.
