## 3 Results and Discussion
### Effect of Thermal Annealing on Hysteresis  
We report the scan-rate-dependent measurements for OECTs where the PEDOT:Tos was annealed for 0, 1, and 4 h. In Figure 3a-c, we show the transfer curves for different scan rates and annealing durations. Figure 3d shows the hysteresis strength \(\psi\) for these devices as a function of the scan rate. We observed a direct correlation between hysteresis strength and annealing time for a fixed V\({}_{\text{GS}}\) scan rate in the kinetic hysteresis regime. For example, at a scan rate of 175 mV s\({}^{-1}\), the 0, 1, and 4 h-annealed devices showed a \(\psi\) value of 2.17, 2.93, and 7.42 V, respectively. However, the devices behaved curiously in the non-kinetic hysteresis regime. Firstly, the non-kinetic hysteresis for the non-annealed device (0 h) was significantly lower (\(\psi=0.51\) V) than for the annealed devices, where \(\psi\) reached a value of approximately 3 V (note that \(\psi\) is a logarithmic quantity and, hence, the difference between the annealed and non-annealed devices was very large). Secondly, the non-kinetic hysteresis for the 1 and 4 h-annealed devices were almost similar at around \(\psi=3\) V, indicating that the effect of annealing was almost complete after 1 h. Finally, the onset of the non-kinetic hysteresis did not show any specific dependence on the scan rate (e.g., the onset of non-kinetic hysteresis for the 0, 1, and 4 h-annealed devices were at 9.82, 85.1, and 7.05 mV s\({}^{-1}\), respectively). This aspect reflected the situation that the transition from the non-kinetic to the kinetic hysteresis was governed by the time constant of ion movement, which may depend significantly on the thickness and conductivity of the solid electrolyte. Figure 3: _Cont._We performed impedance spectroscopy to gain more insight into the two regimes of hysteresis. Typically, the ionic circuit of an OECT is represented by a series circuit of a resistor and capacitors. The resistor accounts for the electrolyte resistance, while the capacitors represent the gate electrolyte and channel electrolyte interfaces. The capacitance of the gate is usually significantly larger and, hence, negligible in the series connection. One can also include a resistor parallel to the capacitor to include Faradaic processes. The ideal capacitor is a simplification, and usually, more complex models need to be used to describe all possible processes (e.g., accounting for different types of ions, their velocity distribution [4], and the non-uniformity of the electrode materials). Furthermore, the description of the electrode by means of a resistor is a simplification, as diffusion in an electrolyte is in general described by a Warburg element (behaving like a resistor at very low frequency and absorbing boundaries [26]). Figure 4 depicts the impedances (source and drain at the same potential and impedance measured to the gate) of all the annealed devices, with the fitting circuit contained as inlets. For non-annealed devices (0 h), the impedance of the channel is mainly described by a pure resistor representing a Faradaic electrode with a capacitive contribution at only a very low frequency (presumably originating from the Warburg element describing the ion migration in the electrolyte). Therefore, it will mostly show kinetic hysteresis (the higher the sweep rate, the stronger the hysteresis is), which is in line with our observations. Moreover, the contribution of the capacitance to the impedance was small, and hence, the kinetic hysteresis was predicted to be the smallest for the non-annealed devices. If the devices were annealed (1, 4 h), the impedance response transformed into the response of a constant phase element (CPE). For the 1 h-annealed device, an additional capacitor was required with the CPE to capture the response. The C and CPE in series imply that only the electrostatic process is there at the beginning. Thus, the electronic-ionic coupling would happen via the same states, but, e.g., the energies of these states change upon annealing, making a Faradaic process possible.