*3.2. Temperature Dependence of Resistance at Various Gate Voltages*

### 3.2.1. α-(BEDT-TTF)2I3

Figure 3a shows the temperature dependence of the four-probe resistance in the EDLT device based on α-(BEDT-TTF)2I3 at various gate voltages. The device exhibits metal–insulator transitions at approximately 130 K, which is slightly lower than that for typical bulk α-(BEDT-TTF)2I3 crystals (135 K). The discrepancy is attributable to the biaxial strain effect that is due to the difference in the coefficient of thermal expansion between α-(BEDT-TTF)2I3 and the PET substrate. At low temperatures, the substrate shrinks and applies compressive strain to α-(BEDT-TTF)2I3, resulting in the reduction in the transition temperature [18]. The resistivity above the transition temperature is consistent with typical bulk crystals (∼ <sup>10</sup>−<sup>2</sup> <sup>Ω</sup> cm) if we apply a typical thickness of the crystal (100 nm). Below the transition, the resistivity is lower than that of typical bulk crystals as the transition is moderate, probably because of the suppression of the lattice deformation.

**Figure 2.** Gate voltage dependence of charge density *p* in (**a**) α-(BEDT-TTF)2I3 and (**b**) α-(BETS)2I3 at 220 K.

**Figure 3.** (**a**) Temperature dependence of the four-probe resistance at various gate voltages in α-(BEDT-TTF)2I3. (**b**) Gate voltage dependence of the sheet conductivity at 50–100 K. (**c**) Arrhenius plots of the field-effect mobility estimated in the range of 0.2 V < |*V*G| < 0.4 V.

Both positive and negative gate voltages enhance the conductance by up to a few times in the insulating region. The conductance enhancement is more significant than the case of FET and occurs at the channel (not only at the contacts) because we performed the four-probe measurements. We evaluated the field-effect mobility *μ*FE, the effective mobility estimated from *μ*FE = (1/*C*)*∂σ*/*∂V*G, where *C* is the capacitance per unit area of the electric double layer. We roughly estimated *C* from the slope (linear approximations for 0.2 V < |*V*G| < 0.4 V) in Figure 2a and obtained *∂σ*/*∂V*<sup>G</sup> from the gate voltage dependence of *σ* (Figure 3b). The derived *μ*FE is approximately 10 cm2/Vs at 100 K, which is three orders of magnitude higher than those in the FET measurements [9]. *μ*FE shows similar thermal activation behaviors to the FETs (Figure 3c), although the values are similar for electron and hole in our EDLT. These values are not the actual carrier mobility values. However, they still indicate the switching performance of the resistance.

Nevertheless, as shown in Figures 3a and 4a, the metal–insulator transition temperature remains almost unchanged by the gate voltage, implying that the suppression of the charge ordering by doping, if any, is limited. Generally, the field effect is confined at the sample surface. Our sample consisted of several tens of conducting molecular layers, and the resistance of the bulk was not very high. Therefore, to determine the temperature dependence of the conductance at the doped surface, we had to extract the gate-induced conductance. Figure 4b shows the temperature dependence of the gateinduced sheet conductivity Δ*σ* = *<sup>L</sup> W* - 1 *<sup>R</sup>* <sup>−</sup> <sup>1</sup> *<sup>R</sup>*0V at various gate voltages (where *W* is sample width, *L* is sample length). Δ*σ* monotonically decreased with cooling at all the gate voltages applied in this study, showing no emergence of metallic conduction, and gate-induced melting of charge ordering was unlikely. As shown in Figure 4a,c, neither the non-doped resistance (*V*<sup>G</sup> = 0 V) nor Δ*σ* shows simple activation behaviors. Additionally, the variable range hopping mechanism does not describe Δ*σ* well either. According to Ivek and Culo [ ˇ 19], the measured resistivity of α-(BEDT-TTF)2I3 can be decomposed as 1/*ρ*measured = 1/*ρ*NNH ∓ 1/*ρ*remaining, where *ρ*NNH is the resistivity of the nearest neighbor hopping (NNH) channel. NNH requires randomly distributed localized states, and *ρ*NNH depends on the temperature-independent activation energy at low temperatures. However, *ρ*remaining depends on the mean-field-like activation energy originating from the charge ordering. In our EDLT device, the Arrhenius plots of Δ*σ* (Figure 4c) indicate that the activation energy is almost independent of *V*<sup>G</sup> at relatively high temperatures, whereas it is dependent on *V*<sup>G</sup> at low temperatures, as shown in Figure 4d. Assuming that the above two-channel conduction model by Ivek and Culo [ ˇ 19] applies also to the doped case, we find that the activation energy for the NNH channel, which depends on the average energy difference between the localized states, decreases with gating. In contrast, the activation energy related to charge ordering is not markedly affected by *V*G. The doped carriers seemingly fill the disorder-induced localized states and do not significantly prevent the formation of charge ordering.
