3.2.2. α-(BETS)2I3

Figure 5a,b shows the temperature dependence of the four-probe resistance and the Arrhenius plots for α-(BETS)2I3 at various gate voltages. We observed large electron doping effects compared to α-(BEDT-TTF)2I3. However, the effects are highly asymmetric against the doping polarity (Figure 5c), where the hole doping slightly reduces the resistance only in the lowest temperature region. *μ*FE under electron doping is 55 cm2/Vs at 40 K and shows a thermal activation behavior that is similar to the α-(BEDT-TTF)2I3 device (Figure 5d). Under electron doping, the gate-induced conductivity Δ*σ* sufficiently exceeds the Mott–Ioffe–Regel conductivity limit in two dimensions (*e*2/*h*, ~38.7 μS), around which the metallic conduction appears in Si-MOSFET [20] and devices based on κ-type BEDT-TTF salts [21,22]. However, Δ*σ* in α-(BETS)2I3 EDLT does not show metallic conduction below the transition temperature of ∼ 50 K, as shown in Figure 6a. The Arrhenius plots of Δ*σ* (Figure 6b) show that unlike in α-(BEDT-TTF)2I3, the activation energy near the transition temperature significantly decreases with increasing positive *V*G. The mechanism is unclear because the insulating state of α-(BETS)2I3 is not a simple charge-ordered state, and the

insulating mechanism is under debate [14–16]. However, the present results may provide clues to understanding the insulating phase of this compound.

**Figure 4.** (**a**) Arrhenius plots of the four-probe resistance at various gate voltages in α-(BEDT-TTF)2I3. The dashed line is a guideline of the slope at low temperatures and is assigned to the NNH hopping conduction in the literature. (**b**) Temperature dependence of the gate-induced sheet conductivity. Note that the data at <sup>|</sup>*V*G<sup>|</sup> <sup>=</sup> 0.1 <sup>V</sup> are not shown because <sup>Δ</sup>*<sup>σ</sup>* <sup>=</sup> *<sup>L</sup> W* - 1 *<sup>R</sup>* <sup>−</sup> <sup>1</sup> *<sup>R</sup>*0V contains large errors when *R* is similar to *R*0V. (**c**) Arrhenius plots of the gate-induced conductivity. Dashed lines are guides to the eye. (**d**) Gate voltage dependence of the activation energy estimated at relatively high (80–100 K) and low (50–60 K) temperatures.

We investigated the Hall effect in α-(BETS)2I3 at 10, 5, and 1.7 K, as shown in Figure 7. In order to eliminate any possible influence of magnetoresistance, the Hall resistance *Rxy* was determined as *Rxy* = *Rxy*(+*B*) − *Rxy*(−*B*) /2. Without gating, *Rxy* is positive and proportional to the magnetic field. The slope (= Hall coefficient *R*H) increases with cooling, although *Rxy* is unmeasurable at 1.7 K due to the high resistance. *Rxy* decreases by *V*<sup>G</sup> = 0.2 V, implying an electron conduction channel on the surface. However, by further electron doping, *Rxy* increases again and almost coincides with the ungated values. We explain below the complicated situation of the Hall effect in our devices [23].

First, *Rxy* of a bulk α-(BETS)2I3 crystal is negative. However, thin crystals on PET substrates show positive *Rxy* because hole carriers are doped by contact charging with the substrate. Therefore, two conduction channels (bulk and the α-(BETS)2I3/substrate interface) already exist without gating. The gate voltage would induce the third conduction channel (ionic liquid/α-(BETS)2I3 interface). It is difficult to distinguish the contribution of each conduction channel to *Rxy*. Nonetheless, as *Rxy* at *V*<sup>G</sup> = 0 V is proportional to the magnetic field, we can regard the two conduction channels (bulk and bottom interface) as one effective *V*G. -independent channel. Then, in principle, we can extract the mobility and the carrier density at the gated surface by fitting the data using the formula

$$R\_{xy} = \frac{\left(\mu\_0^2 n\_0 + \mu\_s^2 n\_s\right) + \left(\mu\_0 \mu\_s B\right)^2 \left(n\_0 + n\_s\right)}{\sigma \left[\left(\mu\_0 |n\_0| + \mu\_s |n\_s|\right)^2 + \left(\mu\_0 \mu\_s B\right)^2 \left(n\_0 + n\_s\right)^2\right]} B \tag{2}$$

where *μ*0, *n*0, *μ*s, and *n*<sup>s</sup> denote the effective mobility and the carrier density at *V*<sup>G</sup> = 0 V, and the mobility and the carrier density at the gated surface, respectively. Using the values of *μ*<sup>0</sup> and *n*<sup>0</sup> derived from *Rxx* and *Rxy* at *V*<sup>G</sup> = 0 V, and the constraint *Rxx* = 1/*e*(*μ*0|*n*0| + *μ*s|*n*s|), we should obtain *μ*<sup>s</sup> and *n*s. However, we could not find any realistic solutions that reproduce the nonlinear *Rxy* at 0.2 V. Furthermore, assuming for simplicity that *Rxy* is proportional to *B* (the terms quadratic to *B* in Equation (2) can be ignored), we obtain hole carriers with *<sup>μ</sup>*<sup>s</sup> = 8.9 cm2/Vs and *<sup>n</sup>*<sup>s</sup> = 6.4 × <sup>10</sup>12/cm2. These values are obviously inconsistent with the charge injection by the positive gate voltage (Figure 2), implying a large discrepancy between the drift mobility and the Hall mobility. The discrepancy is probably due to hopping or one-dimensional (filamentary) conduction at the doped surface. A possible scenario is that as the gate voltage increases, the hopping or one-dimensionality is strengthened, resulting in *Rxy* becoming consistent with the ungated value as the Hall mobility at the doped surface approaches zero.

**Figure 5.** (**a**) Temperature dependence of the four-probe resistance at various gate voltages and (**b**) Arrhenius plots for α-(BETS)2I3. (**c**) Gate voltage dependence of the sheet conductivity at 1.5–40 K. (**d**) Arrhenius plots of the field-effect mobility estimated in the range of 0.2 V < *V*<sup>G</sup> < 0.4 V.

**Figure 6.** (**a**) Temperature dependence of the gate-induced conductivity in α-(BETS)2I3. (**b**) Arrhenius plots of the gate-induced conductivity.

**Figure 7.** Magnetic field dependence of the Hall resistance under electron doping at (**a**) 10, (**b**) 5, and (**c**) 1.7 K.

#### **4. Discussion and Conclusions**

In both compounds, we achieved ambipolar gating effects on the four-probe resistance, indicating that the shift in the band filling in the charge-ordered (and related) insulating state reduces the resistance regardless of the doping polarity. However, we could not observe metallic conduction in the present experimental setup. In α-(BEDT-TTF)2I3, although the apparent activation energy is significantly decreased by the gate voltage, the extracted gate-induced conductivity implies that only the activation energy for the NNH conduction at low temperatures decreases. The doped carriers fill the randomly distributed localized states (due to the displacement of I − <sup>3</sup> anion chains, according to Ivek and Culo [ <sup>ˇ</sup> 19]), and it seems difficult to suppress the charge ordering by further doping in the present device.

In α-(BETS)2I3, the gate-induced conductivity reaches ~140 μS, which largely exceeds the Mott–Ioffe–Regel conductivity limit in two dimensions (*e*2/*h*, ~38.7 μS), around which metallic conduction emerges in various field-effect devices [20–22]. However, we could not observe metallic conduction either. At low electron doping (*V*<sup>G</sup> = 0.2 V), the Hall resistance significantly decreases (by approximately 50% at 10 K), indicating that the electron doping induces partly two-dimensional, band-like transport at the doped surface. Nevertheless, with increasing gate voltage, the Hall resistance approaches the undoped values, suggesting that hopping or filamentary conduction that hardly contributes to the Hall effect is strengthened. Recently, we observed the Shubnikov–de Haas oscillations in

thin single crystals of α-(BETS)2I3 doped by contact charging [23]. Although the doping concentration is comparable (∼ <sup>10</sup><sup>12</sup> cm<sup>−</sup>2), we could not observe the oscillations in the present device, indicating that the present device has a more disordered surface.

Our results contrast those in Mott EDLTs based on κ-type BEDT-TTF salts, where gateinduced metal–insulator transitions and the Hall effect correspond to the reconstructed Fermi surface. However, the situation in this study may be somewhat typical for the electrolyte gating of organic molecular materials. In rubrene EDLTs, both the field-effect mobility and the Hall mobility generate peaks against the gate voltage [24]. Gate voltage application induces charge carriers at the surface. However, with increasing *V*G, the accumulated ions start to form clusters with potential minima that trap the gate-induced carriers [25]. This phenomenon is considered unavoidable in materials with low dielectric constants and narrow bandwidths. To observe more intrinsic field effects, the combination with pressure may be effective because it generally increases the bandwidth. More essentially, the development of a surface treatment method for molecular conductors is necessary to reduce the unevenness of the potential at the gated surface.

**Author Contributions:** Conceptualization, Y.K. and H.M.Y.; methodology, J.P. and T.T.; investigation and analysis, Y.K., H.M. and N.T.; writing, Y.K., H.M. and N.T.; funding acquisition, Y.K. and R.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by MEXT and JSPS KAKENHI, grant numbers JP16H06346, JP19K03730, JP19H00891, JP19K15383, JP19K22127, JP20H05664, JP20H05867, 20H05189, and 20H05862. J.P. also acknowledges support from KONDO-ZAIDAN.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data needed to evaluate the conclusions in the paper are presented in the paper. Additional data related to this paper may be requested from the authors.

**Acknowledgments:** We would like to acknowledge Teijin DuPont Films Japan Limited for providing the PET films and Professor Yutaka Nishio for valuable discussions and advice.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

