Single- versus Dual-Ion Conductors for Electric Double Layer Gating: Finite Element Modeling and Hall-Effect...

Electric double layer (EDL) gating using a single-ion conductor is compared to a dual-ion conductor using both finite element modeling and Hall-effect measurements. Modified Nernst-Planck Poisson (mNPP) equations are used to calculate the ion density per unit area in a parallel plate capacitor geometry with a bulk ion concentration of 215 ≤ c_bulk ≤ 1782 mol/m³. With electrodes of equal size at a 2 V potential difference, the EDL ion density of the single-ion conductor is ∼7 × 10¹³ ions/cm², which is approximately 50% of the ion density induced in the dual-ion conductor. However, this difference is reduced to 8% when the electrode at which the cationic EDL forms is 10 times smaller than the counter electrode. Thus, for a field-effect transistor gated by a single-ion conductor, it is especially important to have a large gate-to-channel size ratio to achieve strong ion doping. The modeled ion densities are validated by Hall-effect measurements on graphene Hall bars gated by a polyethylene oxide (PEO)-based single-ion conductor. The sheet carrier density, n_S, is ∼2 × 10¹³ cm^-2 at V_g = 2 V, which is 3.5 times smaller than the predicted value and has the same order of magnitude as the n_s measured for a PEO-based, dual-ion conductor on the same graphene. The numerical modeling results can be approximated by a simple analysis of capacitors in series, where the EDLs are modeled as capacitors with thickness estimated by the sum of the Debye screening length and the Stern layer. The series of capacitor estimate agrees with the numerical modeling of the dual-ion conductor to within 10% and the single-ion conductor to within 30% from 0.25 to 2 V (c_bulk = 925 mol/m³); similar agreement is observed in the concentration range of 353-1650 mol/m³ for both single- and dual-ion conductors.