Impact of Large Gate Voltages and Ultrathin Polymer Electrolytes on Carrier Density in Electric-Double-Layer-Gated Two-Dimensional Crystal Transistors

Electric-double-layer (EDL) gating can induce large capacitance densities (∼1-10 μF cm^-2) in two-dimensional (2D) semiconductors; however, several properties of the electrolyte limit performance. One property is the electrochemical activity which limits the gate voltage (V_G) that can be applied and therefore the maximum extent to which carriers can be modulated. A second property is electrolyte thickness, which sets the response speed of the EDL gate and therefore the time scale over which the channel can be doped. Typical thicknesses are on the order of micrometers, but thinner electrolytes (nanometers) are needed for very-large-scale-integration (VLSI) in terms of both physical thickness and the speed that accompanies scaling. In this study, finite element modeling of an EDL-gated field-effect transistor (FET) is used to self-consistently couple ion transport in the electrolyte to carrier transport in the semiconductor, in which density of states, and therefore quantum capacitance, is included. The model reveals that 50 to 65% of the applied potential drops across the semiconductor, leaving 35 to 50% to drop across the two EDLs. Accounting for the potential drop in the channel suggests that higher carrier densities can be achieved at larger applied V_G without concern for inducing electrochemical reactions. This insight is tested experimentally via Hall measurements of graphene FETs for which V_G is extended from ±3 to ±6 V. Doubling the gate voltage increases the sheet carrier density by an additional 2.3 × 10¹³ cm^-2 for electrons and 1.4 × 10¹³ cm^-2 for holes without inducing electrochemistry. To address the need for thickness scaling, the thickness of the solid polymer electrolyte, poly(ethylene oxide) (PEO):CsClO₄, is decreased from 1 μm to 10 nm and used to EDL gate graphene FETs. Sheet carrier density measurements on graphene Hall bars prove that the carrier densities remain constant throughout the measured thickness range (10 nm-1 μm). The results indicate promise for overcoming the physical and electrical limitations to VLSI while taking advantage of the ultrahigh carrier densities induced by EDL gating.

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

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.