Electric Double-Layer Doping

• Electric double-layer doping is the modulation of carrier density via the accumulation of mobile ions at a solid interface, achieving sheet densities of 10^13–10^15 cm⁻².
• It has been employed in various devices—ranging from oxide and chalcogenide systems to graphene—to induce effects such as insulator-to-metal transitions and superconductivity.
• Precise control over interfacial electrostatics and capacitance enables tunable electronic structures and emergent phases, with applications in both traditional transistors and novel energy-transfer systems.

Electric double-layer doping is the electrostatic modulation of carrier density produced when mobile ions accumulate at a solid interface and form a nanometer-scale electric double layer whose capacitance is large enough to induce sheet densities from the $10^{13}$ to $10^{15}\,\mathrm{cm}^{-2}$ range, depending on material, electrolyte, and whether the response remains purely electrostatic or crosses into electrochemistry (Takayanagi et al., 2014, Katase et al., 2014, Ueno et al., 2010). In condensed-matter systems this interfacial charge reservoir has been used to drive insulator-to-metal transitions, superconductivity, Hall-sign reversals, bad-metal and non-Fermi-liquid transport, and charge-density-wave reorganization, while closely related interfacial charge-transfer structures reproduce many of the same screened, near-surface electrostatics (Leriche et al., 2020, Liu et al., 2014, Kawasugi et al., 2022).

1. Interfacial electrostatics and capacitance

At oxide/electrolyte interfaces, surface hydroxyls act as amphoteric Brønsted sites, so protonation and deprotonation generate positive or negative surface charge that is compensated by counter-ions in solution. The resulting electric double layer comprises an inner Helmholtz layer, an outer Helmholtz layer, and a diffuse layer; in semiconducting oxides a space-charge region in the solid must also be included. A compact formulation used for such interfaces is

$$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$

with capacitance defined by $C=\partial \sigma/\partial \psi$ (Knijff et al., 2022). For rutile TiO$_2$(110)/NaCl and SnO$_2$(110)/NaCl, reported Helmholtz capacitances are of order $60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$, which is sufficient for carrier accumulation in the $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$ range under volt-scale bias (Knijff et al., 2022).

In device language, the same physics is often written as $Q=CV$ and $n=CV/e$. The ZnO EDLT study made this picture explicit: positive gate bias drives cations toward the ZnO surface, induces electronic charge in the channel, and produces an abrupt reduction of both resistivity and thermopower once the threshold near $10^{15}\,\mathrm{cm}^{-2}$0 V is crossed (Takayanagi et al., 2014). In low-ionic-strength graphene electrolyte gating, the channel-side capacitance is not only ionic. The graphene EGFET study treated the gate coupling as a series combination,

$10^{15}\,\mathrm{cm}^{-2}$1

fixed $10^{15}\,\mathrm{cm}^{-2}$2, and extracted a carrier-density change $10^{15}\,\mathrm{cm}^{-2}$3 from a Dirac-voltage shift of about $10^{15}\,\mathrm{cm}^{-2}$4 V under albumin adsorption (Liaquat et al., 3 Jul 2026). This makes clear that electric double-layer doping is controlled jointly by interfacial ionic structure and, when relevant, the electronic compressibility of the channel.

2. Device realizations and operational modes

Electric double-layer doping has been realized in oxide, chalcogenide, organic, graphene, and granular channels. A recurrent experimental protocol is to apply the gate voltage while ions are mobile and then cool below the freezing or glass-transition temperature of the gate medium so that the interfacial charge distribution is frozen for transport measurements. ZnO devices using PEG/KClO$10^{15}\,\mathrm{cm}^{-2}$5 were gated at $10^{15}\,\mathrm{cm}^{-2}$6 K and measured after freezing below $10^{15}\,\mathrm{cm}^{-2}$7 K; TlFe$10^{15}\,\mathrm{cm}^{-2}$8Se$10^{15}\,\mathrm{cm}^{-2}$9 with DEME–TFSI was written above $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$0 K and then cooled; few-layer graphene with a Li-TFSI-based polymer electrolyte was analyzed below a glass transition near $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$1 K (Takayanagi et al., 2014, Katase et al., 2014, Piatti et al., 2017). Other studies used the same architecture for ultrathin PCCO, bulk polycrystalline MoS$$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$2, and the organic Mott insulator $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$3-Cl, the last of which additionally combined gating with substrate-bending strain to tune bandwidth and band filling simultaneously (Jin et al., 2015, Shimazu et al., 3 Sep 2025, Kawasugi et al., 2022).

Representative realizations are summarized below.

System	Gate medium / range	Reported consequence
ZnO	PEG + KClO$$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$4, $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$5–$$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$6 V	Threshold near $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$7 V; metallic layer about $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$8 nm; $$\frac{1}{C_{\mathrm{EDL}}}= \frac{1}{C_{\mathrm{SC}}}+\frac{1}{C_{\mathrm{H}}}+\frac{1}{C_{\mathrm{GC}}},$$9
TlFe$C=\partial \sigma/\partial \psi$0Se$C=\partial \sigma/\partial \psi$1	DEME–TFSI, up to $C=\partial \sigma/\partial \psi$2 V	Three orders of magnitude conductance modulation at $C=\partial \sigma/\partial \psi$3 K; gate-induced phase transition
$C=\partial \sigma/\partial \psi$4-Cl	Ionic liquid, $C=\partial \sigma/\partial \psi$5 V plus strain	About $C=\partial \sigma/\partial \psi$6 filling change; electron- and hole-doped superconductivity
PCCO	DEME–TFSI, $C=\partial \sigma/\partial \psi$7 to $C=\partial \sigma/\partial \psi$8 V	Multiple Hall-sign reversals; simultaneous enhancement or depression of both carrier types
Polycrystalline MoS$C=\partial \sigma/\partial \psi$9	DEME–TFSI, $_2$0 V	Insulator-to-metal transition; superconducting onset saturating near $_2$1 K
Graphene EGFET	Electrolyte droplet, $_2$2–$_2$3 V	Non-Faradaic Dirac-voltage shifts and mobility suppression

These implementations show that “electric double-layer doping” is not tied to a single channel dimensionality or morphology. It can act on atomically thin channels, few-layer crystals, organic Mott systems, ultrathin cuprate films, and even porous polycrystalline pellets, provided a stable interfacial ionic capacitor can be formed.

3. Reversible electrostatic accumulation and electrochemical modification

A central distinction in the subject is between reversible electrostatic accumulation and electrochemical doping. SrTiO$_2$4 EDLTs provide the clearest operational boundary: at $_2$5 K, gate voltages below about $_2$6 V produced reversible electrostatic charge accumulation, whereas above $_2$7 V persistent conduction remained even after gate removal. In the electrostatic regime the maximum sheet density was $_2$8; in the high-bias regime $_2$9 reached $_2$0 at $_2$1 V and the Hall mobility at $_2$2 K reached $_2$3 (Ueno et al., 2010). AFM and TEM then showed surface undulation, high-density defects near the surface, and dislocation loops several micrometers deep, and the persistent conduction was attributed to oxygen removal and defect formation in a region around $_2$4m thick rather than to a thin accumulation layer (Ueno et al., 2010).

By contrast, several studies deliberately operated inside a non-Faradaic window. ZnO devices recovered their initial current after sweeping between $_2$5 and $_2$6 V and showed no detectable electrochemical reaction under those conditions, while the liquid-gated graphene HSA sensor emphasized reversible and reproducible non-Faradaic operation (Takayanagi et al., 2014, Liaquat et al., 3 Jul 2026). In such cases the gate mainly redistributes charge at the interface, and turning the bias off removes the added carriers.

FeSe-based EDL structures demonstrate a third regime: deliberately using the double layer to drive electrochemistry. In single-crystalline FeSe, FeSe$_2$7Te$_2$8, and FeSe$_2$9S$60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$0 films on LaAlO$60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$1, gate bias of $60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$2 V together with elevated-temperature electrochemical etching created a reacted, electron-doped surface layer, possibly by DEME$60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$3 intercalation or by DEME$60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$4 adsorption at the surface, and this reacted layer exhibited the high-$60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$5 state analyzed in that work (Shikama et al., 2021). The literature therefore treats reversibility, gate-current transients, Hall-thickness estimates, and post-mortem structural probes as decisive diagnostics; a large conductance change by itself does not establish a purely field-effect origin (Ueno et al., 2010).

4. Electronic-structure control and emergent phases

In metallic transition-metal dichalcogenides, electric double-layer doping is often the benchmark for how far electrostatic band filling can be pushed. For monolayer NbSe$60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$6, EDL-FET doping is limited to approximately $60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$7, a regime in which superconductivity and the $60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$8 CDW are strengthened without clear evidence for a change of ordering vector. The misfit compound $60\text{–}100\,\mu\mathrm{F\,cm^{-2}}$9, however, behaves as a rigidly doped NbSe$10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$0 monolayer with $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$1 electrons per Nb, or approximately $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$2, and a $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$3 eV Fermi-level shift; in that ultra-heavy-doping regime the $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$4 CDW is replaced by short-coherence-length $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$5 order (Leriche et al., 2020). This comparison makes the EDL window both a powerful tuning range and a clearly defined upper benchmark.

Interfacial charge-transfer systems can realize closely related electrostatics without an external liquid gate. In FeSe/SrTiO$10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$6, the transferred charge resides at the interface in a manner directly analogous to an electric double layer: the single-layer film takes all transferred charge into one FeSe layer and becomes superconducting once the S-phase doping exceeds about $10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$7 electrons per Fe, whereas double-layer FeSe is hard to dope because the same interface charge is distributed across more layers and screened away from the top surface (Liu et al., 2014). The same interfacial logic also underlies the marked disparity between single-layer and multilayer behavior.

Correlated systems have been a particularly productive arena. In Fe-vacancy-ordered TlFe$10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$8Se$10^{13}\text{–}10^{14}\,\mathrm{cm^{-2}}$9, DEME–TFSI gating produced up to three orders of magnitude conductance modulation at $Q=CV$0 K, reduced the Arrhenius activation energy from $Q=CV$1 meV to $Q=CV$2 meV, and generated resistance humps near $Q=CV$3 and $Q=CV$4 K that were interpreted as a gate-induced phase transition from a Mott-insulating background toward a more delocalized state, possibly associated with magnetic or orbital-selective-Mott physics (Katase et al., 2014). In the organic Mott insulator $Q=CV$5-Cl, approximately $Q=CV$6 filling change at $Q=CV$7 V enabled both electron- and hole-doped superconductivity with almost identical transition temperatures around $Q=CV$8 K, while the normal state displayed strong doping asymmetry: a low-temperature Fermi liquid only on the electron-doped side and hole-doped pseudogap-like behavior tied to the flat part of the anisotropic-triangular-lattice band (Kawasugi et al., 2022).

Ultrathin PCCO illustrates how sensitively a multiband correlated metal can respond. Gate voltages between $Q=CV$9 and $n=CV/e$0 V produced multiple sign reversals of Hall resistivity in both the normal and mixed states, while two-band analysis indicated that electron and hole carrier concentrations are always enhanced or depressed simultaneously in electric fields rather than anticorrelating as in a simple AFM reconstruction picture (Jin et al., 2015). In a different materials class, electric double-layer doping of bulk polycrystalline MoS$n=CV/e$1 drove an insulator-to-metal transition and a superconducting onset whose temperature rose with conductance and saturated around $n=CV/e$2 K, showing that gate-induced superconductivity is not restricted to exfoliated or single-crystalline channels (Shimazu et al., 3 Sep 2025).

5. Screening, thickness, and the spatial profile of doping

Because the accumulated charge is interfacial, screening length and channel thickness are fundamental variables. The FeSe/SrTiO$n=CV/e$3 dichotomy is an especially direct illustration: ARPES at $n=CV/e$4 eV probes a depth of about $n=CV/e$5 Å, comparable to one or two FeSe layers, yet double-layer films remain dominated by the magnetic/insulating N phase because the charge reservoir on the SrTiO$n=CV/e$6 side is spread across all FeSe layers in an uneven manner, with the interface-nearest layer more doped and the farther layer less doped (Liu et al., 2014). In this picture, electric-double-layer-like doping is not only a matter of total transferred charge; its partition across depth determines the observed phase.

In ZnO, the interfacial metallic layer was estimated to be about $n=CV/e$7 nm thick by combining the critical sheet density $n=CV/e$8 with the Mott criterion $n=CV/e$9 (Takayanagi et al., 2014). In porous polycrystalline MoS$10^{15}\,\mathrm{cm}^{-2}$00, however, the actual ionic-liquid-wetted area exceeds the projected area, so an apparent sheet density based on geometric area can substantially overestimate the local carrier density on each grain; that study therefore used $10^{15}\,\mathrm{cm}^{-2}$01 as an empirical proxy for effective doping rather than a nominal $10^{15}\,\mathrm{cm}^{-2}$02 (Shimazu et al., 3 Sep 2025). These examples emphasize that “sheet density” can be straightforward in flat channels and ambiguous in rough or granular ones.

The ionic layer itself can also become the dominant scatterer at high accumulated density. In few-layer graphene gated with a Li-TFSI-based polymer electrolyte, mobility decreased with increasing $10^{15}\,\mathrm{cm}^{-2}$03 on both sides but much more strongly for electron doping; DFT-based extraction of scattering lifetimes traced the asymmetry to the small Li$10^{15}\,\mathrm{cm}^{-2}$04 cation versus the large TFSI$10^{15}\,\mathrm{cm}^{-2}$05 anion, and the 4-layer devices were more strongly perturbed than the 5-layer devices because the disorder source is at the surface (Piatti et al., 2017). This is an important corrective to the idealized view of EDL doping as a pure density knob: the gate medium can also be a strong, polarity-dependent source of scattering.

A more formal electrostatic statement appears in the scaling theory of electrically doped 2D transistors. Solving the 2D Poisson equation yields a characteristic length $10^{15}\,\mathrm{cm}^{-2}$06 for zero gate spacing and $10^{15}\,\mathrm{cm}^{-2}$07 with $10^{15}\,\mathrm{cm}^{-2}$08 when spacing is included, leading to the conclusion that physical oxide thickness and gate spacing, rather than equivalent oxide thickness, are the critical design parameters (Ilatikhameneh et al., 2015). This suggests that in electric-double-layer structures the nanometric physical separation embodied by the double layer itself, rather than an EOT analog, sets the sharpness of electrostatic doping.

6. Characterization, modeling, and conceptual extensions

The subject is defined as much by its metrology as by its devices. Hall measurements and charge-displacement methods are the standard route to $10^{15}\,\mathrm{cm}^{-2}$09 and $10^{15}\,\mathrm{cm}^{-2}$10 in oxide and layered channels, while temperature-dependent transport distinguishes bad metals, Fermi liquids, activated regimes, and superconducting states (Ueno et al., 2010, Katase et al., 2014, Takayanagi et al., 2014). Surface-sensitive probes such as ARPES, STM, and QPI then determine whether the induced state is well described as a rigid band shift or whether a new ordered phase has appeared, as in the heavily doped NbSe$10^{15}\,\mathrm{cm}^{-2}$11 misfit system (Leriche et al., 2020).

Direct observation of ionic charging has also become possible. Electric-double-layer-modulation microscopy uses dark-field scattering to measure a potentiodynamic optical contrast proportional to the accumulated charge of polarizable ions at the interface, while its time derivative represents the nanoscale ionic current; the reported sensitivity corresponds to ion current densities of a few attoamperes, or the exchange of only a few hundred ions (Namink et al., 2019). This turns the EDL itself into an observable object rather than an inferred capacitance.

Atomistic modeling has clarified why different interfaces respond so differently. DFT-based molecular dynamics of TiO$10^{15}\,\mathrm{cm}^{-2}$12(110)/NaCl and SnO$10^{15}\,\mathrm{cm}^{-2}$13(110)/NaCl related Helmholtz capacitance to water orientation, proton exchange, and adsorption mode, with dissociative water adsorption on SnO$10^{15}\,\mathrm{cm}^{-2}$14 giving substantially larger $10^{15}\,\mathrm{cm}^{-2}$15 and asymmetric differential capacitance (Knijff et al., 2022). In liquid-gated graphene, Brownian Dynamics of HSA adsorption showed multiple orientations with heterogeneous charge distributions and dipole alignments; combined with a transport model, this led to the use of inverse mobility $10^{15}\,\mathrm{cm}^{-2}$16 as a sensitive metric of disorder-enhanced scattering inside the electric double layer (Liaquat et al., 3 Jul 2026). The common theme is that the microscopic structure of the ionic or molecular layer is inseparable from the macroscopic doping response.

The electric-double-layer concept also extends beyond transistor transport. Calculations for clean gold surfaces treated the intrinsic surface double layer generated by electron spill-out as a surface dipole with $10^{15}\,\mathrm{cm}^{-2}$17, whose coupling to the electromagnetic field can enhance extreme-near-field heat transfer at sub-$10^{15}\,\mathrm{cm}^{-2}$18 nm separations by several orders of magnitude (Volokitin, 2020). A plausible implication is that electric double-layer doping should be understood not only as a high-capacitance route to carrier accumulation, but as a broader strategy for engineering interfacial electric fields, screening, and surface dipoles across transport, spectroscopy, and energy-transfer phenomena.