## Main

Electrolyte-gated transistors offer low operational voltages and high output currents, as well as a range of other attractive features1,2,3,4. A variety of artificial synapses and memristive systems have, for instance, been developed using such devices and by exploiting the spatiotemporal dependency of ionic motion5,6,7,8,9,10,11. As ions in dielectrics are driven by gate biases to approach or move away from the semiconductor/dielectric interface, the transistors exhibit transient currents that can emulate various synapse-like behaviours including paired-pulse facilitation, short-term memory and long-term memory12,13,14. The accumulation of ions can also induce large capacitances due to electric double layers and pseudocapacitance15,16. By using these effects, combined with devices based on two-dimensional materials, the turn-on properties of transistors have been pushed to below the thermionic limit17,18,19,20, that is, a reversed subthreshold slope below 60 mV dec–1 at room temperature. With such features, electrolyte-gated transistors offer new approaches to create dense, low-power integrated circuits; sensitive biosensors and gas sensors; and compact and powerful neuromorphic computing networks21,22,23,24,25.

Despite this progress, insight into the underlying physics of devices and their various capabilities remains limited. In contrast to a static system, the ion-dynamic capacitance of the electrolyte is not a constant but a function of bias and time. The electrostatic potential also does not drop linearly within the dielectric but mainly drops at the electrolyte/semiconductor interface26, which increase the complexity of the spatiotemporal evolution of ion concentrations, electrostatic potential, effective capacitance and charge accumulation in the channel.

In this Article, we report a compact theory for time- and gate-dependent current in transistors with solid-state electrolytes. The theory predicts that the features of plasticity, high apparent mobility, sharp subthreshold swing and memristive conductance could appear on demand in a single transistor by programming the ion distribution or sweeping speeds. We validate this with numerical simulations. We then fabricate such multimode transistors using thin films (10 nm thick) of semiconducting indium oxide (InOx) and thin films (40 nm thick) of the solid-state electrolyte aluminium oxide (AlOx) or zirconium oxide (ZrOx). We also show, in software, that multimode devices could be harnessed to create neural networks that function in different modes as needed.

## Physics of ion-dynamic capacitance

The device structure, density of ions p(x, t) (cation, cm−3) and electrostatic potential V(x, t) are illustrated in Fig. 1a,b. The p and V values under constant bias change from the initial to the transient and steady states (Fig. 1b). In quantity, p and V are spatiotemporally coupled in the drift–diffusion equation based on the drift flux density Sdrift and diffusion flux density Sdiffusion:

$$\begin{array}{l}\frac{{\partial p\left( {x,t} \right)}}{{\partial t}} = - \nabla S_{{{{\mathrm{diffusion}}}}} - \nabla S_{{{{\mathrm{drift}}}}} = \left[ {D_{{{\mathrm{i}}}}\frac{{\partial ^2p\left( {x,t} \right)}}{{\partial x^2}}} \right]\\ - \left[ {\mu _{{{{\mathrm{ion}}}}} E\left( {x,t} \right)\frac{{\partial p\left( {x,t} \right)}}{{\partial x}} + \mu _{{{{\mathrm{ion}}}}} p\left( {x,t} \right)\frac{{\partial E\left( {x,t} \right)}}{{\partial x}}} \right],\end{array}$$
(1)

where Di is the diffusion coefficient, E(x, t) = –∂V(x, t)/∂x is the electric field and µion = (Die)/(kBT) is the ionic mobility (with elementary charge e, Boltzmann constant kB and temperature T). The analytical solution of equation (1) and Poisson equation for the unconstrained or steady situation are provided in Supplementary Note 1. For simplicity, we mainly consider the time-dependent ion density at the semiconductor/dielectric interface as p(0, t) = pi, the dimensionless potential drop u (Fig. 1b), induced capacitance C and total charges Qi. To consider the large potential drop near the interface, the dimensionless potential u is used for the following discussions. We refer to the typical dispersive process (with energy distribution)27 and the electric double layer theory28, and develop a set of approximated solutions for them (Supplementary Note 2).

$$\frac{{\partial p_{{{\mathrm{i}}}}}}{{\partial t}} = - \left( {p_{{{\mathrm{i}}}} - p_{{{{\mathrm{i}}}}\infty }} \right)\frac{\beta }{\tau }\left( {\frac{t}{\tau }} \right)^{\beta - 1}$$
(2)
$$u = {{{\mathrm{ln}}}}\left( {\frac{{\gamma _1 - 1 - \sqrt {1 + 2\gamma _1\gamma _2 - 2\gamma _1} }}{{\gamma _1 - 2\gamma _2}}} \right)$$
(3)
$$C = C_0\frac{{{{{\mathrm{cosh}}}}\left( {\frac{u}{2}} \right)}}{{1 + 2\gamma _1{{{\mathrm{sinh}}}}^2\left( {\frac{u}{2}} \right)}} \sqrt {\frac{{2\gamma _1{{{\mathrm{sinh}}}}^2\left( {\frac{u}{2}} \right)}}{{{{{\mathrm{ln}}}}\left[ {1 + 2\gamma _1{{{\mathrm{sinh}}}}^2\left( {\frac{u}{2}} \right)} \right]}}}$$
(4)
$$Q_{{{\mathrm{i}}}} = \left( {p_{{{\mathrm{i}}}} - n_{{{\mathrm{i}}}}} \right)et_{{{\mathrm{E}}}}$$
(5)

In equation (2), the time constant τ, power factor β and pi∞ are described by τ = η/(|Vox|Di), β = β0|Vox/1|α and pi∞ = pi,max[1 – Aexp(–Vox/V0)], respectively, where η, β0, α, pi,max, A and V0 are constants, because the process is driven by voltage Vox and the rate is limited by diffusion coefficient Di. In equations (3) and (4), γ1 is the initial-to-steady density ratio γ1 = (pi0 + ni0)/pi,max, γ2 is the initial-to-transient density ratio γ2 = pi0/pi and C0 is the Debye capacitance $$C_0 = \sqrt {\varepsilon _0\varepsilon _{{{\mathrm{r}}}}e^2\left( {p_{{{{\mathrm{i}}}}0} + n_{{{{\mathrm{i}}}}0}} \right)/\left( {4\uppi k_{{{\mathrm{B}}}}T} \right)}$$. When applied with constant bias, equation (2) turns into an integral form (Supplementary Note 2 and Supplementary Fig. 4). The possible ion transfer from electrolytes into semiconductors is considered by a transferred ratio λ1 (0 ≤ λ1 < 1).

The pi, u and C values with various Vox or Di values are calculated by equations (2)–(4) in the case without interfacial ion transfer (λ1 = 0) and is verified by the numerical simulation (Supplementary Fig. 2). With a constant low Vox or a high Vox (Fig. 1c,d), u and C increase with time as pi accumulates (white areas) and then saturate or drop once pi saturates (red areas). With a triangle wave of gate bias, the interfacial ions are driven to accumulate or release with the anticlockwise hysteresis (Fig. 1e), with u and C changing accordingly (Supplementary Fig. 3). As pi increases, C increases until the maximum where u is denoted as uM (Fig. 1f). If pi continues to increase, the piled-up ions would spread into the bulk due to their volumes (steric effect) and the effective capacitor thickness $$L_{{{{\mathrm{eff}}}}} \propto L_{{{\mathrm{D}}}}\sqrt {2\gamma _1u}$$ is increased with decreased C (Fig. 1f, bottom; blue arrow), where LD is the Debye length28. Alternatively, if pi decreases, the dielectric film acts toward a parallel-plate capacitor (Fig. 1f, bottom; red arrow). In either case, the effective capacitor thickness increases and C decreases, giving the gull-wing-shaped Cu relation (Fig. 1f, dashed curves). If decreasing the sweep rate s or increasing diffusion coefficient Di, the Cu curves would cover wider ranges as indicated by the increased Δu (Fig. 1f, from top to bottom). The evolution leads to complex CVg relations (Fig. 1g) that are crucial to achieve multimode transistors.

The compact model equations (2)–(5) could be combined with the field-effect transistor (FET) equations to give current–voltage (IV) relations (Supplementary Fig. 4), where the charges of ions Qi also cause shift in the flat-band voltage VFB against its initial value VFB0, that is, VFB = VFB0 − Qi/C. The theory can be extended by using the non-zero transferred ratio λ1 to describe that some ions transferred from the solid-state electrolytes into semiconductors (for example, Faraday charge transfer) dope semiconductors and affect the conductivity29. It can also be extended by using the condition Di,nDi,p (or Di,nDi,p) to cover the case that only one type of ion is mobile (Supplementary Note 4). The theory predicts that multimode operation could be obtained in a single transistor with an ionic dielectric and will be presented together with experiments later.

## Ions in solid-state electrolytes

To achieve multimode transistors, we fabricated a commonly used metal-oxide dielectric, AlOx, by a sol–gel process followed by annealing at a low or high temperature (300 or 500 °C, respectively). The AlOx film forms an abrupt interface with the highly crystalline indium oxide semiconductor to allow transistor fabrication, as revealed by transmission electron microscopy (TEM) with energy-dispersive spectrometry mapping (Fig. 2a). To identify the ions, the X-ray photoelectron spectroscopy was measured (Fig. 2b), where both O1s peak and Al2p peak of the 300 °C-annealed AlOx film (‘low T’) shift positively compared with those of the 500 °C-annealed film (‘high T’). By referencing the peak positions of aluminium compounds, the shift in O1s and Al2p peaks towards higher energies in low-T AlOx is possibly due to the formation of Al(OH)3 or AlOOH after dehydration condensation30. Hydrogen ions possibly act as the movable ions to give the electrolytic properties. The 27Al nuclear magnetic resonance (NMR) was measured to examine the Al environment (Fig. 2c), where three resonances corresponding to the tetrahedral (~72 ppm), pentahedral (~38 ppm) and octahedral (~9 ppm) Al coordination are found. In low-T AlOx, Al(O)6 decreases from 88% to 79%, whereas Al(O)4 increases from 9% to 15%. Because Al(O)4 has greater acidity than Al(O)6 and it causes ionic polarization31, the conversion of Al(O)6 to Al(O)4 indicates an increase in H+ concentration. The 3.7 ppm left shift of the Al(O)4 peak in low-T AlOx possibly contributes to stronger magnetic shielding induced by the high H+ concentration32.

The low-T AlOx film exhibits the frequency- and voltage-dependent capacitance following the theoretically predicted uC relations (Fig. 2d,e), implying it meets the required ionic electrolyte properties predicted in our model. The electrochemical impedance spectroscopy data at various bias voltages (Fig. 2f,g) follow the Randles cell including electric double layer capacitances33,34,35, in contrast with that of thermally grown SiO2 following a standard resistor–capacitor cell (Supplementary Fig. 5). The electrochemical impedance spectroscopy and cyclic voltammograms are comprehensively analysed with models in Supplementary Note 3 and the estimated parameters of ions are as close to those in the literature (Supplementary Figs. 68)36,37.

## Multimode transistors

The theory (equations (2)–(5)) predicts multimode operation could be obtained by presetting the ion concentration pi (for example, with Vg programming), varying the diffusion rate Di or changing the sweep rate s = ∂Vg/∂t (Fig. 3a–d) and validated by numerical simulation (Fig. 3e–h). On potentiation with different amplitudes or widths of pulses, the transistor shows short-time plasticity (STP) or long-time plasticity (LTP) (Fig. 3a,e), or an enhanced current and apparent mobility after a high gate bias, that is, the ultrahigh-apparent-mobility mode (Fig. 3b,f). By further increasing s (or sweep range of Vg), the hysteresis curve shows an ultrasharp reversed subthreshold slope SS of about 30 mV dec–1 in both forward and backward curves, that is, the subthermionic SS mode (Fig. 3c,g); or even the hysteresis with negative transconductance, that is, the memristive mode (Fig. 3d,h). In experiments, we used a very thin semiconductor InOx film (10 nm) and the above solid-state electrolyte AlOx film (40 nm) or ZrOx and to fabricate bottom-gate, top-contact FETs. The maximum of leakage current is lower than 7% of Id. As shown in Fig. 3i–l, all the abovementioned modes could be obtained by presetting Vg or changing s. The above multimode characteristics maintain at least ten months after storage, indicating good long-term stability. The features have been repeated in more than 20 devices in different batches (Supplementary Note 5). The consistent simulation and experimental results validate the theoretical predictions and applicability of strategy.

The complex transistor modes—tunable plasticity mode, ultrahigh-apparent-mobility mode, subthermionic SS mode and memristive mode—are summarized in Fig. 4a, and the evolution of electrostatic potential and charges are illustrated in Fig. 4b–d.

Tunable plasticity mode: this occurs when ions are gradually accumulated and Δu gently increases with ΔuuM (Fig. 4a, purple segment). As C gently increases (Fig. 1g, top), the electrostatic potential V(x) and interfacial ions pi gently increase (Fig. 4b–d, mode I). The number of ions participating in the operation can be easily controlled by adjusting the amplitude and number of Vg pulses. With a small (large) preset pi or large (small) Di, potentiation is short (long), enabling STP (LTP) in the synaptic behaviour.

Ultrahigh-apparent-mobility mode: when ions synchronously increase with the Vg sweep, Δu substantially increases towards uM (Fig. 4a, orange segment), C sharply increases (Fig. 1g, middle), and substantial carriers are induced with a large potential drop near the interface (Fig. 4b–d, mode II; simulation in Supplementary Fig. 18). As C in equation (3) is comparable with the Debye capacitance C0, it can substantially exceed the geometric capacitance Cox = ε0εr/dox for extracting apparent mobility µ = gmL/(WCoxVd), where gm = ∂Id/∂Vg. For example, C0 is 9.0 μF cm–2 if pi0 = 1020 cm−3 and would approach Cox = 0.2 μF cm–2 only if pi0 < 1017 cm−3 (Supplementary Fig. 19). For simplification, in the case that pi is much less than the maximum values, the ratio between the apparent mobility μ and real μ0 is approximated as

$$\frac{\mu }{{\mu _0}} = \frac{1}{{C_{{{{\mathrm{ox}}}}}}}\frac{{\partial Q_s}}{{\partial V_{{{\mathrm{g}}}}}} \approx \frac{\theta }{{C_{{{{\mathrm{ox}}}}}}} \frac{V_{{{\mathrm{g}}}}{\beta _0t_\mathrm{E}^2}}{\eta } \propto \frac{{D_{{{\mathrm{i}}}}p_{{{{\mathrm{i}}}}0}}}{s},$$
(6)

where the characteristic capacitance is θ = e(2/γ1 – 1/γ2)pi0Di/(stE) Dipi0/s (Supplementary Note 7) and tE is the thickness of the electric double layer. Apparent μ will increase with reducing s, increasing pi or enlarging Di. The simulation results (Fig. 4e and Supplementary Figs. 20 and 21) effectively follow equation (6) as well as the experimental results obtained from reducing s (Fig. 4f and Supplementary Fig. 22), presetting pi (Fig. 4g and Supplementary Fig. 23), or varying the ion concentration in dielectrics31. This also means that the real carrier mobility in transistors with ionic dielectrics could not be determined by only measuring the quasi-static capacitances38. The high-apparent-mobility mode increases the current density but the current decay gradually due to the thermally activated ion diffusion (Supplementary Fig. 25)39,40. As the decay time (500 s) is much longer than the subsecond Vg pulse for programming (Supplementary Fig. 23), this mode can be maintained without the need to frequently refresh.

Subthermionic SS mode: when ions are synchronously released with Vg sweep, u increases and then decreases (Fig. 4a, green segment). As the ions accumulated at the interface are released to the bulk with decreased pi and potential V (Fig. 4b–d, mode III), the current sharply changes; if the rate of ion release matches the rate of Vg sweep, a negative ∂Vox/∂Vg would appear with SS < (kT/e)ln10 (Supplementary Fig. 29). A higher matching degree, characterized by the response of ion-induced potential u to Vg (that is, ∂u/∂Vg), leads to more ions released to the bulk and a smaller SS (Supplementary Figs. 30 and 31). Note that the subthermionic SS can be obtained during the forward curve, backward curve or both curves, if the ions are synchronously released with Vg scanning (Supplementary Note 4 and Supplementary Fig. 12). This theory is confirmed by simulations and experiments (Fig. 3g,k and Supplementary Figs. 3236). The SS is approximated as

$$\mathrm{SS} = \frac{{\partial V_{{{\mathrm{g}}}}}}{{\partial {{{\mathrm{log}}}}_{10}I_{{{\mathrm{d}}}}}} = \frac{{kT}}{e}{{{\mathrm{ln}}}}10/\left( {1 - \frac{{\partial V_{{{{\mathrm{ox}}}}}}}{{\partial V_{{{\mathrm{g}}}}}}} \right) \approx \frac{1}{{1 + \left( {a\theta - b} \right)/C_0}}\frac{{kT}}{e}{{{\mathrm{ln}}}}10,$$
(7)

where Vox = Vg − φs and a and b are constants (Supplementary Note 8). The simulation results follow equation (7) well (Fig. 4e). The experimental results further verify that smaller SS could be obtained by programming more interfacial ions to match the gate-field switching by varying the range of Vg scanning or sweep rate s (Fig. 4h,i and Supplementary Figs. 3436). Combining equations (6) and (7), the characteristic capacitance θDipi0/s could be taken as the key parameter to govern the transition from conventional to unconventional transistor characteristics, featuring very high apparent μ and ultrasharp SS.

Memristive mode: when ions are post-saturated, Δu could exceed uM (Fig. 4a, pink segment). As C reaches the maximum and then decreases due to the steric effects of ions (Fig. 1g, bottom, and Supplementary Fig. 37), the potential V near the interface decreases, resulting in a decrease in Id (Fig. 4d–f, mode IV). The detailed mechanisms are explained with the evolution of ion concentration and electric field (Supplementary Note 9). This mode disappears if ions substantially transfer from the electrolyte into the semiconductor and the steric effect disappears (Supplementary Note 4). The observation of such a mode in experiments implies that ion transfer may not be notable. During the forward sweep in the experiment, the FET changes from the low-resistance state to the high-resistance state at Vg ≈ 6 V (Fig. 3i). The feature with negative gm can be intensified if θDipi0/s increases (Supplementary Fig. 39). The resistance reverses when the state variable pi is close to the maximum, resembling that in memristors41. Specifically, the Id = gm(pi, Vg, t) × (Vg – Vth) relationship follows that of the extended memristor42, because gm is the function of pi with ∂pi/∂t = f(pi, Vg, t). During the backward sweep, Id intersects with the forward curve, also similar to the pinched hysteresis loop as the key feature of memristors claimed elsewhere42. To obtain such a mode, the initial-to-steady density ratio γ1 should be small to allow u to reach uM within the measurement (Supplementary Fig. 38).

The above modes could be coupled to generate second-order features. Mode I with plasticity and mode II with high apparent μ could coexist and enable a visualized synapse in the form of thin-film transistor (TFT)–light-emitting diode (LED) integration, where luminance could be held after gate-off by the excitatory postsynaptic current (EPSC)—a potentiated current triggered by a potential spike signal in a presynaptic neuron43,44 (Supplementary Fig. 42 and Supplementary Videos 1 and 2). Mode I and mode III could be combined to generate the leaky-integrate-and-fire (LIF) behaviour emulating biological neurons45,46. Consecutive pulses shift Vth and simultaneously change gm, inducing the subthreshold to above-threshold transition and abrupt increase in Id. A shorter time of stimuli to trigger the firing process can be obtained by changing several device parameters (Supplementary Fig. 44). In both theoretical calculation and experimental measurements, the LIF behaviour is obtained (Supplementary Fig. 43). In general, to reproduce all these modes, the change in ion concentrations for both ion species should be large enough to give a prominent dynamic capacitance with the interfaces suitable for accumulating ions. In this study, the low-temperature processed AlOx limits the choice of semiconductors to some extent. By far, we have observed all the four operation modes only in transistors with solution-processed or vacuum-deposited indium oxide (Supplementary Fig. 41). Nevertheless, the presented devices enable multimode operations by using the non-crystalline electrolytes with simple fabrication.

## Multimode neural networks

The multimode transistors can enable multimode neural networks: STP for artificial neural networks (ANNs), LTP for recurrent neural networks (RNNs) and LIF behaviour for spiking neural networks (SNNs).

### ANN

With short gate pulses (2 V; duration, 20 ms; period, 40 ms), the increased conductance G = I/V recovers soon (STP; Fig. 5a) and could serve as the weight of the neuron. The experimental results are used to generate the cumulative probability distribution function (CDF) of G and its error ΔG (Fig. 5b), forming the weight update rule under potentiation or depression pulses. The device conductance in STP (the same below for LTP and LIF) were measured and written into the software for training the neural networks, which perform the image recognition tasks. A backpropagation ANN was built to classify the handwritten digits (Fig. 5c)47,48,49,50, giving an accuracy of 85% for large digits (28 × 28 pixels) and 93% for small digits (8 × 8 pixels) after 40 epochs (Fig. 5d).

### RNN

With long positive gate pulses (2 V; duration, 0.5 s; period, 1.0 s), G remains at the demanded values (LTP; Fig. 5e), because substantial interfacial ions remain. The experimental results of LTP are used to achieve a reservoir computing system for RNN, where G of a reservoir neuron (that is, a transistor) changes in response to the input spatiotemporal signals (Fig. 5f). The original images were cut into 22 rows × 20 pixels and turned to pulse streams as the input into the reservoir, leading to the changed G. The 88 × 10-sized fully connected readout layer is trained by backpropagation (Fig. 5g). After training 60,000 images, the RNN achieves a recognition test accuracy of 87.13% (Fig. 5h).

### SNN

The experimental LIF results of a transistor (Fig. 5i) are used as a neuron mimicking the membrane potential of a time series (Fig. 5j)51: V[t + 1] = wX[t] + ζV[t] – S[t]Vth_spike, where ζ is the decay rate of membrane potential; w is the weight matrix; X[t] is an input voltage, spike or unweighted input current; output spike S[t] is generated if V[t] > Vth_spike. The reset voltage is appended after each output spike. The original images were rate coded into 200 pulse patterns (each with a time step), which converts input intensity into a firing rate or spike count51 (Fig. 5k). For each neuron, the input and output are spikes. After training about 1,000 iterations (60,000 images), the SNN achieves a recognition test accuracy of 90.76% (Fig. 5l).

The above modes could be achieved based on the same multimode transistor, and therefore, a single network can switch among different modes as needed. If considering variations in device performance (Fig. 5d and Supplementary Fig. 46), 10% variations in conductance values lead to a decrease in accuracy of about 10% and 5% for ANN and RNN, respectively. Compared with the ANN, the RNN uses much fewer activated neuron-like transistors as connections by integrating calculations in the reservoirs. As the weights of inputs and connections in the reservoir are fixed, only the weights of the readout layer need to be trained, enabling the reservoir computing system to avoid some gradient-descent problems and reduce training cost52,53,54. Although the ANN and RNN use current levels, the SNN uses sparse current spikes with high information density and consumes longer time but much lower energy cost55,56. From a hardware application perspective, the conductance after a long time decay can be quickly refreshed by a subsecond pulse at a frequency much lower than the operation speed. Compared with other electronic devices, such as ferroelectric FETs, phase-change memory and resistive memory, the realization of various neural networks shows the potential of multimode transistor in neuromorphic computing (Supplementary Fig. 47).

## Conclusions

We have reported the development of multimode transistors based on ion-dynamic capacitance. This capacitance could be described by a compact theory validated by numerical simulations. This showed that the characteristics of tunable synaptic weight, high apparent mobility, sharp subthreshold swing and memristive conductance could appear in a single transistor by programming the interfacial ion concentrations or matching the scan speed with ion motions. We then fabricated such multimode transistors using common solid-state electrolyte films, and experimentally confirmed this range of behaviours. Some of the features can also coexist to generate other characteristics including the LIF neuron. Furthermore, we showed in software that the multimode transistors can be used to create neural networks that can be switched between different modes—conventional ANNs, RNNs and SNNs —as needed.

## Methods

### Film characterization

Cross-sectional TEM images and energy-dispersive spectrometry maps were obtained with the JEM 2100F system operated at 200 kV, with the samples prepared on silicon using focused-ion-beam techniques. The chemical structures of AlOx and ZrOx films on silicon were characterized by X-ray photoelectron spectroscopy (Thermo Fisher ESCALAB 250Xi) using a monochromatized Al Kα source with a step size of 0.05 eV. All the binding energies were referenced to the C1s peak at 284.6 eV of the surface adventitious carbon. The AlOx powders were used for the NMR experiments. The powders were prepared by drop casting appropriate precursor solutions on Si substrates at 120 °C for 2 min. This process was repeated about 40 times. Then, the samples were annealed on a hot plate at 300 or 500 °C for 30 min. The mass of the final sample is about 15 mg. The 27Al NMR experiments were conducted at 600 MHz (14.1 T) on a Bruker Avance III 600 spectrometer using a 1.3 mm Bruker probe. The resonance was calibrated using Al(NO3)3 at 0 ppm.

### Device theory

The apparent device mobility is extracted by FET characterization that contains the geometric capacitance calculated by the usually used dielectric constant Cox: µ = L/(WVdCox) × ∂Id/∂Vg. The ratio between μ and true carrier mobility μ0 is derived in Supplementary Note 7 and validated by numerical simulations (Supplementary Fig. 21). All the capacitance parameters including dynamic capacitance, capacitance component in the electrochemical impedance spectroscopy equivalent circuit and characteristic capacitance are summarized in Supplementary Table 5. The reversed subthreshold slope SS is calculated by SS = (∂φs/∂logId)/(1 – ∂Vox/∂Vg), where Vox = Qi/C. The SS is approximated as described in Supplementary Note 8 and validated by numerical simulations (Supplementary Fig. 33). For demonstration, a transistor calculator is encoded in an HTML file with a user interface and provided in the Supplementary Information. Readers can use it to check how the main parameters affect the device operation mode.

### Device simulation with technology computer-aided design

In numerical simulations, an electrolyte layer (40 nm) with mobile cations and anions (1020 cm−3) is under an n-type semiconductor (carrier mobility μ0 of 15 cm2 V–1 s–1). Numerical simulations were carried out using technology computer-aided design tools (Supplementary Note 2; parameters are listed in Supplementary Table 4). The simulation of the electrolyte-gated transistors and the analysis of IV curves, charge and ion distribution, potential and electric field are provided in the Supplementary Information.

### Device fabrication

The 0.2 mol l–1 InOx precursor was prepared by dissolving indium nitrate hydrate in deionized water. The 0.2 mol l–1 AlOx (ZrOx) precursor was prepared by dissolving aluminium nitrate hydrate (zirconium oxynitrate hydrate), nitric acid and ammonium hydroxide in hydrogen peroxide. The metal–insulator–metal capacitors were fabricated as follows. After being stirred and filtered, the AlOx (ZrOx) precursor was spin coated on the heavily doped silicon wafer and annealed on the hot plate at 300 °C (230 °C) for 30 min. The process was repeated five times to deposit an ~40 nm film. The Al top electrodes were deposited by thermal evaporation through a shadow mask. The AlOx/InOx TFTs were fabricated after the deposition of AlOx. The InOx precursor was spin coated on AlOx and annealed at 230 °C for 2 h. After the photolithography process, the channel layer was patterned with a channel width of 96 μm and channel length of 24 μm. Finally, Al was deposited and lifted off to form the source and drain electrodes. Conventional TFTs were fabricated by a similar method, but AlOx was annealed at 500 °C (Supplementary Note 12).

### Device characterization

The cyclic voltammograms and IV curves of the TFT were measured using an Agilent B1500A semiconductor parameter analyser in air and at room temperature. The sweep rate was adjusted by setting the step number and step delay time. The mobility in the linear regime and reversed SS are extracted by Id = WµCox(Vg – Vth)Vd/L and SS = 1/(∂log10Id/∂Vg), respectively. The electrochemical impedance spectroscopies were measured by a Zahner electrochemical workstation. The a.c. amplitude was set as 100 mV. The potentiostatic was turned on and the d.c. voltage was set from −1 to 3 V. The frequency was set from 0.1 Hz to 1 MHz. The capacitance at 1 kHz was used to calculate the apparent mobility of TFTs. The results of varying Vg and sweep rate to obtain different apparent mobility μ or SS values in the InOx/AlOx and InOx/ZrOx transistors are shown in Supplementary Notes 7 and 8. The temperature-dependent transistor characteristics were performed in vacuum with a temperature controller. Different batches of devices were fabricated with the same process and measured. The subsecond gate pulses are generated from the DG1032Z signal generator.

### Neural networks

This work was simulated in Python 3.8.12 and the codes are available via GitHub. (1) ANN. An ANN was established in the CrossSim platform47. A three-layer backpropagation network with 784 input neurons, 300 hidden neurons and 10 output neurons was used for handwritten digit classification. Two datasets, namely, a small image (8 × 8 pixels) from the UCI Machine Learning Repository49 and a large image (28 × 28 pixels) from the Modified National Institute of Standards and Technology database, were used to train the network, and the dataset distribution of training and testing is shown in Supplementary Table 6. With Gaussian white noise (20% standard deviation), the accuracy became 80% for large digits and 85% for small digits. (2) RNN. Schematic of the training process of the reservoir computing system is shown in Supplementary Fig. 45a. The original images were binarized first, then cut into 22 rows × 20 pixels to remove any invalid pixels. Each row was divided into four groups with each group containing five pixels; thus, the image was converted into 88 pulse streams. The reservoir layer was simulated by the LTP device model. As for the readout layer, we chose the SoftMax function $$S(y_{{{\mathrm{i}}}}) = \mathrm{e}^{y_{{{\mathrm{i}}}}}/\mathop {\sum }\nolimits_{{{{k}}}} \mathrm{e}^{y_{{{{k}}}}}$$ as the activation function and cross-entropy $$L = - 1/N\mathop {\sum }\nolimits_{{{\mathrm{i}}}} \hat y_{{{\mathrm{i}}}}\log \left( {S_{{{\mathrm{i}}}}} \right)$$ as the loss function. (3) SNN. Schematic of the training process of the SNN is shown in Supplementary Fig. 45b. Each neuron of the SNN was inspired by spike inputs and would generate spike outputs based on the LIF model. The loss function is the spike-count-based cross-entropy that the spikes at each time step are accumulated and then passed through the cross-entropy loss function. The SNN work is simulated by Python packages PyTorch and snnTorch51.