Introduction

Scaling-down of complementary metal–oxide–semiconductor (CMOS) field-effect transistors (FETs) is a mainstream approach for reducing power dissipation in the rapidly developing field of information technology1,2,3,4. However, CMOS technology still faces a great challenge of feature size <5 nm, due to the degradation of the off-state leakage current induced by short-channel effects (i.e., direct source–drain punch through, and a loss of gate electrostatic control)3,4,5,6,7,8. An efficient way to minimize power consumption is to achieve a steep subthreshold swing (SS) with a fast-switching rate at a reduced supply voltage7,9. The emerging two-dimensional (2D) transition metal dichalcogenides10,11,12, e.g., atomically thin molybdenum disulfide (MoS2)5,8,13, are promising channel materials for future electronic chips with scaling dimensions and ultralow off-state currents, due to the high electron effective mass, low dielectric constant, and large bandgap10,11,12,13. Furthermore, the atomic-scale thickness and smoothness of MoS2 also significantly improve the electrostatic gate control capability according to its characteristic scaling length and can efficiently lower the supply voltage8,10. However, the electrons in the source usually represent a thermal Boltzmann distribution with a potential barrier, which restricts the gate modulation capacity to 60 mV decade−1, as determined by the thermal voltage (kT/q)6,7. Hence, to break the “Boltzmann tyranny”, enabling atomic-scale FETs with steep subthreshold behavior and still maintaining high on/off current ratio, is critical for the development of ultralow-power electronics.

Several strategies have been proposed to obtain an SS of sub-60 mV decade−1, such as band-to-band tunneling8, impact ionization14, nanoelectromechanical switching15, Dirac-source16, negative capacitance (NC)17,18,19,20, and negative differential resistance (NDR)21,22. The demonstrated threshold-switching behavior acting as an internal amplifier offers a shortcut to conquer the Boltzmann limit and triggers the FET to switch with a sub-kT/q slope. In particular, the NDR effect in threshold-switching FET is highly predictable and quantifiable for constructing steeply switchable electronic devices with high performance9,21. When compared to a common insulator–metal–transition device (e.g., VO2)21,23, a new type of metal filamentary threshold switch (TS), which generally consists of Ag (or Cu) as an active electrode or dopant in a solid electrolyte, has been demonstrated a lower leakage current and much steeper switching characteristics24,25,26,27, and can contribute to suppressing the off-state leakage current of conventional FETs with an abrupt SS22,28. The seamless device architecture based on a 2D FET and TS may realize the simultaneous achievement of efficient electrostatic control, small sub-thermionic SS, and low leakage current, leading to efficiently minimizing power dissipation.

Here, we present an atomic threshold-switching MoS2 FET (ATS-FET) with sharp on/off switching properties and ultralow energy consumption. The ATS-FET is endowed with an abrupt amplification capacity via integrating an abrupt variable-resistance Ag atomic TS with an atomically thin MoS2 channel. The channel thickness and metal filament at the atomic scale are critical to reducing the supply voltage. The common HfO2 insulator functions as the dielectric layer for the FET and the electrolyte for the TS, which is promising for future monolithic integration of the ATS-FET configurations with facile fabrication processes. The NDR effect according to the abrupt resistance transition of the TS induces an internal voltage amplification across the MoS2 channel, which enables the MoS2 FET to significantly overcome the fundamental thermionic limitation. According to the atomic thickness of the MoS2 channel and the Ag atomic conductive filament (Ag filament), the superior electrical performances, such as on/off current ratio >106, ultralow cutoff current at 1 × 10−13 A μm−1, an average SS (SSaverage) of sub-5 mV decade−1 (median), and very small hysteresis, are achieved in the ATS-FET. We systematically investigate the influence of the NDR effect on the internal amplification phenomena and evaluate the improved electrical performance of the ATS-FET. The proposed ATS-FET has great potential to be extended to scalable and monolithic steep-slope transistor arrays and is of great significance in energy-efficient and high-performance electronic switches with ultralow-power dissipation.

Results

ATS-FET design

Figure 1a shows a schematic illustration of the ATS-FET by integrating an Ag atomic TS in series with a MoS2 FET. The FET shares the same HfO2 dielectric with the TS (acting as the electrolyte in the TS). Triangle-shaped MoS2 nanoflakes are first synthesized on a SiO2/Si substrate by chemical vapor deposition (CVD). The source/drain electrodes (Cr/Au) top-contacted with the MoS2 are prepared via standard e-beam lithography (EBL), thermal evaporation, and lift-off process. The common HfO2 thin film is deposited with atomic layer deposition (ALD), functioning as both the dielectric layer of the FET and the electrolyte of the TS. The Ag atomic layer is patterned on HfO2 by a standard liftoff process. Top gate and drain contacts are defined at the desired position via EBL and metallization. The structural design of the common HfO2 layer simplifies the fabrication process, while ensuring a high-κ dielectric performance for FET operation and good electrochemical kinetics for threshold switching. The fast formation and spontaneous rupture of the atomic Ag filament in the TS will lead to abrupt on/off switching in the ATS-FET with an ultralow SS (Fig. 1a).

Fig. 1: Ultralow-power steep-slope 2D MoS2 field-effect transistor with Ag atomic threshold-switching (ATS-FET).
figure 1

a Schematic illustration of the ATS-FET, consisting of a MoS2 FET and an Ag/HfO2 based TS. The enhanced performance of the ATS-FET is essentially attributed to the abrupt switching transition of the TS. b The equivalent circuit schematic of the ATS-FET, which can be considered as a baseline MoS2 FET in series with a TS device. VD is the drain-to-source voltage across the TS and the MoS2 FET; VG is the gate-to-source voltage across the MoS2 FET. c, d Schematic band diagrams of the ATS-FET under thermal equilibrium with VG bias, including c VG < VT and d VG > VT. Electrons pass through the contact barriers via thermionic emission or tunneling; and across the electrolyte barrier via hopping. e Optical image of the ATS-FET device structure, exhibiting that the TS stack (cross-point area: 2 × 2 μm2) in series with the channel of the MoS2 FET. The red-dashed triangle indicates the MoS2 channel material. Scale bar: 50 μm. f Raman spectrum of the CVD synthesized MoS2 nanoflake. The peaks of in-plane E2g and out-of-plane A1g vibrational modes are at 386.2 and 406.6 cm−1, respectively.

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Figure 1b depicts the equivalent circuit diagram of the ATS-FET, which can be considered as a baseline MoS2 FET in series with a TS device. The supply voltage (or drain-to-source voltage, VD) drives the TS and the MoS2 channel, while the gate-to-source voltage (VG) controls the switching characteristics of the ATS-FET. The supply voltage variably distributes between the TS and FET, corresponding to a voltage drop of VD for the whole device and VD′ for the MoS2 FET, respectively. Based on the series TS configuration, VG can tune the Fermi level of the MoS2 channel and lead to efficient control of the channel resistance, which dominantly determines the voltage drop between the FET and TS in the series configuration. The band diagrams of the ATS-FET for a typical VG (compared with the threshold voltage, VT) are illustrated in Fig. 1c, d. The HfO2 electrolyte layer in the series TS can be considered as a variable barrier for electron transport according to the applied VG, which determines the voltage drop on the MoS2 channel and the TS component. For VG < VT, the Fermi level of MoS2 is slightly shifted downward (the MoS2 channel resistance is maintained at a high level). The current across the TS is insufficient to trigger the bridging of the Ag filament. The HfO2 electrolyte layer acts as a large barrier to blocking the transport of electrons. When VG > VT, the MoS2 Fermi level is effectively shifted downwards (the MoS2 channel resistance transits to a low level). The current across the TS could induce the Ag filament formation, leading to an abrupt current increase (the mechanism will be discussed below in detail). An optical image of the ATS-FET device is shown in Fig. 1e. The TS stack (Au/Ag/HfO2/Au) is connected in series to the FET, sharing its top electrode as the drain electrode of the ATS-FET. Figure 1f shows the Raman spectrum of a CVD synthesized MoS2 nanoflake excited with a 532 nm laser. The peaks of the in-plane E2g and out-of-plane A1g vibration modes at 386.2 and 406.6 cm−1, respectively, indicate that the as-grown MoS2 is a monolayer.

ATS-FET versus the baseline FET

The transfer characteristics (ID–VG) of the ATS-FET and the baseline MoS2 FET are presented in Fig. 2a. As is clearly shown, when VG sweeps from −3 to 3 V and back to −3 V, the baseline MoS2 FET exhibits an on/off current ratio of 105 and a very small hysteresis (grey square curves). The minimal SS (SSmin) in forward and reverse sweeps are characterized to be 118.3 and 120.9 mV decade−1, respectively, which are both above the thermionic limit of 60 mV decade−1 at room temperature (Fig. 2b). In contrast, the ATS-FET shows more superior electrical properties, including a higher on/off current ratio (5 × 106), a lower off-state current (1 × 10−13 A μm−1), and a much steeper SS (<5 mV decade−1). It is remarkable that, in the ATS-FET, the series integration of a TS in the baseline MoS2 FET enables to produce an internal amplification to overcome the fundamental thermionic limitation of the Boltzmann distribution of electrons. More impressively, the exponentially increased transfer curves of the baseline MoS2 FET can transit to the nearly vertical transfer curves with much steeper slopes for the ATS-FET (Fig. 2a).

Fig. 2: Device performances of the ATS-FET.
figure 2

a Transfer curves from the ATS-FET and FET with the same 2D MoS2 channel (channel width: 10 μm; channel length: 2 μm). Solid symbols indicate the forward sweep, while open symbols indicate the reverse sweep. b SS from the ATS-FET and FET both in forward and reverse sweeps. The FET operates well above the fundamental thermionic limitation, while the ATS-FET has a large range of the drain current where the minimal SS is 2.5 mV decade−1. c The off-state leakage current and SS can be simultaneously reduced in the ATS-FET, indicating the ultralow-power steep-slope phenomenon in the ATS-FET. d ID–VG characteristics measured at room temperature and at VD = 0.2 V at slow/fast gate voltage sweep speeds. The VG steps were set to 3 and 30 mV, respectively. e Transfer characteristics (ID–VG) measured at room temperature and at VD = 0.2 and 0.3 V. f Output characteristics (ID–VD) measured at room temperature at VG from −2 to 2 V with a step of 1 V.

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In the series combination, VD is divided between the MoS2 channel and the TS corresponding to their individual resistances. The off-state (or leakage) current of ATS-FET is commonly determined by the ultrahigh resistance of the TS, leading to a further decrease of ID to a lower level of 1 × 10−13 A μm−1. Initially, at a low VG, the ID flowing through the MoS2 channel and TS is insufficient to induce the switching of TS. As VG increases (i.e., forward sweep), the MoS2 channel resistance shows a gradual decrease until ID approaches a critical threshold (Ith-TS), which is capable to induce the switching on of TS (to low-resistance state, LRS). And consequently, the total resistance of the ATS-FET dramatically decreases and triggers an abrupt ID increase. On the contrary, as VG decreases (i.e., reverse sweep), the MoS2 channel resistance shows a gradual increase until ID reduces to another critical threshold (Ihold-TS), which could reversely induce the switching off of TS (back to high-resistance state, HRS) and causes a rapid drop of ID. Hence, hysteresis in the transfer curve can be found as a result of the difference in VG corresponding to the two critical thresholds (Fig. 2a). Different from that of the baseline FET (clockwise), the hysteresis of the ATS-FET resembles an anticlockwise transition that is caused by the series integration of the TS.

From the subthreshold region of the ATS-FET (in Fig. 2a), the extracted SSmin in forward and reverse sweeps are 2.5 and 4.5 mV decade−1, respectively, as shown in Fig. 2b. Besides, the ATS-FET has a large range of ID (over four decades) where the average SS (SSaverage) is 3.0 mV decade−1 in the forward sweep. It is considered that the NDR effect originating from the volatile threshold-switching behavior in the atomic Ag filament device induces an efficient internal voltage amplification across the atomically thick MoS2 channel, and contributes to inducing a record and significantly reduced SS, which is much smaller than the values previously reported for a tunnel FET (TFET) at 31.1 mV decade−1 (ref. 8), an NC-FET at 41.7 mV decade−1 (ref. 19), a Dirac-source CNT FET (DS-FET) at 35 mV decade−1 (ref. 16), and an ion liquid gating FET at 50 mV decade−1 (ref. 29). Moreover, the subthreshold characteristics of various types of the steep-slope MoS2 FETs are outlined in Supplementary Table 1. A record on SSmin of 0.3 mV decade−1 and SSaverage of 1.3 mV decade−1 (over three decades) is also achieved in the ATS-FET at room temperature.

Both reductions in off-state current and SS in the ATS-FET

Power dissipation is a fundamental issue for advanced CMOS technology, which faces two severe challenges: the increasing difficulty for the supply voltage scaling, and the rising leakage currents causing on/off current ratio degradation6,7. The energy efficiency of a logic operation can be estimated through the total switching energy (Etotal) consisting of dynamic (Edynamic) and static (Estatic) parts, defined as:

$$\begin{array}{*{20}{l}} {E_{{\mathrm{total}}}} \hfill & = \hfill & {E_{{\mathrm{dynamic}}} + E_{{\mathrm{static}}}} \hfill \\ {\,} \hfill & = \hfill & {\alpha C_{\mathrm{L}}V_{\mathrm{D}}^2 + I_{{\mathrm{off}}}V_{\mathrm{D}}\tau _{{\mathrm{delay}}}} \hfill \\ {\,} \hfill & \approx \hfill & {C_{\mathrm{L}}V_{\mathrm{D}}^2\left( {\alpha + \gamma 10^{\frac{{ - V_{\mathrm{D}}}}{{\mathrm{SS}}}}} \right)} \hfill \end{array},$$
(1)

where CL is the switched capacitance, τdelay is the delay time, α is the activity factor, and γ is a fitting parameter7. It can be inferred from the above equations that the steeper SS and a lower off-state current in FETs enable further scaling of the supply voltage and a corresponding reduction in total power dissipation. As shown in Fig. 2c (orange region), the integration of the TS with the baseline MoS2 FET helps to significantly suppress the off-state leakage currents by ~30 times, attributing to the ultrahigh resistance of the TS in the off-state (~1 TΩ). Besides, SSmin of the ATS-FET in forward and reverse sweeps have been demonstrated to greatly decrease to 2.5 and 4.5 mV decade−1, respectively. Both of them are far lower than the fundamental thermionic limitation and those of the baseline MoS2 FET (close to 50 times reduction, the cyan region of Fig. 2c).

Electrical properties of the ATS-FET

To exclude the effects of the VG sweeping rate on the ultralow SS, the transfer characteristics (ID–VG) of the ATS-FET are measured at slow and fast VG sweep speeds of 3 and 30 mV s−1, respectively. As illustrated in Fig. 2d, identical steep-slope switching characteristics with high on/off current ratios over 106 are observed at different VG sweep speeds. The SS, VT, off-state current, and on/off ratio are all independent of the VG sweeping rate. In addition, the transfer characteristics (ID–VG) of the ATS-FET at VD = 0.2 and 0.3 V are shown in Fig. 2e. In the forward sweep, the SSaverage at VD = 0.2 and 0.3 V are characterized to be 4.5 mV decade−1 (over five decades) and 6.0 mV decade−1 (over four decades), respectively. Meanwhile, VT of the ATS-FET shows a negative shift from −1.14 to −1.59 V, which is determined by the balances between the supply voltage and the relevant potential drops on the FET and TS during the VG sweeping. At a higher VD, the TS favors a tendency for the turn on state; consequently, the abrupt resistance change is less efficient, and it is easier for the TS to be switched on at a lower VG. In the reverse sweep, the ID of the ATS-FET decreases until it reaches the critical threshold Ihold-TS (<5 × 10−11 A μm−1), leading to the instantaneous switching off of the TS. And hence, the ATS-FET shows similar abrupt switching characteristics in the subthreshold region regardless of VD. The output characteristics (ID–VD) of the ATS-FET for different VG are characterized, as shown in Fig. 2f. The channel current ID increases from 6.7 × 10−8 to 2.1 × 10−6 A μm−1 as VG increases from −2 to 2 V in the linear/saturation region, showing an increase in the channel conductance with increasing VG. Distinguishable on- and off-states are observed in different VD regions (VD < Vth-TS or VD ≥ Vth-TS, Vth-TS is the threshold voltage of the TS), as shown in Fig. 2f. As VD increases, when VD < Vth-TS, the conductance of the ATS-FET is primarily determined by the TS, even though the MoS2 channel is in a LRS; when VD ≥ Vth-TS, the conductance of the ATS-FET is coordinated by the MoS2 channel. Similarly, as VD decreases, the conductance of the ATS-FET shows a sudden reduction when VD ≤ Vhold-TS (Vhold-TS is the hold voltage of the TS). Moreover, the output characteristics of another ATS-FET and its baseline FET at different VG (from −2 to 2 V) in linear scale are also demonstrated in Supplementary Fig. 1. It is clearly observed that the abrupt switching on/off behavior of TS contributes to causing the steep-slope phenomenon of the 2D FET.

Ag atomic threshold switching

The excellent subthreshold characteristics of the ATS-FET are attributed to the series integration of high-performance TS device. Therefore, it is critical to achieving a TS device with superior threshold-switching behavior. The typical I–V characteristic of the as-fabricated TS device at a compliance current (Icc) of 100 nA is shown in Fig. 3a. The TS exhibits volatile threshold-switching behavior with a small threshold voltage of the TS (Vth-TS = ~0.26 V), an ultralow leakage current (<1 pA), and a high on/off current ratio (>106). The TS device switches from the off-state to the on-state at an applied voltage (Va) larger than Vth-TS (green curve in Fig. 3a), while it switches to the off-state at Va less than the hold voltage (Vhold-TS; grey curve in Fig. 3a). The TS device yields an extremely steep on/off switching slope <0.5 mV decade−1, and Vth-TS ranges between 0.205 and 0.265 V in the cyclic tests. Energy-dispersive X-ray spectroscopy (EDS) line profiles of the cross-sectional TS stack layers are shown in Fig. 3b. The inset is a high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image. The sphere-shaped Ag layer, HfO2 dielectric layer, and top/bottom electrode (TE/BE) layers can be clearly observed, with the Ag atomic-scale layer accumulated at the interface of TE/HfO2.

Fig. 3: Ag atomic threshold-switching (Ag/HfO2-based TS).
figure 3

a Typical I–V characteristic of the TS device at a compliance current (Icc) of 100 nA in forward (green)/reverse (grey) voltage sweeping, exhibiting ultralow leakage currents (<1 pA). b Energy-dispersive X-ray spectroscopy (EDS) line profiles (including Ag, Hf, and O elements) of the TS stack layers along the red line shown in a cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image. Scale bar: 10 nm. c Simulation for the formation and rupture procedures (on/off) of the atomic Ag filament in the TS device with an applied voltage of 0.4 V.

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To investigate the effect of the filament morphology on the switching dynamics, the formation and rupture of the Ag filament at a Va of 0.4 V are illustrated in Fig. 3c via a Monte Carlo simulation (the flow chart is shown in Supplementary Fig. 2). The on-/off-state of the TS is determined by the formation/rupture of Ag filament with volatile threshold-switching behavior. The HfO2 electrolyte layer of the TS can be considered as a variable barrier for electron transport. The Ag nanoparticles diffusion into HfO2 matrix contributes to electrons transport along the nanoparticle chain (i.e., filament), and the adjacent Ag nanoparticles can act as electron traps for thermionic emission or tunneling30. As shown in Supplementary Fig. 3, the Arrhenius curve is used to explain the temperature dependence of the leakage current of a TS device. The charge transport of the TS at HRS is governed by a combination of Frenkel-Poole (F-P) emission and trap-assisted tunneling (TAT) process31,32,33. Specifically, in the high-temperature region (>200 K), the current strongly depends on the temperature, indicating the F-P emission mechanism. In contrast, in the low-temperature region (<200 K), the current shows weak temperature-dependent behavior due to the existence of the TAT mechanism.

By applying a large voltage on the TS, the abrupt formation of the Ag filament commonly induces the NDR effect across the TS. The measured I–V characteristics of the TS device in voltage-sweeping and current-sweeping modes are shown in Supplementary Fig. 4, indicating good performances for current-controlled (or S-type) NDR behavior. The NDR effect is further illustrated with a control sample (the TS connected with a resistor RL, Supplementary Fig. 5a) to study the distribution of the voltage drops during the on/off switching process of the TS. The NDR effect induces an abruptly decreased voltage drop (VTS − ΔVNDR) across the TS device, and consequently an amplified voltage drop (VL + ΔVNDR) across the series resistor (Supplementary Fig. 5a). The decrease in the voltage drop (−ΔVNDR) across the TS device can be extracted from the AC I–V characteristics (Supplementary Fig. 5b). According to the analysis of the control sample, it can be predicted that the NDR effect can induce a similar internal voltage amplification by replacing the resistor with a MoS2 FET.

Monitoring the internal amplification in the ATS-FET

The equivalent circuit diagram of the ATS-FET can be considered as two variable resistors connected in series, as shown in Fig. 4a. We try to disclose the working mechanism of the ATS-FET by using mathematical derivation and simulation with a semi-quantitative model34,35,36, and the simulation is illustrated in Supplementary Fig. 6 and Note 1. Taking the highly nonlinear I–V characteristics both of TS and baseline MoS2 FET into consideration, the node voltage (VD′) and the channel current (ID) can be solved as the intersections of output characteristics (ID–VD′, black lines) of the baseline MoS2 FET and the I–V curve (ID–VD′, red line) of TS device for different VG (see Supplementary Fig. 6c). Impressively, the simulated transfer curves extracted from Supplementary Fig. 6c are in good agreement with the experimental data, as depicted in Fig. 4b. From a physical viewpoint, the steep SS phenomenon is caused by the NDR effect of TS, and it can be understood by a concept of internal amplification gain (β = dVD′/dVG), which is defined to describe the relationship between VD′ and VG. According to the definition of subthreshold swing, SS can be written as

$${\mathrm{SS}} = \frac{{\partial V_{\mathrm{G}}}}{{\partial {\mathrm{log}}_{10}(I_{\mathrm{D}})}} = \frac{{\partial V_{\mathrm{G}}}}{{\partial V_{{\mathrm{D}{\prime}}}}} \times \frac{{\partial V_{{\mathrm{D}}{\prime}}}}{{\partial {\mathrm{log}}_{10}(I_{\mathrm{D}})}} = \frac{{\frac{{2.3kT}}{q}}}{{\frac{1}{n} + \frac{\beta }{{\exp \left( {\frac{{qV_{{\mathrm{D}}{\prime}}}}{{kT}}} \right) - 1}}}} \\ \approx \frac{{2.3kT}}{q} \times \frac{{\exp \left( {\frac{{qV_{{\mathrm{D}}{\prime}}}}{{kT}}} \right) - 1}}{\beta }\\ \approx 0\,{\mathrm{mV}}\,{\mathrm{decade}}^{ - 1},\,{\mathrm{when}}\,\beta \to \infty ,$$
(2)

where VD′ is the output voltage at the internal node D′, β is the internal amplification gain, n is the ideal factor, q is the basic electron charge, k is the Boltzmann constant, and T is the absolute temperature. Ideally, β is approximated to be infinity (i.e., ∆VG = 0) in the forward switching process, and thus SS will be approximated to be zero. However, due to the inevitable limitation by the accuracy of the testing instrument, the measured SS is >0 mV decade−1.

Fig. 4: ATS-FET with an internal amplification across the MoS2 channel.
figure 4

a The equivalent circuit schematic for the electrical measurements. VD′ and ID in red are the output parameters that need to be simultaneously recorded with the increase of the input VG (blue). b The experimental and simulated transfer (ID–VG) characteristics of the ATS-FET at VD = 0.3 V, indicating the simulated results are in good agreement with the experimental data. c The relations between the gate voltage (VG) and the internal voltage (VD′) for two VD schemes, including VD (= 0.2 V) < Vth-TS and VD (= 0.3 V) > Vth-TS. The inset is the linear scale from the data shown in the dashed grey rectangle. d, e VD′ changes as a function of ID for the two VD schemes. The NDR effect induces an amplification of VD′ across the MoS2 channel. f The relation between the average SS and the internal amplification gain (β = dVD/dVG). The inset indicates the sharp increase in VD′ with respect to the applied VG occurring in the region of the abrupt switching due to the NDR effect.

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To verify and further elaborate the internal amplification induced by the NDR, we monitor the output voltage at the internal node D′ (VD′) and analyze the voltammetry characteristics under current sweeping at two different VD. According to Vth-TS at ~0.26 V, we reasonably select two typical VD values (0.2 and 0.3 V, i.e., VD < Vth-TS and VD > Vth-TS, respectively). As shown in Fig. 4c, the abrupt increases in VD′ are clearly observed under both VD (VD < Vth-TS and VD > Vth-TS). As VG sweeps over VT, the redistribution of the effective potential drops on the MoS2 channel and the TS pulls up (increases) VD′ according to the drain voltage superposition effect. The VD′ drop on the MoS2 channel is amplified according to the NDR effect caused by the TS transition from the off-state to the on-state. Notably, the trends of the variation in VD′ are obviously distinguishable for different VD. VD′ at VD = 0.3 V shows an initial decrease with a subsequent increasing trend, while VD′ at VD = 0.2 V only shows an increase at the pull-up point. The pull-up VG value also shifts from −1.45 to −1.04 V as VD decreases from 0.3 to 0.2 V (inset of Fig. 4c). The underlying reason is explained by the voltammetry characteristics under current sweeping. For VD < Vth-TS (Fig. 4d), the TS is initially in the off-state at ID < 1 × 10−12 A μm−1. To maintain a low current in the series circuit, VD′ is therefore kept at a low level to minimize the current in the MoS2 FET. As ID increases, VD’ slightly increases. When ID is large enough (exceeding 1.6 × 10−12 A μm−1) to trigger the Ag filament formation in the TS, the resistance of the ATS-FET abruptly decreases with VD′ representing a steep increment (ΔVNDR). In contrast, VD′ is initially at a high level (0.263 V) for VD > Vth-TS (Fig. 4e). This may be because the supply voltage applied from the drain electrode is transiently imposed on the TS component and triggers the bridging of the Ag filament. The instantly increased device current results in a high VD′ at the beginning. Then, VD′ dramatically decreases with a subsequent slight increasing trend as ID sweeps. When ID exceeds 1.4 × 10−12 A μm−1, VD′ represents a steep increment (ΔVNDR). As the supply voltage in Fig. 4e is larger than that in Fig. 4d, the trigger current for the Ag filament would be relatively smaller, which is consistent with the results in Fig. 4c.

Furthermore, the internal amplification gain (β = dVD′/dVG) extracted from the abrupt switching region is ~22.2 for a low supply voltage at VD = 0.2 V (the inset of Fig. 4f), corresponding to the SSmin of 2.5 mV decade−1 and the SSaverage of 3.0 mV decade−1 over four decades of ID. As the internal amplification gain increases to 28.6, the SSaverage can be further reduced to a record of 1.3 mV decade−1 (Fig. 4f). The internal amplification gain is considered a significant parameter for designing steeper-slope FETs with lower energy consumption.

Based on the above discussion, the internal voltage amplification in the ATS-FET according to the voltage snapback (ΔVNDR) induced by the NDR effect is directly observed in this work. From the point of view of charge carriers, the free electrons transported in the ATS-FET are blocked by the barrier of the HfO2 electrolyte at the beginning (VG < VT). When VG reaches VT, ID increases in an abrupt fashion as a result of the Ag filament formation. Hence, the ATS-FET can in principle overcome the fundamental thermionic limitation of 60 mV decade−1 at room temperature.

Improved ATS-FET with much-reduced hysteresis and SS

Hysteresis is commonly undesirable for transistors in logic applications37. Technically, the achievable ATS-FET with small hysteresis (or hysteresis-free) and ultralow subthreshold characteristics is capable to offer the promising potential for ultralow-power logic circuit applications. However, the ATS-FET described above exhibits large hysteresis of 0.5–1 V (Fig. 2), which in essence needs to be greatly reduced. Some device optimization methods were used to reduce the hysteresis, such as annealing, and passivation, as previously reported37,38. To suppress the hysteresis of the ATS-FET, we also present an effective approach of device optimization by using the TS device with highly ordered Ag nanodots, which could contribute to shrinking the switching window (e.g., reducing the difference between Vth-TS and Vhold-TS) and improving Ihold-TS of TS. The newly presented TS device is fabricated with a HfO2 layer of 10 nm, an active electrode of highly ordered Ag nanodots, and followed by a process of rapid thermal annealing. It is critical to treat the atomic Ag layer with rapid thermal annealing to make the Ag atoms accumulate in a spherical shape, which is preferential for interstitial dopants in HfO2 to guarantee the volatile threshold-switching behavior even at a high-compliance current26. With the compliance currents (Icc) defined from 10 nA to 50 μA, the TS device shows abrupt and volatile threshold-switching behavior (Supplementary Fig. 7a). And the TS device also exhibits good stability in the cyclic test (Fig. 5a), achieving a reduced switching window of 0.12–0.24 V and small variations both in Vth-TS and Vhold-TS (Supplementary Fig. 7b). Furthermore, by connecting such TS device to a MoS2 FET, an improved ATS-FET is demonstrated to have much-reduced hysteresis and SS in a highly reproducible manner. The output characteristics (ID–VD) of the improved ATS-FET for different VG are shown in Supplementary Fig. 8. Fifty continuous cycles of the output characteristics (at VG = 2 V) in Fig. 5b can also verify the stable and repeatable operations of the ATS-FET. From the transfer characteristics in Fig. 5c, we can see that the improved ATS-FET shows reduced hysteresis of <0.15 V at different VD (ranging from 0.7 to 1.1 V). More impressively, the nearly negligible hysteresis (10 mV) is observed at the VD of 0.7 V, meanwhile the SSmin in forward and reverse sweeps are 2.6 and 12.5 mV decade−1, respectively (Supplementary Fig. 9). Further extracting key parameters, including SSforward, SSreverse, hysteresis, and VT, from three ATS-FETs are shown in Supplementary Fig. 10. The SSforward, SSreverse, and hysteresis are all independent of VD, while the VT shows the negative shift with the increase of VD (consistent with that of Fig. 2e).

Fig. 5: ATS-FET with much-reduced hysteresis and SS.
figure 5

a Typical I–V characteristics of the TS device based on highly ordered Ag nanodots in 30 cycles (Icc = 1 μA). The inset is a scanning electron microscopy (SEM) image of highly ordered Ag nanodots. b Output characteristics of the ATS-FET with the newly presented TS at a VG of 2 V in 50 cycles. 2D MoS2 channel (channel width: 2.2 μm; channel length: 1.8 μm). c Transfer characteristics (ID–VG) of the ATS-FET with the newly presented TS at a VD ranging from 0.7 to 1.1 V. d, e Statistical distributions of SSforward, SSreverse, and hysteresis (ΔV) of the ATS-FET in d cycle-to-cycle and e device-to-device variations. f Comparisons of SS–hysteresis (left) and SS–VD (right) in different steep-slope FETs, including the TFET8,39,40, NC-FET18,19,20,41,42,43,44,45,46, phase-FET21,47,48, Ag (or Cu) filament TS-FET22,28,49, resistive-switching FET (RS-FET)50,51, and DS-FET16, and our ATS-FET.

Full size image

Statistical analysis of ATS-FET and the device comparison

To more clearly illustrate the reproducibility of the ATS-FET, we conduct the statistical analysis for the average SS (including SSforward and SSreverse), and hysteresis in cycle-to-cycle (80 cycles) and device-to-device (50 devices) variations. Figure 5d shows the histograms and Gaussian fits for the SSforward, SSreverse, and hysteresis (4.8 and 4.6 mV decade−1; 0.14 V) of the ATS-FET in 80 cycles. Besides, the abrupt switching behavior of the ATS-FET is free of device-to-device deviations. The Gaussian distributions of the SSforward, SSreverse, and hysteresis are plotted in Fig. 5e, showing that the statistical SSforward, SSreverse, and hysteresis mainly distribute at 5.3 mV decade−1, 6.1 mV decade−1, and 0.19 V, respectively.

According to the above-described Eq. (1), VD and SS synergistically contribute to the evaluation of power consumption in the FET device. And hence, it is recommended that both VD and SS are preferred to be minimized, in addition to the suppressed hysteresis in transfer curves. Compared with previous reports of different categories of steep-slope transistors, including the TFET8,39,40, NC-FET18,19,20,41,42,43,44,45,46, phase-FET21,47,48, Ag (or Cu) filament TS-FET22,28,49, resistive-switching FET50,51, and DS-FET16, the relations of SS–hysteresis and SS–VD are both summarized and depicted in Fig. 5f. Capable of achieving steeper SS, reducing hysteresis, and scaling VD, the ATS-FETs show superior performances by using the atomic-scale geometry design with seamless integration of 2D FET and TS. Specifically, the achieved ATS-FET is nearly hysteresis free (10 mV), and has ultralow SSmin of <2.6 mV decade−1, which can satisfy the ITRS requirement for the SS of 25 mV decade−1 in the year of 2027 (ref. 1), and will be promising for future electronics with ultralow-power consuming.

Discussion

In summary, we successfully demonstrate an ATS-FET that significantly overcomes the fundamental thermionic limitation of the SS. This ATS-FET achieves extremely abrupt steepness in the turn on characteristics with a typical SSaverage of 4.5 mV decade−1 for more than five decades of ID at room temperature, and exhibits a significant off-state leakage current reduction to lower the power dissipation. According to the analysis of the I–V dynamics in the ATS-FET both in experiment and simulation, the NDR effect from the TS transition can contribute to inducing an internal VD′ amplification across the MoS2 channel, enabling the ATS-FET to break the “Boltzmann tyranny”.

As a benefit of the active materials in atomic scale (MoS2 and Ag filament), the proposed ATS-FET permits the critical scaling of the supply voltage and exhibits superior electrical performances, as well as greatly suppressed off-state current (Supplementary Fig. 11). In addition, the VD can be readily scaled by reducing the HfO2 thickness of TS, but the abrupt SS behavior can be maintained independent of the variable HfO2 thickness (Supplementary Fig. 12). The geometry design with seamless integration of FET and TS is promising for the potential monolithic integration of the ATS-FET in wafer scale. In this work, the sharp on/off switching properties with ultralow SS in the ATS-FET is originated from the threshold-switching behavior with an internal voltage amplifier, which is universal and applicable to other emerging 2D semiconducting materials related FETs and even different types of transistor devices. To meet the practical applications of logic circuits (also illustrated in the ITRS), the ATS-FETs are available with additional optimization from technical aspects, e.g., further decreasing off current, SS and hysteresis, and improving on/off ratio and reliability. Based on the simulated analysis (Supplementary Fig. 13 and Note 2), the ATS-FET with hysteresis-free behavior is possible to be achieved. Alternatively, in the case of the steep-slope FETs with hysteresis, they could be potentially used as memory devices52 or some specific logic circuits, e.g., Schmitt trigger53. Looking forward, the achievement of an ultralow-power steep-slope ATS-FET would coordinate with the scientific research of short-channel devices to efficiently reduce power dissipation, which is highly desirable for next-generation energy-efficient integrated circuits and ultralow-power electronics.

Methods

Device fabrication

The MoS2 nanoflakes were initially synthesized on highly p-doped rigid silicon (Si) substrates with a thermally grown 275 nm-thick SiO2 layer through CVD. Copolymer and polymethyl methacrylate was spin-coated at a speed of 4000 r.p.m. and then baked on a hot plate at 150 °C. Subsequently, the source–drain electrodes of the MoS2 transistor and the BEs of the TS were simultaneously defined with a standard EBL process, thermal evaporation of Cr/Au (10/40 nm), and lift-off process. A dielectric HfO2 layer of 5–20 nm was fabricated via ALD (PICOSUN/SUNALE R-200) approach. A pre-deposited seed layer of 1 nm of Al via thermal evaporation could help to obtain a high-quality dielectric film. The top gate electrodes of the MoS2 transistor were defined by a second EBL process and metallization of Cr/Au (10/40 nm). The top electrodes of the TS were defined by a third EBL process and metallization of Ag/Au (3/40 nm).

For the TS device with highly ordered Ag nanodots, an ultrathin AAO template was transferred onto the prepared layers after the step of ALD, and then patterned an Ag thin film (4 nm), and followed by a process of rapid thermal annealing (500 °C for 30 s) after the removal of AAO template. The bottom and top electrodes were fabricated following the above-described process. The as-fabricated TS device can be connected to a baseline FET (MoS2, monolayer or multilayer) to construct the ATS-FET.

Materials characterization and electrical measurements

The Raman spectrum was measured by a HORIBA/LabRAM HR Evolution spectrograph with a 532 nm excitation laser. The cross-sectional HAADF-STEM image and EDS line profiles of the TS were obtained by STEM (FEI Tecnai F20). The SEM image was captured by a FEI Nova 450. And the EBL was performed by the FEI Nova 450 with a Raith pattern generator. The electrical measurements of the transistors were performed on a probe station equipped with a semiconductor parameter analyzer (Agilent B1500A) in an ambient atmosphere at room temperature.