# Spiking neurons from tunable Gaussian heterojunction transistors

## Abstract

Spiking neural networks exploit spatiotemporal processing, spiking sparsity, and high interneuron bandwidth to maximize the energy efficiency of neuromorphic computing. While conventional silicon-based technology can be used in this context, the resulting neuron-synapse circuits require multiple transistors and complicated layouts that limit integration density. Here, we demonstrate unprecedented electrostatic control of dual-gated Gaussian heterojunction transistors for simplified spiking neuron implementation. These devices employ wafer-scale mixed-dimensional van der Waals heterojunctions consisting of chemical vapor deposited monolayer molybdenum disulfide and solution-processed semiconducting single-walled carbon nanotubes to emulate the spike-generating ion channels in biological neurons. Circuits based on these dual-gated Gaussian devices enable a variety of biological spiking responses including phasic spiking, delayed spiking, and tonic bursting. In addition to neuromorphic computing, the tunable Gaussian response has significant implications for a range of other applications including telecommunications, computer vision, and natural language processing.

## Introduction

The energy efficiency of spiking neural network (SNN)-based artificial intelligence (AI) can be enhanced by neuromorphic hardware, consisting of spiking neuron-synapse circuits. Since conventional silicon-based complementary metal-oxide-semiconductor (CMOS) transistors do not intrinsically emulate the time-dependent conductance of ion channels in biological neurons, complicated multi-transistor circuits are required for CMOS-based SNNs, thus limiting very-large-scale integration (VLSI) density1,2,3,4,5,6,7,8. For example, CMOS-based neuron circuits that achieve multiple spiking modes require at least 20 transistors that must adhere to stringent design constraints in addition to current-based addressing of several branches per neuron1,2,3. Alternatively, IBM TrueNorth9 and SpiNNaker10 utilize digital processing of spiking neurons that is seemingly more conducive to VLSI design. However, due to limited chip area, digital cores must multiplex several spiking neurons, which compromises the parallelism of a biological spiking network.

To address the limitations of silicon-based SNN circuits, alternative materials are being explored that allow the encoding of neuromorphic functionality directly at the device level. While memristors11, memtransistors12,13, domain-wall memories14, metal-insulator-transition (MIT) devices15, multi-gated transistors16,17, and Gaussian synapses18 have been developed for scalable implementation of synaptic functions, approaches for realizing spiking neurons are relatively lacking. For example, neuristors based on MIT devices have been reported, but this design suffers from low gain and limited output swing19,20. A diffusive memristor coupled with a capacitor has further been shown to exhibit a spiked response, but this demonstration lacks the biophysical characteristics of a neuron spike and runtime neural dynamic adaptation21. Leaky integrate and fire spiking neurons have also been achieved by combining a memristor with CMOS transistors22, but the number of necessary circuit elements remains large. In addition, leaky integrate and fire spiking neurons have been proposed using the magneto-electric effect23, but this implementation dissipates energy continuously, resulting in poor energy efficiency. A spiking neuron exploiting the abrupt state transition and hysteresis in ferroelectric field-effect transistors has also been shown24, but this approach is limited to spike frequency adaptation, whereas biological neurons exhibit a variety of other spiking behaviors (e.g., phasic and tonic spiking or bursting)25. Ferroelectricity is also highly susceptible to temperature variations26, which creates instabilities in ambient operating conditions. Finally, photonic implementations of spiking neurons have recently been discussed based on phase-changing materials27. While this strategy is promising for high speed and high bandwidth neural processing, the optical spiking neuron does not exhibit biophysical characteristics.

In contrast, devices fabricated from low-dimensional materials take advantage of weak electrostatic screening to enable gate-tunable electronic properties that hold promise for spiking neurons. In particular, the incorporation of atomically thin semiconducting materials into gate-tunable p-n heterojunctions results in an antiambipolar response with Gaussian transfer curves28,29,30,31,32,33,34,35,36,37,38. While this behavior has been used for analog signal processing37,39, logic devices30,35,38, and photodetectors28,32,34, the single-gated geometries used previously do not provide sufficient control over the Gaussian current-voltage characteristic to enable efficient neuromorphic functionality. Here, we report the scalable fabrication of dual-gated Gaussian heterojunction transistors (GHeTs) based on mixed-dimensional van der Waals heterojunctions40 consisting of monolayer molybdenum disulfide (MoS2) grown via chemical vapor deposition (CVD) and solution-processed semiconducting single-walled carbon nanotubes (CNTs). The dual-gated geometry provides full tunability of the Gaussian transfer curve, thereby enabling simplified circuits that exhibit a variety of neuronal spiking responses including phasic spiking, delayed spiking, and tonic bursting that hold promise for neuromorphic computing and related AI technologies.

## Results

### Device fabrication

Monolayer MoS2 was specifically selected as the n-type material for our p-n heterojunction because of its atomically thin nature, processing stability, and large-area compatibility via CVD. Solution-processed CNTs were the ideal candidate for the second semiconducting material because of their p-type/ambipolar characteristics, ability to conform over arbitrary nonplanar surfaces, and desired band alignment with MoS228,41. Therefore, a recently reported self-alignment method37 was adapted to large-area photolithography to enable the fabrication of dual-gated GHeTs from MoS2 and CNTs. As shown in Fig. 1a, the undercut profile in developed negative photoresist combined with directional metal evaporation and conformal atomic layer deposition (ALD) of a dielectric oxide results in an encapsulated metal electrode with a self-aligned dielectric extension. Atomic force microscopy (AFM) is used to evaluate both the quality and length of the dielectric extension as shown in Fig. 1b. The height profile in Fig. 1c corresponding to the dashed line in Fig. 1b shows a sub-exposure-wavelength dielectric extension of ~300 nm. The steps in the height profile correspond to the ALD Al2O3 (~35 nm) and metal electrode (~50 nm).

Optical micrographs of the fabrication process are shown in Fig. 1d. (i) CVD-grown monolayer MoS242 is transferred onto a self-aligned local bottom gate (BG, outlined in black) and patterned (outlined in pink) using reactive ion etching (RIE). (ii) A self-aligned bottom contact (BC) is then fabricated on MoS2 followed by an additional patterning and growth of a thin Al2O3 dielectric (outlined in green, distinct from the self-aligned Al2O3 dielectric) on part of the MoS2 to act as an etch mask for subsequent RIE processing. (iii) The metal top contacts (TC) are then deposited directly on top of the BC followed by transfer of a network of semiconducting CNTs43,44 over the entire substrate, after which RIE is used to define the CNT network (purple lines) with deterministic overlap of the MoS2 region. (iv) Finally, an Al2O3 dielectric is grown via ALD over the entire substrate, and local top gates are patterned over the junction region. Three-dimensional renderings of the fabrication process shown in Fig. 1e correspond to: (i) MoS2 is transferred onto the bottom gate (BG) and etched; (ii) Bottom contact (BC) is deposited on MoS2 (dielectric extension in dashed circle); (iii) Top contact (TC) is deposited on the BC followed by semiconducting single-walled carbon nanotube (CNT) network transfer and etching; (iv) ALD Al2O3 is used to cover the entire device structure, after which the top gate (TG) is deposited and patterned. Note, the ALD etch mask outlined in green in Fig. 1d (ii) is intentionally not shown in Fig. 1e to better illustrate the self-aligned and semi-vertical device architecture but is shown in Supplementary Fig. 1. In this dual-gated semi-vertical device, the multiple current paths through the semiconducting materials increase the versatility of device operation (see Supplementary Fig. 2).

### Electrical characterization

Dual-gated control transistors from the constituent semiconductors were characterized to confirm the desired individual material properties. Transfer and output measurements of the 50 µm MoS2 and CNT dual-gated devices are shown in Supplementary Fig. 3 and Supplementary Fig. 4. The MoS2 devices exhibit n-type behavior while the CNT devices exhibit ambipolar behavior. Both materials show dual-gate tunability of threshold voltages, indicating that the heterojunction should also exhibit dual-gate-tunable diode properties and the desired antiambipolar response.

The GHeTs were first characterized by biasing the bottom and top gates independently with the source voltage (VS) grounded. Figure 2a shows selected output curves corresponding to different top gate voltages (VTG) for VBG = 0 V. The top gate modulates the output response of the GHeT from a rectifying diode at VTG = –6 V (orange) to an inverted polarity rectifying diode at VTG = 6 V (purple) due to band-to-band tunneling between the MoS2 and CNTs as has been previously reported37,41,45. Supplementary Fig. 5 shows additional sets of output curves corresponding to VBG = 6 V and –6 V. To further characterize the GHeT rectifying behavior, Fig. 2b shows the rectification ratio (defined here as ID at VD = 1 V divided by ID at VD = –1 V) extracted from the corresponding transfer curves. The top and bottom gates are both able to modulate the diode rectification ratio. For VTG > 0 V, the rectification ratio can be tuned by over two orders of magnitude, including reversal of the rectification direction (i.e., rectification ratio < 1) for VTG > 2 V. For VTG < 0, modulation by the bottom gate is more evident with tunability of the rectification ratio by over two orders of magnitude at VTG = –6 V. The rectification ratios for VBG from 6 V to –6 V with 1 V increments are shown in Supplementary Fig. 6. The GHeT transfer curve as a function of VTG for independent biasing where VBG is held constant throughout the measurement is shown in Fig. 2c. As the VBG setpoint is varied, the peak position of the antiambipolar response can be tuned from VTG = 2 V to VTG = –3 V (see Supplementary Fig. 7 for additional curves). Note that the behavior to the right of the peak is correlated to electrostatic control of the CNT film while the behavior to the left of the peak is correlated to electrostatic control of the MoS2. Thus, the top gate can fully modulate the CNTs at all VBG, as evidenced by a distinct OFF state at VTG ~4 V in Fig. 2c and the negative transconductance (gm) from the peak voltage to VTG = 4 V shown in Supplementary Fig. 8. Due to low dielectric screening by CNT networks45, the top gate can partially modulate the n-type MoS2 as evidenced by positive gm in Supplementary Fig. 8 for VBG < 0 V and negative VTG. For VBG > 0, the negative bias field from the top gate through the CNT network is not sufficiently strong to fully deplete the MoS2 that has been driven into accumulation by the bottom gate, resulting in loss of dual-gate control for the left side of the antiambipolar response. The corresponding GHeT transfer curve and plot of gm as a function of VBG (see Supplementary Fig. 9) indicate that the bottom gate can fully modulate MoS2 for all biases but is unable to fully modulate the CNT network completely at any bias due to stronger dielectric screening of the bottom gate bias by the continuous MoS2 monolayer. The loss of dual-gate control for independent biasing indicates that the current flows primarily through the overlap region of the GHeT (see Supplementary Fig. 2).

Alternatively, the GHeT can be operated in a dependent biasing scheme to combine the modulation of the CNTs by the top gate and the modulation of the MoS2 by the bottom gate, resulting in enhanced electrostatic control of the device response. Since the Al2O3 dielectric layer for both gates is ~35 nm thick, the fields from the top gate and the bottom gate are equivalent for the same bias. Figure 3a shows the transfer response of the GHeT when VBG and VTG are changed together throughout the measurement with a constant offset ranging from –3 V to 3 V while VS is grounded. Rectification ratios extracted from the corresponding transfer curves for dependent gate operation can be tuned by over three orders of magnitude as shown in Supplementary Fig. 10. The Gaussian fits of the antiambipolar response (see Supplementary Fig. 11) illustrate that changing the offset between the gates from –3 V to 3 V can shift the peak position from VTG = –3 V to 0.5 V without a loss of symmetry in the antiambipolar response and without a substantial loss in the peak current. As shown in Supplementary Fig. 12 for VTG – VBG = 0 V, 85% of working devices fabricated over an 0.5 × 0.5 cm area exhibit a Gaussian transfer response. The average peak position of these 14 devices was −0.42 V ± 0.55 V, and the average full-width-half-maximum (FWHM) was 2.92 V ± 0.48 V.

Combining VD modulation with dual-gate tunability results in further control over the peak height, position, and FWHM of the GHeT antiambipolar response. Figure 3b shows that for dependent operation of the gates at VTG – VBG = 0 V, variable VD modulates the peak height while maintaining the peak position with minimal change in FWHM. On the other hand, by changing the dependent gating offset VTG – VBG from 3 V to –3 V and VD from 0.8 V to 0.4 V, the peak position can be tuned while maintaining the peak height and FWHM as shown in Fig. 3c. Finally, Fig. 3d shows that the peak height and peak position can be maintained while the FWHM is varied by switching between dependent and independent gate operation. Independent modulation of peak height, position, and FWHM confirms that the mixed-dimensional MoS2-CNT GHeT possesses a fully tunable Gaussian transfer response in a single heterojunction device.

### Spiking neuron demonstration

The ability to tune the antiambipolar response of the GHeT enables a variety of applications including Hodgkin-Huxley (HH) spiking neurons46. A circuit-level representation of the HH model for biological neurons is shown in Fig. 4a where Na+ ions injected into the neuron lead to spike generation in the membrane potential, Vm, while released K+ ions reset Vm. Capacitance, Cm, and leakage conductance, gL, represent the bilayer of the neuron membrane. The conductance of the Na+ (K+) ions channels is modeled by gNa (gK). Figure 4b, c show the temporal evolution of gNa and gK as described by the HH model. The activation of the K+ ion channel is delayed and gK increases with increasing Vm. The time-dependent evolution of gK can be represented by the delayed turn-on of an n-channel metal-oxide semiconductor (NMOS) transistor where a voltage, Vm, is applied to the gate through a resistive-capacitive load. Meanwhile, the behavior of the Na+ ion channel is more complex and requires a peaked time-dependent response, where the peak conductance increases but the delay to reach the peak conductance is reduced with increasing Vm. To efficiently capture the more complex transient behavior of gNa, the dual-gated GHeT antiambipolar response is exploited as described in Supplementary Fig. 13.

Figure 4d details the full circuit used for the experimental spiking neuron demonstration based on a single MoS2-CNT GHeT device, n-type field-effect transistors (T1 and T2), and a few passive elements (R1, R2, C1, and C2). Voltage sources, V3 and V5, were connected at the source electrodes of T1 and T2 to allow threshold voltage programmability for the field-effect transistors. The GHeT and circuit components T1-R1-C1 emulate gNa, while circuit components T2-R2-C2 emulate gK (see Supplementary Fig. 14). Before application of a synaptic current, the GHeT is in an OFF state due to a large positive gate bias (~V1), corresponding to position 1 in Supplementary Fig. 15 and Supplementary Table 1. For sufficiently high Isyn, C1 and C2 integrate Isyn and the OFF current of the GHeT (IOFF). In other words, the voltage at the GHeT source, Vm, increases with time proportional to Isyn + IOFF (position 2 in Supplementary Fig. 15). As Vm exceeds the threshold voltage of T1, the voltage applied to the gates drops quickly from V1 to near 0 V, resulting in a negative relative gate voltage, VTG – Vm. This condition drives the GHeT from its OFF state to the peak ON state, going through the region of negative transconductance. The increased current, IPEAK, causes a sharp increase in the slope of Vm in proportion to Isyn + IPEAK. As Vm continues to increase, VTG – Vm continues to decrease, thereby accessing the left side of the Gaussian response and resulting in a decreasing current and positive gm (position 3 in Supplementary Fig. 15). At this point, Vm has reached the threshold voltage of T2, and the delayed gK channel is able to dominate and reset Vm below the threshold voltage of T1 (position 4 in Supplementary Fig. 15). This spiking and resetting behavior, experimentally shown in Fig. 4e, will continue as long as Isyn + IOFF is sufficiently high.

Figure 4f shows that simulations performed on the Cadence Virtuoso platform using the Spectre simulator for a prototypical GHeT (brown dashed) agree with the experimental spiking response of the circuit (blue) with a temporal FWHM that is ~200 ms. The energy consumption of this GHeT-based spiking neuron circuit is ~250 nJ per spike, which can be reduced by orders of magnitude by decreasing the channel width, circuit capacitances (C1 and C2), and gate dielectric thickness of the GHeT as well as by custom design and on-chip integration of T1 and T2 transistors. These modifications will also substantially increase the operating speed of the spiking neuron circuit. The measured gate voltage and current from the GHeT during the full 30 sec of constant spiking are shown in Supplementary Fig. 16, thereby confirming that the GHeT is responsible for the spiking behavior. In addition to capacitance values and Isyn affecting the spiking response (Supplementary Fig. 17), experimental results in Supplementary Fig. 18 and simulation results in Supplementary Fig. 19 show that the offset between the gates can be used to further control the spiking response. In particular, constant spiking only occurs when the circuit operating region (4 V to –1 V) contains both negative and positive gm values near IPEAK of the Gaussian transfer response, demonstrating that the antiambipolar response is required to correctly mimic gNa in the HH model of a spiking neuron.

Additional simulations show that multiple biological spiking neuron responses can be achieved with GHeT-based circuits by modifications to how the GHeT is biased by the top and bottom gates. Simulations using the experimental circuit (see Supplementary Fig. 20), where the GHeT experiences dependent biasing, show that constant spiking occurs for a constant Isyn of 40 nA (Fig. 5a), whereas, if Isyn increases linearly from 0 to 80 nA, then the spiking frequency increases (Fig. 5b). A slight modification to the GHeT-based circuit that allows for independent gate biasing (see Supplementary Fig. 21) enables additional functionality such as spike latency, integrator, and phasic spiking responses. For example, Fig. 5c illustrates spike latency where a single neuron spike occurs after a 0.4 sec Isyn pulse of 50 nA. The integrator response in Fig. 5d shows that a neuron spike occurs when the 0.4 sec Isyn pulses of 35 nA are within 0.3 sec of each other (first set of pulses) but does not occur when the pulses are 1.6 sec apart (second set of pulses). In this circuit, a constant Isyn of 40 nA results in a single neuron spike, mimicking phasic spiking (Fig. 5e). Further modification of the circuit to connect the top and bottom gates through an inverter, diode, resistor, and capacitor (see Supplementary Fig. 22) results in phasic bursting for a constant Isyn of 40 nA (Fig. 5f). Incorporating a Schmitt Trigger and two additional transistors (see Supplementary Fig. 23 and Supplementary Fig. 24) results in tonic bursting (Fig. 5g) and dampened tonic bursting (Fig. 5h) for a constant Isyn of 40 nA. With incremental modifications to the original circuit, these simulations highlight the versatility of GHeT-enabled circuits to have runtime programmability of spiking threshold and spiking modes that are desirable for spiking neuron applications.

## Discussion

By creating a device with intrinsic neuronal responses, it is possible to significantly simplify spiking neuron implementations. In particular, the use of mixed-dimensional MoS2-CNT van der Waals heterostructures and a semi-vertical, dual-gated geometry results in a smaller device footprint with superior electrostatic control compared to other antiambipolar demonstrations. Not only is the fundamental behavior of the Na+ ion channel of a biological neuron captured by the GHeT in a simple circuit, but by exploiting the dual-gated programmability both through independent and dependent biasing, it is possible to achieve eight different biological neuron responses, five of which are achieved using a single GHeT, two transistors, two capacitors, and two resistors. Additionally, the fabrication process for GHeT-based spiking neurons is compatible with previous demonstrations of monolayer MoS2 memtransistor-based synapses12,13, enabling scalable implementations of biomimetic neuromorphic platforms.

More broadly, since CMOS transistors cannot natively mimic the Gaussian response demonstrated here, CMOS-based digital designs implement Gaussian functions with complex circuits and look-up tables while analog CMOS circuits suffer from limited programmability and high bias current47. Thus, the tunable GHeT Gaussian antiambipolar response is applicable to hardware-level implementations of spiking neurons as well as other artificial learning paradigms. For example, several natural language processing algorithms require Gaussian functions to build statistical distributions of speech and phoneme characteristics48. Similarly, neural networks used in machine learning often account for uncertainties in Bayesian inference using weight densities represented by a mixture of Gaussian functions49. GHeTs are also likely to be useful for highly efficient computer vision algorithms in artificial neural networks that rely on the tunability and intrinsic filtering ability of a Gaussian response50. Given that the complexity of CMOS-based implementations is a bottleneck for many learning models, the simplification of the Gaussian response to a single GHeT circuit element is expected to accelerate the realization of AI-based technologies.

## Methods

### Fabrication of Gaussian heterojunction transistors

All photolithography steps were performed on a Suss MABA6 Mask Aligner with an exposure wavelength of 365 nm and an exposure intensity of 9 mW cm-2 using resist developer RD6 (Futurrex, Inc.) and liftoff for 1 h in Remover PG (MicroChem) at 70 °C unless specified otherwise. The devices were fabricated on undoped Si/300 nm SiO2 substrates. Following the self-aligned process described in Fig. 1a using negative resist (NR9-1000PY, Futurrex), the bottom gate metal of 10 nm Cr/10 nm Au/4 nm Al was thermally evaporated (Kurt J. Lesker, Nano 38) followed by atomic layer deposition (ALD, Cambridge Nanotech ALD S100) of ~35 nm of Al2O3 grown at 100 °C. The 4 nm of Al oxidizes readily in ambient conditions and acts as a seeding layer for the growth of the ALD dielectric on the Au metal surface. A monolayer of MoS2 grown on a sapphire substrate using solid-precursor CVD was then transferred onto the local bottom gate structure using a wet polycarbonate-assisted transfer process. The MoS2 monolayer was patterned using a positive resist bilayer of polymethylglutarimide (PMGI, MicroChem) and S1813 (MicroChem), and etched by reactive ion etching (RIE, Samco RIE-10NR) using 50 sccm Ar at 13.3 Pa and 50 W for 20 sec. The PMGI/S1813 bilayer was used to minimize S1813 resist residue on the remaining MoS2 monolayer but required overnight liftoff. After repeating the self-aligned process, the encapsulated bottom contacts (4 nm Ti/40 nm Au/4 nm Al, 35 nm Al2O3) were patterned and deposited on the etched MoS2 monolayer. The portion of the final MoS2 film that is designed not to be covered by the film of semiconducting single-walled carbon nanotubes (CNTs) was protected from further etching by a patterned region of ~5 nm Al2O3. The top contacts (10 nm Cr/70 nm Au) were deposited on top of the encapsulated bottom contacts in preparation for the CNT film. The optimized concentration (~10 tubes per µm transferred) of solution-processed P2 single-walled semiconducting CNTs with 99% semiconducting purity obtained via density gradient ultracentrifugation was vacuum filtered onto a cellulose membrane (VMWP, 0.05 µm pore size, Millipore Sigma) and acetone-bath transferred overnight on the entire substrate. The film of CNT was patterned using S1813 and etched by RIE using 20 sccm O2 at 26.5 Pa and 100 W for 15 sec. The substrate was rinsed briefly (<30 sec) with acetone to remove all but a few nanometers of the residual S1813 film. The S1813 residue acts as an encapsulant to minimize doping of the CNTs from the top gate dielectric ALD of ~35 nm Al2O3 that was deposited over the entire substrate. The top gate metal (10 nm Cr/60 nm Au) was then patterned and deposited to overlap the entire device region.

### Materials characterization and electrical measurements

The thicknesses of the different device layers were characterized by atomic force microscopy (AFM) in ambient using an Asylum Cypher AFM. All electrical measurements were performed in ambient on a Cascade MicroTech semi-automated probe system using a Keithley 4200 semiconductor analyzer.

### Statistics

Devices were fabricated over an area of 0.5 × 0.5 cm with 85% yield. The IDVTG antiambipolar response for 14 distinct devices is shown in Supplementary Fig. 12b. Values for the histograms in Supplementary Fig. 12c were obtained by fitting the raw data to

$$y = y_0 + Ae^{ - 0.5\left( {\frac{{x - x_{\mathrm{c}}}}{w}} \right)^2}$$
(1)

where xc is the peak position and w is the FWHM. The average peak position was -0.42 V ± 0.55 V, and the average FWHM was 2.92 V ± 0.48 V. Source data underlying Supplementary Fig. 12c are provided as a Source Data file. Note, the data presented in Figs 2 and 3 correspond to the same device.

### Spiking neuron demonstration

The experimental demonstration of a constant spiking neuron was achieved from the circuit in Fig. 4d using V1 = 4 V, V2 = 1 V, V3 = –230 mV, V4 = 3 V, V5 = –280 mV, R1 = 100 kΩ, R2 = 1 MΩ, C1 = 440 nF, C2 = 220 nF, Isyn = 1 nA and commercial field-effect transistors, BSR802N L6327 (Mouser). Circuits simulations were performed using the Cadence Virtuoso platform using Spectre simulator with a look-up table-based Verilog-A model developed for a prototypical MoS2-CNT GHeT as well as for the commercial transistors based on experimental charge transport characteristics. Other passive and active elements were obtained from the Analog library available within Virtuoso. Supplementary Table 2 contains the parameters used in the simulations of the GHeT-based circuits used in Figs 4 and 5.

## Data availability

The data that supports the findings of this study are available within the paper and its supplementary files or available from the corresponding author upon request. The source data underlying Supplementary Fig. 12c are provided as a Source Data file.

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## Acknowledgements

This research was supported by the 2-DARE program (NSF EFRI-1433510) and the Materials Research Science and Engineering Center (MRSEC) of Northwestern University (NSF DMR-1720139). CVD growth of MoS2 was supported by the National Institute of Standards and Technology (NIST CHiMaD 70NANB14H012). Charge transport instrumentation was funded by an ONR DURIP grant (ONR N00014-16-1-3179). H.B acknowledges support from the NSERC Postgraduate Scholarship-Doctoral Program. M.E.B., W.A.G.R., and H.B. acknowledge support from the National Science Foundation Graduate Research Fellowship Program. This work utilized the Northwestern University Micro/Nano Fabrication Facility (NUFAB), which is partially supported by Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205), the Materials Research Science and Engineering Center (DMR-1720139), the State of Illinois, and Northwestern University.

## Author information

M.E.B. and M.C.H. conceived the device structure and designed all the experiments. A.T., M.E.B., and V.K.S. conceived the circuit for the spiking neuron. A.S. and A.T. performed circuit simulations. V.K.S., M.E.B., and W.A.G.R. designed the photomask. M.E.B. optimized the fabrication process, measured and analyzed all the device data, and implemented the circuit experimentally. S.G. assisted with device fabrication. W.A.G.R. assisted with CNT processing. W.A.G.R. and H.Y. contributed to the experimental circuit demonstration. H.B. and K.S. conducted growth and transfer of MoS2. All authors wrote the manuscript and discussed the results at all stages.

Correspondence to Mark C. Hersam.

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### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks Qing Wan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Beck, M.E., Shylendra, A., Sangwan, V.K. et al. Spiking neurons from tunable Gaussian heterojunction transistors. Nat Commun 11, 1565 (2020). https://doi.org/10.1038/s41467-020-15378-7