Three-terminal device (source, drain and gate) of flash memory1 increases circuit complexity and requires long gate channel length which limits integration density. Furthermore, the presence of a thick and rigid blocking oxide layer leads to high power consumption2,3 and restricts scaling up in the vertical direction, and limits the flexibility and stretchability of the devices for applications4,5. Two-terminal memory devices have been proposed to overcome such limitations: Phase-change random-access memory (PRAM)6,7,8 and resistive random-access memory (RRAM)2,9,10. Due to the absence of gate electrode, two-terminal memories can have extremely short channel length to achieve high memory integration. Furthermore, two-terminal memories can behave as memristor9 that have potential for applications of semi-non-volatile memories and learning networks that require a synapse-like function9,10. However, the biggest challenge for two-terminal memories are low reliability and high leakage off-current because of thermally activated hopping transport through trap states (Poole–Frenkel conduction)11,12,13,14,15, resulting in low on/off ratio and off-state power consumption.

Meanwhile, van der Waals heterostructures based on two-dimensional (2D) materials such as graphene, semiconducting transition metal dichalcogenides and insulating hexagonal boron nitride (h-BN) exhibit peculiar electronic16,17,18,19,20 and optoelectronic properties21,22,23,24,25, and furthermore can provide transparency, flexibility and stretchability19,21,23,26,27. The h-BN layer, with a large bandgap of 5.97 eV, is used as a high-quality insulator20,28 and tunnelling barrier17,24.

Here, we propose a two-terminal tunnelling random access memory (TRAM) using a vertically stacked MoS2/h-BN/Gr heterostructure. With appropriate thickness of h-BN, charges can tunnel through h-BN layer and be stored in the floating gate by large potential difference between drain and floating gate, while the stored charges in graphene cannot tunnel out to source electrode due to the absence of potential difference, thus allowing for charge storage in the floating gate. Our TRAM demonstrates an ultralow off-state current (10−14 A), leading to ultimately high on/off ratio (over 109). In addition, we do not use gate electrode and thick, rigid blocking insulator and instead use an ultrathin h-BN (<10 nm) with high Young’s modulus and breaking strength, which is certainly advantageous for high flexibility, stretchability and scalability in the vertical direction. Our device performs excellent stretchability with no significant electrical performance degradation up to 19% strain, which will be used for wearable and body-attachable electronics in the near future.


Device structure and memory characteristic of TRAM

Figure 1a demonstrates the structure of TRAM with MoS2 on the top, h-BN in the middle and graphene at the bottom. Two Cr/Au electrodes were contacted with the monolayer MoS2 channel for source and drain (Supplementary Figs 1 and 2). Figure 1b shows the band diagrams of drain/h-BN/graphene in programme (Vds≤−6 V) and erase states (Vds≥6 V). The atomistic model (left side Fig. 1c) and cross-sectional bright-field scanning transmission electron microscope image show that the fabricated heterostructure is atomically flat and free from interlayer contaminants (right side Fig. 1c). Each layer was identified by energy-dispersive X-ray spectroscopy. Elements of Mo and S for MoS2, N for h-BN and C for graphene were observed in each stacking position.

Figure 1: Device structure and memory characteristics of the TRAM.
figure 1

(a) Schematic of the two-terminal TRAM with monolayer MoS2 as a semiconducting channel at the top, h-BN as a tunnelling insulator in the middle and monolayer graphene as a floating gate, charge tunnelling between drain and graphene is shown by red arrow. (b) Band diagrams of drain (D)/h-BN/graphene (Gr), the dashed line arrows indicate the tunnelling direction of electrons and holes. Electrons are tunnelled from the drain to graphene at the Vds≤−6 V (Programme) and holes are tunnelled from h-BN to graphene at Vds≥6 V (Erase) states. (c) Atomistic schematic for the TRAM heterostructure of the monolayer MoS2/multilayer h-BN/monolayer graphene (left side) and cross-sectional bright-field scanning transmission electron microscope image and energy-dispersive X-ray spectroscopy elemental mapping of the TRAM heterostructure with 10-nm h-BN (right side). Scale bar is 5 nm. (d) Typical IV curve of the TRAM with 5.5-nm thick h-BN. The current sweep by sweeping Vds is shown as a dashed line. The current sweep can be separated into four stages: (i) Programme, (ii) Read, (iii) Erase and (iv) Read. Channel length and channel width of the device are 4 and 2 μm, respectively. (e) Repeated Erase/Read/Programme/Read sequence with a drain voltage of +6 V/+0.1 V/−6 V/+0.1 V, respectively. The pulse width was 0.01 s.

Charging and discharging processes in the graphene are conducted by controlling drain voltage (Fig. 1d), well distinguished from conventional floating gate memory (CFGM) that operates by the gate voltage with three terminals (Supplementary Fig. 3)29,30. For a voltage sweep from 0 to ±8 V (sweeping directions indicated by the arrow in Fig. 1d), the resistivity of MoS2 changes from high-resistance (OFF) state to low-resistance (ON) state and back to OFF state, yielding a current hysteresis. This hysteresis behaviour is reproducible during the subsequent series of voltage sweeps. Figure 1e demonstrates a series of memory cycles using the repeated voltage pulses of −6, 0.1, 6 and 0.1 V as programing (i), reading (ii), erasing (iii) and reading (iv) operations, respectively. A non-destructive read state with an ON/OFF ratio over 104 was achieved, which can also be inferred from the current hysteresis loop shown in Fig. 1d. To ensure the hysteresis of our devices originating from charging in graphene and the real current flows through MoS2 channel, graphene was grounded and no hysteresis was observed (Supplementary Fig. 4).

Proposed operation principle of TRAM

Such high TRAM performance originates from the asymmetric potential drop built in two contacts between source/floating gate and drain/floating. Figure 2a–c shows the schematic band diagrams (Fig. 2a), charge tunnelling (Fig. 2b), and the simulated potential profile (Fig. 2c) in the programme states, read in off-state (Fig. 2d–f), erase (Fig. 2g–i), and read in on-state (Fig. 2j–l), corresponding to the respective i, ii, iii and iv stages in Fig. 1d,e. The geometry and parameters of the simulation model are shown and discussed in Supplementary Note 1, Supplementary Figs 5 and 6 and Supplementary Tables 1 and 2. Typical channel length of our device is about 2 μm. In fact, we performed two simulations for two channel lengths: 30 nm and 2 μm. The potential distributions in both channel lengths were almost similar to each other (Supplementary Fig. 7). Therefore, we used the simulation model with the channel length of 30 nm for better eye capturing. In the electrostatic potential simulation of the programme (bottom panel of Fig. 2a), the large potential difference and the corresponding large electric field were constructed between drain and graphene, whereas the negligible potential difference and the corresponding low electric field (Supplementary Fig. 8a) were exhibited between source and graphene. A large potential drop between the graphene and drain by −6 V drain bias enables electron tunnelling from drain to graphene, and electrons are spread out through the entire graphene (Fig. 2b). Meanwhile, electrons in graphene cannot tunnel out to MoS2 or source because of the small potential drop at the contact (Fig. 2c). The asymmetric potential drop originates from the highly resistive MoS2 that competes with tunnelling probability through the thin h-BN film, which is a key concept to store charges in graphene.

Figure 2: Numerical simulation of potential distribution in TRAM and the schematic band diagram.
figure 2

Schematic illustration of band diagram, memory operation and simulated electrostatic potential at the states of Programme (ac), Read in Programme state (df), Erase (gi) and Read in Erase state (jl). The dashed line arrows indicate the tunnelling direction of electrons and holes from drain into graphene. The solid line arrows indicate the spreading of electrons and holes at graphene after tunnelling.

The reading process of the programme state is shown in Fig. 2d–f. Because the trapped electrons in the programme state charge the graphene, the graphene potential could be dropped to maintain −2.27 V (Supplementary Note 1). The small potential difference (Fig. 2f) and the corresponding low electric field (Supplementary Fig. 8b) are shown at both the drain–graphene and source–graphene junctions, which are low enough to prevent leakage of the trapped electrons in the floating gate. Meanwhile, the trapped electrons generate a negative electric field and deplete the majority electron carriers in the MoS2, resulting in a highly resistive state. Consequently, the MoS2 performs the programme state (off-state). At +6 V, drain bias (Fig. 2g–i and Supplementary Fig. 8c) holes are tunnelled from drain and trapped in graphene, generating a highly conductive inversion channel in the MoS2 (Fig. 2j–l and Supplementary Fig. 8d), performing an erase state (on-state). Consequently, a large electrical hysteresis is formed by tunnelling and trapping electrons and holes in graphene by a simple drain-bias sweep, fundamental difference from the three-terminals flash memory CFGM (Supplementary Note 2 and Supplementary Fig. 9). By calculating carrier concentrations in graphene and MoS2 (Supplementary Note 3, Supplementary Fig. 10), the carrier concentration of graphene floating gate at Read in Erase state are 1.2 × 1013 cm−2, higher than that of undoped graphene. MoS2 channel shows a carrier concentration of 1.0 × 1013 cm−2, higher than typical carrier density of MoS2 channel, congruent with higher source–drain current in our device.

The h-BN layer thickness dependence

To investigate the thickness dependence of h-BN film on tunnelling current, we fabricated TRAM devices with various h-BN thicknesses from 3.5 to 12 nm. The tunnelling threshold voltage increased in proportion to the h-BN thickness (Fig. 3a). The thin h-BN (3.5 nm) device exhibits a measurable low-bias conductance, which is attributed to direct tunnelling through the thin h-BN film. Meanwhile, the devices with 5.5, 7.5 and 10 nm thick h-BN film show the threshold voltage at ±2, ±5 and ±7 V, respectively, at a current limit of 10−13 A (Supplementary Fig. 11). Over the threshold voltage regime, the tunnelling current becomes nonlinear, which is attributed to Fowler–Nordheim tunnelling31. The tunnelling behaviour depending on the h-BN thickness largely influences charge trapping in graphene, as illustrated in Fig. 3b.

Figure 3: Tunnelling current through h-BN layer.
figure 3

(a) Tunnelling current characteristics between drain electrode and graphene floating gate for various h-BN thicknesses. (bd) Schematics of electron tunnelling between electrode and floating gate at different h-BN thicknesses. A too-thin h-BN layer allows for charge tunnelling on both contacts, and no charges are stored in the graphene (b); a too-thick h-BN layer prohibits tunnelling current at all (d). An appropriate thickness of the h-BN layer is necessary to invoke the asymmetric potential drop so that charges can be stored in the graphene without appreciable leakage current (c).

Figure 4a–e shows 2D colour images of on/off ratio for various thicknesses of h-BN layer (Supplementary Figs 12–16). For a thin h-BN (3.5 nm), on/off ratio was low in any drain sweep as discussed previously (Fig. 4a). At appropriate h-BN thicknesses of 5.5 nm (Fig. 4b) and 7.5 nm (Fig. 4c), high on/off ratio was obtained above the tunnelling threshold voltages of 2 and 5 V, respectively, and increased up to over 108 (red colour area) at reasonable tunnelling threshold voltages. For a 10-nm h-BN, the threshold voltage exceeded 7 V and the obtained on/off ratio was not high because of insufficient tunnelling current via the thick h-BN insulator (Fig. 4d). For a 12-nm h-BN, the on/off ratio was 1 because of no tunnelling current through such a thick h-BN (Fig. 4e). Figure 4f shows a three-dimensional plot of on/off ratio in terms of drain sweep voltage and h-BN thickness. The highest on/off ratio is exhibited at an h-BN thickness 5.5–7.5 nm. However, a 7.5-nm device maintained a better on-current retention than a 5.5-nm h-BN device because of the reduced leakage current at thicker h-BN film (Supplementary Fig. 17).

Figure 4: The h-BN thickness dependence of TRAM.
figure 4

(ae) Colour plots of on/off ratio values as a function of source–drain voltage (x-axis) for a given maximum sweeping voltage (y-axis) with indicated h-BN thickness. (f) On/off ratio as functions of Vds and thickness.

Memory performance of TRAM

We further investigated the memory performance with a 7.5 nm h-BN film. Figure 5a shows a typical IV characteristic with a sweep range of ±8 V. The memory window (VW) of our TRAM was shown at Vds=0–4 V, revealing an on-current of 10−4–10−3 A and off-current of 10−14 A (on/off ratio over 109). The off-current and on/off ratio of TRAM (red star), RRAM32 (black circle) and PRAM33 (blue square) are plotted in Fig. 4b. Our TRAM shows 103–104 times lower off-state leakage current (left panel of Fig. 5b) and 103 times higher on/off ratio (right panel of Fig. 5b) because of the effective charge tunnelling through crystalline h-BN layer and storing charges in graphene layer, which can reduce the off-state power consumption, avoid the data sensing error caused by circuit noise and allow the multi-level cell for storing more than a single bit information. P-RAM and R-RAM can be suitable for high integration due to their vertical geometry. However, small on/off ratio limits their application for multi-level memory. Our device demonstrated 100–1,000 times larger on/off ratio than P-RAM or R-RAM, which is encouraging for multi-level memory applications, as demonstrated in Supplementary Fig. 18. Arithmetically, single four-level TRAM can replace two two-level P-RAM or R-RAM. This may compensate for integration density of the planar structure.

Figure 5: Memory performance of TRAM.
figure 5

(a) IV curve of the TRAM with 7.5-nm thick h-BN. Channel length and channel width of the device are 4 and 2 μm, respectively. The arrows indicate the current sweeping direction. Memory window from 0 to 4 V is shown with blue colour. (b) The plot of off current (left panel) and on/off ratio (right panel) along with reading voltage (VR) normalized by memory window (VW). (c) Retention characteristics of TRAM with 7.5-nm thick h-BN after programme (Vds=−8 V) and erase (Vds= 8 V) for 5 s, Vreading=0.01 V. (d) Endurance characteristics of the TRAM. Programme and erase were carried out by −6 V and +6 V with a pulse width of 0.1 s and a reading voltage of 0.1 V.

In memory characterization, the on and off currents showed no appreciable change, while maintaining an on/off ratio of 104 during a prolonged time scale (>104 s) (Fig. 5c), similar to the retention characteristic of gate-bias induced CFGM (Supplementary Fig. 19). The advantages of our TRAM compared with CFGM are demonstrated in Supplementary Fig. 20 and Supplementary Note 4. In the endurance test, excellent memory durability and stability were exhibited with an on/off ratio of 105 over 105 cycles (Fig. 5d) by retaining a large hysteresis (Supplementary Fig. 21). In addition, our TRAM showed high reproducibility, fast programme/erase operation (<5 ms) and temperature stability over 510 K (Supplementary Figs 22–24). To confirm that our TRAM can operate without a control gate, we measured the IV characteristics of the device with and without grounded Si. In both cases, the memory behaviour was identical (Supplementary Fig. 25). We fabricated another device that has no metal pad on graphene layer. There was no difference between with and without metal pad (Supplementary Fig. 26).

Flexibility and stretchability

The absence of a gate electrode and thick blocking insulator as well as an ultrathin thickness (<10 nm) using 2D materials with high Young’s modulus and breaking strength34,35,36 is certainly advantageous for both high flexibility and stretchability. We fabricated TRAM on flexible polyethylene terephthalate (PET) substrate to investigate the flexibility (Fig. 6a,b). IV characteristics show again the clear memory behaviour with an on/off ratio over 8 × 107 at Vds=−0.5 V (Fig. 6c). This indicates that the memory behaviour originates not from the drain–Si coupling effect but from the drain–floating gate coupling effect. In the bending test, the on/off ratio was reduced from 108 to 104 with the applying bending strain of 0.15%, which could be attributed to poor contact between metal/channel and/or metal/h-BN/Gr; however, the ratio was maintained to 104 to 0.5 % (maximum strain in PET bending), as expected from the strains of the used materials34,35,36, as shown in Fig. 6d.

Figure 6: Flexibility of TRAM.
figure 6

(ab) Optical images of TRAM on PET flexible substrate of a 7-nm thick h-BN layer, scale bar is 10 μm. (c) IV characteristic of memory device fabricated on PET substrate. (d) On- and Off-current of TRAM with applying strain at a given voltage of −0.5 V.

To further extract data for stretchability, we fabricated TRAM devices on a stretchable substrate of polyimide (PI)/polydimethylsiloxane (PDMS) (Fig. 7a,b). The formation of wrinkles of thin-layered materials37 was inevitable during fabrication process (see Methods section). Because of this, the on/off ratio was reduced to 103 after transfer of the device onto PDMS substrate (Fig. 7c black curve). This reduction of on/off ratio is mainly attributed to mechanical degradation of van der Waals contacts or metal electrode caused during the transfer process (Supplementary Fig. 27a). Nevertheless, the IV curve showed a stable memory hysteresis in the forward and reverse drain sweeps until 19% strain, and the on/off ratio was maintained at 103 without degradation (Fig. 7d). The device fails to operate at a strain above 20%, where the leakage current of the tunnelling insulator surges (Supplementary Fig. 27b). It should be noted that the high stretchability of our device does not result from intrinsic properties of 2D materials but from the nature of the wrinkled structure37.

Figure 7: Stretchability of TRAM.
figure 7

(ab) Optical images of TRAM on PI/PDMS stretchable substrate before and after stretching 20% along the length direction. Scale bars are 10 μm. The device is wrinkled or crumpled after transfer. The boundaries of MoS2, h-BN and graphene area are marked by white, blue and red colours, respectively. (c) IV curve of the device on PI/PDMS before stretching (black curve) and after stretching at certain strains (coloured). (d) On-current (black) and off-current (red) with tensile strain at a given voltage of 1 V. Memory function disappears at 20% strain. A 10-nm thick h-BN layer was used for the tunnelling insulator in (a).


In summary, we have demonstrated a TRAM with two terminals, which is gate-free and blocking insulator-free device. In this way, our TRAM can achieve not only highly reliable memory performance, such as high on/off ratio up to 109, long retention time (>104 s), stable endurance (>105 cycles) and multilevel feasibility, but also excellent stretchability with no appreciable electrical performance changes up to 19% strain because of the absence of a rigid blocking insulator and large apparent strain from the wrinkled structure on PI substrate. Our memory device can be useful for next-generation of wearable, body-attachable electronics in the near future.


The fabrication of MoS2/h-BN/Gr heterostructures

For the fabrication of the vertical heterostructures of the graphene/MoS2/h-BN device, the graphene was grown via chemical vapour deposition, transferred onto a Si/SiO2 (300 nm SiO2) substrate, and patterned into 10 × 50 μm strips as a floating gate using a photolithography and oxygen-plasma etching process. The h-BN and MoS2 flakes were then transferred onto the graphene strips through a dry transfer approach22. This method includes the mechanical exfoliation of the required flakes onto a dual-layer polymer stack polyvinyl alcohol (PVA) and polymethyl methacrylate. The bottom polymer (PVA) layer is dissolved in water and the resulting membrane is inverted and positioned above the target flake. The metal electrodes for probe contact were patterned on the MoS2 by e-beam deposition of Cr/Au (30/70 nm) followed by e-beam lithography.

For fabricating flexible devices on PET, we first stacked Gr/h-BN/MoS2 heterostructure on SiO2/Si wafer, and then floated them with polymethyl methacrylate binder on hydrofluoric acid etchant by etching SiO2 sacrifice layer. The stack was washed three times by floating in deionized water and then transferred onto PET substrate. The source and drain electrodes were then patterned by e-beam lithography.

For stretching test devices, a thin PI film was formed on the SiO2/Si wafer by spin-coating polyamic acid followed by annealing. The graphene/h-BN/MoS2 heterostructures and source–drain electrodes were formed by a dry transfer method and e-beam lithography, respectively, on the prepared PI film-coated Si wafer. A 10-nm thick h-BN layer was used for the tunnelling insulator. The TRAM-loaded PI film was detached from the Si wafer by etching the sacrificial SiO2 layer with hydrofluoric acid acid solution and then transferred onto the PDMS substrate.


A SPA400 (SEIKO) was used to record the AFM images. Electrical transport measurements were conducted with a probe station and source/measure units (Keithley 4200 and Agilent B2900A). For the stretching test, one side of the PI/PDMS substrate was fixed and the other side was pulled to stretch. All electrical measurements were performed in high vacuum (10−6 Torr).

Electrostatic simulation

Device simulation was carried out by the Comsol Multiphysics package using the electrostatic module. The Laplace equation with given boundary conditions for voltages was numerically solved by the finite element method.

Data availability

The data that support the findings of this study are available from the corresponding author upon request

Additional information

How to cite this article: Vu, Q. A. et al. Two-terminal floating-gate memory with van der Waals heterostructures for ultrahigh on/off ratio. Nat. Commun. 7:12725 doi: 10.1038/ncomms12725 (2016).