When we set out to study how electrons tunnel through atomically thin materials, we initially expected that materials with larger bandgaps would show stronger insulating behaviour. In reality, the situation turned out to be much more complicated. Early reports from other groups (including Nobel laureate Prof. K. Novoselov’s team1) showed puzzlingly large current densities through few-layer (ranging from monolayer to four-layer) hexagonal boron nitride (hBN), a two-dimensional (2D) material with a bandgap of around 6 eV2. At the same time, many studies on monolayer-hBN-based atomristors reported current densities that were several orders of magnitude lower3-7. These contradictions motivated our investigation. We wanted to understand the origin of these very different current levels and clarify what really happens in real monolayer-2D-material-based devices.
In our experiments, we fabricated dozens of micro- and nano-scale devices, each consisting of hBN flakes or films sandwiched between metallic electrodes, such as Ru, Au, and graphite. We first carefully recreated past experimental structures, starting with very thin, monolayer hBN and then moving to thicker stacks. The results were revealing. We found that surface roughness of bottom electrode can strongly alter the leakage current when an electric field is applied. We also showed that, in multilayer 2D materials, the bandgap and the density of atomic defects are key factors governing leakage current. However, in monolayer 2D materials, leakage current is mainly determined by the effective sample thickness, which can be understood as the electrode-to-electrode distance.
For example, monolayer hBN contacted with Ru, which has a surface roughness of ~0.308 nm, showed roughly 60 times lower current than monolayer hBN contacted with graphite, which has a surface roughness of ~0.153 nm, under otherwise identical device structures in terms of gap-free interfaces between graphite electrodes and hBN layer. At the device level, we fabricated several samples with area of 1 µm², and we observed that19-layer hBN contacted with Au, which has a surface roughness of ~1.30 nm, showed about 1.5 times lower current than 19-layer hBN contacted with graphite. These results further show that, when the dielectric becomes extremely thin, the bottom electrode roughness can have a dominant impact on the tunnelling current.
In short, the leakage current through a monolayer-hBN-based atomristor with metal electrodes, such as Au, can be very different from that expected for an ideal material stack with a perfect monolayer hBN interface (e.g., hBN/graphite). This difference can arise simply because nano-voids form between monolayer hBN and the rough bottom electrode, which increases the effective electrode-to-electrode distance and strongly suppresses tunnelling current.
To better understand how the electrode-to-electrode distance controls tunnelling current in the monolayer limit, we further fabricated several mechanically exfoliated monolayer samples, including hBN, MoS2, and WS2, using graphite as the bottom electrode to form a cleaner and more ideal interface. One of the major challenges, and also one of the key breakthroughs of this study, was obtaining statistically meaningful data from such ideal monolayer structures. This required the transfer of clean and relatively large monolayer flakes, larger than 10 × 10 µm2, onto graphite flakes, which is experimentally difficult. For each sample, we performed around 100 I-V measurements with a current limit of 110 pA. We measured onset voltages of 0.005 ± 0.0007 V for monolayer hBN (~0.34 nm), 0.018 ± 0.007 V for monolayer MoS2 (~0.634 nm), and 0.12 ± 0.04 V for monolayer WS2 (~0.79 nm). Notably, although monolayer hBN has a much wider bandgap than MoS2 and WS2, it exhibited significantly higher current and a lower VON. This observation further supports our conclusion that, in the monolayer limit, thickness, or more precisely the electrode-to-electrode distance, plays the dominant role in determining quantum tunnelling, even more than intrinsic material properties such as bandgap.
Looking forward, these findings have important implications for future 2D electronics. They show that evaluating a 2D material only by its intrinsic properties, such as bandgap or defect density, is not sufficient when the material is only monolayer thick (< 1 nm). At this limit, the full device structure matters: the electrode roughness, the interface quality, the presence of nano-voids, and the actual electrode-to-electrode distance can all change the measured leakage current by orders of magnitude. This means that reliable 2D-material-based electronics will require not only high-quality 2D materials, but also carefully engineered electrodes and interfaces. For atomristors and other ultra-thin electronic devices, controlling these hidden structural factors may be as important as designing the switching layer itself. By identifying these factors and separating their contributions, our work provides a clearer framework for understanding leakage current in monolayer 2D materials and for building more reliable 2D-material-based devices in the future.
References
- Britnell, L. Gorbachev, R. V. Jalil, R, et al. Electron tunneling through ultrathin boron nitride crystalline barriers. Nano letters, 2012, 12(3): 1707-1710.
- Cassabois G, Valvin P, Gil B. Hexagonal boron nitride is an indirect bandgap semiconductor. Nature photonics, 2016, 10(4): 262-266.
- Wu X, Ge R, Chen P A, et al. Thinnest nonvolatile memory based on monolayer h‐ Advanced Materials, 2019, 31(15): 1806790.
- Kim M, Pallecchi E, Ge R, et al. Analogue switches made from boron nitride monolayers for application in 5G and terahertz communication systems. Nature Electronics, 2020, 3(8): 479-485.
- Yang S J, Dahan M M, Levit O, et al. Reconfigurable low-voltage hexagonal boron nitride nonvolatile switches for millimeter-wave wireless communications. Nano Letters, 2023, 23(4): 1152-1158.
- Ge R, Wu X, Liang L, et al. A library of atomically thin 2D materials featuring the conductive‐point resistive switching phenomenon. Advanced Materials, 2021, 33(7): 2007792.
- Yuan Y, Pazos S, Li J, et al. On-chip Atomristors. Materials Science & Engineeringg: R: Reports, 2025, 165: 101006.