Quantum tunnelling and leakage current across two-dimensional materials

Leakage current is a physical phenomenon that critically affects the operation and reliability of mainstream electronic devices and heterostructures for diverse applications. Two-dimensional materials are being integrated into the structure of ultrascaled electronic devices, but the leakage current across them is still not well understood. Here we analyse the leakage current across hexagonal boron nitride (hBN), molybdenum disulfide and tungsten disulfide of different thicknesses, and compare it with industrial-quality SiO₂/n⁺⁺Si samples. The samples are analysed at the nanoscale and at the device level, and the experimental data are complemented with computational modelling assisted by technology computer-aided design and density functional theory. First, we demonstrate that the surface roughness of the bottom electrode dramatically alters the leakage current when an electric field is applied. Second, we show that in multilayer two-dimensional materials, the energy bandgap and density of atomic defects are key factors that determine the leakage current; however, in monolayer two-dimensional materials, the leakage current is mainly determined by sample thickness, understood as the electrode-to-electrode distance. Consequently, leakage current across monolayer hBN is higher than that across monolayer molybdenum disulfide and tungsten disulfide despite hBN having a bandgap nearly three times larger, due to its approximately 50% lower thickness. Third, we establish an equivalence (in terms of leakage current) between hBN and SiO₂ films of different thicknesses, which can be used to predict the performance and reliability of two-dimensional-material-based nano-electronic devices, such as transistors and memristors.