研究目的
To study resonant electron tunnelling through the localised states in few atomic-layer boron nitride barriers sandwiched between two monolayer graphene electrodes and to determine the energy, linewidth, tunnelling transmission probability, and depth within the barrier of more than 50 distinct localised states.
研究成果
The study observed resonant electron tunnelling between graphene monolayers through individual localised states in the hBN tunnel barrier. The theoretical model determined the energy, linewidth, tunnel coupling coefficients, and spatial coordinate of individual localised states in the barrier region. A three-step percolative inelastic process was also observed, providing insights into the future exploitation and control of electron tunnelling through localised states in hBN.
研究不足
The study is limited to localised states with energies in the range ?0.3 to 0.3 eV due to the application of strong electric fields up to ~±300 mV/nm across the barrier to avoid electrical breakdown. The areal density of tunnel-active defects in the devices is quite small, around 4 orders of magnitude smaller than the electron sheet densities in the graphene electrodes at zero bias and gate voltages.
1：Experimental Design and Method Selection:
The study uses gated tunnel transistors to investigate resonant electron tunnelling through localised states in hexagonal boron nitride (hBN) barriers. The theoretical model combines the Landauer-Büttiker conductance formula with Fermi’s golden rule and an electrostatic model of the device.
2：Sample Selection and Data Sources:
The devices incorporate either one or two gate electrodes, providing precise control of the density and chemical potentials of the carriers in the graphene layers. The active area for current flow in Device 1 is ~50 μm2, and in Device 2, it is ~25 μm2.
3：List of Experimental Equipment and Materials:
The devices were fabricated using a conventional dry-transfer procedure, with graphene and hBN layers mechanically exfoliated onto a Si/SiO? substrate. Cr/Au contact pads were mounted on the graphene electrodes, and a top hBN capping layer was covered by a Cr/Au layer serving as a top gate electrode.
4：Experimental Procedures and Operational Workflow:
The tunnel current and differential conductance were measured with a small amplitude AC modulation voltage at zero DC bias over a range of gate voltages. The measurements were used to determine the energy and spatial position of each of the localised states.
5：Data Analysis Methods:
The data were analyzed using a theoretical model that includes the quantum capacitance of graphene and an electrostatic model of the device. The model was used to fit the measured data and determine the tunnel barrier thickness, the thickness of the insulating hBN layer, and the energy and spatial position of the localised states.
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