| Summary: | In this thesis, the form of the current-voltage characteristics and the resulting current oscillations in graphene-hexagonal boron nitride heterostructures are explored by means of theoretical investigation and are supported by experimental observations. The conditions for resonant tunnelling and the effect of device and circuit parameters are examined through simulation of the charge dynamics using the Bardeen Transfer Hamiltonian method. Studies of the effect of induced moir\'e patterns between the crystallographically aligned graphene and the boron nitride lattices are also undertaken, with recommendations for future investigation.
It is theoretically shown that samples containing two layers of graphene, separated by hexagonal boron nitride tunnel barriers, produced higher frequency oscillations when the graphene lattices are aligned. This was found to be due to the decrease in wavefunction overlap in the misaligned samples, which is not compensated by the higher density of states available for tunnelling. Chemical doping of the graphene layers are also found to increase the frequency, as it allows the Dirac cones to be brought into alignment for resonant tunnelling with a higher number of states available. It is known that the mismatch in lattice constant between the graphene lattice and the hexagonal boron nitride lattice creates a moir\'e pattern. This, in turn, induces additional Dirac points in the band structure and thus leads to new features in the current-voltage characteristics.
The theoretical simulations presented in this thesis are substantiated by recently-published experimental results, and provide insight into possible future high-frequency, room-temperature solid state oscillators and amplifiers. In conclusion, the mechanisms for resonant tunnelling in multiple graphene heterostructures are identified and demonstrated in this work, and provide promising evidence for novel high frequency technologies and further research.
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