Electronic transport in graphene: 2D materials, composites, and 3D printed structures - Gosling, Jonathan. H. (2023)
In this thesis, the charge-carrier mobility in graphene, limited by multiple sources of electron scattering, is studied under the framework of the Boltzmann transport equation using the Born approximation for scattering potentials. Two congruent methods are explored: deterministic discontinuous Galerkin, and stochastic Direct Simulation Monte Carlo, to solve the full Boltzmann equation. Such temporal simulations, showcasing the transient dynamics from thermal equilibrium to a new steady-state under electrostatic perturbation, reveal the profound effects of the Joule heating capabilities of graphene, where the electrons behave as an electron gas with weak external lattice coupling. Mobility curves reveal the nature of electronic transport with changing electron population, and under varying physical parameters. As modelled for impurity dominated graphene, we find a “universal” connection between the carrier mobility and variation of conductivity with carrier population, applicable for both pristine graphene and graphene heterostructures. Ultimately, such universality relies on universality at the Dirac point. When thermally excited phonons and charge carriers become important, the behaviour around the Dirac point should be carefully considered. We show how thermal effects on the low-energy electron distributions affect the width of the total resistivity curve with respect to variations of carrier density, and how this affects the measured mobility and it’s temperature dependence. Twisting between constituent layers of hexagonal lattices alters the periodic lattice potential, forming secondary Dirac points and band gaps within the low-energy spectrum of a single graphene layer. We show how this can limit conductivity with and without external lattice perturbations. We find intriguing features, such as negative differential conductance, at electron energies around the secondary Dirac points, due to Bloch oscillating electrons. 3D printing provides a potential solution for scalable and efficient manufacturing of 2D materials and heterostructures. Flakes deposited via inkjet printing form percolating networks. Results reveal how the macroscopic electrical properties, characterised by the hopping and tunnelling between individual flakes, are strongly influenced by the distribution of flakes and by complex meandering electron trajectories, which traverse multiple printed layers.