Electronic Conduction in Disordered Carbon Materials
Authors:   , Cheah Chun Yee 
Published: November 2021

<p>Graphene, consisting of a single layer of carbon atoms, is being widely studied for its interesting fundamental physics and potential applications. The presence and extent of disorder play important roles in determining the electronic conduction mechanism of a conducting material. This thesis presents work on data analysis and modelling of electronic transport mechanisms in disordered carbon materials such as graphene. Based on experimental data of conductance of partially disordered graphene as measured by Gómez-Navarro et al., we propose a model of variable-range hopping (VRH) – defined as quantum tunnelling of charge carriers between localized states – consisting of a crossover from the two-dimensional (2D) electric field-assisted, temperature-driven (Pollak-Riess) VRH to 2D electric field-driven (Skhlovskii) VRH.  The novelty of our model is that the temperature-dependent and field-dependent regimes of VRH are unified by a smooth crossover where the slopes of the curves equal at a given temperature. We then derive an analytical expression which allows exact numerical calculation of the crossover fields or voltages. We further extend our crossover model to apply to disordered carbon materials of dimensionalities other than two, namely to the 3D self-assembled carbon networks by Govor et al. and quasi-1D highly-doped conducting polymers by Wang et al. Thus we illustrate the wide applicability of our crossover model to disordered carbon materials of various dimensionalities.  We further predict, in analogy to the work of Pollak and Riess, a temperature-assisted, field-driven VRH which aims to extend the field-driven expression of Shklovskii to cases wherein the temperatures are increased. We discover that such an expression gives a good fit to the data until certain limits wherein the temperatures are too high or the applied field too low. In such cases the electronic transport mechanism crosses over to Mott VRH, as expected and analogous to our crossover model described in the previous paragraph.  The second part of this thesis details a systematic data analysis and modelling of experimental data of conductance of single-wall carbon nanotube (SWNT) networks prepared by several different chemical-vapour deposition (CVD) methods by Ansaldo et al. and Lima et al. Based on our analysis, we identify and categorize the SWNT networks based on their electronic conduction mechanisms, using various theoretical models which are temperature-dependent and field-dependent. The electronic transport mechanisms of the SWNT networks can be classed into either VRH in one- and two-dimensions or fluctuation-assisted tunnelling (FAT, i.e. interrupted metallic conduction), some with additional resistance from scattering by lattice vibrations.  Most notably, for a selected network, we find further evidence for our novel VRH crossover model previously described. We further correlate the electronic transport mechanisms with the morphology of each network based on scanning electron microscopy (SEM) images. We find that SWNT networks which consist of very dense tubes show conduction behaviour consistent with the FAT model, in that they retain a finite and significant fraction of room-temperature conductance as temperatures tend toward absolute zero. On the other hand, SWNT networks which are relatively sparser show conduction behaviour consistent with the VRH model, in that conductance tends to zero as temperatures tend toward absolute zero. We complete our analysis by estimating the average hopping distance for SWNT networks exhibiting VRH conduction, and estimate an indication of the strength of barrier energies and quantum tunnelling for SWNT networks exhibiting FAT conduction.</p>