title: Computational study of electron transport in nanocrystalline graphene
Creators: name: Perera, Delwin
Publisher: name: UNSPECIFIED
Year: 2023

description: Over the last years graphene research has branched into many fields and sub-fields spanning from pure theory to technology. A first climax of this development was the Nobel Prize in Physics 2010. Since then new milestones have been reached increasingly focussing on the technological application of graphene. Ideally, the extraordinary properties of graphene could be directly transferred from laboratory to commercial devices. Such a straight route, however, does not exist in most cases. Designing and manufacturing graphene-based electronic devices on large scales rather poses additional questions and challenges. A major challenge is the control of dislocations and grain boundaries in graphene. These defects are typically caused by large-scale synthesis methods such as chemical vapour deposition. Defects often deteriorate pristine material properties like mechanical strength, electric conductivity or electron mobility. In this sense they are clearly undesired, but defects offer new possibilities as well. They can be used to tune for example mechanical or electronic properties and defect engineering has become an increasingly pursuit research area. In this work, we study a specific type of defect in graphene: grain boundaries at the nanometer scale. Graphene grain boundaries are extended defects but in contrast to three-dimensional materials they are line not area defects. The reduced dimensionality relates them closely to dislocations and other topological defects. Topological defects, generally, change the connectivity between atomic sites without necessarily changing the coordination. This strongly affects the electronic properties of graphene and offers possibilities to engineer electron transport that contrast with commonly used methods like doping or chemical modifications. A second source to modulate transport properties is mechanical strain. The piezoresistive effect, i.e. the change of electric response upon mechanical strain, is a well-known example. In graphene the piezoresistive effect offers interesting application possibilities in the form of transparent strain sensors due to graphene’s optical transparency and mechanical flexibility. The piezoresistive effect in graphene is also an interesting crossing point between electromechanical properties and their interaction with grain boundaries. Nanocrystalline graphene (NCG) shows a pronounced piezoresistivity suggesting that the high grain boundary density contributes somehow to it. Uncovering the role of grain boundaries for electron transport is invaluable, both theoretically and experimentally. Transport at the length scales relevant in NCG offers a quite interesting opportunity: The problem can be investigated theoretically by quantum-mechanical methods while still accessible to experimental probes. Such a complementary investigation is interesting in itself. We must acknowledge, however, that the theoretical treatment in this thesis, still uses several simplifications that cannot be mimicked in experiments, directly. First we study how the grain boundary structure influences electron transport in graphene bicrystals. We find that there are generally two transport regimes within the ballistic transport approximation: an energy gap region and, at energies beyond this gap, an ohmic region. The size of the energy gap depends on the bicrystal geometry and can be zero for some bicrystals. The gap region is insensitive to structural variations while the ohmic region is quite sensitive. This insight motivates a purely geometric picture of the emergence and size of transport gaps in graphene bicrystals. Moreover, this picture can be extended to describe a gap modulation by mechanical strain. It is therefore a useful bridge from bicrystals to piezoresistivity in graphene nanocrystals. The final topic considered in this thesis is an approximation of electron transport in nanocrystals under a uniaxial external strain. The approximate nature lies mainly in the model construction: We use hexagonally shaped grains to establish simple orientation relations between adjacent grains and to reduce the number of additional degrees of freedom. By combining conventional two-terminal transport calculations and transport samples embedded in complex absorbing potentials we find that the grain boundary network exhibits pronounced metallicity at low energies. This indicates that the enhanced piezoresistivity of NCG may be attributed to a finite-size effect. While a conclusive description of mechanically modulated conductivity in NCG could not be presented, our work establishes important technical insights into ballistic transport calculations of extended structures in general and transport across graphene grain boundaries in particular.