Characterizing two dimensional materials and their hybrids

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Numerous two dimensional materials are investigated namely graphene, as the progenitor of monolayer materials, and the emerging family of transition metal dichalcogenides (TMD)s. This work is conducted predominately using density functional theory (DFT) with calculations carried out to produce over 200 unique monolayer structures. Several of these materials, in particular graphene, molybdenum dichalcogenides and platinum dichalcogenides are studied in depth, focusing on elastic, electronic and optical properties. Indentation calculations of large graphene sheets are optimised using empirical force fields and then examined using the higher level modelling of DFT. These demonstrate the possibility of pretension existing in the experimental analogs and suggest a compensating behaviour of such pretension in the empirical formula that was originally used to obtain the elastic properties. In addition the first atomistic modelling and characterization for the indented graphene wrinkles phenomena is given for large sheets. The elastic properties of graphene are then compared to that of MoS₂ and PtX₂ where X = S; Se; Te revealing a higher elasticity in the platinum based monolayers. Electronic calculations of the dichalcogenides show a similar responses for PtX₂ to MoS₂ with orbital quantization as the bulk approaches monolayer. Analysis of the PtX₂ band structure allows the determination of effective hole and electron masses. It was observed that the platinum dichalcogenides posses exceptionally large holes and favourably large exciton binding energies with the latter determined by calculating the exciton wave function. An alternative explanation of the relative phase stability of the TMDs is provided, utilising the crystal orbital overlap (COOP) for all TMDs in trigonal-prismatic and octahedral coordination. In addition, transition between these phases is investigated with the calculated barrier energies given for several systems including a proposed α phase. Optical calculations of the different phases are included to emphasize the unique properties of each atomic coordination. Phonon calculations are performed and formation energies compared to summarize the entire family of TMDs by their relative and individual stability for the trigonal-prismatic, octahedral and distorted octahedral coordinations. The details of which are used in a custom neural network to ascertain correlations between material parameters. These results show a weak correlation between several properties that can be somewhat improved when considering multiple input properties at once. This can ultimately help guide the selection of hybrid heterostructure constituents.
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