Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.


Physics and Astronomy

Degree Program

Physics, PhD

Committee Chair

Yu, Ming

Committee Co-Chair (if applicable)

Jayanthi, Chakram

Committee Member

Jayanthi, Chakram

Committee Member

Sumanasekera, Gamini

Committee Member

Fu, Xiao-An

Author's Keywords

Semi-empirical approach; Materials design; Low Dimensional Boron Nanostructures; Band Gap Engineering


This dissertation will explore the potential of a semi-empirical Hamiltonian, developed by the research group at the University of Louisville, in predicting the existence of new families of low-dimensional boron nanostructures based on icosahedral α-B12 clusters, and in tuning the band gaps of h-BN sheets with graphene domains and holey graphene. This semi-empirical Hamiltonian models electron-electron and electron-ion interactions using environment-dependent (ED) functions, and ion-ion interactions via usual pairwise terms. Additional features of our approach are that it uses a linear combination of atomic orbitals (LCAO) framework to describe the Hamiltonian and it calculates the charge distribution around a site self-consistently (SC). Throughout this dissertation, we will refer this semi-empirical Hamiltonian using the acronym SCED-LCAO. Our first application on boron nanostructures using SCED-LCAO revealed that one and two-dimensional nanostructures (referred as α, δ4 and δ6 sheets) based on icosahedral α-B12 clusters were structurally stable. A relative stability with respect to δ6 was also determined for the two-dimensional sheets with the strength of the stability in the order of �4 < � < �6. The infinite one-dimensional chain (which is the least stable among the low dimensional Boron structures predicted) as well as δ4 and δ6 sheets are found to have semiconducting properties while α sheet has metallic properties. With recent reports on the synthesis of an ultra-thin layer of α-tetragonal B50 structure, we delved into a second project that focused on investigating the structural stabilities and properties of a single layer of α-tetragonal B50. We found that, the α-tetragonal B50 does not keep its two-dimensional nature but prefers to exhibit symmetry breaking. Our prediction is inconsistent with experimental observations but this may be due to experiments discerning double or multi-layer structures of α-tetragonal B50. We note that the stability of multi-layer α-tetragonal B50 structure requires further investigation. A third application studied includes the band gap engineering on h-BN sheet by creating in it graphene domains of different shapes (triangular, circular, hexagonal and rectangular) and sizes with the aim of reducing the energy gap of pristine h-BN. For this project, the parametrization of the SCED-LCAO Hamiltonian corresponding to the nitrogen element was developed as a first step towards the investigation of pristine h-BN sheets and h-BN sheets embedded with graphene domains. The results of our study of h-BN sheets embedded with graphene domains reveal that the density of states are dependent on the shapes and sizes of the graphene domains and that hexagonal and circular graphene domains are good candidates for engineering the gap of a pristine h-BN sheet. A fourth application of SCED-LCAO method focused on a study of the band gap of holey graphene sheets, i.e., graphene sheets carved with different types of geometrical holes. We found holey triangular graphene sheets to have the smallest possible energy gap with its biggest size being the most stable and having 0.11 �� for gap. Holey circular graphene sheet has also a stable structure with a possible gap of 0.35 �� while the most stable structure among the holey rectangular sheets was found to have a gap of 0.4 ��. Computational studies undertaken in this dissertation demonstrate that the SCED-LCAO method is a powerful technique for designing materials with desired properties, which can guide the experimentalists to synthesize novel complex materials. The novel structures and properties predicted in this work for boron icosahedra chains and sheets, holey graphene sheets and h-BN with graphene domains await experimental confirmation.