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Materials Design and Band Gap Engineering of Complex University of Louisville ThinkIR: The University of Louisville's Institutional Repository Electronic Theses and Dissertations 8-2016 Materials design and band gap engineering of complex nanostructures using a semi-empirical approach : low dimensional boron nanostructures, h-BN sheet with graphene domains and holey graphene. Cherno Baba Kah Follow this and additional works at: https://ir.library.louisville.edu/etd Part of the Condensed Matter Physics Commons Recommended Citation Kah, Cherno Baba, "Materials design and band gap engineering of complex nanostructures using a semi- empirical approach : low dimensional boron nanostructures, h-BN sheet with graphene domains and holey graphene." (2016). Electronic Theses and Dissertations. Paper 2491. https://doi.org/10.18297/etd/2491 This Doctoral Dissertation is brought to you for free and open access by ThinkIR: The University of Louisville's Institutional Repository. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The University of Louisville's Institutional Repository. This title appears here courtesy of the author, who has retained all other copyrights. For more information, please contact [email protected]. MATERIALS DESIGN AND BAND GAP ENGINEERING OF COMPLEX : LOW NANOSTRUCTURES USING A SEMI-EMPIRICAL APPROACH , h DIMENSIONAL BORON NANOSTRUCTURES - BN SHEET WITH GRAPHENE DOMAINS AND HOLEY GRAPHENE By Cherno Baba Kah M.S, University of Louisville, 2013 M.S, Clark Atlanta University, 2011 B.S, University of The Gambia, 2009 A Dissertation Submitted to the Faculty of the College of Arts and Sciences of the University of Louisville in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics Department of Physics and Astronomy University of Louisville Louisville, Kentucky August 2016 Copyright 2016 by Cherno Baba Kah All rights reserved MATERIALS DESIGN AND BAND GAP ENGINEERING OF COMPLEX NANOSTRUCTURES USING A SEMI-EMPIRICAL APPROACH: LOW DIMENSIONAL BORON NANOSTRUCTURES, h-BN SHEET WITH GRAPHENE DOMAINS AND HOLEY GRAPHENE By Cherno Baba Kah M.S, University of Louisville, 2013 M.S, Clark Atlanta University, 2011 B.S, University of The Gambia, 2009 A Dissertation approved on July 20, 2016 by the following Dissertation Committee: Dr. Ming Yu (Dissertation Director) Dr. Chakram S. Jayanthi Dr. Gamini Sumanasekera Dr. Xiao-An Fu ii DEDICATION This dissertation is dedicated to the loving memories of my parents Al Hadji Mbackeh Kah and Adji Isatou Jallow for all their sacrifice and guidance during the short time they lived with us and for teaching us to believe and trust in Allah, as well as to always work hard to achieve success. This is also dedicated to my newly born daughter Adji Aissatou (I can't wait to hold you in my arms); may you live a successful life full of blessings and in line with the teachings of the Prophet Muhammad (SAW). iii ACKNOWLEDGMENTS To attend a graduate school 4510 푚푖푙푒푠 away from my home country is only possible with the help and guidance of the creator Allah. His grace manifested in my case through Professor Ming Yu, my PhD advisor. I would like to express my deepest appreciation to Professor Ming Yu for accepting me in her research group and taking me under her wing and making me understand the research methodologies used in my PhD dissertation topic. She has been truly patient in guiding me through the techniques and concepts of the SCED- LCAO method used in this dissertation, and, in particular, she transmitted her deep understanding of Condensed Matter Physics and the computational tools required to succeed in this field to me. Without her persistent support, this work might not have become a reality. I would also like to thank the department of Physics and Astronomy of the University of Louisville for giving me the chance to attain a status that I never imagined even in my wildest dreams and for the support throughout my studies. My acknowledgments also go to Professors Chakram Jayanthi, Gamini Sumanasekera and Xiao-An Fu for accepting to be part of my dissertation committee and for the various suggestions and discussions. I would also want thank Professor Shi-Yu Wu for timely and helpful ideas on SCED-LCAO fitting and MD codes. Avery special thanks to Professors Chakram Jayanthi and Christopher Davis for all the help they gave me to get me funded throughout the course of my study. I would also want to iv express my gratitude to the McSweeney family for their support that funded my graduate fellowship for three years. I would also like to acknowledge the support received from the Dillon fellowship, the graduate teaching assistantship from the Physics and Astronomy Department and the tuition scholarship received from SIGS (through the dissertation completion award) during Spring 2016 semester that enabled me to complete my dissertation. I would also like to express my appreciations to all the professors within the department of Physics and Astronomy, the supporting staff, especially, Ms. Mary Gayle Wrocklage and Ms. Rea Diehlmann. I would also like to thank Dr. Lutz Haberzettl for the technical support, especially, the support that he gave when I needed to connect to the university computer servers from home. Throughout my time in the department, I met lot of students who influenced me positively in different ways and it would not do justice to them if I do not acknowledge them. In particular, my appreciations go to Dr. Paul Tandy, Dr. George Anderson, Ms. Congyan Zhang, Mr. Harrison Simrall, Mr. Tarek Afaneh, Mr. Jafar Ghithan, Mr. Saliya Kirigeeganage, Mr. George Schuhmann, Mr. Allan Lasky-Headrick and many more. I would like to thank all my siblings Ndeye Yagou, Serigne Mamadou, Aminata, Mame Marie, Mame Maty, Cherno Muhtarr and Maimouna. My thanks also go to aunty Oumie and uncle Mam Cherno as well as to all my uncles, aunts, cousins and friends for always being supportive despite the long distance between us. Finally, I would like to convey my special appreciation to my wife Aminata Kone Kah for her understanding and patience during the last phase of my PhD studies. v ABSTRACT MATERIALS DESIGN AND BAND GAP ENGINEERING OF COMPLEX NANOSTRUCTURES USING A SEMI-EMPIRICAL APPROACH: LOW DIMENSIONAL BORON NANOSTRUCTURES, h-BN SHEET WITH GRAPHENE DOMAINS AND HOLEY GRAPHENE Cherno Baba Kah July 20, 2016 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 vi determined for the two-dimensional sheets with the strength of the stability in the order of 훿4 < 훼 < 훿6. 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 vii 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 푒푉 for gap. Holey circular graphene sheet has also a stable structure with a possible gap of 0.35 푒푉 while the most stable structure among the holey rectangular sheets was found to have a gap of 0.4 푒푉. 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.
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