Electronic and optical properties of graphene and graphene antidot structures
Translated title
Elektroniske og optiske egenskaber af grafen og grafen antidot strukturer
Authors
Thomsen, Morten Rishøj ; Brun, Søren Jacob
Term
4. term
Education
Publication year
2013
Submitted on
2013-06-07
Pages
93
Abstract
Denne afhandling modellerer de elektroniske egenskaber ved rent grafen med en tight-binding-tilgang, en forenklet model af, hvordan elektroner bevæger sig mellem naboatomer. Grafen opfører sig som et semimetal og har en lineær båndstruktur nær Dirac-punktet i Brillouin-zonen. Vi lineariserer båndstrukturen i dette område (Dirac-approksimationen) for at udlede analytiske udtryk for flere egenskaber. Da mange elektroniske anvendelser kræver et båndgab, introducerer vi det på to måder: gennem en matematisk model for “gapped graphene” og gennem et grafen-antidotgitter (GAL), en realistisk struktur med et periodisk mønster af huller (antidots). I den samlede model for GAL’er beskrives antidot-områderne som gapped graphene, mens resten af materialet behandles som rent grafen; begge dele understøttes af Dirac-approksimationen. Derudover modellerer vi, hvordan elektroner spredes ved grafen-antidotbarrierer (GAB’er) ved hjælp af Green’s tensor area integral equation method (GTATIEM). Vi fokuserer på barrierer, hvor antidots er arrangeret i et heksagonalt mønster, og undersøger, hvordan spredningen skalerer med strukturens størrelse for at kunne approximere effekter i store systemer.
This thesis models the electronic properties of pristine graphene using a tight-binding approach, a simplified description of how electrons move between neighboring atoms. Graphene behaves as a semimetal and has a linear band structure near the Dirac point of the Brillouin zone. We linearize the bands in this region (the Dirac approximation) to derive analytical expressions for several properties. Because many electronic applications require a band gap, we introduce one in two ways: via a mathematical “gapped graphene” model and via a graphene antidot lattice (GAL), a realistic structure with a periodic pattern of holes (antidots). In our combined model for GALs, the antidot regions are treated as gapped graphene while the remaining areas are pristine; both are framed by the Dirac approximation. We also model how electrons scatter at graphene antidot barriers (GABs) using the Green’s tensor area integral equation method (GTATIEM). We focus on barriers with antidots arranged in a hexagonal pattern and examine how scattering scales with size to enable approximations for large structures.
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