Electronic and optical properties of graphene and graphene antidot structures

Thomsen, Morten Rishøj ; Brun, Søren Jacob

4. term

Nanotechnology, Master

2013

2013-06-07

93 pages

De elektroniske egenskaber af ren grafen modelleres ved brug af tight-binding. Grafen er halvmetallisk med en lineær båndstruktur nær Dirac punktet i Brillouin zonen. En linearisering af båndstrukturen, kendt som Dirac approksimationen, bruges til at opstille analytiske udtryk for adskillige egenskaber. Det er nødvendigt at introducere et båndgab i grafen for at kunne bruge det til flere elektroniske anvendelser. Det er muligt at intoducere et båndgab i grafen, rent matematisk, ved hjælp af en "gapped graphene" model. Det er desuden muligt at introducere et båndgab i grafen ved at lave grafen antidot gitre, som er mere realistiske at fabrikere. Sammen med Dirac approksimationen bruges gapped grafen modellen til at opstille en model til at beskrive grafen antidot gitre. Antidot områderne modelleres som gapped graphene, men resten af strukturen modelleres som ren grafen. Derudover bruges GTAIEM til at modellere spredning gennem en grafen antidot barriere. Vi fokuserer på grafen antidot barrierer med antidots arrangeret i et sekskantet mønster inde i barrieren. En undersøgelse af spredningsfænomenernes skalerbarhed bruges til at tilnærme spredningen forårsaget af store strukturer.

The electronic properties of pristine graphene are modeled using a tight-binding approach. Graphene is a semimetal with a linear band structure near the Dirac point of the Brillouin zone. A linearization of the band structure, called the Dirac approximation, is used to set up analytical expressions for several properties. For many electronic applications, it is necessary to introduce a band gap in graphene. A gapped graphene model may be used to introduce a band gap in a purely mathematical way, whereas a graphene antidot lattice (GAL) may be used to introduce a band gap in a realistic structure. Together with the Dirac approximation, the gapped graphene model forms the basis of the model describing these GALs, where the antidot regions are modeled as gapped graphene and the rest of the structure is modeled as pristine graphene. Additionally, the scattering through graphene antidot barriers (GABs) is modeled using a Green's tensor area integral equation method (GTATIEM). We focus on GABs with a hexagonal arrangement of antidots inside the barrier. An investigation of the scalability of the scattering phenomena is used to approximate the scattering caused by large structures.

Grafen ; Antidot ; Elektroniske egenskaber ; Optiske egenskaber ; GTAIEM ; Green's funktioner ; Elektronspredning

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