石墨烯超晶格之電子傳輸特性

Electronic Transport Properties of Graphene Superlattices

趙秉祥(Bing-Siang Chao)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.11222

摘要

本論文建構了石墨烯超晶格裡電子的傳播行為模型，推演出電子在結構裡的穿透率，並藉由穿透率為媒介推導超晶格中的電流、微分電導以及范諾因數等公式。本文注意到石墨烯超晶格結構會產生新的狄拉克點，其發生在均零波數上，且其位置不受晶格常數變化，只會隨著超晶格的層與層間寬度比與位能障壁高而改變，並且均零波數能隙會隨晶格常數與位能障壁高的增加而開闔，但其位置並不會隨晶格常數變化而只會與入射角有些微相關，除此之外提高超晶格的周期數有助於凸顯在能隙上穿透率跌落的幅度，以及當超晶格摻有其他雜質或是亂序時，均零波數能隙的位置仍會較其他位置的能隙穩定，在其中還有可能會產生缺陷模態，造成在能隙中產生穿透率以及電導突起的現象，藉由以上幾點讓新狄拉克點的存在有助於科學家設計出以石墨烯為基底的電子元件。

關鍵字

石墨烯 ； 緊束縛法 ； 克萊恩傳輸 ； 超晶格 ； 范諾因數

並列摘要

The behaviors of electrons in graphene superlattice such as transmission spectra, current, differential conductance, and Fano factor has been studied by using tight-binding method, Dirac-like Hamiltonian approximation, and transfer-matrix method. It’s found that there are some new Dirac points in graphene superlattices. New Dirac points occur at zero-averaged wave-number. Besides, their locations don’t change when lattice constants are changing. In fact, they only change with layer width ratios of superlattices and barrier heights of superlattices. The zero-averaged wave-number gaps are opened or closed when lattice constants are changing. But the positions of the gaps don’t also change when lattice constants are changing. However, they change slight with the angles of incidence. In addition, the magnitudes of transmission decrease with the increasing numbers of cells. Moreover, even though there are defects or disorders in grpahene superlattices, the positions of zero-averaged wave-number gaps are more stable than the other gaps. Defect modes which cause special transmission and conductance peaks in zero-averaged wave-number gaps are probably also generated. All characteristics mentioned above can be used to design graphene-based electronic devices.

並列關鍵字

graphene ； tight-binding method ； Klein tunneling ； superlattice ； Fano factor

參考文獻

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