碳組成許多不同的物質,像是鑽石和石墨。但彼此之間最大的不同就是碳是導體而鑽石是絕緣體,原因就在於鍵結。鑽石中的碳原子彼此形成三維的sp3的共價鍵,而石墨在平面結構是二維的sp2鍵結的共價鍵,垂直方向自由的pz鍵結的金屬鍵形成 π 能帶,層與層之間微弱的凡得瓦力,使得石墨具導電性。 石墨的研究已經幾十年了。在1981年M. S. Dresselhaus和G. Dresselhaus以tight-binding理論模擬石墨的能帶以及A. Grüneis在2008年以TB-GW描述石墨的能帶。在我的論文當中,我將會探討以角解析光電子能譜量測石墨的電子結構。不同於石墨烯是二維的結構,石墨是三維的結構, z ̂ 方向的位置不同會影響石墨能帶的變化。對於石墨能帶中兩個 π 鍵形成的價帶隨著入射的光子能量不同,對應在 z ̂ 當中位置的不同,進而影響兩個 π 價帶之間分裂、合併的週期關係。並且以tight-binding理論描述兩個 π 價帶所形成的費米面。我主要的目的是以tight-binding理論模擬出一套tight-binding參數對於束縛能較大即為較遠理費米能階的價帶做出好的模擬;並且,以此參數對束縛能較小即為較靠近費米能階的價帶做描述,觀察在束縛能小的能帶描述的狀況。
Carbon composes lots of material, like diamond and graphite. But the biggest difference is that graphite is a conductor while diamond is an insulator, because of the bonding. The carbon atoms in the diamond hybridize into the three-dimension sp3 covalent bonding, however the carbon atoms hybridize into two-dimension sp2 covalent bonding in-plane and the delocalized pz bonding results in metallic bonding which forms the π band. The interaction between layer and layer is the weak van der Waals' force so that graphite is a conductor. Graphite has been researched for decades. M. S. Dresselhaus和G. Dresselhaus used the tight-binding theory to describe the band structure of graphite in 1981 and A. Grüneis used the TB-GW to describe the band structure of graphite. In my thesis I will discuss the electronic structure of graphite measured by ARPES. Unlike graphene, graphite is a three-dimension material the different position along z ̂ direction, the different the band structure of graphite will be. To graphite, the two valence π bands with the different incident photon energy which respect to different position along z ̂ direction, results in the periodically merge or split of two valence π bands. In addition I will use the tight-bind theory to describe the Fermi surface result from two valence π bands. The major goal is obtain a set of tight-binding parameters that could well-described Fermi surface at high binding energy, moreover using the same parameters to describe the Fermi surface at low binding energy. Then discuss the describing at low binding energy.