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.

Chapter 1
1. M. S. Dresselhaus and G. Dresselhaus, Intercalation compounds of graphite , Adv. Phys. 30, 139 (1981)
2. A. Grüneis, Tight-binding description of the quasiparticle dispersion of graphite and few-layer graphene, PRB 78, 205425(2008)
Chapter 2
1. Stefan H fner, Photoelectron Spectroscopy, Springer
2. Geim, A. K. et al. Graphene: status and prospects. Science 324, 1530 (2009)
3. Booster, National Synchrotron Radiation Research Facility, Website of NSRRC
4. National Synchrotron Radiation Research Center, Introduction to synchrotron radiation. Website of National Sunchrotron Radiation Research Center
5. Damascelli, A. Probing the electronic structure of complex systems by ARPES, Phys. Scr. 109, 61-74 (2004)
6. Dominic, A. Ricci, Photoemission studies of interface effect on thin films properties, Ph. D. thesism, University of Illinois at Urbana-Champaign (2006)
7. Chia-Jen Hsu, Angle-resolved photoemission study of interlayer spacing in bilayer graphene and graphite, thesis
8. K. Sugawara, Fermi surface and edge-localized states in graphite studied by
high-resolution angle-resolved photoemission spectroscopy, PHYSICAL
REVIEW B 73, 045124 2006
9. Rong-Li Lo, Panel 1, Chapter 1, Surface Physics

Chapter 3
1. Chia-Jen Hsu, Angle-resolved photoemission study of interlayer spacing in bilayer graphene and graphite, thesis
2. A. Grüneis, Preparation and electronic properties of potassium doped graphite single crystals, pss-RRL (2008)
3. A. Grüneis, Tight-binding description of the quasiparticle dispersion of graphite and few-layer graphene, PRB 78, 205425(2008)
4. M. S. Dresselhaus and G. Dresselhaus, Intercalation compounds of graphite , Adv. Phys. 30, 139 (1981)

Chapter 4
1. Chia-Jen Hsu, Angle-resolved photoemission study of interlayer spacing in bilayer graphene and graphite, thesis
2. Song Y. F., et al, Performance of an ultrahigh resolution cylindrical grating monochromator undulator beamline. Rev. of sci. inst. 77, 085102 (2006)
3. Y. Baskin and L. Meyer, Lattice Constants of Graphite at Low Temperatures, PHYSICAL REVIEW VOLUM E 100, NUM BER 2