近代材料科學中，調控材料性質(例如 :電性、磁性、光學性質...等等)最有效方法之一，即在具備週期條件之晶格結構中，引入晶格缺陷(包括 :空缺、摻雜、晶格錯位...等等)。相較於實驗方法(透過新穎技術及濃度控制以製備摻雜晶體)，理論計算則是利用超晶胞(supercell)方法，建立原子層級之摻雜晶體模型。然而，進行超晶胞計算，將隨所對應之布里淵區(Brillouin Zone)縮小所致之能帶摺疊效應，而失去計算所得之能帶結構與無摻雜晶體能帶之關聯性。因此，我們的研究工作是結合基底轉換與倒空間展開方法，將超晶胞的能帶結構展開。展開後的能帶結構圖，可以讓我們直接看出摻雜對於能帶結構的影響(如：對稱性破壞、能帶寬度變化…等等)，而計算結果可直接與ARPES實驗比較。此工作將探討三類不同的結構 : IV族半導體摻雜結構、III-V族缺陷結構與二維(2-D)石墨烯結構。 In modern materials science, introducing the impurities (such as, vacancies, dopants, lattice dislocations, etc.) inside a periodic lattice structure is the most effective approach to manipulate the fundamental characteristics of materials, including electronic , magnetic and optical properties. Corresponding to the progress of modern experiments by means of novel techniques and sample preparation of doping crystals, theoretical atomic-level simulation of doping structures can be performed within a supercell scheme. However, the connection between the corresponding structures of doped and undoped compounds will be obscured by zone-folding induced reduction of Brillouin zone in a supercell calculation.. Thus, it is our task to unfold the supercell band structure by combining the basis transformation and momentum space unfolding methods. The unfolded band structure enables us to observe directly the impacts of doping on the band structure such as symmetry breaking and band width modification. A direct comparison between the first-principles unfolded band structure calculations and ARPES measurements can be achieved.. In this thesis, we will study the following three systems: group IV semiconductor doping, group III-V defects and 2D graphene structures.
