以第一原理能帶展開理論研究摻雜效應對二維材料電子結構之影響

論文提要內容：對於現今二維材料的蓬勃發展，摻雜效應能使其材料有微妙的變化。摻雜效應會破壞原本晶體的週期性，進而能使材料有更多樣的發展和應用。利用超晶胞(supercell，SC)方法解決計算中非週期性系統，是常見的方法:隨著超晶胞越大，相對應的布里淵區(Brillouin Zone，BZ)即隨之變小；比較無摻雜之單元晶胞(primitive cell，PC)與SC計算，SC不僅含較多之電子數，而使得其BZ內的能帶數目增加，而且SC中的能帶，會因摺疊BZ而產生糾纏現象。所以，利用能帶展開理論，可以展開糾纏的能帶；此外，我們也引入混合泛函近似(hybrid functional)以及準粒子GW修正，模擬多電子系統之遮蔽效應。，因而，通過此計算之電子能帶結構，將可直接與角分辨光電子能譜曲線(ARPES)做比較。本論文中，我們分別計算三種二維系統:石墨烯摻雜氮化硼、二硫化鉬摻雜硒、以及二硒化鎢摻雜鉻與硒空缺。在石墨稀摻雜氮化硼中，討論相同濃度不同的摻雜組成，以及不同濃度摻雜情況下，對於其摻雜形成能(formation energy)及電子能帶結構之影響。另一方面，我們發現二硫化鉬在不同晶格常數條件下，有不同的能隙特性；接著，也探討摻雜硒後，對於其形成能與能隙的影響。最後，探討二硒化鎢摻雜鉻與硒空缺；可以透過軌道投影，分析較局域化的能帶，並研究改變摻雜鉻與硒空缺之距離，所造成的影響。

關鍵字

二維材料；摻雜；能帶展開；混合泛函近似

並列摘要

For 2D crystal structures which original planar periodicity is disturbed through the introduction of external influence of defects, a supercell (SC) scheme is a common practice with longer periodic boundary conditions in the computational exploration of aperiodic systems. However, the expansion of primitive periodic cell (PC) in the SC approximation induces a Brillouin Zone (BZ) shrink through the zone folding and usually gives rise to a massively entangled band structures in a tiny size BZ of large SC structures. To probe the weak influence contributed by the imperfection of crystals, we discuss how to visualize supercell band structures in hybrid density functional theory more effectively by incorporating unfolded spectral weights which can be compared with angle-resolved photoemission spectra (ARPES) of 2D materials, such as graphene, silicene, etc. In this thesis, we performed the first-principles unfolding calculations to study the defect effects in the electronic band structures of 2D materials: graphene doped with BN, MoS2 doped with Se, and WSe2 doped with Cr and Se-vacancy (VSe).