在2004年Andre Geim的研究團隊在偶然的情況下，重複使用膠帶黏貼石墨，使之撥離出單層石墨烯(Graphene)的樣品，且在觀測石墨烯後，發現了許多令人驚豔的物理性質，因而吸引許多科學家投入對二維材料的探索。為了探究二維新穎材料的基礎特性，我們將以第一原理密度泛函微擾理論，計算單、雙層石墨烯及單、雙層與多層氮化硼以及氮化硼/石墨烯異質結構，其電子結構、晶格的振動模式及拉曼光譜。 本篇論文首先介紹密度泛函理論(Density Functional Theory)與密度泛函微擾理論(Density Functional Perturbation Theory)，並說明拉曼光譜的理論基礎與第一原理計算方法。接著模擬計算石墨烯與氮化硼六角結構單層與雙層系統，也探討單層氮化硼結構中，聲子LO-TO 分裂 (Longitudinal Optical-Transverse Optical splitting)效應，並通過多層結構探討層間作用力。此外，我們也研究氮化硼/石墨烯異質結構的穩定堆疊結構、電子結構及晶格振動特性。 我們藉由計算低頻剛體層狀振動模式之頻率，估計層狀結構中之層間作用力強度大小，進而發現氮化硼/石墨烯異質結構層間之作用強度，比為氮化硼層大。而在異質結構中，因為層間耦合作用較弱，導致高頻區聲子模態，明顯由個別原子層所主導，此一特性，亦說明異質結構之聲子能譜，可視為單層氮化硼聲子與單層石墨烯聲子之組合，惟其主要相異處，在於光支頻低頻區的聲子模態，對應於相異原子層間之相對運動。 Graphene is considered the foundation of exciting new science in two-dimensional layered materials. However, the zero-band-gap properties limit its applications in building nano-optoelectronic devices. Recently, monolayer hexagonal boron nitride (BN), a layered material similar to graphene, has been synthesized successfully as a two-dimensional dielectric or substrate material for graphene based electronics. Further van der Waals heterostructures, composed of various isolated graphene-like atomic layers, extend a wide range of novel device designs. In this thesis, we study the electronic structures, vibrational properties, and interlayer interaction of few-layer hBN and hBN/graphene nanostructures by carrying out first-principles total energy calculations and Raman calculations within the framework of Density Functional Perturbation Theory(DFPT). We find high-frequency intralayer vibrations of these layered materials are dominated by each individual layer which is originated from the weak interlayer coupling. Furthermore, based on DFPT and spring model calculations, we find the interlayer interaction of few-layer hBN/graphene heterostructure is stronger than that of few-layer hBN nanosheets.
