石墨烯被認為是令人振奮的新興二維材料科學基礎，但其零能隙的特性，侷限了在奈米光電元件上的應用。類似石墨烯的六角晶格層狀材料:單層氮化硼(BN)，成功地被合成介電或基板材料，成為以石墨烯為基礎的電子元件。更進一步，由兩層類石墨烯原子厚度，組成凡德瓦力複合層狀結構，可以在設計新穎元件上，延伸出更廣泛的應用 在本篇論文中，我們以第一原理密度泛函微擾理論，對少層氮化硼以及氮化硼與石墨烯的兩層複合材料，進行電子結構與振動特性研究。由於層狀結構具有高度的各向異性，我們也探索了氮化硼的少層及複合層結構，在平面應力效應下，對其電子能帶結構及拉曼光譜的影響。實際上計算的結果與最新實驗的量測相當吻合。 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 and vibrational properties of few-layer BN sheets and hetero-bilayer of BN and graphene by using density functional perturbation theory. According to the highly anisotropic character of these layered materials, we also investigate the biaxial stress effects on electronic band structures and Raman spectra of few-layer and hetero-bilayer BN nano sheets. Indeed, our calculating results are in good agreement with very recent experimental observation.