本論文採用第一原理之密度泛函理論，對一維奈米碳材料進行物理特性研究，最初區域摺疊法依據奈米碳管之螺旋性，所歸類之電性結構已無法再遵循，因此其應用上之預測將會有明顯變化，必須藉由第一原理了解其電學性質與電子場發射間之相互關係。
選擇極小管徑之奈米碳管作為場發射源，然而特殊的深寬比特性，使其電學性質以奈米碳管之曲率效應作為主要依據，表現出較低之費米能，因此相對獲得較高之功函數，有別於超級針對場發射會帶來助益之構想；相同極小管徑下，有限管長之冒口端幾何重構，促使(3,0)和(5,0)之冒口結構分別轉變為sp3-like和sp2特徵，重構結構將會影響費米能附近之佔據態和非佔據態，透過冒口端之侷限態將可改善無限管長之奈米碳管的電子場發射。
摻雜對奈米碳管電性之影響，透過八種可能的B/N co-doping形式，找到硼和氮元素以相連成對的型式置換管壁兩顆碳原子，其形成能表現遠低於將硼和氮元素以分離形式進行摻雜。電性結構分析顯示，扶手椅型奈米碳管受B/N co-doping，將會使其轉變為半導體性；反之，原本為半導體性之鋸齒型奈米碳管，受摻雜作用後其能隙則獲得縮小，唯獨曲率效應較大之(4,0)和(6,0)則呈現金屬性；另一個考量因素，隨著摻雜濃度增加，B/N co-doping奈米碳管之能隙僅在一固定範圍內震盪，並無明顯影響；實際摻雜過程，是無法確保雜質影響的雜化現象，因此利用B-rich或N-rich對B/N co-doping奈米碳管進行雜化，其電性結構將獲得改變，表現出受子或施子狀態，此特徵行為是受費米能偏移至低能價帶區或高能導帶區進行佔據所導致的。
硼和氮元素除了以摻雜方式表現，也可與碳元素以一定化學計量比例合成為BC2N奈米管，而極小管徑(5,0)表現為金屬性，其餘扶手椅型和鋸齒型之BC2N奈米管均為半導體性；在區域II之能隙，主導操控著電子場發射效應，與功函數呈現相對應關係，因此鋸齒型BC2N奈米管之能隙與功函數均表現出sawtooth-like的特徵，隨者(n,0)內之指數n來決定，反觀在區域I，卻呈現相反關係，與極小管徑奈米碳管之狀態相似；而整體電子場發射過程，其電子的貢獻主要來自於硼元素鄰近之碳原子的p軌域價電子，其餘合成元素之電子貢獻則相對較為弱勢。
一維奈米碳材料透過摻雜和合成之技術，將影響其結構幾何和電學性質的改變，對其應用上將可帶來多樣化發展，未來將可以作為奈米尺度電子元件的理論參考依據。

The first principle theory is employed to investigate the physical properties of one-dimensional nano carbon materials, for instance of pristine and doped carbon nanotubes, and BC2N nanotubes. However, the classification rule of electronic structures in carbon nanotube was demolished by previous experimental studies, depending on the curvature effects rather than the chirality. Consequently, many applications might be changed due to above misjudgment. Therefore, the thesis is focused to investigate the relations between the electron structures and field emission of one-dimensional nano carbon materials.
The carbon nanotubes are used in field emission source due to their unique high aspect ratio. For the infinite ultra small carbon nanotubes, the high work function will be obtained by the accompanying decrease of the Fermi energy, different to the concept of the super tip. On the contrary, for the open-ended carbon nanotubes, the no-bonding valence electrons induced at the mouth layer after geometrical relaxations are corresponding to the variation of work functions. The localized states at the mouth layer of the open-ended (3,0) and (5,0) exhibit the stable sp3-like and sp2 structures, which will influence the occupied and the unoccupied states near the Fermi level and improve the field emission properties of infinite carbon nanotubes.
From eight possible B/N co-doping configurations, it is found that the one with substitutional B and N atoms located at neighboring sites has the smaller formation energy than that with separate B/N atoms. The electronic structure of armchair carbon nanotubes evolves from metallic to semiconducting as a result of B/N co-doping, whereas the energy gaps of the intrinsically semiconducting nanotubes are reduced significantly. On the contrary, the small zigzag nanotubes always remain metallic properties due to their large curvature effects except (5,0) after B/N co-doping. As the atomic concentration of B/N co-doping is increased, the energy gaps of carbon nanotubes oscillate around a constant level, which is much lower than the energy gap of BC2N nanotubes. Moreover, the B/N co-doped carbon nanotubes with B- or N-rich impurity exhibit the characteristics of an acceptor or donor, respectively, since their electronic structures are significantly influenced by the occupied states in the valence and conduction bands due to the shifting of Fermi level.
From the synthesis technology, the composite BC2N nanotubes can be fabricated with the specific stoichiometry, different to doping or substitution process. Most of BC2N nanotubes are semiconducting besides (5,0), which presents the metallic behavior and has a larger work function. In the region II, the work function of zigzag BC2N nanotubes, corresponding to their energy gap, shows an interesting sawtooth-like feature, depending on n is odd or even. During the field emission, the p-orbital of carbon atom near boron atom contributed more electrons emitting to vacuum level than other elements of BC2N nanotubes.
The one-dimensional nano carbon materials through synthesis and substitution technologies influence the geometrical optimization and electronic structures, which bring more potential applications. Therefore, the development of future high-performance nanoscale electronic devices might refer to these theoretical studies.

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