由於石墨烯具有獨特且優異之電子與光學性質，其在各種光電元件的應用上被認為是極具發展潛力之二維奈米碳材料。然而，在實際的應用上石墨烯必須依附於基材，而石墨烯與基材間的相互作用通常會降低石墨烯的電子遷移率。因此，了解基材的表面結構與其內部所含之缺陷、雜質如何對石墨烯的電子性質產生影響便成為當前極為重要之研究課題。由於製程的相容性以及其本身所具有之諸多優點，二氧化矽是目前奈米元件中最常被使用作為基材的絕緣介電材料。在本研究中，我們即利用第一原理計算探討當二氧化矽基材內含有磷、砷以及錫等摻雜物時，基材內部的微結構變化與表面性質如何對石墨烯的電子性質產生影響。
在論文的第一部份，我們首先探討含有磷摻雜之二氧化矽基材對石墨烯電子性質產生之影響。我們的結果顯示磷原子在二氧化矽基材中可能會以數種不同的結構與鍵結形式存在，其中部分的鍵結形式甚至會伴隨二氧化矽本質的結構缺陷產生。這些摻雜物以及伴隨而生的本質缺陷可能會在二氧化矽能隙中產生電子佔據或未佔據之缺陷能態，其部分可能成為石墨烯電子之施體或受體，因而造成石墨烯與二氧化矽基材間產生電荷移轉的現象。結構分析的結果顯示，含有磷摻雜之二氧化矽基材中約有40%的摻雜結構會對石墨烯產p型摻雜的效果。另外，我們的結果也顯示，二氧化矽基材表面結構的差異可能會引起缺陷能態相對於真空能階(vacuum level)距離的改變，進而影響其與石墨烯間電荷轉移的程度與效果。例如當含磷摻雜基材表面吸附水分子時，OH朝下之偶極矩會增加基材對石墨烯產生p型摻雜之效應，並降低或甚至消除n型摻雜的可能性；相反地，當基材表面吸附之水分子OH基朝上時，其原本對石墨烯所具有之p型摻雜效應會被降低，或甚至反轉而產生n型摻雜的效果。這樣的效果與當含磷摻雜之基材表面生成矽醇基(silanol group)時對石墨烯產生的影響類似。
接著我們探討含砷摻雜之非晶二氧化矽基材對石墨烯電子性質之影響。結構分析的結果顯示雖然砷與磷為同族元素，磷與砷原子的原子半徑大小以及電負度等基本性質之差異可能會造成兩者在二氧化矽結構中形成不同傾向的鍵結形式。另外，砷摻雜在二氧化矽基材中所引入的缺陷能階與真空能階的距離普遍較磷摻雜為大，使得絕大部分與砷摻雜結構相關的無電子佔據缺陷能階皆低於狄拉克點，因而導致對石墨烯產生較磷摻雜為顯著的p型摻雜效應。也因此緣故，有將近有70%的砷摻雜結構不容易受到基材表面結構或水分子存在的影響而明顯改變其對石墨烯所產生之p型摻雜效果。
最後我們探討錫摻雜二氧化矽基材對石墨烯電子性質之影響。與磷、砷摻雜最大不同的地方是實驗上有觀察到摻雜之錫原子再經退火處理後有可能會以β-錫金屬析出或以金紅石二氧化錫團簇形式存在於二氧化矽基材中。所以在本研究中，我們分別針對這兩種結構對石墨烯電子性質所可能產生之影響進行探討。我們計算的結果顯示由於β相錫金屬的功函數略小於石墨烯，β-錫金屬與石墨烯間的交互作用有可能會使石墨烯產生n型摻雜效果。另外，我們的結果也顯示當石墨烯置放於二氧化錫基材表面時，基材表面的五配位錫原子有可能會捕捉石墨烯上的電子而對石墨烯產生p型摻雜的效果。然而，當基材表面產生氧空缺時，氧空缺所產生的缺陷能態會與基材導帶下緣之能態相互作用，因而造成導帶下緣往高能量端位移，使得其原本對石墨烯所具有之p型摻雜效果消失。本研究成果可對石墨烯應用在光電奈米元件的材料設計及製程改善方面提供更多可能的方向與參考。

Graphene, a monolayer of graphite, is a promising candidate for novel carbon-based devices due to its outstanding physical properties and unique electronic properties. In practical applications, graphene must be adsorbed on a substrate. Considering the process compatibility and the optical contrast to the graphene layer, SiO2 remains one of the predominant choices for the substrate materials in nanoelectronic devices. However, the interaction between graphene sheets and the SiO2 substrates could lead to the degradation of the carrier mobility, which eventually limits its performances. Therefore, understanding the modulation of the electronic properties of graphene via the dopants or defects in underlying SiO2 substrates is an important issue. In this thesis, we present a first principles study on revealing the doping effect on graphene from P, As, and Sn impurities in the SiO2 substrates.
In the first part of the thesis, the effects of phosphorus-doped SiO2 substrates on the electronic properties of the graphene sheets were discussed. Various bonding configurations of P dopants were observed, and some of the bonding configurations could even associate with the formation of intrinsic defects of SiO2. Those dopant configurations and associating intrinsic defects could induce occupied or unoccupied defect states in the substrates. Some of them could even lead to charge transfer of graphene. We found that about 40% of the defect configurations could induce p-type doping effects on graphene. Furthermore, manipulation of the surface structures of SiO2 can modulate the energy levels induced by P and the related defect states relative to the Dirac point of graphene. For example, while water molecules are absorbed on the surface of phosphorus-doped SiO2, the dipole moments of the downward OH-groups could enhance the p-type doping effects on graphene. On the contrary, the upward OH-groups may reduce the p-type doping effects and even induce n-type doping. Those effects are similar to that induced by surface silanol groups.
In the second part of the thesis, the characteristics for graphene on arsenic-doped SiO2 were analyzed. First, we found that although arsenic and phosphorus are both the Group VA elements in the periodic table, the preferences for the bonding configurations in SiO2 are largely different. Moreover, since the energy level for the unoccupied defect states induced by arsenic are generally lower than that induced by phosphorus, the p-type doping effects becomes even more significant, and the surface condition can merely affect the preferences for charge transfer.
In the third part of the thesis, we consider the impacts of tin-doped SiO2 substrate on the electronic properties of graphene. Unlike the phosphorus- and arsenic-doped SiO2, tin atoms tend to segregate around the surface and form metallic tin clusters or tin oxides after high temperature annealing. Therefore, our simulations were performed by placing graphene sheets on pure tin (β-Sn) and tin oxides (rutile SnO2). Our calculated results show that the work function of β-Sn is around 0.16~0.19eV lower than that of graphene, indicating that β-Sn nanoclusters embedded in SiO2 could induce n-type doping on graphene monolayer. For rutile SnO2 substrate, our calculations also show that the five-coordinated Sn atoms on the surface would trap the electron, resulting in remarkable p-type doping on graphene. Upon the existence of O vacancy on substrate surface, the interaction between conduction band and the defect state of vacancy may push the bottom of conduction band to a higher energy level. Hence, the presence of O vacancy can notably reduce the doping effect on graphene from the SnO2 substrate.

誌謝 i
摘要 ii
Abstract iv
目錄 vi
第一章 緒論 1
1.1研究背景 1
1.2研究目的與方向 2
第二章 文獻回顧 5
2.1石墨烯之基本性質 5
2.2含缺陷或摻雜物之基材對石墨烯電性影響 7
第三章 理論基礎與計算條件 11
3.1波恩-歐本海默近似法(Born-Oppenheimer approximation) 11
3.2密度泛函理論 (Density Functional Theory, DFT) 12
3.2.1 Thomas-Fermi Model 12
3.2.2 Hohenberg-Kohn方程式 12
3.2.3 Kohn-Sham 方程式 13
3.2.4交換相關泛函(exchange-correlation functional) 15
3.2.5混和密度泛函 16
3.2.6虛位勢法 (pseudopotential method) 17
3.2.7分子動態模擬 (Molecular Dynamics Simulations) 18
3.3 計算條件 18
第四章 摻雜磷之二氧化矽基材對石墨烯之影響 21
4.1 石墨烯之能帶結構 21
4.2磷原子在非晶二氧化矽中之結構討論 25
4.3石墨烯置於摻雜磷之非晶二氧化矽基材 30
4.3.1摻雜磷之dense基材 30
4.3.2表面吸附水之摻雜磷非晶二氧化矽dense基材 51
4.3.3表面含矽醇基(silanol group)之摻雜磷非晶二氧化矽基材 72
4.4總結 84
第五章 摻雜砷之二氧化矽基材對石墨烯之影響 86
5.1摻雜砷在非晶二氧化矽中之結構討論 86
5.2石墨烯置於摻雜砷之非晶二氧化矽基材 89
5.2.1摻雜砷之dense非晶二氧化矽基材 89
5.2.2表面吸附水之摻雜砷dense非晶二氧化矽基材 103
5.2.3表面含矽醇基之摻雜砷非晶二氧化矽基材 119
5.3 總結 126
第六章 摻雜錫之二氧化矽基材對石墨烯之影響 127
6.1 研究目的與方向 127
6.2金屬錫對石墨烯的摻雜影響 130
6.3二氧化錫對石墨烯電子性質之影響 133
6.3.1二氧化錫之基本性質 133
6.3.1石墨烯置於無缺陷之二氧化錫基材 136
6.3.2石墨烯置於含氧空缺之二氧化錫基材 142
6.4 結論 147
第七章 總結 148
參考文獻 150

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