|Abstract: ||以小分子苯環結構向外擴展，形成兩種相異結構如扶手椅形(Armchair, ACn, n= 3 ~ 9) 與鋸齒形(Zigzag, ZZn, n= 1 ~ 8)，n代表外圍圈數，使用SIESTA軟體GGA方法，搭配密度泛函數PBE基底函數DZP進行結構最佳化，並獲得能隙值。計算結果顯示，AC和ZZ結構隨著n數增加，共軛體系增大，能隙值各別從2.49下降至0.87 eV，5.24下降至0.38 eV。利用化學修飾將石墨烯末端氫原子，以不同取代基進行半取代與全取代計算模擬，選取拉電子基-F，-Cl，-CN與推電子基-OH，-SH。取代基不論具推、拉電子性質，皆造成能隙下降，以-SH取代基下降效果最佳，但隨著n數增加其取代基效應減小。同樣利用化學修飾將石墨烯中心結構產生缺陷進行模擬，計算結果顯示，結構會因碳空位缺陷的不同而有合環或扭曲的現象，而使能隙值產生變化。|
同樣以小分子硼氮六圓環結構向外擴展，形成兩種相異結構如扶手椅形(BN-ACn, n= 3 ~ 9) 與鋸齒形(BN-ZZn, n= 1 ~ 8)，n代表外圍圈數，使用相同計算軟體與方法，並獲得能隙值。計算結果顯示，BN-AC結構隨著n數增加，能隙值呈現一波動性下降；而BN-ZZ結構隨著n數增加，共軛體系增大，能隙值各別從6.33下降至4.22 eV。利用化學修飾將硼氮六圓環奈米帶末端氫原子，以不同取代基進行全取代計算模擬，選取拉電子基-F，-Cl，-CN與推電子基-OH，-SH。取代基不論具推、拉電子性質，皆造成能隙下降，以-SH取代基下降效果最佳。
Graphene is one of the most important subject in materials science today. It is a two-dimensional structure of sp2 carbon atoms with very unusual and interesting electronic and mechanical properties. Boron nitride (BN) nanoribbon is also have similar structures like grapheme. In my research, using C6 symmetry extension form a central benzene and hexagonal BN, two different hexagonal shapes of both structure, armchair shape (ACn, BN-ACn, n=3~9)and zigzag shape (ZZn, BN-ZZn, n=1~8) when n represents the number of peripheral rings, can be generated. Using the GGA method of SIESTA package, the optimized geometries and the electronic structures of hexagonal shape graphenes and BN nanoribbons were generated with density functional theory PBE and the DZP basis set. The calculation results show that for both the AC and ZZ graphene structure, the energy gap (Eg = LUMO-HOMO)decreased from 2.49 (n=3) to 0.87eV (n=9), and 5.24 (n=1) to 0.38eV (n=8) respectively; and for both the AC and ZZ BN nanoribbon structure, the energy gap decreased from 4.60 (n=3) to 4.10eV (n=9), and 6.33 (n=1) to 4.22eV (n=8) respectively with increasing n, i.e. increasing conjugation. Chemically modified hexagonal shape graphenes and BN nanoribbons with substitutions at the periphery both structure, were also investigated. Two substitution types, the half- and full-substitution, were calculated and various functional groups, including the electron-donating (-F, -Cl, -CN ), and –withdrawing (-OH, -SH ) were addressed. The calculated energy gap decreases for all of substitutions, no matter graphene or BN nanoribbon. Especially for –SH substituent in the hexagonal shape graphene while such substitution effect becomes less significant gradually with increasing n of the graphene. Last in defect effect of graphene, we observed graphene structure will be distortion and cyclized by some carbon remove, and dfifferent structure can affect energy gap.