本論文將根據第一原理的密度泛函理論來計算單壁奈米碳管的
電子特性與功函數，首先將針對無限長奈米碳管做結構收斂測試，並
對其做能帶結構計算與態密度計算，藉由能帶結構與態密度我們可以
了解奈米碳管的電子特性，進一步可判斷是否為金屬特性或半導體特
性。接著我們對奈米碳管做垂直管軸方向外加電場模擬，由能帶結構
圖觀察其能隙與能帶變化，我們發現半導體性質的奈米碳管，在電場
作用下能隙消失，而此結果使得奈米碳管可以運用於場效應電晶體
上。最後我們對奈米碳管做平行管軸方向外加電場模擬，此時我們著
重於電場對功函數的變化，我們發現奈米碳管功函數隨電場增強而下
降，而這正是奈米碳管場發射的主要因素，並且我們針對不同長度的
奈米碳管比較其功函數受電場影響的變化，發現奈米碳管的長度並無
嚴重影響功函數的變化。

We will compute the electronic properties and work functions of
single-walled carbon nanotube according to the first principle method.
First we find the lowest energy structure of infinitely-long carbon
nanotube by the convergence calculation, and then calculate the density
of states and band structures. Now we can distinguish between metal and
semiconductor of carbon nanotube by it’s density of states and band
structures. Second we simulate carbon nanotube under transverse electric
field. We find that band gap modifications occur to the semiconducting
carbon nanotube under an external electric field by inducing a
semiconductor-metal transition. It can apply to field effect transistors as a
result of semiconductor-metal transition. Finally we simulate carbon
nanotube under vertical electric field. We find that work function
modifications occur to carbon nanotube under an external electric field.
And tube length do not effect the work function modifications.

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