本篇論文我們計算單一電子在奈米碳管中受到一雜質(電洞)吸引的束縛能階。在我們的計算結果中，基態束縛能量與文獻計算無限長碳管中最低的激子束縛能相近，不過在短管軸碳管中則沒有束縛態。另外我們對奈米碳管外加一均勻磁場，再不考慮自旋與磁場偶合之下，可看到雜質能階有隨著一個基本磁通量做週期性變化的A-B效應出現，短管軸碳管的雜質能階有簡併被打開的現象，而長管軸碳管則沒有能階簡併。

In this thesis, we calculate the energy states of one electron attracted by an impurity(hole) in finite carbon nanotubes. Comparing our calculations with Pederson’s result, the ground state energy of the electron (attracted by an impurity in finite carbon nanotube) is close to the exciton binding energy in infinite carbon nanotube, but there is no bound state in short length carbon nanotubes.

Further more, we study energy states under an uniform magnetic along the z axes. The energy levels of the impurity vary in periods of an unit magnetic flux. And some of the energy states are degeneracy in short length carbon nanotubes but not in long length carbon nanotubes.

目錄　
　
第一章 導論 ----------------------------------------------- 7
第二章 奈米碳管的幾何結構與能帶理論　------------------------- 9
　2-1 幾何結構　------------------------------------------------ 9
　2-2 石墨能帶結構　------------------------------------------- 10
　2-3 奈米碳管的能帶結構　-------------------------------------- 12
　2-4 奈米碳管的導電性　---------------------------------------- 13
　2-5 電子在奈米碳管中的有效質量　------------------------------ 14
第三章 計算方法 ---------------------------------------------- 17
3-1 電子受雜質吸引的模型 ------------------------------------ 17
　3-2 外加磁場　------------------------------------------------ 19
第四章 計算結果與討論　--------------------------------------- 21
　4-1 電子受雜質吸引的能階分佈 -------------------------------- 21
　4-2 外加磁場下的電子能階分佈　-------------------------------- 22
4-3 結論 ---------------------------------------------------- 23
參考文獻 ------------------------------------------------------- 45
5結構與能帶理論

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