本論文是利用格林函數(Green’s function)計算導線參雜不同類型的雜質或缺陷時，電子電導值的變化。因為研究的對象是小尺寸的導線，所以電子內部的傳輸行為是量子傳輸，與古典的傳輸現象會有很大的不同。論文內所討論的導線包含-(1) 單一個雜質、(２)方形的位能、(3)亂數分布的雜質，其中雜質的位能形式是 函數。先利用薛丁格方程式,解出導線橫向侷限的特徵值及特徵向量。再利用特徵值及特徵向量計算格林函數。而格林函數與穿透機率有關，可計算出穿透機率，接著利用藍道公式(Landauer formula)計算電導值。計算的結果可以得到量子傳輸行為的一些特殊的物理現象。在單一雜質的導線中，可以看到電導值量子化的階梯曲線及受到位能為負的雜質引響，產生凹陷值。方形雜質的導線上則發現，電導值會有共振的現象，與薛丁格方程式處理方形位能井或方形位能障的情況相似。考慮雜質亂數分布導線，取雜質位能為正時，發現電導的波動特性(fluctuation)。這現象可以幫助我們了解一些量子干涉效應。增加一些位能為負的雜質之後，會改變電導值。其中一部分原因是受到準施體能階(quasi-donor level)的影響。我們的計算結果與Bagwell、Kumar等人利用散射矩陣(scattering-matrix)計算電導的研究成果[1,2]相符合。

Green’s Function is used to calculate the conductance in narrow wires which include several types of scatters. The research subjects are narrow wires, so the transport properties of the electrons belong to quantum transport, which is totally different from classic transport. This study discusses about the narrow wires that include: (1) a single scattering center, (2) rectangular potential barrier and (3) random distributed scattering centers. Both repulsive and attractive potentials are considered in each case. The delta function potentials are used for the discrete scattering centers. First, we use the Schrodinger equation to calculate the eigenvalues and eigenfunctions of the confined transverse modes of the narrow wires. Then, we use them to calculate the Green’s function in order to calculate the transmission probability. After that, we use the Landauer formula to calculate conductance. The results display the physical phenomena of quantum transport. The stepwise increases of quantum conductance are found for these wires. For a single attractive defect in the wire, there is a dip in the conductance caused by the existence of the quasi-donor level. For the rectangular barrier in the wire, there are resonances in the conductance which are similar to those of the potential barrier and well in quantum mechanics. For the random positive defects in the wire, there appears fluctuation in the conductance. This phenomenon helps us to understand the quantum interference effects. By changing part of the defects from repulsive to negative, the conductance is modified. There are some dips in the conductance due to the quasi-donor levels. The results are consistent with the work of Bagwell and Kumar [1, 2], who use the Scattering-Matrix to calculate conductance。

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