由於半導體材料(GaAs-AlAs-GaAs)中處於不同能帶的電子有不同的質量，所以在本篇論文中我們引用有效質量倒數的張量(reciprocal effective mass tensor)概念，來研究半導體中電子傳遞的行為。
首先，我們將這概念應用在一維的量子穿隧的問題，探討在同一導電帶中(Γ valley)，不同能量的電子穿透過材料的機率為何?接著將問題延伸到兩個導電帶之間(Γ valley和Χ valley)的散射問題，並且採用耦合(mixing)的概念，把兩個原本不相關的導電帶給聯繫在一起。同時地，我們也計算當不同能量的電子穿透材料時，在不同的導電帶所得到的穿透係數，接著並調整耦合的強度，分析此強度與穿透係數的關係。
最後，我們施一外加偏壓於材料上，使其能帶圖變形，所以當我們將電子射入材料內時，則有電流的產生。在這過程中，我們要探討電流強度與偏壓的關係，以及電流強度與耦合強度有何關聯？此時，我們將會發現一些有趣的現象，如負電阻效應(Negative Differential Resistance)等等。

In semiconductors, electrons have different effective mass in different energy bands. Thus, in this thesis, we use the concept of reciprocal effective mass tensor to study the transiting behavior of electrons in semiconductors.
First, we apply this concept to problems of quantum tunneling in one dimension, and studying the probability of electrons with different energies in the same valley (Γ valley) through semiconductors. Next step, we extend 1-D problems to scattering problems between two valleys (Γ valley and Χ valley). And we use the concept of mixing to combine the two valleys which have no relation originally. At the same time, we also calculate the transmission coefficients of electrons with different energies in different valleys through semiconductors. And we change the intensity of mixing to analyze the relation between the intensity and transmission coefficients.
Finally, we give an additional bias on semiconductors to make the band diagrams deformed. This bias will cause current occurred when electrons emit through semiconductors. In this process, we can discuss the relation between intensity of current density and bias, and that between intensity of current density and intensity of mixing. Thus we will find some interesting phenomena, such as negative differential resistance (NDR) and etc.

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