半導體一直是研究的熱門課題，本篇論文研究GaAs和AlAs兩種III-V族半導體的介面散射現象。在本篇論文中，我們首先介紹使所用的塊材其晶體結構和計算塊材能帶結構的緊密束縛方法(tight-binding method)。然後，利用緊密束縛模型結合轉移矩陣法找到連結兩種不同塊材的方法，用以探討GaAs的電子經過介面時，散射到其它能谷的機率。我們計算當GaAs/AlAs以(001)和(111)兩種不同方向作接合時，電子從GaAs中入射到AlAs在各點所產生的穿透量和反射量，我們發現當塊材以(001)方向接合，電子能量小於2.8eV時，電子較容易在Γ1點和X3點間移動；我們並且調整連結兩種塊材的參數的濃度以觀察改變參數對介面散射結果所造成的影響。我們嘗試以波函數的對稱性來解釋在介面散射所得到的結果，但結果顯示波函數的對稱性和介面散射的現象並無關係。

Recently, electronic properties of semiconductor had been an intensively interested topic and related researches had been prolific. Various categories of semiconductor devices are made of hetero-junction – an interface between two different semiconductors. The performance of a semiconductor device is very much depended on the behavior of electrons across the hetero-junction.

This thesis aims to explore the interface scattering of an electron across an interface between GaAs and AlAs. We first employ the tight-binding method to construct their bulk energy band structures, and then use the transfer matrix to connect the electronic wavefunctions in both sides. Some interface related tight-binding parameters are introduced within the transfer matrix across the heterojunction. The transmission and reflection coefficients into various energy valleys are studied as functions of the interface parameters.

We calculated the transmission coefficient and the reflection coefficient of different energy valleys with an incident Γ electron from the GaAs Layer under two different interface geometries, along the (001) and (111) directions. In the (001) direction, theΓelectron is scattered into the X valley due to the interface, and in the (111) direction, it’s scattered into the L valley.

We report our results for electron with energy from 1.5 eV to 2.8eV, and try to explicate the connection between transmissions and symmetrical properties; however, we fail to observe simple relations between transmission and symmetrical properties. It requires further investigation in the future study.

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