即使莫爾定律至今仍然是被信賴的經驗法則，人們仍擔心尺寸微縮趨勢不再如同該定律所言，製程技術不斷受到考驗，同時隨著電晶體數目指數上升，元件的整體功率也持續地升高。在這樣的情況下，對於製程技術外其他改善元件特性的研究持續地受到重視。
如何在相同製程技術的情況下去改善電晶體電特性的研究是現今模擬的趨勢，藉由結構變化來提高奈米等級之互補式金氧半元件的性能，諸如雙閘極，三閘極或鰭式電晶體的設計。對於材料特性影響元件的研究，如同能帶結構、晶體方向、量子效應及電子遷移率也是一大研究方向。
此論文旨於探討不同晶體表面方向對超薄基體元件的影響。首先，我們藉由將緊束縛理論從描述晶體各向同性質之塊材推導至在指定晶體方向被限制在量子等級厚度的極薄結構，運用至矽與鍺兩種材料，再根據能帶理論去求得電子在該結構中指定方向的等效質量與能障能量差異，接著將所得到的量子參數應用於雙閘極金氧半場效應電晶體中，利用非平衡態格林函數方法來模擬元件在量子彈道傳輸下的電壓電流轉移特性曲線去觀察元件的電特性，以分析討論通道材料晶體表面方向對於元件的影響。

The trend of size shrinking is no longer as straightforward as traditional Moore's Law in the past. How to improve the electrical characteristics of transistors is still highly considered as a major target of today's investigation. The structural evolution, planar MOSFETs, fin-FET and gate-all-around MOSFET it to improve the gate electrostatic control of the nanoscale complementary metal-oxide-semiconductor (CMOS). Also, the impact of the material properties of the device, as band structure, crystal orientation, quantum confinement effect, and carrier mobility, is an essential topic in the direction of research.
This thesis intends to investigate the impact of crystal surface orientation on the band structure of the ultra-thin body (UTB) and the electrical characteristics of a MOSFET based on the UTB. First, we introduce the empirical tight-binding (ETB) theory for the bulk material. Then we generalize the ETB model to a material with the UTB structure, where has one direction confined in a nanoscale thickness in a specified crystal direction. Based on the ETB calculated band structure, we obtain several material parameters, such as electron effective masses and band offset at different valleys and spatial directions, which are essential for quantum transport simulations. Apply the obtained quantum parameters to the device structure. With non-equilibrium Green's function (NEGF) method and quantum ballistic transmission assumption, we simulate the electrical characteristics of double-gate (DG) MOSFETs based on the UTB. Finally, we analyze and compare the impact of the crystal surface orientation of the channel material in the same channel direction on the electrical characteristics of the devices.

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