半古典傳輸模擬是一種利用勞倫茲力來計算電子在不同二維材料中隨著不同磁場以及不同載子濃度會有不同運動情形的模擬方法 [1]。

本論文討論了利用半古典傳輸模擬出的幾種情況，一開始的材料設定為石墨烯，並且從硬牆邊界開始分析，我們可以得到電子在其中傳輸的軌跡，接著利用TMF做出來的圖可以不同磁場和載子濃度的影響。接著我們還進行了更多的測試，例如：將邊界改成軟牆、改變裝置形狀、加入電場以及把石墨烯更換成其他不同的二維材料。經過所有測試之後，我們將結果與量子傳輸模擬的結果進行比較。

本研究表明，半經典模擬的結果與量子模擬的結果高度吻合。此外，硬牆測試與軟牆測試的結果也非常一致。

透過半古典傳輸模擬我們可以觀察到一些利用量子傳輸模擬沒辦法，舉例來說我們可以看出電子在撞到邊界的時候會有什麼特別的行為。

Semiclassical transport simulation is a way using Lorentz force to calculate how electron moves in different 2D materials with different magnetic field and carrier density [1].

This thesis is about Semiclassical transport for some cases, starting with the hardwall simulation in graphene, we can get the trajectories of the electron, further more we can do the Transverse Magnetic Focusing (TMF) for different magnetic field and carrier density. And then try to do more test such as changing boundaries into softwall, changing the shape of the device, adding electric field, and changing different materials. After all the test, we take the results to compare with the results of the Quantum transport simulation.

This work shows that the results from Semiclassical simulation are highly match with the results from Quantum simulation. Also the hardwall test and softwall test agree with each other very well.

By using semiclassical transport simulation, we can see some things that are not show in quantum transport simulation such as we can see how the electron act when hitting the boundary.

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