這篇論文主要探討了對相同面積下各種不同邊長比例和各種不同邊界性質的量子點的D'yakonov-Perel'自旋弛豫值。對於不同邊長比例的量子點，我們更深入探討兩種不同的邊界性質：完全光滑和完全粗糙的。而應用在論文研究的主要方法為半古典的路徑積分數值模擬法，內容概要是這樣的：在第一章中，我們探討了論文研究的緣由，並對這篇論文作了簡單初步的介紹。接著在第二章中，我們推導出一些論文相關的實用公式。作法是由一些基本的有關Rashba的自旋軌道交互作用推導，再利用半古典的路徑積分理論延伸，從而得到具有Rashba的自旋軌道交互作用的電子在二維自由空間的能量的本徵值及本徵態。在第三章，我們解釋論文中數值模擬的方法，分別使用不同的自旋軌道耦合能量來測量，並實際說明了自旋弛豫極化的過程及最後的結果。在第四章，我們將第三章的光滑面改為完全粗糙面，用第三章同樣的方法來操作。在第五章，我們分別探討了單顆電子不同軌跡的自旋演化結果，這樣的結果有助於我們瞭解在第三章和第四章所得到的終結自旋極化值為正的原因。在第六章，我們則對論文的結果作了一番討論並導引出一些結論。主要有：我們發現具有完全光滑邊界的量子點有較慢的自旋弛豫。除此之外，在所有的同樣邊界性質的量子點中，正方形的量子點具有最大的終結自旋極化值。因此我們可以說明，在本文所提到的所有量子點系統中，正方形的量子點是最佳的自旋資訊儲存系統。

This thesis studies the D'yakonov-Perel' spin relaxation in various rectangular quantum dots with different side length ratios of the same area. The boundaries include smooth and rough cases. The method used was semiclassical path integral simulation. In Chapter 1, a brief introduction for the thesis is given. Thereafter, Chapter 2 derives some useful formulas for this study. It begins with the fundamental theory for classical spin evolution induced by the Rashba SOI and its semiclassical
version in path integral formalism and followed by the eigenstates and the eigenvalues of the Hamiltonian with Rashba SOI in the 2D free space. Chapter 3 explains our simulation method and demonstrates the spin polarization relaxation scenarios and their final residual polarization values in different spin-orbit coupling strengths in smooth systems. Chapter 4 extends the study from smooth systems to rough systems. In Chapter 5, the properties of the spin evolution along individual trajectories are studied. The result helps us understand the positive residual spin polarization in chapters 3 and 4. In Chapter 6 some discussions and conclusions are given. We found that the smooth boundary systems have a slower spin relaxation. Furthermore, the square quantum dot has a largest residual spin polarization. Therefore, among all smooth rectangular quantum dots of the same area, the smooth square is the best system for spin information storage.

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