Abstract
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.