正方形GaAs量子点中类氢杂质结合能的数值模拟..doc

摘 要 在有效质量近似下，利用一维有效势模型，采用有限差分法作为数值计算方法，求解正方形量子点中类氢杂质的结合能，应用MATLAB编程进行数值模拟，研究了外加电场、量子点尺寸以及杂质位置对各能级结合能大小的影响。首先考虑杂质不存在时，电子在基态以及在五个激发态的能量随电场大小的变化。结果表明：各能级能量随电场以及量子尺寸的增大而减小。随之，考虑杂质置于量子点中心时，杂质结合能以及五个激发态结合能随电场、量子尺寸的关系。电场对各能级的结合能影响不同，有的能级的结合能随电场的增大而减小，有的能级的结合能随着电场的增大而先增大后减小。然而，各能级结合能随量子点尺寸的增加而减小。最后，改变杂质的位置，讨论杂质位置对各能级结合能的影响。结果表明：结合能对杂质的位置有很强的依赖性。 关键字：量子点；类氢杂质；有限差分法；结合能 Abstract Within the effective mass approximation, binding energies of hydrogen impurity in the square quantum dots are investigated by use of one-dimensional effective potential model and the finite-difference method. Numerical simulation by using MATLAB program, investigate the influence of applied field, the size of impurity and the impurity position on the binding energy at different energy level. First considering the impurity does not exist, the electron in the ground state and in five of the excited state energy vary with the magnetic of the electric field. Results show that the banding energy decreases with increasing electric field as well as quantum size. Then, we put the impurity at the centre of the quantum dot, investigate the influence of applied field and the size of impurity on binding energy at ground state and five excited state. Binding energy effect of electric field in each level is different, at some level, the binding energy decreases with the increase of electric field, at other level binding energy decreases after the first increases with the increase of electric field. However, the binding energy level decreases with the increase of the quantum dot size. Finally, change the position of the impurity, discuss the influence of impurity position on each level of the binding energy. The results show that the binding energy has a strong dependence to the position of the impurity. The keyword: Quantum dots; Hydrogen impurities; Finite-difference method; binding energies 目录 第1章 概述 1 1.1 量子点的几本概念及其应用 1 1.2 量子力学的创立和发展 2 1.3 研究意义及展望 3 1.4 本章小结 4 第2章 GaAs量子点中杂