Measuring the Probability Density of Quantum Confined States

为了分析电子-电子相互作用对量子限制态概率密度测量的影响，编制了一个计算机程序，通过对角化哈密顿矩阵，数值计算量子点中n-电子的精确态。然后使用计算机程序计算了包含单个或N个电子的圆形、椭圆形和三角形量子点中的电子结构。在圆形量子点中，由于壳层填充和自旋极化半填充，附加能量随N的变化呈现出清晰的结构。然而，在椭圆量子点中，由于不对称约束势导致简并的单粒子态分裂，结构被削弱。利用精确对角化计算的特征态，计算了量子点的隧穿矩阵元素。对于具有N个电子（从N=1到4）的GaAs量子点，通过纵向声声子发射计算了能量弛豫时间，其中窄量子阱中的电子受到抛物线限制势的限制。通过考虑电子之间的库仑相互作用对电子状态进行了数值计算，并利用费米黄金法则估计了弛豫时间。随着电子数量的增加，能级变得密集，弛豫通道的数量急剧增加。通过对所有弛豫通道的弛豫时间的评估，发现有几个弛豫过程通过初始态和最终态之间的一些中间态被间接过程加速。

In order to analyze the effect of electron-electron interaction on measuring the probability density of quantum confined states, a computer program has been made which numerically calculates the exact N-electron states in a quantum dot by diagonalizing the Hamiltonian matrix.Electronic structures in circular, elliptic and triangular shaped quantum dots containing single or N electrons have then been calculated using the computer program. In a circular quantum dot, the addition energy shows a clear structure as a function of N due to the shell filling and the spin polarized half filling. In an elliptic quantum dot, however, the structure is found to be diminished, which is attributed to the splitting of the degenerated single-particle states due to the asymmetric confining potential. Tunneling matrix elements through a quantum dot have been calculated by using the eigen states evaluated with the exact diagonalization.Energy relaxation time through longitudinal-acoustic phonon emission has also been calculated for a GaAs quantum dot with N electrons (from N=1 to 4), where the electrons in a narrow quantum well are confined by a parabolic confining potential. The electronic states are numerically evaluated by taking into account of the Coulomb interaction between the electrons, and the relaxation time is estimated by using the Fermi's golden rule. As the number of electrons increases, the energy levels become dense, and the number of relaxation channels drastically increases. From the evaluation of the relaxation time associated with all the relaxation channels, several relaxation processes are found to be accelerated by indirect process through some intermediate states between the initial and the final states.