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Measuring the Probability Density of Quantum Confined States

测量量子限域的概率密度

基本信息

批准号：
08650380
负责人：
MORI Nobuya
金额：
$ 1.22万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

项目摘要

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.

为了分析电子-电子相互作用对量子受限态几率密度测量的影响，编制了一个计算机程序，通过对哈密顿矩阵对角化，精确计算了量子点中N个电子的态，并利用该程序计算了圆形、椭圆形和三角形含单电子和N个电子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的半填充，附加能随N的变化呈现出清晰的结构。而在椭圆量子点中，由于非对称限制势的存在，简并单粒子态的分裂导致了这种结构的减弱。利用精确对角化计算的本征态计算了量子点的声子发射矩阵元，并计算了N个电子（N=1 ~ 4）的GaAs量子点的声子发射能量弛豫时间，其中窄量子阱中的电子受抛物型限制势的限制.通过考虑电子之间的库仑相互作用的电子状态的数值计算，和弛豫时间估计使用费米的黄金法则。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。从与所有的弛豫通道的弛豫时间的评估，几个弛豫过程被发现是通过一些中间状态之间的初始和最终状态的间接过程加速。