| Summary: | 碩士 === 國立交通大學 === 物理研究所 === 89 === The progress of semiconductor technology fabricates devices
in the nano-scales successfully. The scale is close to the atomic size that the quantum behaviors of electrons are very important. Scales, temperatures, external field now have subtle influences on the system. And we realized that investigations often can only be explained with quantum mechanics.
A semiconductor quantum dot is a structure of three dimensinal confinements. In this article we will discuss the behaviors of an impurity in the vertical quantum dot with static electromagnetic field. The concentration of dopants allows us to simplify the many-body problem to be tractable. Since the effective mass approximation remains valid for band structures of GaAs with shallow donors, the problem can be solved as a hydrogenic atom confined in a well-described harmonic potential.
The Schrodinger equation of the system can not be solved analytically, therefore efficient numerical simulations are important. We use the Gauss-Legendre-Lobatto pseudospectral
method to solve the problem. The well-located grid points and
well-behaved wave functions on the boundaries greatly improve the realiability and accuracy of our results.
Finally, our results are compared with published perturbation treatment. We also present the ground- and excited state energy levels. The outcomes would be helpful on optical spectral measurements.
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