Energy spectrum of an off-center hydrogenic impurity in an elliposiod quantum dot

• Main Authors: C.F. Kao, 高健富
• Other Authors: T.J. Yang
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/03411488553580762335

碩士 === 國立交通大學 === 電子物理學系 === 83 === In this thesis we study the electronic eigenenergies of ground state and the first excited state of a hydrogenic impurity in a quantum dot. The potential at the boundary of the quantum dot in our present work is set to be infinite. And we survey this problem in three case. (i) the tendency of change of the eigenenergies when the impurity is located at the center of this dot (ii) the change of elliptical quantum dot is shifted along a principal axis (iii) the change of eigenenergies when the volume of the quantum dot is fixed but the shape of quantum dot is gradually changed from sphere to ellipsoid. The calculation method used in our work is based on the theory proposed by Gorecki and Brown in 1989. We extend the original ideal of Gorecki and Brown to include more basis functions to evaluate the eigenvalue. And our improved especially when the position of method can also get excited energies which makes the G-B's variational method more general to other problems. From the coefficients of basis functions and the equal-value contour surface of eigenfunctions got in our numerical calculation, we show the effect from coulomb potential and that from boundary pontential compete with each other. And we also find the size effect of quantum dot apparently influence the eigenenergies.