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|Title:||Efficient method for calculating electronic states in self-assembled quantum dots|
Maksym, P. A.
|Citation:||Physical Review B, 2003, 68 (23), 235308.|
|Abstract:||It is demonstrated that the bound electronic states of a self-assembled quantum dot may be calculated more efficiently with a harmonic-oscillator (HO) basis than with the commonly used plane-wave basis. First, the bound electron states of a physically realistic self-assembled quantum dot model are calculated within the single-band, position-dependent effective mass approximation including the full details of the strain within the self-assembled dot. A comparison is then made between the number of states needed to diagonalize the Hamiltonian with either a HO or a plane-wave basis. With the harmonic-oscillator basis, significantly fewer basis functions are needed to converge the bound-state energies to within a fraction of a meV of the exact energies. As the time needed to diagonalize the matrix varies as the cube of the matrix size this leads to a dramatic decrease in the computing time required. With this basis the effects of a magnetic field may also be easily included. This is demonstrated, and the field dependence of the bound electron energies is shown.|
|Rights:||This is the author's final draft of the paper published as Physical Review B, 2003, 68 (23), 235308. The final version is available from http://prb.aps.org/abstract/PRB/v68/i23/e235308. Doi: 10.1103/PhysRevB.68.235308|
|Appears in Collections:||Published Articles, Dept. of Physics and Astronomy|
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