Electron energy level calculations for cylindrical narrow gap semiconductor quantum dot

Jacobi–Davidson methods for cubic eigenvalue problems

“…Thus,Ã( ) and A( ) have the same ÿnite spectrum except the eigenvalues in ( ). Furthermore, dividing Equation (8) by 3 and using the fact that…”

“…Figure 1 illustrates the schema of the QD structure. Moreover, the model is based on the e ective-mass envelopefunction approximation with one conduction band, the BenDaniel-Duke boundary conditions, and non-parabolic e ective mass depending on both energy and position [1][2][3]. On the boundary of the QD, the ÿnite hard-wall 3D conÿnement potential is induced by real discontinuity of the conduction band.…”

“…The diameter and the height of the cylindrical QD considered here are 15 and 2:5 nm, respectively, whereas that of the matrix are 75 and 12:5nm, respectively. The QD size is chosen so that it is approximately comparable with that of the experimental model presented in Reference [23] and the non-parabolic e ect of the band structure is signiÿcant [3]. Furthermore, the semiconductor band structure parameters used in the numerical computations are c 1 = 0:000, g 1 = 0:235, 1 = 0:81, P 1 = 0:2875, c 2 = 0:350, g 2 = 1:590, 2 = 0:80, and P 2 = 0:1993.…”

“…In applications, a set of the eigenvalues embedded in the interior of the spectrum of a large-scale eigenvalue problem are often of interest. For example, a semiconductor quantum dot model with non-parabolic band structure described by the three-dimensional (3D) Schr odinger equation [1][2][3] can result in a cubic eigenvalue problem of (1) with order up to 211 400 from the ÿnite di erence approximation (see Section 3). And we are concerned only with several smallest positive real eigenvalues (energy states) and their associated eigenvectors (wave functions).…”

Nonparabolicity and dielectric effects on addition energy spectra of spherical nanocrystals

“…Intersubband spin-density excitations in QWs have been addressed using the Kohn-Sham equations with energy-dependent effective mass. 8 Extensive single particle studies of different shaped QDs, [9][10][11] quantum rings, 12 and artificial molecules 13 have also been carried out. Recently, the energy-dependent effective mass approach has reproduced experimental effective masses obtained from optical transition energies in QWs 14 and provided quantitative interpretations of capacitance voltage spectroscopy experiments.…”