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Off‐Center Neutral and Negatively Charged Donor Impurities in Semiconductor Heterostructures: Fractal Dimension Method
Author(s) -
Mikhailov I.D.,
Betancur F.J.,
Escorcia R.A.,
SierraOrtega J.
Publication year - 2002
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200211)234:2<590::aid-pssb590>3.0.co;2-e
Subject(s) - wave function , ground state , physics , heterojunction , quantum mechanics , hydrogen atom , electron , condensed matter physics , atomic physics , group (periodic table)
We reduce the problems of the on‐ and off‐center D 0 and D — S‐states in semiconductor heterostructures to the similar ones in an isotropic effective space with variable fractional dimension starting from the variational principle. The dimension of this space is defined as a scaling parameter that relates the radii of a set of spherical boxes to the charge densities within induced by the free electron ground state in the heterostructure. Explicit expressions for the effective space dimensionality in a quantum well (QW), quantum‐well wire (QWW) and a quantum dot (QD) are found by using this definition. To solve the wave equations for the free electron ground state in the heterostructure and for the hydrogen‐like atom S‐states in the fractional‐dimensional space, we use the numerical trigonometric sweep method. The three‐parameter Hylleraas trial function is used to solve the similar problem for a negative‐hydrogen‐like ion in the effective space. Ground state binding energies for off‐center neutral and negatively charged donors in QWs and spherical QDs are calculated. Our results are in a good agreement with those of the variational and Monte Carlo methods. In addition, novel results for the D — binding energy as a function of the cylindrical GaAs/Ga 0.7 Al 0.3 As QWW radius and the magnetic field intensity are presented. It is found that the D — binding energy in the wire increases from 0.055 Ry* up to about 1.230 Ry* as the radius decreases to 30 Å. It is also shown that the magnetic field produces a considerable enhancement of negative‐donor binding energy in QWW only for radii greater than 100 Å.