Doping of semiconductors by impurity atoms has widespread technological applications in microelectronics and optoelectronics. It provides further means to control the performance of related devices [1]. Donors have been used in some elegant quantum computing proposals that draws upon the vast expertise of the semiconductor device industry [2]. One of the proposals that renewed interest in the quantum mechanics of donors is the Kane qubit [3] in which information is encoded into the nuclear spins of donor atoms in doped silicon electronic devices, and engineers the donor electron wave function by electrodes to manipulate information.

 Due to the development of nanoscience and nanotechnology, the study of donor related electronic and optical properties in semiconductor quantum dots (QDs) has been of great interest in the past [4–8]. It has been found that donor related properties in semiconductor QDs depend significantly on the materials, geometries (sizes and shapes), shapes of the confinement potentials and also dopant positions. External perturbations, such as applied electric and magnetic fields, hydrostatic pressure and temperature, also modify significantly the confined states of the donors [6,9–14]. To control and modulate the output of the doped-QDs-based optoelectronic devices, a combined application of these external perturbations in semiconductor QDs, such as a combination of the electric field with the magnetic field, has drawn increasingly attentions recently [15–20]. When the electric and magnetic fields are applied perpendicular to each other in a QD system, as reported in a recent paper [20] of our group, competition effects appear. These competition effects on the donor binding energy have been found to be strongly dependent on the QD geometric characteristics (dot sizes and aspect ratios) and also the strength and orientation of the two fields [20]. When another external perturbation is also simultaneously present in the QD system under the influence of perpendicular electric and magnetic fields, a question, which will arise, is that how a given perturbation influences the competition effects.

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