Properties Of Negatively Charged Donors In Parabolic Quantum Well Wires Under Magnetic Fields

The ground state of a negatively charged donor (D-) in a parabolic GaAs quantum-well wire in the presence of a magnetic field is investigated using the finite difference method within the quasi-one-dimensional effective potential model. The magnetic effects on the binding energies of the ground state of a D- ion are calculated for various parabolic potentials. The average distance between the electrons and the donor ion, and the average distance between the two electrons are also calculated, respectively, as a function of the strength of the parabolic potential and the magnetic field. We find that the interplay of the spatial confinement and the magnetic confinement of electrons in quantum-well wires leads to complicated behavior of the binding energies of the D- ion. In the case of strong spatial confinement, the binding energies of the D- ion are insensitive to the magnetic fields and diverge as the parabolic potential approaches infinity. This indicates that the main contribution to the binding energies of the D- ion comes from the spatial confinement of the electrons, which prevails over the magnetic confinement. In the intermediate range of spatial confinement, the effect of the magnetic confinement of electrons combines with the effect of the spatial confinement. The effect of the magnetic confinement on the binding energies of the D- ion becomes more apparent as the parabolic potential decrease. In the weak spatial confinement range, the binding energies of the D- ion increase with increasing magnetic field and converge asymptotically to the value of the D- ion in bulk material as the parabolic potential approaches zero. We also find that the average distance between the two electrons, as well as the average distance between the electron and the donor ion, gets shorter as the extra confinement increases. This indicates that the two electrons become more strongly bound as the extra confinement increases. The confinement, on one hand, pushes the electrons closer to the donor ion, but on the other hand, forces the electrons to get close to each other. Thus, there are two competing trends: the increase of the electron-donor ion attraction and the increase of the electron-electron repulsion, which almost balance each other. Our calculation shows that the binding energies of the D- ion in ground state increase as the spatial and magnetic confinement increase. This indicates that the increase of the electron-donor ion attraction dominates the increase of the electron-electron repulsion as the extra confinement increases for the ground state of a D- ion in a parabolic quantum-well wire.Moreover, we have adopted the Thomas-Fermi model to investigate the screening effect on the properties of the D- ion in a parabolic quantum-well wire. We found that the screening effect enlarged the average distance between the particles of the system. Therefore, it decreases the binding energy of the system. The D- ion in the parabolic quantum-well wire becomes unbind as the screening parameter increases, and the value of critical screening parameter increases with the increasing extra confinement.