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Polaronic shifts of the donor binding energies in an electric field in a quantum well are presented here. The properties of a polaron in a quantum well are investigated within the second-order perturbation theory. GaAs/Ga_1-xAl_xAs quantum well is chosen as an example to calculate the polaron energy. Since this system is a weak polar material, the electron-lattice coupling constant is small so this effect is considered by second-order perturbation theory. The polaronic effects are suppressed when an electric field is coupled. The diamagnetic susceptibility is also calculated and the results are compared with the results obtained using other approximation methods.

Using a variational approach, the binding energy of shallow hydrogenic impurities in a semimagnetic parabolic quantum dot is calculated within the effective mass approximation. The binding energy is computed for Cd_1-xinMn_xinTe/Cd_1-xoutMn_xoutTe structures as a function of the dot size in an external magnetic field. The results show that the impurity binding energy (i) increases with the reduction in dot sizes (ii) decreases when the magnetic field is increased for a given dot and (iii) increases to a maximum value at 100 Å and then decreases as the size of the dot increases beyond 100 Å for a realistic model. Spin polaronic shifts are estimated using a mean field theory. These results are compared with the existing literatures.

The binding energy of shallow hydrogenic impurities in parabolic GaAs/GaAlAs quantum dots is calculated as a function of dot radius in the influence of magnetic field. The binding energy has been calculated following a variational procedure within the effective-mass approximation. Calculations are presented with constant effective-mass and position dependent effective masses. A finite confining potential well with depth is determined by the discontinuity of the band gap in the quantum dot and the cladding. The results show that the impurity binding energy (i) increases as the dot radius decreases for the infinite case, (ii) reaches a peak value around 1R^* as the dot radius decreases and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well for the infinite case, and (iii) increases with the magnetic field. Also it is found that (i) the use of constant effective mass (0.067 m₀) is justified for dot sizes ≥ a* where a* is the effective Bohr radius which is about 100 Å for GaAs, in the estimation of ionization energy and (ii) the binding energy shows complicated behavior when the position dependent mass is included for the dot size ≤ a*. These results are compared with the available existing literatures.

The binding energy of a shallow hydrogenic impurity of a spherical quantum dot confined by harmonic oscillator-like and by rectangular well-like potentials, using a variational procedure within the effective mass approximation, has been determined. The calculations of the binding energy of the donor impurity as a function of the system geometry, and the donor impurity position have been investigated. The binding energy of shallow donor impurity depends not only on the quantum confinements but also on the impurity position. Our results reveal that (i) the donor binding energy decreases as the dot size increases irrespective of the impurity position, and (ii) the binding energy values of rectangular confinement are larger than the values of parabolic confinement and (iii) the rectangular confinement is better than the parabolic confinement in a spherical quantum dot.