Neutral Donor Bound Exciton In Quantum Wells Line Nature

In the effective mass approximation, using the one-dimensional equivalent potential model and simple two-parameter wave function, theground state binding energy of excitons bound to a neutral donor (D0,X) ininfinite rectangle GaAs quantum-well wires (QWWs) as a function of the wire width is calculated variationally in different position of the impurity (at the center, at the boundary and at the corner). The results are satisfactory.Firstly, the binding energies of excitons and impurity state in infinite rectangle GaAs quantum-well wires are calculated variationally. The results obtained basically are in good agreement with the ones gained from the previous theories and experiments.Secondly, the one-dimensional equivalent potential model is used to turn the excitons and impurity state in infinite rectangle GaAs quantum-well wires into the effective one-dimensional excitons and impurity, thenthe parameters (aD rD ax and rX) versus the quantum-well wires width are calculated.As to (D0,X) in infinite rectangle GaAs quantum- well wires, theone-dimensional equivalent potential model is still utilized. In the model, the following variational wave function is chosen:In the wave function , both the Coulombic correlation among the particles and the effect of the interchanged term caused by the same particles are taken into consideration. Where a and B are the twovariational parameters. and the aD rD ax and rx are determined bythe equations obtained from the variation of the energy of excitons and impurity state. By the complicated mathematical calculating, the energyequation of (D0,X) is achieved, the variational parameters a and B can be determined based on the energy equation of (D0,X) which is mentionedabove, thus the binding energy of (D0,X) versus the quantum-well wireswidth can be obtained. The average interparticle distance as functions of the wire width is also calculated, with the results being satisfactory.At last, the results are discussed in detail. The conclusions are as follows:( i ) The binding energy decreases as the wire size increases, and the binding energy is considerably larger in narrow well width. As the wirewidth increases, the binding energy of (D0,X) decreases and begins toapproach the GaAs bulk value. The reason why peak value has not appeared is adoption of the infinite potential in quantum-well wires.( ii ) In comparison with the binding energy of the (D0,X) in thequantum-wells (QWs) and the binding energy of biexciton (XX) in the QWWs at the same condition, the results obtained can be proved to be reasonable.(Hi) The binding energies of the (D0,X) system as a function of the length of one side (Lx = L) fixed while the other side (Ly=W) varied iscalculated. It can be obtained that the binding energies are more correlated to the cross-sectional area of the wire than the size of the rectangular cross section.( iv ) The average interparticle distance increases as the wire size increases, the changing tendency of the average interparticle distance reverse to the binding energy. When the average interparticle distance takes its smaller value, the binding energy takes its greater value. The bindingenergy of (D0,X) yields a reduction as the average interparticle distanceincreases. The average distance of donor-electron is much less than that of donor-hole, which is due to the Coulomb potential, and it is consequent that the average distance of electron-hole is less than that of electron-electron.