Infinitely Deep Gaas Quantum Well Wires Biexciton Nature

In the effective mass approximation, using the one-dimensional equivalent potential model and a simple two-parameter wave function, the binding energy of the biexciton in the infinite rectangle GaAs quantum-well wires (QWWs) as a function of the wire width is calculated variationally. The reasonable results are obtained.Firstly, the binding energies of excitons in the infinite rectangle GaAs quantum-well wires are calculated variationally. The results obtained basically are in good agreement with the ones of the previous theories and experiments.Secondly, the one-dimensional equivalent potential model is used to turn the excitons in infinite rectangle GaAs quantum- well wires into theeffective one-dimensional excitons, then the parameters α_x and γ_xversus the quantum-well wires width are calculated.As to the biexciton in infinite rectangle GaAs quantum- well wires, the one-dimensional equivalent potential model is still utilized. In the model, the following variational wave function is chosen,In the wave function Φ, both the Coulombic correlation among the particles and the effect of the interchanged term caused by the same particles are taken into consideration. Where α and β are the twovariational parameters, and the α_x and γ_x are determined by theequations obtained from the variation of the energy of excitons state. By the complicated mathematical calculating, the energy equation of the biexcitonis achieved, the variational parameters α and β can be determined based on the energy equation of the biexciton which is mentioned above, thus the binding energy of the biexciton versus the quantum-well wires width can be obtained.The average interparticle distance are also calculated as functions of the wire width. The results obtained are satisfying.At last, the results are discussed and compared in detail with previous theoretical results. The conclusions are as follows:(1) The binding energy of the biexciton decreases as the wire size increases, and it is considerably larger in narrow well width. As the wire width increases, the binding energy of the biexciton decreases and begins to approach the GaAs bulk value. The reason why peak value has not appeared is due to the adoption of the infinite potential in quantum-well wires. In comparison with the binding energy of the biexciton in the quantum-wells(QWs) and the binding energy of (D0,X) in the QWWs at the same condition,the results obtained can be proved to be reasonable.(2) The binding energies of the biexciton system as a function of thelength of one side (L_x=L) fixed while the other side (L_y=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.(3) 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 the biexciton yields a reduction as the average interparticle distance increases. The average distance of electron-electron and hole-hole are also much less than that of electron-hole, which is due to the difference of the Coulomb potential.