Gaas-al The <sub> X </ Sub> 1-x </ Sub> As Quantum Well Of Ga <sub> Charged Exciton Nature

In the effective mass approximation, using the two-dimensional equivalent potential model and a simple two-parameter wave function, we calculate variationally the ground state binding energy and correlation energy of positively and negatively charged excitons in finite deep GaAs-Al0.33Ga0.67As quantum wells. The results show fairagreement with the previous experimental results.Firstly, we calculate variationally the binding energy and correlation energy of excitons in finite deep GaAs-Al0.33Ga0.67Asquantum wells. In the calculation, we consider the effect of effective mass and dielectric constant mismatch in the two materials. The results we obtained are basically conformed to the ones obtained from the previous theory and experiment.Secondly, we use the two-dimensional equivalent potential model to turn the excitons in quantum well into the effective two-dimensional excitons, and calculate the parameters ax and yx versus the quantum well width.To the positively and negatively charged excitons in finite deep GaAs-Al0.33Ga0.67As quantum wells, we still use thetwo-dimensional equivalent potential model. In this model, we choose the variational wave function as follows:V(p1,p2,p3) = R213e-e-+(1-2). In this wave function, we consider the whole Coulombiccorrelation among the particles, and the effect of the interchanged term caused by the same particles. Where a and are the two variational parameters, and the parameters of ax and yx are determined by the two equations obtained from the variation of the energy of excitons. By the complicated mathematical calculating, we obtain the energy equation of charged excitons, from which we can determine the variational parameters a and , thus the complex energy of charged excitons can be calculated, and the binding energy and correlation energy of charged excitons can be obtained versus the quantum well width.At last, the results are discussed and compared in detail with previous experimental and theoretical results. The conclusions are as follows:(i) The binding energy of charged excitons versus the quantum well width is basically conformed to the previoustheoretical results. The peak appears at about 30 A width, and the value is about 3meV, which larger than the previoustheoretical results. But compared with the present experimental data, our results show fair agreement with them, (ii) The correlation energy of charged excitons versus the quantum well width is also basically conformed to the previous results. The absolute values are slightly smaller than the previous theoretical data, but the curve tendency is in agreement with them.