| In the effective mass approximation, the binding energy of the exciton bound to a neutral donor (D~0,X) in infinite GaAs quantum-well wires(QWWs) is calculated variationally by using a three-parameter wave function. The coulomb interaction terms are treated exactly in their full three-dimensional forms throughout the calculation. Using a two-dimensional Fourier expansion of the coulomb potential removes the numerical difficulty with the 1/r singularity and considerably reduces the computational effort. Inaddition, we also calculate the binding energies of (D~0,X) when the donor isin different positions (at the centre, at the boundary and at the corner). The average interparticle distances in the square QWWs are discussed.Firstly, using the method of Fourier expansion of the coulomb potential, 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 same method is used to the (D~0,X) system, then theparameters versus the quantum-well wires width are calculated. We can obtain the binding energy of the system.The average interparticle distance as functions of the wire width are also calculated, with the results being satisfactory.At last, the results are discussed in detail. The conclusions are as follows:(l)The binding energy of (D~0,X) system as a function of the wire size(L-W) is shown in Fig.5. It can be seen that the binding energy decreases as the wire size increases. The difference between our results and that of Ref. [27] is that our results are larger than those in Ref. [27] when L(W) is less than 100 Angstrom, when L(W) is greater than 100 Angstrom, our results are smaller. As the wire size approaching the less width, the wave function can not penetrate the potential barrier, since the infinite potential wells are used, the greater the binding energy, the stronger the particles is bound. As the wire width increases, the binding energy depends on the position of dopant, theconfinement potential can be ignored, the binding energy of (D~0,X) decreases and begins to approach the GaAs bulk value. (2)The Fig. 6 shows the binding energy of (D~0,X) for three differentpositions of the impurity (at the centre (O), at the boundary (A), and at the corner (B)) of the square cross section of the GaAs wires of infinite potential barrier. As can be seen, the binding energy is much larger when the impurity is located at the centre of the wire than that of the other two positions of the impurity. This is because the particle wave functions vanish at the boundaries and thus their contributions to the energy are smaller when the impurity is at the boundary or the corner. (3)In Fig.7, one side L of QWWs is fixed while the other side W is varied,we show the binding energies of (D~0,X) in asymmetric QWWs. It is clear thatthe binding energies decrease as the wire expands in one direction while kept to be fixed in the other directions. The trends are consistent with the result obtained when L equals W. Then we obtain the conclusion: the bindingenergies of (D~0,X) in QWWs are relative to cross section, not only dependson one direction. (4)By calculating the binding energy, the variational parameters in the wave... |
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