The Energy Of An Exciton In A Wurtzite GaN/Al_xGa_1-xN Quantum Well

In this paper The anisotropy of the band mass of the hole and The anisotropy of optical phonon mode and the effect of phonon frequency changing with vector are considered in a wurtzite GaN /AlxGa1-xN quantum well. The ground state energy and binding energy of an exciton in a wurtzite GaN /AlxGa1-xN finite quantum well and in a wurtzite GaN /AlN infinite quantum well are calculated by a Lee-Low-Pines(LLP)variational method. The ground state energy and binding energy of a heavy-hole exciton and a light-hole exciton as function of well width and Al composition x are given In this paper .The ground state energy and the binding energy in a wurtzite GaN /AlxGa1-xN quantum well are compared with the results in a Zinc blende quantum well. In the above calculation process, the static dielectric constant and high-frequency dielectric constant are respectively used.The results show that the ground state energy and binding energy of a heavy-hole exciton or a light-hole exciton in a wurtzite GaN /AlxGa1-xN quantum well decreases when the well width increases; and the energy decreases rapidly at a narrow well, then decreases slowly and is close to the values of an exciton in three-dimensional GaN materials at large well width. the ground state energy and binding energy of a heavy-hole exciton or a light-hole exciton in the infinite quantum well are significantly larger than the corresponding values in the finite quantum well at smaller well widths,but the corresponding values are almost the same in these two kind of quantum wells at large well widths.The numerical results indicate that the ground state energy and binding energy of a heavy-hole exciton or a light-hole exciton in a wurtzite GaN /AlxGa1-xN quantum well increases when Al composition x increases; and it is more visible in narrow well (such as 4nm),but it is slowly in at large well width (such as 12nm).The binding energy of an exciton with the effect of polaron are significantly smaller than the results of a bare exciton, and the contribution from the electron-phonon interaction to the energy of an exciton is obvious(about 10% -16% lower). the ground state energy and binding energy of a heavy-hole exciton are less than the corresponding values of a light-hole exciton . The ground state energy of an exciton in wurtzite GaN /AlxGa1-xN quantum well is less than the results for a Zinc blende GaN /AlxGa1-xN quantum well. The binding energy of an exciton in wurtzite GaN /AlxGa1-xN quantum well is larger than the results for a Zinc blende GaN /AlxGa1-xN quantum well.the ground state energy calculated using the static dielectric constant was significantly higher than the corresponding values calculated using high-frequency dielectric constant, the binding energy calculated using the static dielectric constant was significantly lower than the corresponding values calculated using high-frequency dielectric constant. Variational Parameterλdecreases when the well width increases.