Exciton energy in a wurtzite GaN/Al_xGa_(1-x)N quantum well

Considering the anisotropy of the band mass for holes and the optical phonon mode,and the variation of phonon frequency with wave vector,the ground state energy and binding energy of an exciton in wurtzite GaN/AlxGa1-xN quantum well(QW) are calculated by a Lee-Low-Pines(LLP)variational method.The ground state energy and binding energy of a heavy-hole exciton as functions of well width and Al composition x are given.The ground state energy and the binding energy in a wurtzite GaN/Al0.3Ga0.7N quantum well are compared with those in a zinc blende quantum well.The results show that the ground state energy and binding energy of a heavy-hole exciton in a wurtzite GaN/Al0.3Ga0.7N quantum well decrease with the well width increases.The ground state energy and binding energy of a heavy-hole exciton in the infinite quantum well are significantly larger than those in the finite quantum well at smaller well width,but the corresponding values are almost the same in these two quantum wells at larger well width.Tthe ground state energy and binding energy of a heavy-hole exciton in a wurtzite GaN/AlxGa1-xN quantum well increase when Al composition x increases.The binding energy of an exciton with the effect of polaron is significantly smaller than that of a bare exciton.The ground state energy of an exciton in wurtzite GaN/Al0.3Ga0.7N quantum well is smaller than that in a zinc blende GaN/Al0.3Ga0.7N quantum well,while the binding energy of an exciton in wurtzite GaN/Al0.3Ga0.7N quantum well is larger than that in a zinc blende GaN/Al0.3Ga0.7N quantum well.