Fractal dimension method for exciton in cylindrical GaAs/AlxGa1−xAs core-shell-cap nanowires

By use of the fractal dimension method, the binding energies of heavy-hole exciton and light-hole exciton in cylindrical GaAs/AlxGa1−xAs core-shell-cap nanowire are explored. In this study, the exciton is confined in GaAs shell of the GaAs/AlxGa1−xAs core-shell-cap nanowire for a given aluminum concentration of x = 0.3. The numerical results of heavy-hole exciton binding energy, light-hole exciton binding energy and fractal dimension parameter are worked out as functions of shell width and core radius. It has been shown by the calculated results that heavy-hole exciton binding energy and light-hole exciton binding energy firstly increase and then decrease as the shell width increases. When the core radius increases, both the heavy-hole exciton binding energy and light-hole exciton binding energy increase gradually. Exciton problems in GaAs shell of the cylindrical GaAs/AlxGa1−xAs core-shell-cap nanowire are solved in a simple manner to avoid complex and lengthy calculations by using the fractal dimension method.