Fractal dimension study of polaron effects in cylindrical GaAs/Al x Ga 1− x As core–shell nanowires

Polaron effects in cylindrical GaAs/Al x Ga1-xAs core–shell nanowires are studied by applying the fractal dimension method. In this paper, the polaron properties of GaAs/Al x Ga1-xAs core–shell nanowires with different core radii and aluminum concentrations are discussed. The polaron binding energy, polaron mass shift, and fractal dimension parameter are numerically determined as functions of shell width. The calculation results reveal that the binding energy and mass shift of the polaron first increase and then decrease as the shell width increases. A maximum value appears at a certain shell width for different aluminum concentrations and a given core radius. By using the fractal dimension method, polaron problems in cylindrical GaAs/Al x Ga1-xAs core–shell nanowires are solved in a simple manner that avoids complex and lengthy calculations.