Polaron effect influenced by thicknesses of GaAs film and Al_xGa_1−xAs substrate

The binding energy and effective mass of a polaron confined in a GaAs film deposited on Al_xGa_1-xAs substrate are studied theoretically within the framework of the fractional-dimensional approach and by using a correctional length of confinement. The numerical results for the polaron binding energy and effective mass in the GaAs film deposited on Al_xGa_1-xAs substrate are obtained as functions of the film thickness and substrate thickness. Through the correctional length of confinement, the problem of the original fractional-dimensional approach for the jumps of the polaron binding energy and mass shift with increasing the film thickness is solved. Our calculations show that the polaron binding energy and mass shift decreases monotonously as the film thickness increases. It is also shown that the polaron binding energy and mass shift both have their maxima as the substrate thickness increases.