Fractional-dimensional space approach for the polaron in a GaAs film deposited on AlxGa1−xAs substrate

Within the framework of the fractional-dimensional space approach, the binding energy and the effective mass of a polaron confined in a GaAs film deposited on the AlxGa1−xAs substrate for different aluminum concentration at different values of substrate thickness are investigated. Analytical expressions allowing a very simple estimation of the corresponding polaron binding energy and mass shift are found. As functions of the film thickness, the numerical results for the polaron binding energy and mass shift in the GaAs film deposited on the AlxGa1−xAs substrate structure are obtained. Our calculations show that the polaron binding energy and mass shift both have their maxima in a GaAs film deposited on the AlxGa1−xAs substrate. It is shown that the polaron binding energy and mass shift for different aluminum concentration have a maximum at a certain film thickness for the sample with a given substrate thickness.