Novel method to determine effective length of quantum confinement using fractional-dimension space approach

The binding energy and effective mass of a polaron confined in a GaAs film deposited on an Al_xGa_1-x As substrate are investigated, for different film thickness values and aluminum concentrations and within the framework of the fractional-dimensional space approach. Using this scheme, we propose a new method to define the effective length of the quantum confinement. The limitations of the definition of the original effective well width are discussed, and the binding energy and effective mass of a polaron confined in a GaAs film are obtained. The fractional-dimensional theoretical results are shown to be in good agreement with previous, more detailed calculations based on second-order perturbation theory.