Simple analytical method for calculating exciton binding energies in semiconductor quantum wells

We present a very simple method for calculating exciton binding energies in quantum-confined semiconductor structures. The aim of the model calculation, which is developed in the framework of the fractional-dimensional space, is not to compete with the very advanced ones already proposed, but, on the contrary, to avoid tedious and expensive calculations, to obtain, with good accuracy, the exciton binding energy in most of the confined structures where the exciton can be associated with a specific pair of electron and hole subbands. Our main result is an analytical expression for the exciton binding energy, free of any adjustable parameter. Furthermore, in the cases where the 1s and 2s transition energies can be experimentally measured, the method permits one to obtain the exciton binding energy without any hypothesis or calculation.