Exciton binding energy in semiconductor multiple quantum well (MQW) systems is analyzed with both the variational method and the perturbation theory. The intrinsic deficiency of the use of the two-dimensional exciton envelop wave function is clearly demonstrated. Using a GaAs/Al x Ga 1−xAs MQW as an example to calculate the exciton binding energy with a variational three-dimensional trial envelop function, we found that in many realistic samples the spatial extension of an exciton covers a region of several lattice constant dA + dB, where dA is the barrier width and dB is the well width.
Comment on “Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials”