Excitons
The exciton states are computed using the approach from [ChuangOpto1995]. The explanation below only covers the most important aspects of the model, for detailed derivation please refer to the [ChuangOpto1995] book. The exciton computation is only available for 1D systems.
Model
Assuming the effective mass approximation for the electron and hole, the Schrödinger equation for the exciton can be written as:
where
The wavefunciton of the exciton, formed by electron
where
where
The solution of the equation for
where
Averaging model parameters
The model depends on dielectric constant
Excitons in multiband Hamiltonians
The computation of the exciton in the case of 8-band