Franz-Keldysh effect in semiconductor built-in fields

Franz-Keldysh effect is expressed in the smearing of the absorption edge in semiconductors under high electric fields. While Franz and Keldysh considered a limited case of externally applied uniform electric field, the same effect may be caused by built-in electric fields at semiconductor surfaces and interfaces. While in the first case, the bands are bent linearly, in the latter case, they are bent parabolically. This non-linear band bending poses an additional complexity that has not been considered previously. Here, we extend the linear model to treat the case of a non-linear band bending. We then show how this model may be used to quantitatively analyze photocurrent and photovoltage spectra to determine the built-in fields, the density of surface state charge, and the doping concentration of the material. We use the model on a GaN\AlGaN heterostructure, and GaAs bulk. The results demonstrate that the same mechanism underlies the band-edge response both in photocurrent and photovoltage spectra and demonstrate the quantitative use of the model in contactless extraction of important semiconductor material parameters.