Band-edge absorption characteristics of semi-insulating indium phosphide under unified Franz-Keldysh and Einstein models

The foundational Franz-Keldysh effect and Einstein model are applied in this work to characterize semiconductor band-edge absorption-and its departures from ideality. We unify the Franz-Keldysh and Einstein models to fully characterize the field-induced tunneling of photoexcited electrons from degenerate valence bands into the conduction band, with encroachment into the band gap arising as an Urbach tail. Our unified model is implemented for semi-insulating indium phosphide (SI-InP) with strong agreement seen between the theoretical and experimental results for varied photon energies and electric fields.