Electroabsorption characteristics of semi-insulating indium phosphide as applied to optoelectronic modulation

In this work, we explore the band edge absorption characteristics of semiconductors as applied to optoelectronic modulation-with careful consideration to the departures from ideality in the semiconductors. To this end, we develop a rigorous model of electroabsorption in semiconductors that characterizes the electric-field-induced constriction/narrowing of the bandgap and the resulting increase in absorption of photons, whose energies are slightly below the bandgap energy. The model unifies the Franz-Keldysh effect, characterizing the electric-field-induced tunneling of photoexcited electrons from valence band states to conduction band states, and the Einstein model, quantifying the encroachment of valence and conduction band states into the bandgap. Careful consideration is given here to the nonidealities in the semiconductor, which arise within the valence band as degenerate states, due to light and heavy holes, and within the bandgap, as encroaching Urbach tail states. We apply the model in characterizing optoelectronic modulation of 980-nm photons with semi-insulating indium phosphide (SI-InP), and we see strong agreement between our theoretical and experimental results over a wide range of electric fields and photon energies. Ultimately, the findings show that optoelectronic modulation can be had with large modulation depths over short propagation lengths through the semiconductor. This opens the door to highly effective implementations of optoelectronic modulators in emerging free-space optical communication systems-given that such modulators do not allow for prolonged (guided-wave) propagation and have thus exhibited small modulation depths.