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Franz-Keldysh effect

The Franz-Keldysh effect is a change in optical absorption by a semiconductor when an electric field is applied. The effect is named after the German physicist Walter Franz and Russian physicist Leonid Keldysh (nephew of Mstislav Keldysh).

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As originally conceived, the Franz-Keldysh effect is the result of wavefunctions "leaking" into the band gap. When an electric field is applied, the electron and hole wavefunctions become Airy functions rather than plane waves. The Airy function includes a "tail" which extends into the classically-forbidden band gap. (picture needed) According to Fermi's Golden Rule, the more overlap there is between the wavefunctions of a free electron and a hole, the stronger the optical absorption will be. The Airy tails slightly overlap even if the electron and hole are at slightly different potentials (slightly different physical locations along the field). The absorption spectrum now includes a tail at energies below the band gap and some oscillations above it. It should be noted that this explanation omits the effects of excitons, which may dominate optical properties near the band gap.

The Franz-Keldysh effect occurs in uniform, bulk semiconductors, unlike the quantum confined Stark effect, which requires a quantum well. Both are used for electroabsorption modulators. The Franz-Keldysh effect usually requires hundreds of volts, limiting its usefulness with conventional electronics.

References

W. Franz, Einfluß eines elektrischen Feldes auf eine optische Absorptionskante, Z. Naturforschung 13a (1958) 484-489.
L. V. Keldysh, Behaviour of Non-Metallic Crystals in Strong Electric Fields, J. Exptl. Theoret. Phys. (USSR) 33 (1957) 994-1003, translation: Soviet Physics JETP 6 (1958) 763-770.
L. V. Keldysh, Ionization in the Field of a Strong Electromagnetic Wave, J. Exptl. Theoret. Phys. (USSR) 47 (1964) 1945-1957, translation: Soviet Physics JETP 20 (1965) 1307-1314.
R. Williams, Electric Field Induced Light Absorption in CdS, Phys. Rev. 117 (1960) 1487-1490.
J. I. Pankove, Optical Processes in Semiconductors, Dover Publications Inc. New York (1971).