Franz Keldysh Effect

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The Franz Keldysh Effect ( FKE ) is a change in the fundamental absorption of a semiconductor in the presence of an electric field . It was described almost simultaneously by Walter Franz and Leonid Keldysch in 1957/58 and first observed in 1960 by Richard Williams on cadmium sulfide (CdS). A further explanation was given in 1964 by Keldysch.

description

Illustration of the Franz-Keldysh effect.

The change in fundamental absorption is caused by a reduction in the effective bandgap energy . Without an electric field, a photon with an energy below the band gap energy passes through the semiconductor because it does not have enough energy to be absorbed. It does not have enough energy to lift an electron from the valence band to the conduction band .

If an electric field is applied to the semiconductor, the strip edges tilt. The wave function of the charge carriers and thus their probability of being present now decay exponentially into the forbidden zone between the bands. That is, the probability of finding an electron in the band gap decreases according to an exponential function. A valence electron that is to be lifted into the conduction band by an absorbed photon with a photon energy slightly below the band gap energy must tunnel through a triangular energy barrier. Solutions of the Schrödinger equation for such a triangular potential offer Airy functions . The barrier height depends on the band gap energy and the photon energy, the thickness depends on the electric field. The Franz Keldysh effect is thus a photon-assisted tunneling process. The thickness of the barrier decreases with increasing field, so that the tunnel probability increases.

Change in absorption due to the Franz Keldysh effect.

With an increasing electric field , the absorption coefficient for photon energies smaller than the band gap energy increases. This corresponds to a shift of the absorption edge to lower energies. The greatest change in the absorption coefficient at low field strengths occurs due to the exponential dependence in the immediate vicinity of the absorption edge. On the other hand, high field strengths only cause comparatively small further changes. Overall, the shift and flattening of the absorption edge towards larger wavelengths can be observed. At higher energies, an oscillatory decaying behavior of the differential absorption can be observed. The reason for these so-called Franz Keldysh oscillations is also the quantum mechanical tunnel effect , which also influences the photon absorption above the band edge.

The Franz Keldysh effect occurs in bulk semiconductors . In contrast, the quantum-enhanced effect in quantum well structures Stark effect (Engl. Quantum confined Stark effect , QCSE ). Both effects are used for light modulation in electro-absorption modulators in the communications technology used. The necessary field strengths are a few hundred kilovolts per centimeter. These field strengths can be easily achieved with diode structures (example: pin diode structure with 300 nm thick i-zone, electrical voltage applied in reverse direction : 3 V, so the electrical field strength in the i-zone is 100 kV / cm).

literature

  • JI Pankove: Optical Processes in Semiconductors. Dover Publications Inc., New York 1971.

Individual evidence

  1. ↑ W. Franz: Influence of an electric field on an optical absorption edge. In: Z. Naturforschung 13a, 1958, pp. 484-489.
  2. ↑ LV Keldysh: In: J. Exptl. Theoretically. Phys. (USSR) 33, 1957, pp. 994-1003.
    translated: Behavior of Non-Metallic Crystals in Strong Electric Fields. In: Soviet Physics JETP 6, 1958, pp. 763-770.
  3. ^ R. Williams: Electric Field Induced Light Absorption in CdS. In: Phys. Rev. 117, 1960, pp. 1487-1490.
  4. ↑ LV Keldysh: In: Exptl. Theoretically. Phys. (USSR) 47, 1964, pp. 1945-1957.
    translated: Ionization in the Field of a Strong Electromagnetic Wave. In: Soviet Physics JETP 20, 1965, ISSN  0038-5646 pp. 1307-1314.
  5. ↑ F. Cerdeira, C. Vázquez-López, E. Ribeiro, PAM Rodrigues, V. Lemos, MA Sacilotti, AP Roth: Franz-Keldysh oscillations in the photomodulated spectra of an In 0.12 Ga 0.88 As / GaAs strained-layer superlattice . In: Physical Review B . tape 42 , no. 15 , 1990, pp. 9480-9485 , doi : 10.1103 / PhysRevB.42.9480 .