Franz–Keldysh effect

The Franz- Keldysh effect (FKE ) is a fundamental change in the absorption of a semiconductor in the presence of an electric field. It was in 1957/58 almost simultaneously described by Walter Franz and Leonid Keldysh and first observed in 1960 by R. Williams of cadmium sulfide ( CdS). A further statement was made in 1964 by Keldysh.

Description

The change in the fundamental absorption is caused by a reduction in the effective band gap energy. No electric field passes through a photon having an energy less than the band gap energy of the semiconductor, because it does not have sufficient energy to be absorbed. So it does not have enough energy to remove an electron from the valence band into the conduction band to raise.

An electric field is applied to the semiconductor, so tilt the strip edges. The wave function of the charge carriers and thus their probability sound now exponentially in the forbidden zone between the bands. That is, the probability of finding an electron at the band gap decreases in accordance with an exponential function. A valence electron to be lifted by a absorbed photon with a photon energy slightly below the band gap energy in the conduction band must tunnel through a triangular energy barrier. Solutions of the Schrödinger equation for such a triangular potential offer this Airy functions. The barrier height depends on the band gap energy and the photon energy, the thickness of 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 tunneling probability increases.

With an increasing electric field, the absorption coefficient for photon energies less than the band gap energy increases. This corresponds to a shift of the absorption edge to lower energies. The biggest change of the absorption coefficient at low field strengths is due to the exponential dependence close to the absorption edge. In contrast, large field strengths give rise to only relatively small further changes. Total of the displacement and flattening of the absorption edge to longer wavelengths is observed out. At higher energies is a decaying oscillatory behavior of the differential absorption observable. The reason for this so-called Franz -Keldysh oscillations is also the quantum mechanical tunnel effect, which affects the absorption of photons above the band edge.

The Franz -Keldysh effect occurs in bulk semiconductors. In contrast effect in quantum well structures of quantum -enhanced Stark effect ( engl. quantum confined strong effect, QCSE ). Both effects are used for light modulation in electroabsorption modulators in communication engineering. The necessary field strengths up to a few hundred kilovolts per centimeter. These field strengths can be personalized with diode structures easily implement (example: pin diode structure with 300 nm thick i-region, applied in the reverse direction voltage: 3 V, so is the electric field strength in the i- Zone 100 kV / cm).

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