Franz-Keldysh effect
Encyclopedia
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
).
As originally conceived, the Franz-Keldysh effect is the result of wavefunction
s "leaking" into the band gap. When an electric field is applied, the electron
and hole
wavefunctions become Airy function
s rather than plane waves. The Airy function includes a "tail" which extends into the classically forbidden band gap. 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. This explanation does, however, omit the effects of exciton
s, 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 Electro-absorption modulator
s. The Franz–Keldysh effect usually requires hundreds of volt
s, limiting its usefulness with conventional electronics – although this is not the case for commercially available Franz–Keldysh-effect electro-absorption modulators that use a waveguide geometry to guide the optical carrier.
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
when an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
is applied. The effect is named after the German physicist Walter Franz
Walter Franz
Walter Franz was a theoretical physicist who independently discovered the Franz-Keldysh effect.Franz was a student of Arnold Sommerfeld at the University of Munich. He was granted his Ph.D. in 1934...
and Russian physicist Leonid Keldysh (nephew of Mstislav Keldysh
Mstislav Keldysh
Mstislav Vsevolodovich Keldysh was a Soviet scientist in the field of mathematics and mechanics, academician of the USSR Academy of Sciences , President of the USSR Academy of Sciences , three times Hero of Socialist Labor , fellow of the Royal Society of Edinburgh . He was one of the key figures...
).
As originally conceived, the Franz-Keldysh effect is the result of wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
s "leaking" into the band gap. When an electric field is applied, the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
and hole
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
wavefunctions become Airy function
Airy function
In the physical sciences, the Airy function Ai is a special function named after the British astronomer George Biddell Airy...
s rather than plane waves. The Airy function includes a "tail" which extends into the classically forbidden band gap. According to Fermi's Golden Rule
Fermi's golden rule
In quantum physics, Fermi's golden rule is a way to calculate the transition rate from one energy eigenstate of a quantum system into a continuum of energy eigenstates, due to a perturbation....
, 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. This explanation does, however, omit the effects of exciton
Exciton
An exciton is a bound state of an electron and hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and some liquids...
s, which may dominate optical properties near the band gap.
The Franz–Keldysh effect occurs in uniform, bulk semiconductors, unlike the quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
confined Stark effect
Stark effect
The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift. In general one distinguishes first- and second-order Stark effects...
, which requires a quantum well. Both are used for Electro-absorption modulator
Electro-absorption modulator
Electro-absorption modulator is a semiconductor device which can be used for modulating the intensity of a laser beam via an electric voltage...
s. The Franz–Keldysh effect usually requires hundreds of volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
s, limiting its usefulness with conventional electronics – although this is not the case for commercially available Franz–Keldysh-effect electro-absorption modulators that use a waveguide geometry to guide the optical carrier.