Photogalvanic effect

The photogalvanic effect (PGE) describes a purely optically induced current in semiconductors . To generate electricity, only optical excitation is required, no other external fields (e.g. electrical fields ). The term PGE is a phenomenological term and only describes the occurrence of a current regardless of its microscopic origin. The PGE can be divided into different sub-categories: according to the excitation polarization (linear and circular), the processes involved (e.g. surface effects, photodrag effect, material symmetry ) and the charge carrier density matrix (diagonal and off-diagonal elements). In general, the PGE is described by the electrical susceptibility of the second order , so the generated current direction depends, among other things. a. on the orientation of the polarization.

The term photogalvanic should not lead one to think of a photogalvanic cell or the Becquerel effect , in which electrodes are immersed in an electrolyte in a galvanic test arrangement . The PGE is also not to be confused with the internal photoelectric effect .

description

Phenomenologically, the PGE can be described by:

${\displaystyle j_{\lambda }=\sum _{\mu ,\nu }\chi _{\lambda \mu \nu }E_{\mu }E_{\nu }^{*}}$

where is the complex electric field of the optical excitation. The excitation energies must be able to enable inter- or intra-band transitions . ${\displaystyle E{\mu \nu }}$

The complex conjugation of and represents the expansion coefficient, which is a third degree tensor . is symmetry dependent. ${\displaystyle E_{\mu }}$ ${\displaystyle \chi _{\lambda \mu \nu }}$ ${\displaystyle \chi _{\lambda \mu \nu }}$

Examples

Some examples for all allowed tensor elements are

- Gallium arsenide as an example of the crystal system : ${\displaystyle {\bar {4}}3m}$

${\displaystyle \chi _{xyz}}$and all permutations of x, y, z. All tensor elements have the same strength.

${\displaystyle x}$, , Corresponding to the primitive crystal axes [100], [010] and [001]. ${\displaystyle y}$ ${\displaystyle z}$

- Cadmium selenide as an example of the crystal system : ${\displaystyle 6mm}$

${\displaystyle \chi _{zzz},\chi _{zxx},\chi _{xzx}=\chi _{xxz},\chi _{xzx}=-\chi _{xxz}}$

${\displaystyle z}$lies here along the optical axis . and can be chosen arbitrarily so that they form an orthogonal coordinate system. ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle x,y,z}$

Classifications

polarization

A distinction is made between linear and circular polarization (LPGE and CPGE) of the optical field. The LPGE is allowed if applicable

${\displaystyle \chi _{\lambda \mu \nu }=\chi _{\lambda \nu \mu }}$

the CPGE if applicable

${\displaystyle \chi _{\lambda \mu \nu }=-\chi _{\lambda \nu \mu }}$.

In general it can be said that the CPGE requires a much lower crystal symmetry than the LPGE.

Charge carrier density matrix

Charge carrier bands in semiconductors can be spatially separated. This separation can lead, assuming spatial asymmetry, that charge carriers have a preferred spatial direction at a band transition and thus generate a current. This current is also called a shift current. Optical excitation and asymmetrical scattering processes can cause asymmetry in the momentum space. This current is also called the ballistic component of the PGE or injection current. With interband excitation in bulk material, the LPGE with the displacement current and the CPEM with the injection current are almost identical. In the case of intra-band and intersub-band excitations (e.g. from light to heavy perforated bands), the LPGE also contains ballistic components.

literature

• Wolfgang Weber: Terahertz laser-induced photogalvanic effects in semiconductor quantum films and their application . Regensburg 2008, DNB  990350975 , urn : nbn: de: bvb: 355-opus-10469 (dissertation, University of Regensburg).

Individual evidence

1. ^ ^{A b} V. L. Alperovich, VI Belinicher, VN Novikov, AS Terekhov: Photogalvanic effects investigation in gallium arsenide . In: Ferroelectrics . tape 45 , no. 1 , 1982, pp. 1-12 , doi : 10.1080 / 00150198208208275 .
2. ^ ^{A b c d e f} J. E. Sipe, AI Shkrebtii: Second-order optical response in semiconductors . In: Physical Review B . tape 61 , no. 8 , February 15, 2000, p. 5337-5352 , doi : 10.1103 / PhysRevB.61.5337 .
3. ↑ K. Kalyanasundaram: Dye-sensitized solar cells . EPFL Press, 2010, ISBN 978-1-4398-0866-5 ( limited preview in Google book search).
4. ↑ N. Laman, M. Bieler, HM van Driel: Ultrafast shift and injection currents observed in wurtzite semiconductors via emitted terahertz radiation . In: Journal of Applied Physics . tape 98 , no. 10 , November 15, 2005, p. 103507 , doi : 10.1063 / 1.2131191 .