photoelectromotive force[¦fōd·ō·i¦lek·trō′mōd·iv ′fȯrs]
(or photo-emf), an electromotive force (emf) that is produced in a semiconductor when electromagnetic radiation, which consists of photons, is aborbed in the semiconductor. The production of a photo-emf is known as the photovoltaic effect and is caused by the spatial separation of charge carriers generated by the radiation; such carriers are called photocarriers. The separation of photocarriers occurs during the diffusion and drift of the carriers in electric and magnetic fields. Such diffusion and drift is caused by, for example, nonuniform photocarrier generation, inhomogeneity of the crystal, the effect of an applied magnetic field, or uniaxial compression.
A photo-emf that is produced in the bulk of a homogeneous semiconductor and results from the nonuniform generation of photocarriers in the semiconductor is called a diffusion photo-emf, or Dember photo-emf. When a semiconductor is nonuniformly illuminated or is exposed to radiation that is strongly absorbed and thus rapidly attenuated within the crystal, the photo-carrier concentration is high near the illuminated surface but low or zero in the dark parts. The photocarriers diffuse from the illuminated surface to the region where the concentration is lower. If the mobilities of conduction electrons and holes are not the same, a space charge arises in the bulk of the semiconductor, and a Dember photo-emf is produced between the illuminated and dark parts. The magnitude of the Dember photo-emf between two points 1 and 2 of a semiconductor may be calculated on the basis of the equation
where k is the Boltzmann constant, e is the charge of the electron, T is the temperature, μe is the electron mobility, μh is the hole mobility, σ1 is the electrical conductivity at point 1, and σ2 is the conductivity at point 2. For a given intensity of illumination, the greater the difference between the electron and hole mobilities and the lesser the dark conductivity of the semiconductor, the greater the Dember photo-emf. Radiation that generates only majority carriers in a semiconductor does not produce a Dember photo-emf because, in this case, the emf in the bulk of the semiconductor is balanced by the emf produced at the semiconductor-electrode contact; the two emf s are equal in magnitude and opposite in sign. The Dember photo-emf in conventional semiconductors is small and has no practical application.
A depletion-layer or barrier photo-emf is produced in chemically inhomogeneous or nonuniformly doped semiconductors and at metal-semiconductor contacts. In the inhomogeneous region in a semiconductor, an intrinsic electric field exists which accelerates the minority carriers generated by the radiation and retards the nonequilibrium majority carriers. As a result, photocarriers of opposite signs are separated in space. The separation of electrons and holes by an intrinsic field is effective when the inhomogeneity is not too smooth, so that over a length of the order of the minority-carrier diffusion length the difference between chemical potentials exceeds kT/e; at room temperature, kT/e = 0.025 electron volts. A depletion-layer photo-emf may be produced in a semiconductor exposed to light that generates both electrons and holes or at least minority carriers. Especially important for practical applications is the depletion-layer photo-emf that is produced in a p-n junction or a semiconductor heterojunction. Such a photo-emf is used in photovoltaic cells and solar cells. Depending on the magnitude of the depletion-layer photo-emf, weak in-homogeneities in semiconductor materials may be detected.
A photo-emf may also be produced in a homogeneous semiconductor when the semiconductor is simultaneously subjected to uniaxial compression and illuminated; in this case, the production of a photo-emf is called the photopiezoelectric effect. The photo-emf is produced at the surfaces perpendicular to the direction of compression, its magnitude and sign depending on the direction of compression and illumination relative to the crystallographic axes. The photo-emf is proportional to the pressure and the radiation intensity. In this case, the photo-emf is caused by the anisotropy of the photocarrier diffusion coefficient produced by the uniaxial deformation of the crystal. When a semiconductor is simultaneously subjected to nonuniform compression and illuminated, a photo-emf may be caused by unidentical pressure-induced changes in the width of the forbidden band in different parts of the crystal; that is, it may result from the elastoresistance effect.
If a semiconductor is placed in a magnetic field and illuminated by light that is strongly absorbed, a photocarrier concentration gradient and a gradient in the photocarrier diffusion flux may arise in the direction perpendicular to the magnetic field. In this case, the electrons and holes are separated by being deflected in opposite directions by the magnetic field (seeKIKOIN-NOSKOV EFFECT).
In 1937, the Soviet physicist B. I. Davydov showed that a photo-emf may be produced when only majority carriers are generated or when radiation is absorbed by conductive electrons, if the energy of the photocarriers differs appreciably from the energy of other charge carriers. Such a photo-emf is usually produced in pure semiconductors with a high electron mobility at very low temperatures. In this case, the photo-emf is caused by the dependence of the electron mobility and diffusion coefficient on the energy of the electrons. In n-type InSb cooled to the temperature of liquid helium, this type of photo-emf is considerable.
When radiation is absorbed by free carriers in a semiconductor, both the photon energy and the photon momentum are absorbed. As a result, the electrons acquire ordered motion relative to the crystal lattice, and a light-pressure photo-emf is produced at the crystal surfaces perpendicular to the radiation flux. The light-pressure photo-emf is small, as is its time constant, which is of the order of 10–11 sec. A light-pressure photo-emf is used in fast-response radiation detectors intended for measuring the power and shape of laser pulses.
REFERENCESRyvkin, S. M. Fotoelektricheskie iavleniia v poluprovodnikakh. Moscow, 1963.
Tauc, Jan. Foto- i termoelektricheskie iavleniia v poluprovodnikakh. Moscow, 1962. (Translated from Czech.)
Fotoprovodimost’: Sb. st. Moscow, 1967.
T. M. LIFSHITS