Corpuscular-wave nature of light. Experiments show that light has double nature. In some phenomena (interference, diffraction and polarization) the wave-like properties of light are observed, in the other phenomena (photo-electric effect, Compton’s effect, luminescence) – particle-like properties. Accordant to Planck’s law the radiation and absorption of light by the matter passes not continuously, but by portions or quanta. In accordance with Einstein theory these quanta can spread in space. The experiment of Bote confirmed the existence of the special particles – of photons. Energy of photon is equal to the energy of quantum of optical radiation, proposed by Planck: E = Ћω = hν.

This energy is determined by frequency of photon or ν = ω/(2π), where ω – cyclic frequency of radiation, h – constant of Planck. Value Ћ = h/2π – Dirac’s constant of Planck.

A photon possesses wave-like properties (by interference and diffraction). Special property of photon to be a wave and particle is named wave - particle duality. Wave-particle duality inherent to all presently known elementary particles. For photons with small frequencies the wave-like properties are determininants. For large frequencies of photons the particle-like properties are more substantial. The sources of quanta are transitions of atoms, molecules and atomic kernels from the excited state into the state with smaller energy. Photons are emitted at accelerated motion of the charged particles, during the processes of disintegration and annihilation of particles.

A photon has impulse-like properties (spin), which is equal to Ћ.  If a photon is taken in, or emitted by the matter, the momentum of impulse of matter is changed on the discrete value of mЋ, where m = 1, 2, 3… The impulse-like nature of photon is confirmed by the presence of pressure of light. The liaison between energy of photon E and his impulse p is set by the special theory of relativity: E = pc,   p = Ћω/с = 2πЋ/λ = Ћk, where λ – wave-length, k – wave number. A photon travels in the direction of propagation of Hertzian wave, therefore the directions of his impulse p and wave vector k coincide: p = Ћk.                                                

When interacting with the matter the photons can be emitted, absorbed and dispersed. Thus the amount of photons is not saved, but the laws of conservation of energy and impulse are executed.

Not all photons can cause heating of body. The short-wave photons can cause such phenomena, as luminescence and photo-electric effect.

Photo-electric effect. The phenomenon of emission of electrons by the matter under action of light is named a photo-electric effect or photoeffect. The experiments fulfilled by G. Hertz and G. Thomson demonstrated, that a photoeffect is submitted to the following conformities to the natural law:

-            the energy of liberated photoelectrons does not rely on the intensity of light;

-            the increase of intensity of light brings to the increase of the amounts of electrons, but not of their velocity;

-            the amount of electrons is proportional to the intensity of light;

-            the velocity of electrons relies only on frequency of falling light; with the increase of frequency the energy of electrons is growing linearly.

It exist an external photoeffect, when the carriers of charge go out of material, and internal photo-electric effect, when the carriers of charge get promoted mobility and, as a result, the conductivity of material grows. The necessary conditions of photoeffect are the following factors: light must be absorbed by photosensitive material and liberate the carriers of charge, which are divided by the electric field within working material. 

These laws of photoeffect can not find explanation at the level of only wave-like nature of light. Albert Einstein’s theory that is based on particle-like nature of light gives a complete explanation of the quantitative and qualitative data received by an experimental way

The picture of mechanism of photoeffect is explained qualitatively by that a photon gives the energy to the electron of matter. If the energy of photon is enough for freeing of electron from forces retaining him within the matter (bounds), electron goes out of this matter. The every disengaged electron absorbs energy of only one photon. The possibility of simultaneous absorption of energy of two photons is very small. The number of disengaged electrons is proportional to the number of absorbed photons, determining the intensity of light, and the energy of electrons linearly relies on frequency ω and does not rely on the number of photons. The number of the disengaged electrons is proportional to the number of absorbed photons determining the intensity of light, and the energy of electrons linearly relies on frequency ω and does not rely on the number of photons. Quantitatively a photoeffect is described by relation of A. Einstein: Ћω = (1/2)mv²_max + A that represents by itself the law of conservation of energy. In this equation m – rest mass of electron, v_max – maximum velocity of electron, A – work of output of electron, that is equal to the minimum energy of light, which must be given to the electron for deleting him outside the matter in a vacuum. The value (1/2)mv²_max = eV - maximal kinetic energy of the disengaged electron, e - charge of electron, V - potential. He is equal to a voltage, which must be applied to the cathode to prevent escaping of the electrons from the matter.

In obedience to equation (4), if the work of output A exceeds the energy of quantum Ћω, an electron can not leave the matter. The frequency ω₀ and wave-length λ₀ describe the red boundary of photoeffect and are determined by terms: ω₀ = А/Ћ, λ₀ = 2πЋс/A. 

For every matter the minimum frequency of photoeffect exists. The threshold of photoeffect is determined by chemical properties and state of surface of matter. For most metals a red boundary of photoeffect is found in the ultraviolet range of light-spectrum. A photoeffect is possible, when ω₀ < ω, або λ₀ > λ.

This formula describes not only a direct photoeffect, in which energy of photons is transformed into kinetic energy of photoelectrons, but also reverse photoeffect, at which photons birth due to kinetic energy of electrons falling onto a surface of matter, for example, metal (process that is observed in x-ray tubes). A photoeffect is practically inertialess.

The number of photoelectrons that are created on one falling photon is called the quantum output of photoeffect. A quantum output is determined by properties of matter and wave-length of radiation. Dependence of quantum output in metals from energy of photons, certain in eV, is called the spectral characteristic of photoeffect. Near the red boundary the quantum output for metals is equal to the value of 10^-4. When the energy of photons is about 10 eV, quantum output grows quickly. The maximum of quantum output is observed on frequencies, for which the coefficient of reflection of light is minimum.

The phenomenon of strong growth of quantum output and photocurrent of saturation in the separate ranges of frequencies of falling radiation is called a selective photoeffect. In this case a quantum output strongly relies on the angle of incidence of light and his polarization. In the case of polarization of radiation in a plane, perpendicular to the plane of falling, a selective photoeffect is maximal and relies on the angle of incidence. The indicated features testify to the influence of wave-like properties of light on an external photoeffect.

In the case of multilayer cathodes (compounds of alkaline metals with the stibium and bismuth, cathodes with semiconductor layers) an external photoeffect is stimulated by absorption of photons by electrons that are found in a zone of conductivity, or at level of admixtures. As a result of small work of output the quantum output of compounds cathodes for visible part of light-spectrum considerably exceeds the quantum output of ordinary metallic cathodes. 

Photoelectrons that move under action of the external electric field form a photocurrent. The all considered types of photoeffect are external, as a result of which the electrons go out of the matter.

There is also an internal photoeffect, at which the electrons, remaining in the matter, change the power state. In semiconductors and dielectrics a part of electrons under action of light passes from valiancy zone into the zone of conductivity. The conductivity of matter is thus growing. Such phenomenon is named photoconductivity. The change of the power state of electrons can cause a change of the internal electric field in a crystal and, as a result, causes an appearance of electromotive force (photo-EMF) on a boundary of two semiconductors or of conductor and metal under their illumination. The conductivity of matter is proportional to the intensity of monochromatic light.

The introduction into the semiconductors of admixtures brings to the decline of frequency as a result of knocking over of electrons from a valance zone into acceptors levels of an admixture. Photoconductivity of n-semiconductor has an electronic nature. Photoconductivity of p- semiconductor has a «hole» nature. Strong absorption of light can lower conductivity of semiconductors as a result of intensification by photons of the processes of recombination of electrons and «holes» and decreasing of concentration of charges carriers. 

A valve (photo-electric) photoeffect become appearent in the origin of EMF as a result of internal photoeffect near the contact between a metal and semiconductor, or two semiconductors of p-type and n-type. Such contact has the one-sided conductivity, related to impoverishment of layers of semiconductors adjoining to the contact, by the carriers of current (electrons, holes).

An internal photoeffect in semiconductors causes a violation of the equilibrium distribution of carriers of current in the region of contact and results in appearance of contact difference of potentials, in other words, results in appearance of electromotive force (photo-EMF). The value of photo-ERS is proportional to the intensity of monochromatic light. A valve photoeffect in p-n- transition represents by itself the direct transformation of energy of electromagnetic radiation into energy of electric current. This phenomenon is used in the photo-electric sources of current (in semiconductor silicon elements, germanium and other). 

In gases the phenomenon of photoeffect results in photoionization of atoms and molecules under action of radiations.

Written by Vasil Sidorov on August 05, 2010 in queltanews.com

Technopark QUELTA,

Nizhyn Laboratories of Scanning Devices

sidorovvasil@gmail.com

References

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3.     Rebrin Y.K., Sidorov V.I. Holographic devices of control of an optical ray. – Kiev:  KHMAES, 1986. - 124 pp.