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Study of spectral dependences of absorption coefficient at the region of absorption by free carriers shows that the introduction of radiation defects in n-GaP crystals leads to the appearance of additional scattering besides of traditional ones. A new scattering mechanism on “frozen” phonons (deformation localized near the radiation defects) is suggested and its behavior in experimental and theoretical aspects taking into account Х
_{1с}-Х
_{3с} transitions at the scattering process has been studied. It was shown that the increase of “frozen” phonons’ concentration results to the growth of this mechanism contribution in the whole scattering and the absorption coefficient by free carriers is described approximately by low
*α ~ ω*
^{-r}, where -1/2 ≤ r ≤ 7/2. Suggested scattering mechanism allows explaining qualitatively the decrease of r. It was established that the dis- ordered by irradiation region effectively decreases the concentration of free carriers, but being a region of increased resistivity, it influences the scattering slightly even at the actual quantum region
.

The basic information about the scattering mechanisms has been obtained from the temperature and field dependences of kinetic coefficients. In respect of electron-phonon scattering mechanisms, the problem primarily consists in finding the electron-phonon coupling constants in the expression for kinetic coefficients as parameters to be determined experimentally. However, the temperature dependences of kinetic coefficients alone are often insufficient to fully define all of above constants. As shown in [

Quantum theory of the absorption by free carriers predicts power degree dependences of absorption coefficient:

where r is determined by the scattering mechanisms [

For n-GaP usually r

This paper presents the results of study the light absorption by free carriers in n-GaP crystals irradiated by high energy (50 MeV) electrons, i.e., a defects concentration and compensation ratio of free carriers in crystals was carried out by introducing radiation defects. Both experimental and theoretical investigations were applied in the course of electron irradiation at various doses and proposed theory explained the experimental data sufficiently.

The measurements of free carrier absorption in n-GaP crystals doped with tellurium (free carrier concentration n = (1.5 - 2) × 10^{17} cm^{−3}) in infrared region (l = 2 - 15 μm) were carried out using UR-20 spectrophotometer at room temperature. The concentration of charge carriers was determined from the intensity of 3 μm absorption band based on the value of the absorption cross-section for X_{1c}-X_{3c} transitions, s = 9 × 10^{−17} cm^{2} [^{2}∙s at room temperature was carried out using a linear accelerator of Yerevan Physics Institute.

_{1}_{с} to the minimum X_{3}_{с} located higher by 0.4 eV; 2) absorption by free carriers.

The curves reveal an absorption band at l = 3 μm (type (1) transition) on the background of uniformly increased with absorption wavelength described by function like (1) due to type (2) transitions. _{A}/N_{D} compensation ratio (N_{A}-acceptors concentration, N_{d}-donors concentration), a/n ratio at l = 6.25 μm in the initial crystal and after electron irradiation. Also, some data from [

It is seen that as a result of irradiation, the concentration of free electrons decreases and the compensation ratio increases. At the same time, a decrease of degree r in the spectral dependence of the absorption coefficient down to 1.13 takes place. Here, a/n ratio after irradiation increases. When irradiating with 50 MeV electrons, point radiation defects and more thermo-stable disordered regions are simultaneously formed in GaP crystals [^{17} el/cm^{2}) and after heat treatment at 525˚C. For the crystals irradiated with so high integral electron fluxes, the free carriers density decreases sharply, in consequence of which no absorption by free carriers is observed. It was shown in [

between curves 1 and 2 (see

It is obvious that whereas only 25% of free electron concentration was recovered after the annealing, the r value in (1) was recovered completely, the a/n ratio also was recovered.

Numbers of samples | D, el/cm^{2} | n, cm^{−3} | N_{A}/N_{D} | a/n × 10^{−17}, cm^{2} | r |
---|---|---|---|---|---|

1 | 0 | 1.7 × 10^{17} | 0.1 | 6 | 1.75 |

1 | 4.3 × 10^{15} | 1 × 10^{17} | 0.4 | 9.2 | 1.36 |

1 | 7 × 10^{15} | 6.7 × 10^{16} | 0.6 | 9.7 | 1.25 |

1 | 8.6 × 10^{15} | 2.2 × 10^{16} | 0.87 | 11.5 | 1.13 |

Data from [ | 0 | 7.2 × 10^{17} | 0.6 | 20 | 1.35 |

2 | 0 | 1.9 × 10^{17} | 0.1 | 10 | 1.86 |

2^{*} | 1 × 10^{17} | 5 × 10^{16} | 0.7 | 10.8 | 1.86 |

^{*}After irradiation, the sample was annealed at 525˚C during 20 min.

The coefficient of absorption by free carriers was calculated by the second order of the perturbation theory [

where i, m, f represent the initial, intermediate and final electron state, respectively,

tionship is determined by the dependence of matrix elements on k, k' vectors. The expressions

to the (2) defines a(w) relationship.

In accordance with [_{1c} and for overlying X_{3c} zone)-can be represented in the following form:

where

where N is the carrier concentration, n is the refractive index. The second term in (3) corresponds to the inclusion of intermediate states in the next conduction band (X_{1c}-X_{3c} virtual transitions), which formally looks like the presence of one more scattering mechanism, called i-scattering [

The above mentioned experimental results show that the degree r in (1) decreases with increasing N_{A}/N_{D} in the case of both doping [

The basic idea of the deformation potential approximation is that the operator of interaction with phonons should be replaced by a quantity characterizing the crystal deformation. It is supposed that the deformation caused by static field arising in the presence of radiation defects, is responsible for local changes in the size and shape of the crystal unit cell much as in the case of the deformation due to lattice vibrations. If the phonons are the sum of normal vibrations, then the static field near the radiation defects can be considered as the sum of a large number of Fourier components corresponding to the “frozen” lattice vibrations. Obviously, their number is proportional to the density of radiation defects.

Scattering on the “frozen” phonons can be taken into account, on the whole, within the framework of the theory of deformation potential. It is known that in this approximation, when describing the electron interaction with one phonon with wave vector

where D_{q}, w_{froz}_{.}, n_{froz}_{.} are the interaction constants, frequency and distribution function of such “frozen” phonons, respectively. For small q _{q} can be expanded to q series:

and similar to the interaction with the photons, if (D_{q})_{q}_{=0} ≠ 0, the transition is “permitted”, and if (D_{q})_{q}_{=0} = 0, the electron-phonon transition is “forbidden”.

For the “frozen” phonons, w_{froz}_{.} and n_{froz.} weakly depend on q, therefore for the permitted transitions

does not depend on q, a_{froz}_{.}(w) is the same as for the acoustic phonons, so these data cannot explain our experimental results.

However, for the “forbidden” transitions

where

For the “forbidden” transitions (D_{q})_{q}_{=0} = 0, and the electron-phonon interaction will be of the first order in q. Note that for all types of phonons apart from acoustic ones, such scattering does not practically contribute to the kinetic phenomena due small q. However, in the case of the absorption of free carriers, where the scattering is no

longer elastic due to presence of high-energy photons

should be also considered.

Assuming that the interaction with the “frozen” phonons is described by the first order terms in q, with the growth of the number of such phonons the scattering on them can be an essential mechanism competing with the scattering on acoustic phonons.

Below, calculation of a(w) for this mechanism is presented similar to the method from [

Substituting

which can easily be represented in the following form:

where

It follows from the form of a_{froz}_{.} that a_{froz}_{.} ~w^{−}^{1/2} (i.e. l^{1/2}), and it is related to the fact that

Therefore, the frequency dependence of the total coefficient of absorption by free carriers, taking into account

the scattering on the “frozen” phonons, should approximately be described by (1) with

be noted, making allowance for all known scattering mechanisms, that naturally, from a large number of terms not all of them make equal contributions to the final result. In addition, i-scattering should be sufficiently intensive as X_{1c}-X_{3c} transition in n-GaP is dipole-allowed. Consideration of all these features allows explaining anomalously low values of r in the frequency dependence of a(w) and the tendency for a decrease in r with increasing the concentration of radiation-induced defects.

The increase in a/n ratio after irradiation shows that the introduced radiation defects in n-GaP crystals lead to the emergence of an additional scattering mechanism. The change in the scattering mechanism is also indicated by a decrease of r in (1) after irradiation.

The comparison of changes in the power degree r as a result of introduction of radiation-induced defects with the impact of introduction of compensating impurity atoms on r (see

It is known that in A^{III}B^{Y} semiconductor compounds, the radiation defects reveal a significant specific deformation per one point defect which is much more than the specific deformation for a substitution impurity atom. Therefore, the above proposed theoretical conclusion that the scattering on the “frozen” phonons can play a significant role in the absorption by free carriers is explained by additional scattering on local deformations.

In this connection it is interesting to note a much greater influence on the basic absorption edge in GaP, exerted by radiation defects in comparison with impurity centers, which is also explained by deformation effects [

The results shown in

The relationships shown in

Revealing high potential barrier [

Norik Е.Grigoryan,Hrant N.Yeritsyan,Vachagan V.Harutyunyan,Narek A.Hakobyan,Eduard A.Aleksanyan,Vahan A.Sahakyan, (2015) Scattering of Conduction Electrons on the Static Deformation Raised by Irradiation in n-GaP Crystals. Journal of Modern Physics,06,1935-1941. doi: 10.4236/jmp.2015.613199