High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma

The results of experimental investigations of distribution functions of nonequilibrium electrons induced by H+ and He+ ion beams with energies 1-2,25 MeV in solid-state plasma of Ge, GaAs and CdTe semiconductors are presented. It is shown, that distribution functions have a power-law character with...

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Published in:Вопросы атомной науки и техники
Date:2003
Main Authors: Zhurenko, V.P., Kononenko, S.I., Kalantaryan, O.V., Kolesnik, V.T., Muratov, V.I.
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Language:English
Published: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2003
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Cite this:High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma / V.P. Zhurenko, S.I. Kononenko, O.V. Kalantaryan, V.T. Kolesnik, V.I. Muratov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 148-151. — Бібліогр.: 20 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Zhurenko, V.P.
Kononenko, S.I.
Kalantaryan, O.V.
Kolesnik, V.T.
Muratov, V.I.
author_facet Zhurenko, V.P.
Kononenko, S.I.
Kalantaryan, O.V.
Kolesnik, V.T.
Muratov, V.I.
citation_txt High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma / V.P. Zhurenko, S.I. Kononenko, O.V. Kalantaryan, V.T. Kolesnik, V.I. Muratov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 148-151. — Бібліогр.: 20 назв. — англ.
collection DSpace DC
container_title Вопросы атомной науки и техники
description The results of experimental investigations of distribution functions of nonequilibrium electrons induced by H+ and He+ ion beams with energies 1-2,25 MeV in solid-state plasma of Ge, GaAs and CdTe semiconductors are presented. It is shown, that distribution functions have a power-law character with one power index on the whole electron energy range of 5÷100 eV being investigated; the corresponding power indices are presented. The yields of secondary electron emission induced by He⁺ ions are measured.
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fulltext УДК 533.9 NONEQUILIBRIUM ELECTRON DISTRIBUTION FUNCTIONS INDUCED BY FAST IONS IN SEMICONDUCTOR PLASMA V.P. Zhurenko, S.I. Kononenko, O.V. Kalantaryan, V.T. Kolesnik, V.I. Muratov Kharkov National university named by V.N. Karazin, sq. Svobody, 4, 61077, Kharkov, Ukraine, e-mail: kononenko@univer.kharkov.ua The results of experimental investigations of distribution functions of nonequilibrium electrons induced by H+ and He+ ion beams with energies 1-2,25 MeV in solid-state plasma of Ge, GaAs and CdTe semiconductors are presented. It is shown, that distribution functions have a power-law character with one power index on the whole electron energy range of 5÷100 eV being investigated; the corresponding power indices are presented. The yields of secondary electron emission induced by He+ ions are measured. INTRODUCTION Universal steady-state nonequilibrium power-law particle distribution functions f=Ap2s (p is a momentum) are exact solutions of kinetic equations with the Boltzmann collision integral. Kats et al. firstly obtained it by means of a group symmetry approach [1]. Such distribution can be realized in solid-state plasma under certain conditions. Entry of an additional kinetic energy into plasma of a solid gives rise to ionizations of medium atoms and production of a plenty of free electrons, which have energies above an equilibrium level [2]. In such conditions it is possible to form of electron distributions differing from equilibrium ones [3, 4]. As it has been shown in a number of theoretical and experimental investigations, under bombardment of high energy ion beams the presence of a particle (energy) flux generated in momentum space by a source (ionization) and a sink (emission of electrons) results in the formation of a steady-state nonequilibrium power-law distribution function of electrons in a solid-state plasma: f(E)=αI1/2E s, (1) where α is a normalizing constant, I is a flux of particles (energy), s is a power index [4, 5]. Here E is a total energy of electrons in a solid: E=ϕ+EF+eU, where ϕ is a work function, EF is a Fermi level, and the energy eU is measured from a vacuum level. Power-law distributions are characterized by the presence of significant part of high energy electrons. For example, the fraction of electrons with energies higher than Ep=18,9 eV (where Ep is energy of a plasma oscillations in beryllium) in the electron distribution induced by 4,9 MeV α-particles in beryllium specimen can exceed 37 % [6]. When velocity of an incident ion v essentially exceeds velocity of each electron of target atom, elastic losses are negligible small, and inelastic losses of energy usually referred to ionization losses or stopping power, are determined by the Bethe-Bloch formula [7]: -dE/dx=(4πZ1 2e4/mv2)Z2N ln(2mv2/I), (2) where m is the mass of an electron, Z1 is the charge of the incident particle, Z2 is the charge of the substance atoms, N is density of target atoms, and I is their mean excitation potential. As appears from the formula (2), in a high energy region ionization losses decrease as v-2. Entry of an additional charge into the quasi-neutral equilibrated system of solid-state plasma results in excitation of electron plasma oscillations - plasmons [8]. Thus, the energy lost by an ion moving in a solid-state plasma, can be transferred to electrons of medium in two different ways: a fraction of the ion energy goes into excitation of plasmons, and the other fraction is converted into the energy of individual electrons in collisions (in particular, in ionizing collisions with atoms) [2]. New free electrons produced have energies which significantly exceed the equilibrium level. The nonequilibrium situation realizable in such a way gives rise to considerable changing of a distribution function of free electrons [4]. It is possibly to obtain information about nonequilibrium electron distributions formed in solid- state plasma by measuring secondary effects that occur during the passage of a charged particle through a solid [6, 9]. The part of the nonequilibrium electrons produced in solid-state plasma, having the proper values and directions of momentum, can escape from the substance or, in other words, a secondary ion induced electron emission (SIEE) takes place. Process of an emission occurs in three stages: 1) production of nonequilibrium electrons; 2) transport of electrons (diffusion) to a surface of a solid and collisions; 3) overcoming potential barrier existing on a surface, and ejection into vacuum. Since well-known Sternglass paper [10] such approach is considered to be most thorough representing the mechanisms of SIEE [11]. The integral characteristic of SIEE is coefficient of SIEE γ frequently termed in the literature as an electronic yield [12]. Electronic yield γ is defined as a relation of a number of secondary electrons Ne emitted to a number of incoming ions Ni: γ=Ne/Ni . (3) The value of electron yield essentially depends on energy of bombarding ions. Now it is considered theoretically and experimentally proved, that for light ion impact electronic yield γ is proportional to the specific ionization losses (electronic energy loss per unit path lengths) in substance dE/dx [10, 12, 13]. Considerably more informative characteristics of SIEE are energy spectra of secondary electrons. The experimental study [14-16] has shown, that energy mailto:kononenko@univer.kharkov.ua spectra of secondary electrons have power-law character. As it has been shown in [9] studying the energy spectrum of the emitted electrons enable to find the shape of the electron distribution function in a solid. The experimentally investigated energy distribution functions of nonequilibrium electrons in a plasma of metals have piecewise power character with different power indices for different energy intervals [5, 16, 17]. The theoretical study [3, 4, 18] and the numerical modeling analysis [19] show that, in a semiconductor plasma, the power-law distribution function corresponding to a constant energy or particle flux in momentum space can exist in the energy range (E- EF) >EF. This distribution is formed by both collisions with electrons in the energy range (E-EF) >EF and collisions with background (equilibrium) electrons. From the expression for the electron emission current density [3, 4, 9, 20] we can see that, in a plasma with a nonequilibrium electron distribution, the electron emission current density is anomalously high, because, the distribution function decreases very gradually in the inertial interval. The conduction characteristics of the medium are governed by the density of the current carriers, so that, in a semiconductor plasma with a nonequilibrium electron distribution, this density is very high, in contrast to the case of an exponentially decreasing equilibrium distribution function [19]. That is why, under the action of intense fluxes of fast particles, the emission and conduction properties of a semiconductor plasma can become anomalous [19]. Experimental study of nonequilibrium electron distribution functions in semiconductor plasma has not been carried out yet. Thus, in this paper we tried to restore such distributions formed in a semiconductor plasma under the bombardment of fast light ions by means of measuring energy spectra of SIEE. EXPERIMENTAL SETUP The investigations of distribution functions and electron yields of secondary electron emission induced by fast light ion beams were carried out on the experimental setup which schematic diagram is represented on Fig. 1. The electrostatic ion Van de Graff accelerator, used as a source of primary particles, permitted to produce hydrogen H+ and helium He+ ion beams with energies from 1 up to 2,25 МeV. A system of target replacement developed by us was dispose inside the experimental chamber. It permits reliable moving and fixation on the beam axis up to 6 targets without vacuum failure. All targets under study 1 had 10 mm diameter and were fixed in copper workholders fastened on holder 2. The ion beam, collimated by means of diaphragm system, impinged on the target and caused backward secondary electron emission from its surface. Plane of the target was perpendicular to beam axis. The diameter of the beam spot on the target was 3 mm. The ion current density was not higher, than 30 µА/cm2. Experiments were carried out with polycrystalline targets prepared of germanium, gallium arsenide and cadmium telluride. The chamber was pumped out with a NMD-0,4-1 magnetic-discharge pump and an NVPR-16D fore vacuum pump with a liquid nitrogen trap, developed for elimination of vacuum oil contamination of chamber constructional elements. In all experiments vacuum system has allowed to provide residual gas pressure in the chamber no more than 10-6 тоrr. 1 2 3 4 5 6 7 8 9 10 R c Fig. 1. Schematic diagram of the experimental setup: 1 – target; 2 - holder of a target; 3 - half-spheres; 4,5 - electrometric amplifiers; 6 - the analog-digital converter; 7 - IBM PC computer; 8 – Faraday cup, 9 - current device F303; 10 - source of sawtooth voltage The secondary electrons emitted from the target surface, hit on the spherical collector consisting of two 100 mm radius hemispheres 3. By means of target replacement system the specimen under study was positioned between two hemispheres at center of the collector. The gap between hemispheres was 15 mm. The input window of the hemisphere was 10 mm diameter. Simultaneously with measuring collector current IC the target current IT was registered. The target current is a sum of the ion beam current IB and a current of the secondary electrons, which have reached the collector: IT = IC+ IB. The measured collector current IC and target current IT amplified correspondingly by electrometric amplifiers 4 and 5, were fed through the analog-to-digital converter 6 to the IBM PC COMPUTER 7. In order to calibrate the measuring system a Faraday cup 8 was disposed behind the back hemisphere. It permits to carry out direct measuring of ion beam current IFC when the targets are brought out of the beam. The dimensions of the Faraday cup were ∅ =20 mm and l=130 mm. Its current IFC was measured by means of current device F303 9. Electron yield was determined by the formula: γ = IC / (IC - IT). (4) Studying energy spectrum of SIEE electrons by means of the spherical analyzer designed for a point source of emission, it is possible to find an explicit shape of the distribution function of electrons inside a solid [9]. When the electron distribution is the power- law function the derivative of emission currents on electron energy dI/dU can be represented as: dI/dU = B⋅(EF+ϕ+eU)s+1, (5) where B is a constant, EF is Fermi level, ϕ is work function, eU is the energy of electrons in vacuum. Hence, the dependence (5) in logarithmic scale represents straight line, which slope ratio is equal to s+1. The energy distributions of secondary emission electrons were measured by means of the spherical collector in a retarding field energy analyzer mode. The retarding field was ranged from 0 to 100 V with 1 V step. The retarding electric field was produced in the space between the target 1 and two hemispheres 3. As the radius of the energy analyzer considerably exceeded target size the electrical field distribution was close to spherical one. The holder of each target 2 was a ceramic tube ∅=5 mm whose outer surfaces were covered by resistive layers. The specific resistance of layer Rc was varied nonlinearly along the tube so that the holder potential did not disturb the electrical field inside the energy analyzer. The target was in contact with one end of the resistive layer, whose another end was grounded. The retarding potential produced by the sawtooth voltage generator 10 controlled by COMPUTER 7 was applied to the target inside a ceramic tube. Thus, the current flowing along the resistive layer produced a potential distribution along the holder. The emitted secondary electrons, being moved on radial trajectories, hit the collector. When the retarding potential is applied to the target only those electrons which energy were sufficient for overcoming retarding field hit the collector. The experiment control program allowed making of 100 measurements of electron emission current for each value of the retarding potential during 7 seconds. Then the averaged value of that current was fed to the COMPUTER and memorized. As a result of that procedure the obtained dependences of the collector current on retarding voltage (5) (retarding curves) allowed to obtain the energy spectrum of SIEE electrons by differentiation of these dependences, and then restored the distribution function. Calculation procedure of the power index s values of electron distribution functions included some operations. At the beginning the "fitting" of electron emission current and differentiation of the retarding curves were carried out. Then the linear approximation of the dI/dU dependences on a total energy of electrons inside a solid (EF+ϕ+eU) plotted in logarithmic scale was performed. According to (5), the slope ratio of the straight lines is equal to (s+1). EXPERIMENTAL RESULTS AND DISCUSSIONS The experimental investigation performed has shown, that for all energies of incident H+ and He+ ions the electron energy distribution functions in solid-state plasma of semiconductors under study have power-law dependence. The typical double logarithmic-scale distribution function of nonequilibrium electrons induced by 1,25 МеV He+ ions from gallium arsenide sample is presented on Fig.2. The experimental points are seen to fit well in one straight line with power index s=-2,9 in the whole vacuum electron energy interval of 5…100 eV. As a result of experimental data processing we have obtained the power index s values of electron distribution functions. The corresponding power indexes for semiconductor samples are presented in Tables 1 depending on primary ion energy. As we have mentioned above the electron distribution functions formed in a metal plasma during the passage of fast light ions have piecewise power character with different power indices for different electron energy intervals [5, 16, 17]. At least two such energy intervals were observed. 10 100 0,1 1 2,01,5 E F +φ +eU, eV log(dI/dU), arb.units log(E F +φ +eU), arb.units Fig.2 Typical log(dI/dU) dependence on log(EF+ϕ+eU) for gallium arsenide bombarded by ions He+ with energy 1,25 МеV. The distribution function has one section on the whole energy interval 5…100 еV with power index s=-2,9 Table 1 Ion Energy, МеV Power index Gallium arsenide Germanium Cadmium telluride He+ 1 - 2,8 - 1,25 2,9 2,8 - 1,5 2,9 2,8 - 1,75 2,6 2,7 2,9 2 2,6 2,8 2,8 2,26 2,7 2,8 2,9 H+ 1 3,1 2,9 3,1 1,25 2,9 2,8 3,0 1,5 2,8 2,9 3,0 1,75 2,8 2,6 2,7 2 2,7 2,6 2,7 2,26 3,0 2,8 2,8 In our opinion, the presence of piecewise character, namely two sections on the distribution function observed for metal samples, perhaps, is connected with the action of two different mechanisms of energy transfer from the moving fast ion to the electron subsystem of the solid: plasma oscillation excitation with subsequent electron production by plasmon ionization and inelastic collisions with substance atoms, leading to direct ionization. The energy of the electron produced by the former mechanism can’t exceed the plasmon energy EP. For semiconductors the energy of plasmons, which are spread in conduction electron medium, is significantly less than ionization potential of substance atoms. In this connection, semiconductors have one power index in the whole energy interval of secondary electrons. An electron yield is considered to be basic characteristic of secondary ion induced electron emission. In our experiments we have measured this quantity too. The results of experimental measurements of the electron yield values for He+ ions are presented in Table 2. Table 2 Ion Energy, MeV Electron yield γ Gallium arsenide Germanium Cadmium telluride He+ 1 - 2,4 - 1,25 2,3 2,3 - 1,5 2,2 2,3 - 1,75 1,7 2,0 2,0 2 2,1 1,9 1,9 2,26 1,9 1,7 1,9 3100 3200 3300 3400 3500 3600 3700 1,7 1,8 1,9 2,0 2,1 2,2 2,3 2,4 2,5 γ , electrons per ion dE/dx, MeV/cm Fig.3. Electron yield from germanium sample as a function of the stopping power dE/dx for He+ projectiles The assumption of a proportionality between the electron yield of SIEE and the stopping power is demonstrated in Fig.3. As evident from this figure, the experimental points of electron yield dependence on the stopping power dE/dx for germanium and He+ projectiles are seen to fit well in straight line. CONCLUSIONS As a result of the experiments performed it is shown, that the nonequilibrium electron distribution functions induced by fast hydrogen and helium ions in solid-state plasma of the semiconductors under study have power- law dependence with one power index on the whole electron energy range of 5…100 eV being investigated. Presumably, earlier observed presence of two electron energy intervals on the distribution function in metal plasma is connected with plasma oscillation mechanism in a solid. For semiconductors the energy of plasmons spreading in free electron medium, is less than ionization potential of substance atoms. Thus, semiconductors have one power index in the whole energy interval of secondary electrons. Thus, the influence of plasma oscillations in solid state plasma on formation of electron distribution functions has been demonstrated. We want to express thanks V.I. Karas’ for continuous interest to work, useful remarks and discussions. Also the authors thank the staff of VG-5 accelerator of NSC KIPT and personally V.M. Mishchenko for arrangement of operation conditions. This work was supported by Science and Technology Center in the Ukraine project no.1862. REFERENCES 1.A.V. Kats, V.М. Kontorovich, S.S. Моiseev, and V.Е. Novikov // Pis’ma Zh.Eksp.TeorFiz. 1975. v. 21. p. 13. 2.N.P. Kalashnikov, V.S. Remizovich, M.I. Ryazanov. Collisions of fast charged particles in solids. Мoscow: Atomizdat, 1980. 3.V.I. Karas’, S.S. Моiseev, V.Е. Novikov // Pis’ma Zh.Eksp.TeorFiz. 1975, v. 21, №9, p. 525-528. 4.V.I. Karas’, S.S. Моiseev, V.Е. Novikov // Zh.Eksp.TeorFiz. 1976, v. 71, №4(10), p. 1421-1433. 5.Е.N. Batrakin, I.I. Zalyubovskii, V.I. Karas’ et. al. // Zh.Eksp.TeorFiz. 1985, v. 89, № 3(9), p. 1098-1100. 6.V.P Zhurenko, S.I. Kononenko, V.I. Karas’ etc. Dissipation of the energy of a fast charged particle in a solid-state plasma // Plasma Physics Reports. 2003, v. 29, №2, p. 130-136. 7.Yu.V. Gott. Interaction of particles with substance in plasma research. Мoscow: Atomizdat, 1978. 8.М. Steel, B. Vural. Wave interactions in solid state plasmas. Moscow: Atomizdat, 1973. 9.V.М. Balebanov, V.I. Karas’, I.V. Karas’ et al. // Plasma Physics Reports. 1998, v. 24, №9, p. 732-749. 10.E.J. Sternglass // Phys. Rev. 1957, V. 108, №1, p. 1. 11.H. Rothard, C. Caraby, A. Cassimi et. al. // Physical Review A 1995, v. 51, № 4, p. 3066-3078. 12.D. Нasselkamp, K.G. Lang, A. Scharmann et al. // Nucl. Instr. and Meth. B. 1981, v. 180, p. 349-356. 13.J. Schou //Phys. Rev. B. 1980, v. 22, p. 2141. 14.W. Meckbach, G. Braunstein, N. Arista // J. Phys. B 1975, v. 8, № 14, p. L344-L349. 15.D. Нasselkamp, S. Hippler, A. Scharmann // Nucl. Instr. and Meth. B. 1987, v. 18, p. 561-565. 16.Е.N. Batrakin, I.I. Zalyubovskii, V.I. Karas’ et al. // Poverkhnost. 1986, № 12, p. 82-86. 17.S.І. Коnonenko // Dopov.NANU. 2001, № 1, p. 87. 18.J.M. Ziman, Electrons and Phonons. Clarendon, Oxford, 1960; Inostrannaya Literatura, Moscow, 1962. 19.V.I. Karas` and I.F. Potapenko // Fizika Plazmy. 2002, v. 28, № 10, p. 908-918 [Plasma Physics Reports. 2002, v. 28, issue 10, p. 837–846]. 20.V.I. Karas’ // Pis’ma Zh. Tekh. Fiz. 1975, v. 1, p. 1020 [Sov. Tech. Phys. Lett. 1, 438 (1975)]. Table 1 Table 2
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1562-6016
language English
last_indexed 2025-12-07T13:26:09Z
publishDate 2003
publisher Національний науковий центр «Харківський фізико-технічний інститут» НАН України
record_format dspace
spelling Zhurenko, V.P.
Kononenko, S.I.
Kalantaryan, O.V.
Kolesnik, V.T.
Muratov, V.I.
2017-01-08T16:58:28Z
2017-01-08T16:58:28Z
2003
High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma / V.P. Zhurenko, S.I. Kononenko, O.V. Kalantaryan, V.T. Kolesnik, V.I. Muratov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 148-151. — Бібліогр.: 20 назв. — англ.
1562-6016
https://nasplib.isofts.kiev.ua/handle/123456789/111170
533.9
The results of experimental investigations of distribution functions of nonequilibrium electrons induced by H+ and He+ ion beams with energies 1-2,25 MeV in solid-state plasma of Ge, GaAs and CdTe semiconductors are presented. It is shown, that distribution functions have a power-law character with one power index on the whole electron energy range of 5÷100 eV being investigated; the corresponding power indices are presented. The yields of secondary electron emission induced by He⁺ ions are measured.
We want to express thanks V.I. Karas’ for continuous interest to work, useful remarks and discussions. Also the authors thank the staff of VG-5 accelerator of NSC KIPT and personally V.M. Mishchenko for arrangement of operation conditions. This work was supported by Science and Technology Center in the Ukraine project no.1862.
en
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
Вопросы атомной науки и техники
Нелинейные процессы
High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
Article
published earlier
spellingShingle High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
Zhurenko, V.P.
Kononenko, S.I.
Kalantaryan, O.V.
Kolesnik, V.T.
Muratov, V.I.
Нелинейные процессы
title High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
title_full High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
title_fullStr High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
title_full_unstemmed High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
title_short High number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
title_sort high number harmonic exitation by oscillators in periodic media and in periodic potential nonequilibrium electron distribution functions induced by fast ions in semiconductor plasma
topic Нелинейные процессы
topic_facet Нелинейные процессы
url https://nasplib.isofts.kiev.ua/handle/123456789/111170
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