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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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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| 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. |
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| 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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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.
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Table 1
Table 2
|
| id | nasplib_isofts_kiev_ua-123456789-111170 |
| 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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