Determination of the spectra of ion He and H₂ bombardment of autoemitter surface
Analytical consideration and numerical calculations of the parameters describing the operating conditions of field electron emitters and the spectra of the ion bombardment of emitting surface are adduced. Based on the analysis of the obtained energy spectra, it is calculated the dependence of the av...
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Mazilov, A.A. 2015-05-29T16:18:55Z 2015-05-29T16:18:55Z 2015 Determination of the spectra of ion He and H₂ bombardment of autoemitter surface / A.A. Mazilov // Вопросы атомной науки и техники. — 2015. — № 2. — С. 35-38. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 02.30.Mv, 68.37.Vj https://nasplib.isofts.kiev.ua/handle/123456789/82437 Analytical consideration and numerical calculations of the parameters describing the operating conditions of field electron emitters and the spectra of the ion bombardment of emitting surface are adduced. Based on the analysis of the obtained energy spectra, it is calculated the dependence of the average energy of bombarding ions of helium and hydrogen on the radius of curvature of the emitter in the process of field current extraction and it is proposed an analytical approximation of the results. Приводятся аналитическое рассмотрение и численные расчеты параметров, описывающих условия эксплуатации полевых электронных эмиттеров и спектры ионной бомбардировки эмитирующей поверхности. На основании анализа полученных энергетических спектров рассчитана зависимость средней энергии бомбардирующих ионов гелия и водорода от радиуса кривизны эмиттера в процессе отбора автоэлектронного тока и предложена аналитическая аппроксимация результатов. Приводяться аналітичний розгляд і чисельні розрахунки параметрів, що описують умови експлуатації польових електронних емітерів і спектри іонного бомбардування поверхні, що емітує. На підставі аналізу отриманих енергетичних спектрів розрахована залежність середньої енергії бомбардуючих іонів гелію й водню від радіуса кривизни емітера в процесі відбору автоелектронного струму та запропонована аналітична апроксимація результатів. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Физика радиационных повреждений и явлений в твердых телах Determination of the spectra of ion He and H₂ bombardment of autoemitter surface Определение спектров бомбардировки ионами He и H₂ поверхности автоэмиттеров Визначення спектрів бомбардування іонами He і H₂ поверхні автоемітерів Article published earlier |
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| title |
Determination of the spectra of ion He and H₂ bombardment of autoemitter surface |
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Determination of the spectra of ion He and H₂ bombardment of autoemitter surface Mazilov, A.A. Физика радиационных повреждений и явлений в твердых телах |
| title_short |
Determination of the spectra of ion He and H₂ bombardment of autoemitter surface |
| title_full |
Determination of the spectra of ion He and H₂ bombardment of autoemitter surface |
| title_fullStr |
Determination of the spectra of ion He and H₂ bombardment of autoemitter surface |
| title_full_unstemmed |
Determination of the spectra of ion He and H₂ bombardment of autoemitter surface |
| title_sort |
determination of the spectra of ion he and h₂ bombardment of autoemitter surface |
| author |
Mazilov, A.A. |
| author_facet |
Mazilov, A.A. |
| topic |
Физика радиационных повреждений и явлений в твердых телах |
| topic_facet |
Физика радиационных повреждений и явлений в твердых телах |
| publishDate |
2015 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Определение спектров бомбардировки ионами He и H₂ поверхности автоэмиттеров Визначення спектрів бомбардування іонами He і H₂ поверхні автоемітерів |
| description |
Analytical consideration and numerical calculations of the parameters describing the operating conditions of field electron emitters and the spectra of the ion bombardment of emitting surface are adduced. Based on the analysis of the obtained energy spectra, it is calculated the dependence of the average energy of bombarding ions of helium and hydrogen on the radius of curvature of the emitter in the process of field current extraction and it is proposed an analytical approximation of the results.
Приводятся аналитическое рассмотрение и численные расчеты параметров, описывающих условия эксплуатации полевых электронных эмиттеров и спектры ионной бомбардировки эмитирующей поверхности. На основании анализа полученных энергетических спектров рассчитана зависимость средней энергии бомбардирующих ионов гелия и водорода от радиуса кривизны эмиттера в процессе отбора автоэлектронного тока и предложена аналитическая аппроксимация результатов.
Приводяться аналітичний розгляд і чисельні розрахунки параметрів, що описують умови експлуатації польових електронних емітерів і спектри іонного бомбардування поверхні, що емітує. На підставі аналізу отриманих енергетичних спектрів розрахована залежність середньої енергії бомбардуючих іонів гелію й водню від радіуса кривизни емітера в процесі відбору автоелектронного струму та запропонована аналітична апроксимація результатів.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/82437 |
| citation_txt |
Determination of the spectra of ion He and H₂ bombardment of autoemitter surface / A.A. Mazilov // Вопросы атомной науки и техники. — 2015. — № 2. — С. 35-38. — Бібліогр.: 12 назв. — англ. |
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AT mazilovaa determinationofthespectraofionheandh2bombardmentofautoemittersurface AT mazilovaa opredeleniespektrovbombardirovkiionamiheih2poverhnostiavtoémitterov AT mazilovaa viznačennâspektrívbombarduvannâíonamiheíh2poverhníavtoemíterív |
| first_indexed |
2025-11-24T11:37:31Z |
| last_indexed |
2025-11-24T11:37:31Z |
| _version_ |
1850845428286750720 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №2(96) 35
DETERMINATION OF THE SPECTRA OF ION He AND H2
BOMBARDMENT OF AUTOEMITTER SURFACE
A.A. Mazilov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: mazilov@kipt.kharkov.ua
Analytical consideration and numerical calculations of the parameters describing the operating conditions of
field electron emitters and the spectra of the ion bombardment of emitting surface are adduced. Based on the
analysis of the obtained energy spectra, it is calculated the dependence of the average energy of bombarding ions of
helium and hydrogen on the radius of curvature of the emitter in the process of field current extraction and it is
proposed an analytical approximation of the results.
PACS: 02.30.Mv, 68.37.Vj
INTRODUCTION
The development of radiation-resistant materials of
reactor building largely complicated by the lack of
knowledge of the nature of radiation effects in the
relatively unexplored region of very high doses. In
works [1, 2] using accelerator simulation technologies
there were investigated in detail the processes of
interaction of fast charged particles with solids: primary
radiation damage of materials, formation and evolution
of dislocation structure. As the result, it was achieved a
significant progress in the development of concepts of
radiation damage of structural materials. However, there
are still insufficiently studied experimentally the
phenomena accompanying the elementary acts of
radiation damage. In this regard, of particular interest
are simulated experiments in situ using field ion
microscopes with built-in sources of accelerated ions
[3, 4]. In such experiments at the atomic level there
were detected processes such as surface diffusion,
activated by low-energy ion bombardment [5, 6], which
play an essential role in radiation damage of materials
of the first wall and divertor of fusion devices and is
widely used at present in nanotechnology of surface
treatment of metals.
For irradiation of solids by low-energy ions in the
chamber of field emission microscope was used method
[7, 8], based on the bombardment of the surface of the
needle-shaped sample by ions formed by electron
impact ionization of atoms (molecules) of gas that fills
the vacuum chamber of the microscope. The resulting
ions are accelerated in a strong electric field and
bombard the surface of the needle-shaped sample. This
technique allows varying in a wide interval of ion
beams parameters up to the minimum, corresponding to
a single ion collision with the surface, allowing the
study of elementary acts of radiation damage. Since
using this method there is no possibility of direct
experimental determination of the intensity of the ion
bombardment of the sample surface, it is necessary to
conduct their numerical calculations. Recently in a
number of works [9, 10], there was established an
analytical framework for calculations of ion
bombardment of needle samples in the process of field
current extraction. However, these calculations was not
took into account found in the work of P.A. Bereznyak
and V.V. Slezov [8] features of the configuration space
region from which ions, generated with zero initial
speed, get to the emitting part of the sample. The
present article shows the results of calculations of the
ion bombardment of the needle samples in the process
of field current extraction that are performed in the
framework of Bereznyak-Slezov theory for a wide range
of irradiation parameters.
RESULTS AND DISCUSSION
1. SIMULATION OF ION SPECTRA
The potential distribution near the surface of the
needle emitter and in the interelectrode space is
satisfactorily described by Bereznyak-Slezov model [8],
originally developed to solve the problem of ion
bombardment of needle-shaped emitters. The authors
convincingly showed that the most part of the ions,
formed in the process of field current extraction,
bombards the side (tapered) part of the emitter. Emitting
region is bombarded mainly from the axial cylindrical
region of radius 4.8r0. However, it should be noted that
due to the large amount of calculations and the limited
memory and speed of used computers, the task was
strictly solved only for one set of parameters specific to
the field emitters.
In this work, we present the results of the analysis
and the numerical values of the relevant parameters
describing the operating conditions of field electron
emitters and the spectra of the ion bombardment of
emitting surface. The calculations were performed using
Bereznyak-Slezov approximation. The equations of
motion of a particle with charge e and mass m,
according to this model are of the form:
0
1
0
rmr
e
;
00
1
rmr
e
; (1)
2
1
222
3
22
2
0
AK CC
V
mr
e
; (2)
22
2
1
22
2
3
22
2
0 AK CC
V
mr
e
. (3)
and are interpreted as the components of
acceleration along the axis and perpendicular to the
axis, respectively. Solving this system in the time scale
τ, it can be set polar coordinate of the point of ion
contact on the edge. Here
mailto:mazilov@kipt.kharkov.ua
36 ISSN 1562-6016. ВАНТ. 2015. №2(96)
V
CC
e
m
r AK
01 . (4)
For determination of the intensity of ion
bombardment, we used the approximation formula for
the configuration area, from which ions, formed with
zero initial velocity, fall on the needle top:
))exp((1
)(
0
1
0
m
m
A
, (5)
where γm = 4.80368; A1 = -2485.07; η0 = -18.6127 and
Δη = 2.7592.
From (5) it follows that the contribution to ion
bombardment of emitting surface is provided by the
ions formed near the surface of the tip, or in a region
close to the symmetry axis. In both cases, for the
number of ions N, bombarding the surface per time unit
the ratio is applicable:
ddr
e
j
kT
p
N
max max
min0
)(
)(
22
3
0
0 ),(
2)( , (6)
)( 00 Vr
e
I
kT
p
kN BS , η >> 10. (7)
Here p is the pressure in the chamber of the microscope,
Pa; k=1.3806488·10
-23
– the Boltzmann constant, J/K;
T – temperature, K; I field current, A; e = 1.602176·10
-19
–
the electron charge, C; σ(V0) – the ionization cross
section, m
2
; kBS – Bereznyak-Slezov factor, is equal to:
ddkBS
1000 )(
0
22
min
0
)(
, (8)
where
2
0
2
0 0
( )
1
( )
( ) ln 1.25 .
( ) 1 ln 1.25
ii
i
i ii
VV
EE V
E V VV
E EE
(9)
Here Σ(η) is reduced ionization cross section; V(η) – the
potential at a given point of the area; Ei – the ionization
potential of the gas; ηmin – the distance where
V(ηmin) = Ei.
Fig. 1 shows the dependence of the numerical
coefficient kBS determining the total number of ions
bombarding the tip per time unit on the radius of
curvature of the shape at the top for helium and
hydrogen. Dots represent calculated values, and the
solid curve is the proposed approximation:
for hydrogen 09618.05.146.15)( 0
rH
BS rk , (10a)
for helium 09664.046.146.13)( 0
rHe
BS rk . (10b)
In numerical calculations, the operating voltage of
the microscope (diode) was determined based on the
condition of constancy of the field strength at the top of
the emitter (F = 5 V/nm). As follows from the Fig. 1,
the coefficient kBS significantly depends on the size of
the emitter. The maximum value kBS is 13.5 that is
consistent with calculations [8] carried out for the tip
with a radius equal to 100 nm.
0 20 40 60 80 100
0
2
4
6
8
10
12
14
16
k B
S
r
0
, nm
H
He
Fig. 1. The intensity of the ion bombardment of the tip
depending on the radius of curvature of the emitter
From Fig. 2 it follows that the dependence of
reduced ionization cross section of helium and hydrogen
Σ(η) from the dimensionless axial coordinates
(cylindrical system) has a sharp maximum near the
shape top (r0 = 100 nm). For large values of coordinates
and until the anode a cross section changes slightly.
0 2 4 6 8 10
0
2
4
6
8
10
r
0
= 100 nm
H2
He
Fig. 2. Reduced ionization cross section of helium and
hydrogen depending on the dimensionless coordinate
directed along the optical axis
The distribution function for the energy of
bombarding ions can be obtained from expressions (7)
and (9):
0 0
( )
( )
max
max2 2
00
(2 1)( )
ln(2 1) .
2
V
V
f d
V
(11)
We have performed calculations for emitters with
different radii of curvature at the top, corresponding to
the typical conditions of the ion microscopy
experiments. As the result, the curves of the energy
distribution of bombarding ions were built.
Fig. 3 shows the energy spectra of ions of helium
and hydrogen, bombarding the hemispherical part of
emitters with radii of curvature of 10, 25, 50 and
100 nm, respectively. These values of the radii of
curvature are typical for experiments with nanoemitters,
samples, used in the traditional field ion microscopy,
studying of the mechanisms of radiation damage of the
ISSN 1562-6016. ВАНТ. 2015. №2(96) 37
surface and operating of the needle nonheated cathodes
in high-resolution electron microscopy.
0 200 400 600 800 1000
0,00
0,01
0,02
0,03
0,04
0,05
0,06
f,
a
.u
W, eV
r
0
= 10 nm
r
0
= 25 nm
r
0
= 50 nm
r
0
= 100 nm
He
0 200 400 600 800 1000
0,00
0,02
0,04
0,06
0,08
0,10
f,
a
.u
H2
W, eV
r
0
= 10 nm
r
0
= 25 nm
r
0
= 50 nm
r
0
= 100 nm
Fig. 3. Spectra of ion bombardment of the emitting part
of the needle-shaped cathode with different radii of
curvature in the process of field current extraction at
the atmosphere of helium and hydrogen
2. CALCULATION OF THE ION
BOMBARDMENT FLUENCE
Fig. 4 shows the dependence of the average energy
of ion bombardment on the radius of curvature of the
emitter in the process of field current extraction in the
atmosphere of helium and hydrogen. The solid curve
corresponds to calculations by the formula (11) obtained
by numerical solution of the trajectory tasks. The dotted
curve is the result of calculations by the approximate
formula proposed in [5]. A comparison of these data
shows an almost identical near the radii of curvature of
the order of 50 nm, i.e., the area where the most ion-
microscopic studies of radiation damage of
autocathodes are carried out. Outside these values, there
is only a slight deviation from the linear dependence,
proposed on the basis of analytical calculations in [5].
To calculate the number of ions N, bombarding the
surface of the tip per time unit (7) it is necessary to
calculate the ionization cross section σ(W) of helium
and hydrogen atoms. We used experimental data values
σ(W) from [11, 12], and approximated them by formula:
2
32
2
2
1 ln)(
A
W
A
WA
AW
AW . (12)
where A1 = 8317·10
-21
; A2 = 24.6; A3 = 0.986 for helium
and A1 = 7130·10
-21
; A2 = 13.595; A3 = 0.92136 for
hydrogen.
0 20 40 60 80 100 120
0
100
200
300
400
500
He
H
<W>=eFr
0
<
W
B
S
>
,
eV
r
0
, nm
Fig. 4. The dependence of the average energy of ion
bombardment on the radius of curvature of the emitter
0 400 800 1200 1600 2000
0
1
2
3
4
W, eV
W
cm
2
He
0 400 800 1200 1600 2000
0
2
4
6
8
10
W
cm
2
W, eV
H2
Fig. 5. The dependence of the ionization cross section
on the electrons energy for helium and hydrogen
Fig. 5 shows the dependence of the ionization
energy cross section on electrons energy for helium and
hydrogen. Dots represent experimental data [11, 12],
and the solid curve is the approximation formula (12).
Solving equation (7) considering (10a), (10b), (12)
in terms of p = 0.01333 Pa; T = 300 K; I = 10
-7
A;
r0 = 30 nm; V0 = 2 kV, we obtain that each surface atom
is subjected to a collision once on time of 152 c by
helium ions and once on time of 66 c by hydrogen ions
(assuming that 1 cm
2
of the tip surface area contains
10
15
atoms). Hence the fluence of ions:
t
r
N
2
02
(13)
38 ISSN 1562-6016. ВАНТ. 2015. №2(96)
for time t = 100 c is ФHe = 6.575·10
18
m
-2
for helium and
ФH = 15.14·10
18
m
-2
for hydrogen.
CONCLUSIONS
A mathematical analysis and numerical calculations
of the parameters describing the operating conditions of
field electron emitters was performed and the spectra of
the ion bombardment of emitting surface were obtained.
There was established that at typical field emission
researches of experimental conditions (F ≤ 5 V/nm,
r0 ≤ 100 nm) ions, formed when r ≤ 10r0, have energy
below the threshold of radiation displacement of lattice
atoms. There was established the dependence of the
numerical coefficient kBS determining the total number
of ions bombarding the tip per time unit from the radius
of curvature of the tip at the top. Based on the analysis
of obtained energy spectra there was calculated
dependence of the average energy of bombarding ions
on the radius of curvature of the emitter in the process
of field current extraction and analytical approximation
results were proposed.
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Статья поступила в редакцию 18.02.2015
ОПРЕДЕЛЕНИЕ СПЕКТРОВ БОМБАРДИРОВКИ ИОНАМИ He И H2
ПОВЕРХНОСТИ АВТОЭМИТТЕРОВ
A.A. Мазилов
Приводятся аналитическое рассмотрение и численные расчеты параметров, описывающих условия
эксплуатации полевых электронных эмиттеров и спектры ионной бомбардировки эмитирующей
поверхности. На основании анализа полученных энергетических спектров рассчитана зависимость средней
энергии бомбардирующих ионов гелия и водорода от радиуса кривизны эмиттера в процессе отбора
автоэлектронного тока и предложена аналитическая аппроксимация результатов.
ВИЗНАЧЕННЯ СПЕКТРІВ БОМБАРДУВАННЯ ІОНАМИ He І H2
ПОВЕРХНІ АВТОЕМІТЕРІВ
О.О. Мазілов
Приводяться аналітичний розгляд і чисельні розрахунки параметрів, що описують умови експлуатації
польових електронних емітерів і спектри іонного бомбардування поверхні, що емітує. На підставі аналізу
отриманих енергетичних спектрів розрахована залежність середньої енергії бомбардуючих іонів гелію й
водню від радіуса кривизни емітера в процесі відбору автоелектронного струму та запропонована
аналітична апроксимація результатів.
http://www.sciencedirect.com/science/article/pii/003960287890256X
http://www.sciencedirect.com/science/article/pii/003960287890256X
http://www.sciencedirect.com/science/journal/00396028
http://www.sciencedirect.com/science/journal/00396028/75/2
http://www.sciencedirect.com/science/journal/00396028/75/2
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