High resolution probe-forming system with spherical aberration correction for nuclear microprobe
A probe-forming system based on a separate orthomorphic quadruplet of magnetic quadrupole lenses with a short working distance is considered, allowing the system demagnification to be significantly increased. Three magnetic octupole lenses are used to correct spherical aberrations. The parameters of...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Zitieren: | High resolution probe-forming system with spherical aberration correction for nuclear microprobe / A.G. Ponomarev, S.V. Kolinko, H.E. Polozhii, V.A. Rebrov // Problems of Atomic Science and Technology. — 2023. — № 3. — С. 153-157. — Бібліогр.: 25 назв. — англ. |
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| author | Ponomarev, A.G. Kolinko, S.V. Polozhii, H.E. Rebrov, V.A. |
| author_facet | Ponomarev, A.G. Kolinko, S.V. Polozhii, H.E. Rebrov, V.A. |
| citation_txt | High resolution probe-forming system with spherical aberration correction for nuclear microprobe / A.G. Ponomarev, S.V. Kolinko, H.E. Polozhii, V.A. Rebrov // Problems of Atomic Science and Technology. — 2023. — № 3. — С. 153-157. — Бібліогр.: 25 назв. — англ. |
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| description | A probe-forming system based on a separate orthomorphic quadruplet of magnetic quadrupole lenses with a short working distance is considered, allowing the system demagnification to be significantly increased. Three magnetic octupole lenses are used to correct spherical aberrations. The parameters of the octupole corrector are calculated using the matricant method. The focusing properties of the system are determined by means of a probe formation optimization process based on the value of the maximum reduced collimated acceptance. The calculations performed showed the feasibility of such a probe forming system for microanalysis and proton beam writing technique.
Розглянуто зондоформуючу систему на базі розподіленого ортоморфного квадруплету магнітних квадрупольних лінз з малою робочою відстанню, що дозволило значно збільшити коефіцієнти зменшення. Для корекції сферичних аберацій застосовуються три магнітні октупольні лінзи. Розрахунок параметрів октупольного коректора виконується методом матрицантів. Фокусуючі властивості системи визначаються за рахунок оптимізації процесу формування зонда на основі величини максимального приведеного колімованого аксептансу. Проведені розрахунки показали, що така система може бути реалізована для застосування в методиках мікроаналізу та протонно-променевої літографії.
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ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145) 153
https://doi.org/10.46813/2023-145-153
HIGH RESOLUTION PROBE-FORMING SYSTEM WITH SPHERICAL
ABERRATION CORRECTION FOR NUCLEAR MICROPROBE
A.G. Ponomarev, S.V. Kolinko, H.E. Polozhii, V.A. Rebrov
Institute of Applied Physics, National Academy of Sciences of Ukraine, Sumy, Ukraine
E-mail: ponom56@gmail.com
A probe-forming system based on a separate orthomorphic quadruplet of magnetic quadrupole lenses with a
short working distance is considered, allowing the system demagnification to be significantly increased. Three
magnetic octupole lenses are used to correct spherical aberrations. The parameters of the octupole corrector are
calculated using the matricant method. The focusing properties of the system are determined by means of a probe
formation optimization process based on the value of the maximum reduced collimated acceptance. The calculations
performed showed the feasibility of such a probe forming system for microanalysis and proton beam writing
technique.
PACS: 41.85.p; 41.85.Gy; 41.85.Lc
INTRODUCTION
The nuclear scanning microprobe is one of the
channels of analytical complexes based on electrostatic
accelerators. Currently, the microprobe is widely used
for non-destructive microanalysis of samples of various
origins [1‒4] and proton-beam writing in the fabrication
of high-quality 3D micro- and nanostructures [5–7].
The spatial resolution of microprobe setups in the
microanalysis mode in techniques such as PIXE, NRA
and RBS is at the level of 1 µm, which is due to the high
current mode of the focused beam of about 100 pA.
Proton beam writing and techniques such as STIM and
IBIC are used in low current mode with a beam current
of about a few fA, here the resolution reaches the sub-
100 nm range. Such spatial resolution parameters are
caused by the low brightness of ion sources used in
accelerators and not high demagnification of probe-
forming systems, which are at the level of 100 [8–11].
Separately, it is worth noting the microprobe setup with
demagnifications of 857×130, which is used exclusively
for proton-beam writing, in which a resolution of
9×30 nm
2
in the mode of 1000 ions per second is
achieved [12]. Improving the resolution for existing
microprobe installations by reducing the size of the
object collimator leads to a significant decrease in the
beam current, and the effect of transparency of the
collimator walls does not lead to the desired result.
One of the way to improve the resolution of
microprobes is to use high demagnification probe
forming systems. However, such systems have very
large spherical and chromatic aberrations. If the
influence of the latter can be limited by improving the
energy spread of the ions in the beam to 10
–5
[13], then
spherical aberrations have to be compensated by a
system of octupole lenses. In [14–17] were considered
octupole correctors in quadrupole probe-forming
systems with low demagnifications, which did not lead
to the desired results. Since these systems have low
spherical aberrations, reducing them leads to a
mismatch between the beam emittance and the
acceptance of the probe-forming system and does not
increase the focused beam current.
In this paper, we consider a probe-forming system
based on a separated orthomorphic quadruplet of
magnetic quadrupole lenses, which has the same
demagnifications in both transverse directions.
Previously, such systems were considered in works [18‒
21] with a large working distance. By reducing the
working distance, a significant increase in
demagnifications is achieved, and spherical aberrations
are compensated by the use of three magnetic octupole
lenses.
1. CALCULATION OF THE OCTUPOLE
CORRECTOR PARAMETERS USING THE
MATRICANT METHOD
Previously [22] showed that spherical aberrations in
quadrupole systems can be completely compensated by
three octupole lenses. To calculate the parameters of the
octupoles, in this work, the matricant method is used,
the general principles of which are described in [23].
The magnetic octupole lens matricant was formed based
on the following calculations.
The scalar magnetic potential of the magnetic
octupole in the local coordinate system has the form
2 2
4 ( )4mu W x y xy . (1)
Magnetic field components
2 3
4 4
2 3
4 4
2 2
4
12 4
12 4
4 ( )
x
y
z
B W x y W y
B W y x W x
B W x y xy
(2)
The trajectory equations of motion of a charged
particle in a magnetic field have the form
2 2 2
2 2 2
(1 ) ( ) 1
(1 )
(1 ) ( ) 1
(1 )
y x z
x y z
e
x x B y x B B x y
p
e
y y B x y B B x y
p
(3)
For the subspace of phase moments in the form
Фх={x,x',xδ,x'δ,x
3
,x
2
x',xx'
2
,x'
3
,xy
2
,xyy',xy'
2
,x'y
2
,x'yy',x'y'
2
}
T
Фy={y,y',yδ,y'δ,y
3
,y
2
y',yy'
2
,y'
3
,yx
2
,yxx',yx'
2
,y'x
2
,y'xx',y'x'
2
}
T
(4)
equations of motion (3) are transformed to the form
,
,
.
,
.
154 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145)
2 24
2 24
4
( 3 ) ,
4
( 3 ) ,
eW
x x y x
p
eW
y y x y
p
(5)
where e is the elementary charge;
22 ( / )p MZe Ze c is a relativistic momentum;
М is the ion mass; Z is the charge number; φ is the
accelerating potential; с is the speed of light.
The procedure of immersion (5) in (4) according to
octupole symmetry gives the system of differential
equations
( )
( ) ,
х y
x y
d
P
dz
(6)
where
0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 ( ) 0 0 0 3 ( ) 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 3 0 0 0 0 0 0 0 0
0 0 0 0 0 0 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0
( )
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2 0 1 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0
z z
P z
0 0 0 0 0 0 0 0 0
3
44 / / ( )pО aОeW p еB pr .
BpО is the induction at the pole of a magnetic octupole,
raО is the octupole aperture radius.
The equation for the matricant of an octupole has a
similar form
О
О
d
P
dz
. (7)
The matricant for a rectangular field model of a
magnetic octupole lens has the form
2 3 4 5 2
2 3 4
2 3
2
1 0 0 / 2 / 2 / 4 20 3 / 2
0 1 0 0 3 / 2 / 4 3
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 1 3 3 0
0 0 0 0 0 1 2 0
0 0 0 0 0 0 1 0
( )
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
O z
3 4 3 4 5
2 3 2 3 4
2 2 3
2
2
/ 4 / 2 / 2 3 20
3 3 / 2 2 3 / 4
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
2 2
1 0
0 1 0 0
0 0 1 2
0 0 0 1
0 0 0 0 1
(8)
where τ=z-z0, z0 is the coordinate of the beginning of the
effective boundary of the octupole field, for the whole
lens τ=Leff, Leff is the effective octupole length.
The complete matricant of the object-target
transformation of coordinates of the phase moments is
constructed as a result of multiplying the elementary
matricant of each optical element, including drift gaps,
quadrupole and octupole lenses. Matricants of magnetic
quadrupole lenses and drift gaps can be found in [23].
The elements of the full matricant responsible for
spherical aberrations depend linearly on the excitations
of the octupole lenses. Then we can write the expression
for the values of the magnetic induction at the poles of
the octupoles in the form
A·b+γ=τ,
where τ1= 1,8x , τ2= 1,14x τ3= 1,8y are the spherical
aberrations, ,x y are a full matricants object-target
transformations of the phase moments coordinates (4),
b is the vector of unknown values of the magnetic
induction at the poles of the octupoles, at which τ=0.
Here matrix A and vector γ are implicitly defined,
which are calculated according to the following
procedure by varying the magnetic induction of each
octupole
(1) (1) (1) (1,1)
1 1 2 2 3 3
(2) (1) (1) (2,1)
1 1 2 2 3 3
i i i i i
i i i i i
a b a b a b
a b a b a b
, i=1,...,3.
Then from two equalities one can obtain explicit
expressions for the elements of the matrix A and the
vector γ
(2,1) (1,1) (2,2) (1,2) (2,3) (1,3)
1 2 3(2) (1) (2) (1) (2) (1)
1 1 2 2 3 3
(1,1) (1) (1) (1)
1 1 2 2 3 3
, , ,
( ).
i i i i i i
i i i
i i i i i
a a a
b b b b b b
a b a b a b
The vector of unknown values of magnetic induction
at the poles of three octupoles, at which spherical
aberrations are equal to zero, is now determined from
the linear equation
A·b+γ=0.
2. PROBE-FORMING SYSTEM ON THE
BASE OF ORTOMORPHIC QUADRUPLET
Fig. 1 shows the layout of magnetic quadrupole and
octupole lenses in the probe-forming system.
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145) 155
Fig. 1. Layout of magnetic quadrupole and octupole
lenses in a probe-forming system with spherical
aberration correction
An orthomorphic quadruplet was chosen as the
probe-forming system due to the fact that it has the
same demagnifications in both transverse directions,
Dx=Dy. This is achieved by powering the quadrupoles
from two power supplies in the form C1D2C2D1, where
C means that the lens is converging, and D is diverging
in the xOz plane, the number indicates which of the two
supplies the lens is connected to. The increase in
demagnification is affected by the geometric parameters
of the quadruplet: the length of the system l, the location
of the first doublet relative to the second one ax (for
ax>>h, the quadruplet is called separated and has
intermediate crossovers in both transverse directions)
and the working distance g. In [24] it was shown that an
orthomorphic quadruplet has the largest
demagnification at g=4 cm. The remaining geometric
parameters of the probe-forming system have the
following values: a0=a1=800 cm, ax=140 cm, effective
field length of quadrupoles L=10 cm, octupoles
i1=i2=i3=2 cm, h=4 cm, j=1 cm, radius apertures of
quadrupoles raQ=0.65 cm, octupoles raO=0.85 cm. For
such a geometry, the parameters of the probe-forming
system without aberration correction at stigmatic
focusing are given in Table for a beam energy of
3 MeV.
Parameters of a probe-forming system based on a
separated orthomorphic quadruplet of magnetic
quadrupole lenses
Magnetic induction
at lens poles, Т
В1Q
В2Q
0.32806630
0.125974694
Demagnification
D=Dx=Dy
574
Chromatic aberration,
µm/mrad
3
Cpx
Cpy
-8023
-604
Spherical aberration,
µm/mrad
3
<x/xˊ
3
>
<x/xˊyˊ
2
>
<y/yˊ
3
>
<y/yˊxˊ
2
>
-208866
370472
14093
370472
Correction of spherical aberrations is provided with
the magnitude of the magnetic induction at the poles of
the octupoles В1О=0.02792804 Т, В2О=0.13491 Т,
В3О=–0.1234434 Т.
The process of microbeam formation on the target
was optimized by the method of maximum reduced
collimated acceptance of the probe-forming system,
which is described in [25]. The reduced acceptance is
determined by the value of the phase volume formed by
rectangular object and aperture collimators, which can
be focused into a spot on a target with fixed dimensions
and has the form
( ) ( ) ( ) 0, 4 /x y x y x y x yr R a , (9)
where 2rx(y), 2Rx(y) sizes of the object and aperture
collimators, respectively.
For a probe-forming system in which spherical
aberrations are fully compensated, the object-target
phase coordinate transformation has the form
t o x о
t o y о
x x D Cp x
y y D Cp y
(10)
where xt,yt are the ion coordinates in the target plane,
, , ,o o o ox y x y are the phase coordinates of the ion in the
object plane, D is the demagnification, Срх,Сру are the
chromatic aberrations, δ is the momentum spread.
For the limit trajectory (10) can be written as
( ) ( ) ( ) ( ) 00.5 ( )x y x y x y x yd r D Cp R r a , (11)
where d is the size of the square beam spot on the target.
Taking into account (11), we can write the
expression for the reduced collimated acceptance
( ) ( ) ( ) ( ) 0 ( )4 (0.5 (1/ / )) / .x y x y x y x y x yr d r D Cp a Cp
(12)
From the condition of maximum collimated
acceptance, we obtain
*
( ) 0
0.5
2(1/ / )x y
d
r
D Cp a
(13)
The final expression for the reduced collimated
acceptance is
2
( )
( ) 0 ( )4(1/ / )
x y
x y x y
d
D Cp a Cp
(14)
Based on (13), the dependence of the size of the
object collimator on the size of the spot of the focused
beam on the target is shown in Fig. 2, which shows that
the sizes are within acceptable limits.
Fig. 2. Dependence of the size of the object collimator
on the size of the focused beam on the target
The value of the current of the focused beam on the
target depending on the size of the spot is shown in
Fig. 3, where the beam current was determined from the
expression I=bα, here the beam brightness at an energy
of 3 MeV is b=100 pА/(µm
2
∙mrad
2
), and the collimated
acceptance was calculated from (9), (14). This figure
shows that the beam current is within acceptable limits
for microanalysis and proton beam writing applications.
,
,
.
.
156 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145)
Fig. 3. Dependence of the focused beam current on its
size on the target
3. CONCLUSIONS
A probe-forming system based on a separated
orthomorphic quadruplet of magnetic quadrupole lenses
with a small working distance is considered. This
allowed the system demagnification to be increased to
564. Such a system has very large spherical aberrations,
making it unacceptable for use. One way of improving
the ion-optical characteristics of such a system is to
correct spherical aberrations using three magnetic
octupole lenses. The approach developed to correct
aberrations using the matricant method allowed the
parameters of the octupoles to be determined.
Optimization of the microprobe formation process using
the value of the maximum reduced collimated
acceptance allowed to determine the size of the object
collimator and the value of the focused beam current for
the probe size in the range of 10…100 nm, which shows
the feasibility of such a system for various applications.
ACKNOWLEDGEMENT
This work was carried out within the framework of
the state program of Ukraine “Research and
development in the field of physical and mathematical
sciences”. State registration number 0120U101035.
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Article received 18.04.2023
ЗОНДОФОРМУЮЧА СИСТЕМА ВИСОКОЇ РОЗДІЛЬНОЇ ЗДАТНОСТІ З КОРЕКЦІЄЮ
СФЕРИЧНИХ АБЕРАЦІЙ ДЛЯ ЯДЕРНОГО МІКРОЗОНДА
О.Г. Пономарьов, С.В. Колінько, Г.Є. Положій, В.А. Ребров
Розглянуто зондоформуючу систему на базі розподіленого ортоморфного квадруплету магнітних
квадрупольних лінз з малою робочою відстанню, що дозволило значно збільшити коефіцієнти зменшення.
Для корекції сферичних аберацій застосовуються три магнітні октупольні лінзи. Розрахунок параметрів
октупольного коректора виконується методом матрицантів. Фокусуючі властивості системи визначаються за
рахунок оптимізації процесу формування зонда на основі величини максимального приведеного
колімованого аксептансу. Проведені розрахунки показали, що така система може бути реалізована для
застосування в методиках мікроаналізу та протонно-променевої літографії.
http://www.sciencedirect.com/science/article/pii/S0168900212012235
http://www.sciencedirect.com/science/article/pii/S0168900212012235
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| id | nasplib_isofts_kiev_ua-123456789-196159 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:47:44Z |
| publishDate | 2023 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Ponomarev, A.G. Kolinko, S.V. Polozhii, H.E. Rebrov, V.A. 2023-12-10T18:08:15Z 2023-12-10T18:08:15Z 2023 High resolution probe-forming system with spherical aberration correction for nuclear microprobe / A.G. Ponomarev, S.V. Kolinko, H.E. Polozhii, V.A. Rebrov // Problems of Atomic Science and Technology. — 2023. — № 3. — С. 153-157. — Бібліогр.: 25 назв. — англ. 1562-6016 PACS: 41.85.p; 41.85.Gy; 41.85.Lc DOI: https://doi.org/10.46813/2023-145-153 https://nasplib.isofts.kiev.ua/handle/123456789/196159 A probe-forming system based on a separate orthomorphic quadruplet of magnetic quadrupole lenses with a short working distance is considered, allowing the system demagnification to be significantly increased. Three magnetic octupole lenses are used to correct spherical aberrations. The parameters of the octupole corrector are calculated using the matricant method. The focusing properties of the system are determined by means of a probe formation optimization process based on the value of the maximum reduced collimated acceptance. The calculations performed showed the feasibility of such a probe forming system for microanalysis and proton beam writing technique. Розглянуто зондоформуючу систему на базі розподіленого ортоморфного квадруплету магнітних квадрупольних лінз з малою робочою відстанню, що дозволило значно збільшити коефіцієнти зменшення. Для корекції сферичних аберацій застосовуються три магнітні октупольні лінзи. Розрахунок параметрів октупольного коректора виконується методом матрицантів. Фокусуючі властивості системи визначаються за рахунок оптимізації процесу формування зонда на основі величини максимального приведеного колімованого аксептансу. Проведені розрахунки показали, що така система може бути реалізована для застосування в методиках мікроаналізу та протонно-променевої літографії. This work was carried out within the framework of the state program of Ukraine “Research and development in the field of physical and mathematical sciences”. State registration number 0120U101035. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology Applications and technologies High resolution probe-forming system with spherical aberration correction for nuclear microprobe Зондоформуюча система високої роздільної здатності з корекцією сферичних аберацій для ядерного мікрозонда Article published earlier |
| spellingShingle | High resolution probe-forming system with spherical aberration correction for nuclear microprobe Ponomarev, A.G. Kolinko, S.V. Polozhii, H.E. Rebrov, V.A. Applications and technologies |
| title | High resolution probe-forming system with spherical aberration correction for nuclear microprobe |
| title_alt | Зондоформуюча система високої роздільної здатності з корекцією сферичних аберацій для ядерного мікрозонда |
| title_full | High resolution probe-forming system with spherical aberration correction for nuclear microprobe |
| title_fullStr | High resolution probe-forming system with spherical aberration correction for nuclear microprobe |
| title_full_unstemmed | High resolution probe-forming system with spherical aberration correction for nuclear microprobe |
| title_short | High resolution probe-forming system with spherical aberration correction for nuclear microprobe |
| title_sort | high resolution probe-forming system with spherical aberration correction for nuclear microprobe |
| topic | Applications and technologies |
| topic_facet | Applications and technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/196159 |
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