Download Computer-Aided-Design of an electrostatic lenses

Magnetic Lens Design using JESS Expert System
Fadhil A. Ali
*Oklahoma State University – School of Electrical and Computer Engineering Department
[email protected]
ABSTRACT
This paper has shown an optimum single magnetic lens design with no permeability. By using dynamic
programming method, and a JESS technique got an expert system to have new calculations of optimum magnetic
flux density and pole pieces reconstruction are proposed in this paper. Also, comparison has presented to show this
work model with a standardized model.
Keywords: Optical design, Optimizations, Artificial intelligence, JESS, Focused Ion Beam
I. INTRODUCTION
Any axially symmetric magnetic field produced by current carrying coils with or without ferromagnetic
materials or by permanent magnets is called a magnetic lens. Manufacturing of magnetic lenses is usually more
complicated than that of electrostatic lenses. The action of a magnetic lens can be understood on the basis of the
Lorentz force. Owing to the interaction of the radial velocity component of the particle with the longitudinal
component of the magnetic flux density acquires an azimuthally component, which in turn interacts with the
longitudinal component resulting in a radial focusing component [1].
Szilagyi, and Ahmad et al. introduced the dynamic programming approach, that got a computer aided design
of an electrostatic FIB system consisting of three electrostatic lenses approximated by the Spline lens model[2,3].
More recently Ali F.A., which introduced an expert system to design two electrostatic lenses column by mixing
dynamic programming and AI techniques [4]. In this paper similar methodology is developed and applied to
present rule-based system by using Java Expert System Shell (JESS expert system).A typical dynamic
programming recursive formulation and an optimization procedure as [5,6]:
Fn (n, s, x) = g |R (n, s, x), F*n-1(s')| …………… (1)
where n is an integer denoting the stage of the problem, s is an integer denoting the state of the system at n, s' is an
integer denoting the state of the system at stage n-1 resulting from the decision x, x is the decision being evaluated
at stage n , R(n,s,x) is the immediate return associated with making decision x at stage n when the state of the
system is s , F*n-1(s') is the return associated with an optimal sequence of the decision at stage n-1 when the state is
s' and g is the minimal function. Figure 1 shows computational grid of the dynamic programming procedure with
the aid of artificial intelligence technique for the present magnetic lens defined over twenty intervals.
1
Computational grid
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-8
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Dynamic function
W(z)/ ∆W
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-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
22.00
21.00
20.00
0.00
Optical axis
Figure 1 Shows computational grid of the dynamic programming procedure with the aid of artificial intelligence
technique for magnetic lens defined over twenty intervals.
In this paper that only one case of a magnetic lens has been designed(i.e. permeability  = 0). Therefore, the
optical properties (i.e. the relative spherical and chromatic aberration coefficients) are characterized and obtained
by a dimensionless parameter (k2d2), where k2 as in paraxial ray equation (2) and d is the field half-width, in which
is determined by the shape of the pole pieces and by the degree of saturation[7].
r " (z) + k2 r (z) = 0 ………………… (2)
where k2= [q Bz2 / 8 m V], Bz - is the axial component of the magnetic flux density , q- is the electric charge ,V-is
the accelerating voltage and m is the mass of charged particles accelerated through a magnetic field. The axial flux
density distribution was optimized as Grivet-Lenz model for magnetic lenses, which it can be used for the
description of unsaturated lenses.
II. Optimum Magnetic Lens Design
The optimized formula of the axial magnetic field distribution (i.e. the axial flux density distribution B(z)) was
obtained by using similar dynamic programming procedure with the aid of artificial intelligence technique within
some modifications as in Ali F.A.[8], a present modified algorithm has shown in figure (2).Figure (3) and table (1)
are shown the optimum field distribution with its first derivative and its optimum formula respectively. The
maximum value has been taken in our work for the axial flux density distribution Bmax is equal to (6.0) mTesla. For
future work optimization will be done to get a formula depending on the magnetic permeability µ in ferromagnetic
materials as a function of the optical axis.
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Star
t
Access Data stored
Import data as
(*.xls)
Calculate the Magnetic Flux Density
r " (z) + k2 r (z) = 0
Plot data in grid within
Optical axis beam angle
range
Yes
Is there another data?
Yes
Knowledge-base
Read data
rule based system
Evaluate individual functions fi
Fn (n, s, x) = g |R (n, s, x), F*n-1(s')|
Calculate partial derivatives f'ij, f"ij
Set initial values
Gik = min | Fijk + Gj (k1)|
Solve the (flux density, trajectories) equations
Set new values and parameters taking new
constraints
Evaluate new individual functions fi
Yes
Has optimum
parameters
been found for
this iteration?
Solve the (flux density) equations Calculate partial derivatives f'ij,
f"ij
Modify parameter
values
Is another
optimization
cycle required?
Yes
Stop
Figure 2 Shows modified algorithm of the present work for optimum magnetic lens
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6.0
4.0
2.0
0.0
0.
96
0.
88
0.
81
0.
73
0.
66
0.
58
0.
51
0.
45
0.
38
0.
30
0.
23
0.
15
0.
08
-2.0
0.
00
the axial flux density distribution (mTesla)
8.0
Optical axis z/L
Figure 3Shows the optimum axial magnetic flux density distribution B(z) with its first derivative for the given
magnetic lens obtained by the dynamic programming procedure and artificial intelligence technique.
Table (1) the optimum magnetic lens formula with its dynamic parameters by using the dynamic programming
procedure and artificial intelligence technique.
Lens Type
magnetic lens (1)
µ=0
Dynamic Parameters
Optimized Flux density
Distribution Formula
a
b
c
d
a*sech (z^c/ b) +d
Bmax
2.0
1.0
0
III. Optimum Magnetic Lens Trajectories
The ion beam trajectories were obtained in Focused Ion Beam system under infinite magnification condition.
Figure (4) shows the trajectory along the relative optical axis for the optimized magnetic field obtained ,while
Figure (5) has shown the relative spherical and chromatic aberration coefficients Cs/fo and Cc/fo respectively, as a
function of the dimensionless parameter k2d2 related to the half-width d for the optimized magnetic field.
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magnetic lens 1
µ=0
1.00
radial displacement (r/L)
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
1 .0
0 .8
0 .7
0 .5
0 .4
0 .3
0 .1
0 .0
0.00
Optical axis z/L
Figure 4. Shows the ion beam trajectories of magnetic lens under infinite magnification condition (for a constant
length L=20 mm)
The relative aberration coefficients
1.20
Cs/fo
Cc/fo
1.00
0.80
0.60
0.40
0.20
0.00
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
2 2
The dimensionless parameter k d
Figure 5. Shows the relative spherical and chromatic aberration coefficients of the optimized magnetic lens related
to the dimensionless parameter k2d2.
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IV. Optimum Magnetic Lens Design
(Pole pieces reconstruction)
The present work single lens design of optimum magnetic lens, has pole pieces reconstruction taken the same
analyzed procedure by using SIMION Simulator 8[9]. The following figures (6) and (7) are shown the profiles of
the pole pieces of the optimized magnetic field in two and three dimensions respectively.
µ=0
NI=96
1.00
0.90
0.80
0.70
r/L
0.60
0.50
0.40
0.30
0.20
0.10
0.
99
0.
88
0.
78
0.
68
0.
58
0.
50
0.
40
0.
30
0.
20
0.
10
0.
00
0.00
Optical axis z/L
Figure 6. Shows the two dimension profile of a pole piece for a magnetic lens with µ=0 and NI = 96 ampere-turns.
(a)
(b)
Figure 7(a) three dimensions graph of the pole piece of a magnetic lens (µ=0). (b) The optimized pole piece profile
of magnetic lens obtained by SIMION 8.
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To make comparison of the present optimum magnetic lens i.e. magnetic lens (1),with a standard Glaser's
model i.e. magnetic lens (2).Figure (8) shows the axial magnetic flux density distribution B(z) with its first
derivative for both.
6.0
Grivet-Lenz model
magnetic-1
Glaser's model
magnetic-2
5.0
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
0.
96
0.
88
0.
81
0.
73
0.
66
0.
58
0.
51
0.
45
0.
38
0.
30
0.
23
0.
15
0.
08
-3.0
0.
00
The axial flux density distribution (mTesla)
7.0
Optical axis z/L
Figure 7 Shows magnetic flux density distributions B(z) with its first derivatives for both magnetic lens (1) & (2).
V. Conclusion
The present investigation has clearly obtained optimized results of a single magnetic lens. By using SIMION 8
the pole pieces reconstruction has been resulted to give the most common standards. As well as the aberration discs
diameters (ds –spherical aberration disc diameter, dc – chromatic aberration disc diameter and dt– total aberration
disc diameter), have shown the values in micro scale (µm) under the infinite magnification condition (0.03,0.13
and 0.133) respectively.
VI. Acknowledgement
I would like to thank OSU – School of Electrical and Computer Engineering Department / Dr.James Stine in his
collaboration. Many thanks to SIMION researchers group at SIMION Company for delivering a test compiler of
SIMION package version 8.With my deepest thanks to SRF Iraq Project / IIE for letting me this chance of research
gate.
VII. References
[1]Lencová B. and Wisselink G.,Program package for the computation of lenses and deflectors, Nucl. Instr. and
Meth. in Phys. Res. ,A 298, 56-66,1990
[2] Szilagyi M., Electron optical synthesis and optimization, Proc. IEEE, vol.73, p.412-418, 1985
[3] Ahmad, A.K., Sabah M.J. and Ahmed A. Al-Tabbakh, Computer aided design of an electrostatic FIB system,
Indian J.Phys.,vol.76B, p.711-714, 2002
[4] Ali F.A., Expert system Design of Two Electrostatic Lenses Column by Mixing Dynamic Programming and AI
Techniques, International Journal of Advancements in Computing Technology,vol.2, 5, 2010
[5] Szilagyi M.,Electron and Ion Optics, Plenum Press, New York, 1988
[6] Steve C. J., Alan W. G., David Y. Wang, and Dilworth D. C., Combination of global-optimization and expertsystems techniques in optical design, Proc. SPIE Vol. 1780, p. 192-196, 1993
[7]Hawkes P.W. and Kasper E., Principle of Electron Optics,vol.1,Academic press, London,1989
[8] Ali F.A., Expert system design of beam spot size measurements in FIB system, IEEE Xplore , 11989664,p.168172,2011
[9] http://www.simion.com
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