pp. 345-360 - Arabian Journal for Science and Engineering

*Address for correspondence:
Department of Physics
University of Baghdad
Baghdad, Iraq
E-mail: drmhj54@yahoo.com
AN ION BEAM TRANSPORT DESIGN OPTIMIZATION IN A
MEDIUM RANGE ION IMPLANTER SYSTEM
Mahdi Hadi Jasim*
Department of Physics, College of Science, University of Baghdad
Baghdad, Iraq
: ﺔـﺻﻼﺨﻟا
ﺪﻳﺪﺤﺗ ﻊﻣ ﻲﻧﻮﻳأﻻا
عرﺰﻟا ﺔﻣﻮﻈﻨﻣ ﻲﻓ ﺔﻠﻗﺎﻨﻟا ﺔﻣﺰﺤﻟا
ﺮﻴﺌﺒﺗ جذﻮﻤﻧ ﻦﺴﺤﺗ زﺎﺠﻧإ
- ﺚﺤﺒﻟا اﺬه ﻲﻓ – ﻢﺗ ﺪﻘﻟ
تﻻدﺎﻌﻣ ﺖﻘُﺘﺷا
ﺪﻗو . نﻮﺤﺸﻤﻟا ﻢﻴﺴﺠﻟا ﻰﻠﻋ ﺮﺛﺆﺗ ﻲﺘﻟا ﺎﻬﺗﺎﻤﻠْﻌَﻣ
ﻊﻣ ﺔﻴﺴﻴﺋﺮﻟا
ﺔﻳﺮﺼﺒﻟا ﺮﺻﺎﻨﻌﻟا لﺎﻤﻌﺘﺳا
تﺎﻳﻮﺘﺴﻤﻟا ﺪﻨﻋ ﺔآﺮﺤﻟا نأ رﺎﺒﺘﻋﻻﺎﺑ
ﻦﻳﺬﺧﺁ
يﺮﺼﺑ ﺮﺼﻨﻋ ﻞﻜﻟ تﺎﻓﻮﻔﺼﻤﻟا ﻊﻣ ﺔﻧﻮﺤﺸﻤﻟا تﺎﻤﻴﺴﺠﻠﻟ ﺔآﺮﺤﻟا
. ﺔﻴﻟﺎﺜﻤﻟا ﻰﻟإ بﺮﻗﻷا ﺔﻣﺰﺤﻟا تﺎﻤﻠﻌﻣ ﻰﻠﻋ لﻮﺼﺤﻟا ضﺮﻐﻟ نﺎﻴﺒﻳﺮﻘﺗ ﺪﻤﺘﻋاو
. ﺎﻬﻨﻣ ﻞﻜﻟ ﺔﻠﻘﺘﺴﻣ نﻮﻜﺗ ﺔﻔﻠﺘﺨﻤﻟا
: ﺪﻌﺒﻟا ﻲﻋﺎﺑر ﺪﻨﻋ ﺔﻣﺰﺤﻟا ﻞﻜﺷ لوﻻا ﺐﻳﺮﻘﺘﻟا ﻲﻓ
( ) ( ) T
out R.σ
in . R
σ =
ﺐﻄﻘﻟا ﻲﻋﺎﺑر)
ﻰﻟوﻷا
ﺔﺟرﺪﻟاو ( ﺐﻄﻘﻟا ﻲﺋﺎﻨﺜﻟا قﺎﻴﺴﻧﻻا ﺰّﻴﺣ)
ﺮﻔﺼﻟا ﺔﺟرد ﻲﻓ ﺔﻣﺰﺤﻟا ﻞﻘﻧ زﺎﺠﻧإو
ﺪﻗو
. ﺔﻴﺋﺎﻀﻔﻟا ﺎﻬﺗﺎﻴﺛاﺪﺣإ ﺔﺣﺎﺴﻣ ﺪﻨﻋ ﻲﺳوﺎﺟ
ﻞﻜﺸﺑ تﺎﻤﻴﺴﺠﻟا ﻊﻳزﻮﺗ نﻮﻜﻳ
ﻲﻧﺎﺜﻟا ﺐﻳﺮﻘﺘﻟا ﻲﻓو
.( ﺲﻴﻃﺎﻨﻐﻤﻟاو
ﻚﻠﺘﻤﻳ ﺎﻤهﻼآو نﻮﺤﺸﻤﻟا ﻢﻴﺴﺠﻟا ﺔﻗﺎﻄﻟ ًاﺮﻴﺛﺄﺗ
ﺮﺜآأ نﻮﻳﻷا
ﺔﻣﺰﺤﻟ عﻮﻄﺴﻟاو ثﺎﻌﺘﺑﻻا تﻼﻣﺎﻌﻣ
تﺎﺑﺎﺴﺣ نأ
ﺪﺟُو
. ﺔﺘﺑﺎﺛ ﺔﻳرﺎﻴﻌﻣ ﺔﻤﻴﻗ
ﺔﻣﻮﻈﻨﻣ ﻊﻣ يﺮﺼﺑ ﺮﺼﻨﻋ ﻞﻜﻟ
ﺔﻴﻤﻴﻤﺼﺘﻟا
تﺎﻤﻠﻌﻤﻟا ﺮﻴﺛﺄﺗو ﻊﻗﻮﻣ ﻒﻳﺮﻌﺗ ﻲﻓ ﻢﻴﻴﻘﺗو ﺔﻧرﺎﻘﻣ ءاﺮﺟا ﻢﺗو
. نﻮﻳﻷا
عرﺰﻠﻟ ةﺮﻓﻮﺘﻣ
Paper Received 26 August 2006; Revised 30 August 2007; Accepted 28 November 2007
Mahdi Hadi Jasim
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 345

346
Mahdi Hadi Jasim
ABSTRACT
An improvement of the transport beam focusing model in an ion implanter system
has been achieved, with the definition of the main optical elements used and their
parameters’ effect on charged particles. The equations of motion of charged particles
and matrices in each optical element have been derived, with consideration of the
motion in different planes. Two assumptions were made in obtaining the optimized
beam parameters. In the first assumption, the four-dimensional beam ellipsoid
( ( ) ( ) T
σ out = R.σ
in . R ), the beam transport is accomplished in zero order (drift space
and dipole) and first order (quadrupole and magnet). In the second assumption, the
particle distribution is normal in the area of its space coordinates. Calculations of the
emittance and the brightness factors of the ion beam are found to be more affected by
the energy of charged particles. The emittance and brightness have constant
normalized values.
A comparison and evaluation was made of the definition of the location and the
effect of the designed parameters for each optical element within the available ion
implantation design system.
Key words: transport beam focusing, ion implanter system, four dimensional beam
ellipsoid, emittance and brightness factors
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008

Mahdi Hadi Jasim
AN ION BEAM TRANSPORT DESIGN OPTIMIZATION IN A MEDIUM RANGE ION
IMPLANTER SYSTEM
1. INTRODUCTION
Ion implantation is a powerful technique for modifying the near surface properties of material, so it is important in
CMOS applications. To design an ion implanter system, the behavior of the ion beam passing through its elements must
be understood. Therefore, it is necessary to study the transport of charged particle ion beams during their passage
through the ion implanter system. Such studies give much information about the charged particle ion beam, such as the
quality of implanted ions, the beam size, and the focusing regions along the ion beam path. Many studies have appeared
in this field, which have mainly resulted in the improvement of the ion implantation systems. Gillespie et al. [1]
developed a set of optical models for a variety of electrostatic lenses and accelerator columns for the computer code
TRACE 3-D. This code is an envelope (matrix) code including space charge often used to model bunched beams in
magnetic transport systems and radiofrequency (R.F.) accelerators when the effects of beam current may be important.
TRACE 3-D uses the first-order transfer matrix (R-matrix) formalism to compute changes in the beam matrix (σ -matrix).
A computer code to measure the beam emittance and beam parameters of the ATR line has been produced by Tsoupas et
al. [2]. This code included a theoretical formalism for the method for the measurement of the beam emittance, and on
how to obtain the σ -matrix using the R-matrix. The transverse linear optics of a charged particle storage ring has been
studied [3]. This present work deals with a 4-dimensional phase space and normalized phase space in two cases. Firstly
it treats the x and y spaces as an invariant subspaces, and, secondly when the x and y spaces are coupled.
This work is aimed to study the behavior of a charged particles ion beam in different elements of the ion implanter
system. The equations of motion of the charged particle beam passing through each element of ion implanter system
have been modeled.
2. THEORETICAL FORMALISM
In this work a beam extracted from a medium-range ion implanter is considered to be an upright ellipse with semi
axes.
The general algebraic equation of an ellipse centered on the origin is:
where M m is a positive definite symmetric matrix ,
T
X M m X = D
(1)
M m =
T
x
X : is the transpose matrix of X , X = , x, x′
are the particle’s position and angular divergence in the radial
x′
direction, respectively.
The shape of the elliptical beam depends on the value of the constant: for B =0, a right plane space ellipse is obtained
which is always defined as a minimum beam size or beam waist [4,5]. The existence of the latter depends on the nature
of the elliptical beam.
Based on Liouville's theorem [6,7] the determinant of the Mm -matrix is equal to unity (D=1). So Equation (1)
becomes:
X T Mm X = 1 (2)
By considering (σ ) as the inverse of Mm -matrix
A
B
C
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 347
B
⎡
⎤
=
−1
σ
=
11 σ
σ M
12
⎢
⎥ , (3)
m
⎢⎣
σ12
σ 22 ⎥⎦
where (σ ) is the phase space matrix, then the equation defining the ellipse may be written as:
T −1 X σ X = 1
(4)

348
Mahdi Hadi Jasim
Or equivalently:
2
2
σ x − 2σ
xx′
+ σ x′
= detσ
(5)
22
12
11
A typical output elliptical beam characterized by
11
,
22
σ σ , and σ
12
is illustrated in Figure 1 [8].
The beam envelope is represented by the maximum spatial extent of the ellipse (xmax = σ 11 ), and also the maximum
angular divergence of the beam within the phase ellipse (x'max = σ 22 ). The parameter ( σ
12
) defines the orientation of
the ellipse relative to the x and x' axes.
The correlation term (r) is given in terms of the off-diagonal elements of σ -matrix [6,9], i.e.
r
ij
=
σ
ij
σ σ
ii jj
. (6)
σ
In the case of a two dimensional ellipse r
12
12
= , the particles of phase space ellipse have a normal Gaussian
σ
11
σ
22
distribution [2]. Under the linear transformation, the normal distribution of particles in the ellipse is transformed into
another normal distribution.
To find the relation between σ -matrices at two positions of the beam line, i.e. σ (out)
) and ( σ (in)
, the equation of
the ellipse can be used at input location:
X
T
( in)
σ ( in)
−1
X ( in)
= 1,
(7)
while at the output location it is:
X
T
( out)
σ ( out)
−1
X ( out)
= 1
(8)
By using a linear transformation, Equation (1) and the identity (RR -1 =1), the equation (7) can be written as:
Also equation (9) becomes:
( RX ( in))
T
( Rσ
( in)
R
T
)
−1
( RX ( in))
= 1
(9)
X
T
( out)(
Rσ
( in)
R
T
)
−1
R(
out)
= 1
(10)
Equation (8) and Equation (10) after inversion can be written as:
σ ( out ) = Rσ
( in)
R
T
(11)
Equation (11) represents the relation between theσ -matrix in two locations of the beam line. Also based on
Liouville's theorem [6, 7], the transformation has preserved the phase space volume of the beam and (det σ (in)
=
det σ (out)
).
The area of phase space ellipse is equal to (π det σ (out)
), therefore, the emittance is:
The normalized emittance isε n = βγε ; where = vi / c
γ = ( 1 − β
2
)
−1/
2
.
ε = detσ
= ( σ σ − σ )
(12)
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008
11
22
2
12
β ; c: velocity of light in vacuum; i
v : ion velocity;

The normalized brightness ( B r ) varies across the beam by:
xn
yn
Mahdi Hadi Jasim
I
Br
π ε ε
2
2
= , (13)
where I is the total ion beam current.
The beam distribution at any point along the transport lines can be described mathematically by a four dimensional
beam ellipsoid ( x, x′
, y,
y′
) which can be expressed by a 4× 4 symmetric matrix ( σ − matrix ), see Figure 1. As shown in
the Appendix (Tables A1, A2, and A3) the terms of theσ − matrix and the transformation Rij − matrix have been
derived. They include the main effective parameters and the beam ellipsoid for different optical elements in the ion
implanter system.
x'
x'int =
Beam centroid
3. RESULTS AND DISCUSSIONS
Based on the theoretical calculations for a 4 × 4 symmetric σ − matrix and its transformation Rij − matrices, an
optimization procedure has been performed for different optical elements in an ion implanter system, as shown in Figure
2. The main input parameters, Table 1, were used to calculate the beam profiles (beam width) for a slit extraction as a
function of the system’s length, as shown in Figure 3, for the horizontal plane and vertical plane, respectively. The
specifications are: bending angle 75 o 2
, R=430mm, slit extraction dimensions = (5 ± 0.04)× (20 ± 0.0006) mm ,
S1=410mm and S2=175mm. The phase space ellipse movement of ion implanter elements is shown in Figure 4 for the
horizontal plane, where the region of divergence or convergence of the ion beam indicates the effect of the acceleration
tube and the deflector units.
The bending magnet works as a strong focusing element through selection of the pole-face
angles( = . 3°
, β = −0.
5°
β act a thin divergence lens in the
α m 20 m ),where the entrance angle α m and exit angle m
horizontal plane and as a thin convergence lens in the vertical plane. The effect of the fringe field on the ion beam is
represented by the reduction of the entrance angle (ψ ) which has a small value in the case of a homogeneous magnetic
field. In the present work, ψ is found to be 0.03°. The minimum and maximum beam paths inside the good field region
allowed a magnetic field strength ranging from 2000 to 4000 G for the extraction voltage range (15–35 kV). The
magnetic field strength reached 0.396T and the magnetic rigidity reached 0.17T.m, for Ar + ion beams.
The maximum acceleration voltage (180 kV) is reached using a high voltage electrostatic accelerator type (HERP
Germany). It is found that an increase in the acceleration energy causes a decrease in non-linearity in the phase space
ellipse at the target for both planes and a decrease in the total area. The decrease in the total area is proportional to the
acceleration voltage ( ) 2 / 1
U
Figure 1. Two-dimensional phase space ellipse based on the σ -matrix [8]
U .
o
detσ
σ11 x'max = σ 22
xmax = σ 11
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 349
σ12
σ11
xint =
σ
Slope =
σ
x
detσ
σ 22
12
11

350
Mahdi Hadi Jasim
The effect of triplet quadrupole lenses has been studied in comparison with the upright phase space ellipse in the
extraction region which shows a divergence effect in the horizontal plane. The triplet quadrupole lens consists of three
quadrupole parts with dimensions described in Table 1. However, in the vertical plane there is no clear effect of the
quadrupole lens due to the small value of initial angular divergence (y').
The deflector causes deflection of the desired charged particle beam with an angle proportional to the potential
difference between the deflector plates. The deflector causes a shift in the distance and in the angular divergence of the
phase space ellipse in both horizontal and vertical planes, as shown in Figure 4.
The lengths of free regions were calculated and found to be consistent with the minimum physical element to element
separation as well as with the overall implanter system. The length of the first field free region has a strong effect on the
total area of ion beam at the target as shown in Figure 5. From this figure the minimum value of the total area of ion
beam at the target is 237.29 mm 2 and that means the silicon wafer area (5cm in diameter) is covered at least by eight
regions with homogenous doping.
At the target region, the ion beam has divergence properties in both the horizontal and vertical plane as shown in
Figures 6 and 7. This region shows a shift in the phase-space ellipse due to the influence of the deflector.
80
Bending
system
410
Acceleration
tube
Bending
line
175
75 o
Decelerator
Ion source
1000
Lenses tube
3
945
Scanner
Target
(not to scale )
Figure 2. Top view of ion implanter system with the calculated optimized positions for each optical element (all dimensions in
mm)
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008
25
6.66 o
Electron
shower
1150
300
1000

Mahdi Hadi Jasim
Table 1. The Specific Optimization Values for the Optical Element Used in the Ion Implantation System and
Evaluation of the Available Designed Values in IMIIIS.
Optical element
Parameters
Fixed Optimizati
Slit Extractor
Homogenous
Magnet Analyzer
Accelerating tube
Quadrupole Triplet
Deflector plates
Drift free space
between the optical
elements
Extraction voltage (kV)
Extraction current (mA)
xo (mm)
x'o (rad.)
yo (mm)
y'o (rad.)
Entrance angle (degree)
Deflection angle (degree)
Exit angle (degree)
Fringing field effect angle (degree)
Magnet radius (mm)
Magnet rigidity (T. m)
Magnet field strength (T)
Magnet gap (mm)
Acceleration voltage (kV)
Final energy of charged particle(keV)
Acceleration tube length (mm)
Length (mm)
Distance between the lenses (mm)
Operation voltage (V)
Distance between electrodes (mm)
Total length (mm)
Length (mm)
Plates distance (mm)
Potential difference (V)
Deflection angle (degree)
S1-First free region length (mm) S2-
Second free region length (mm)
S3-Third free region length (mm)
S4-Fourth free region length (mm-)
S5-Fifth free region length (mm)
* Iraqi Ministry of Industry ion implantation system (IMIIIS).
Design values*
15–35
2.23
5
.04
20
on values
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 351
.0006
-----
75
-----
-----
430
0.2276
0.5293
80
0-180
215
1000
-----
-----
-----
-----
-----
------
------
------
------
------
------
------
------
------
15-35
2.23
5
0.04
20
0.0006
20.3
75
–0.5
0.03
430
0.17032
0.396
80
0-180
215
1000
100
20
250
30
440
4. CONCLUSION
Equations of motion of the charged particles and the matrices in each optical element have been derived, with the
consideration that the motions in different planes are independent of each other. An optimization of the beam parameter
design at the target wafer has been obtained using two assumptions; a four-dimensional beam ellipsoid equation and the
normal distribution of ion beam particles in the area of its space coordinates. Also, it is concluded that the emittance and
the brightness factors of the ion beam are constant unless there is a change in the ion beam energy.
An optimization analysis has been adopted to evaluate the Iraqi Ministry of Industry ion implantation system, which
+
reflects the results form the design revision for each element. Using Ar ions the optimum values are 30–180 keV and
2.23 mA. The maximum value of normalized emittance for the present configuration system is 0.077 mm.mrad, while
the normalized brightness of the emittance is equal to 0.356 A/(mm.mrad) 2 , and the current- normalized brightness is
2.
256 ×
10
−4
A/(mm.mrad)
2
.
500
30
3000
6.66
410
175
3
3
25

352
Mahdi Hadi Jasim
1
Beam width in x and y
directions (mm)
40
20
0
-20
-40
0 1000 2000 3000
Length (mm)
Horizontal plane
Vertical plane
Figure 3. Beam profiles for a 75 o homogenous magnetic analyzer for a slit extraction system
with an α = 20. 3
o
, = −0.
5
o
m βm
, ψ =0.03°, S1=410mm and R=430mm in IMIIIS
2 3 4 5 6 7 8 9
Figure 4. Phase space ellipse movement along the ion implanter in horizontal plane. 1. Extraction system, 2. first field free
region, 3. 3.75 ° magnetic analyzer, 4. second field free region, 5. acceleration tube, 6. third field free region, 7. triplet
Quadrupole, 8. forth field free, region, 9. deflector and Fifth free region
Figure 5. Effect of first free region length S1 (slit extraction-magnetic analyzer length) on the total area of ion beam at the
target
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008

Brightness (mA/(m.rad. 2 ))
X' (rad.)
0.13
0.12
0.11
0.10
(a) Beam profile map
20 25 30 35 40
X (mm)
(c) Beam profile image
Brightness (mA/(m.rad. 2 ))
Mahdi Hadi Jasim
0.00
10 20 30 40 50
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 353
X' (rad.)
0.08
0.06
0.04
0.02
0.13
0.12
0.11
0.10
Figure 6. Horizontal phase space profile at the target region
20 25 30 35 40
X (mm)
(b) Beam profile contours
X (mm)
(d) Beam Gaussian curve

354
Mahdi Hadi Jasim
Brightness (mA/(m.rad. 2 ))
Y' (rad.)
0.125
0.120
0.115
0.110
0.105
(a) Beam profile map
20 25 30 35 40
Y (mm)
(c) Beam profile image
0.00
10 20 30 40 50
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008
Y' (rad.)
Brightness (mA/(m.rad. 2 ))
0.125
0.120
0.115
0.110
0.105
0.08
0.06
0.04
0.02
Figure 7. Vertical phase space profile at the target region
20 25 30 35 40
Y (mm)
(b) Beam profile contours
Y (mm)
(d) Beam Gaussian curve

APPENDIX
Table A1. The σ– Matrix of the Beam Ellipsoid Terms in an Ion Implanter System
Optical Elements
Drift space
Magnet analyzer
Magnet edge
Good field region
σ − matrix Terms in Radial and axial directions
σ 11
x
σ 12
x
2
( o)
= σ x11(
i)
+ 2Sσ
x12(
i)
+ S σ x 22(
i)
( o)
= σ x 21(
o)
= σ x12(
i)
+ Sσ
x 22(
i)
( o)
= σ 22(
i)
σ x 22 x
Axial terms are similar to radial terms but replace x by y
σ 11(
o)
= σ 11(
i)
x
σ x11(
i)
σ x12(
o)
= + σ x12(
i)
f
σ 21(
o)
= σ 12(
o)
x
σ x11(
i)
2σ
x12(
i)
σ x 22(
o)
= + + σ 22(
)
2
x i
f f
σ 11(
o)
= σ 11(
i)
y
σ y11(
i)
σ y12(
o)
= − + σ y12(
i)
f
σ 21(
o)
= σ 12(
o)
y
σ y11(
i)
2σ
y12(
i)
σ y 22(
o)
= − + σ 22(
)
2
y i
f f
exit edge
Ro
Ro
= , f y =
β tan( β −ψ
)
Mahdi Hadi Jasim
Ro
=
tan( α −ψ
)
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 355
x
x
y
y
x
x
y
Ro
H int : entrance edge f x =
tanα
1
2
+ σ x 22(
i).
sin kxl
2
k
σ 21(
o)
= σ 12(
o)
+ σ 22(
i).
cos k l
y
f
x
2 1
σ x12(
i).
cos kxl
+ σ x 22(
i).
sin kxl.
cosk
xl
k
m
x
y
2 2
σ x11(
o)
= σ x11(
i).
cos kxl
+ σ x12(
i).
cosk
xl.
sin kxl
k
σ 12(
o)
= −σ
11(
i).
k . cosk
l.
sin k l −σ
12(
i).
sin k l +
x
x
x
x
x
x
x
x
2
x
x
x
2
x
2
x
σ 22(
o)
= σ 11(
i).
k . sin k l − 2σ
12(
i).
k . sin k l.
cosk
l
Terms in the axial direction are similar to radial terms but x must be
replaced by y
x
x
m
x
x
,
m
f
x
y
x
x
2
m
x
x

Mahdi Hadi Jasim
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008
356
Ratio
Energy
Particle
U
U
R
H
R
i
o
o
o
i
R
R
L
R
i
o
i
R
L
i
R
L
i
o
o
r
r
x
x
x
x
x
r
r
a
r
x
x
x
r
a
x
r
a
x
x
,
:
int
)
(
22
)
(
22
)
(
12
)
(
21
)
(
22
)
1
(
2
)
(
12
)
(
12
)
(
22
)
1
(
4
)
(
12
1
4
)
(
11
)
(
11
2
1
2
2
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
=
=
+
+
=
+
+
+
+
=
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
Terms in
axial direction are similar to radial terms but x must be replaced by y
Accelerating tube
1
)
(
33
)
(
23
)
(
32
)
(
13
)
(
31
)
(
23
)
(
22
).
1
(
)
(
12
).
1
(
4
)
(
11
.
4
)
(
22
)
(
12
)
(
21
.
2
1
)
(
13
.
2
1
)
(
22
.
).
1
)(
2
1
(
)
(
12
).
1
(
)
(
12
).
2
1
(
2
)
(
11
).
1
(
2
)
(
12
.
4
1
)
(
22
.
.
)
2
1
(
)
(
12
.
)
2
1
1
)(
1
(
2
)
(
11
).
1
(
)
(
11
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
=
=
=
=
+
−
+
−
−
=
=
=
+
−
−
+
−
+
−
−
−
−
=
+
−
+
−
−
+
−
=
o
o
o
x
o
o
o
i
i
L
o
L
o
o
o
L
o
L
i
L
i
i
i
L
o
L
i
L
i
L
i
o
x
x
x
x
x
x
x
d
x
d
x
x
x
d
x
d
x
d
x
x
x
d
x
q
x
q
x
q
x
x
σ
σ
σ
σ
σ
α
σ
α
σ
α
σ
α
α
σ
α
σ
σ
σ
α
σ
α
σ
α
α
σ
α
σ
α
α
σ
α
α
σ
α
σ
α
σ
α
α
σ
α
σ
Electrostatic deflector

Mahdi Hadi Jasim
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 357
)
(
22
)
3
2
).(
).(
(
21
4
)]
3
2
(
).[
(
11
4
)
(
22
)
(
12
)
(
21
)]
1
(
1
).[
2
).(
(
22
2
)]
1
(
1
).[
2
).(
3
2
(
)
4
1
).(
(
12
)
3
2
)(
).(
(
11
2
)
(
12
)]
1
(
1
.[
)
2
).(
(
22
4
)]
1
(
1
)[
2
).(
(
12
4
)
(
11
)
(
11
)
(
22
)
3
2
)(
)(
(
21
4
)]
3
2
(
).[
(
11
4
)
(
22
)
(
12
)
(
21
))
1
(
1
).(
2
)(
(
22
2
))]
1
(
1
)(
2
).(
3
2
.(
4
1
)[
(
12
)
3
2
).(
).(
(
11
)
(
12
)]
1
(
1
[
)
2
).(
(
22
4
)]
2
1
(
1
).[
2
).(
(
12
4
)
(
11
)
(
11
4
2
4
2
2
4
4
2
2
2
2
4
2
4
2
2
4
4
2
2
2
2
i
L
s
L
i
L
s
L
i
o
o
o
L
s
s
L
i
L
s
s
L
L
s
L
i
L
s
L
i
o
L
s
s
L
i
L
s
s
L
i
i
o
i
L
s
L
i
L
s
L
i
o
o
o
L
s
s
L
i
L
s
s
L
L
s
L
i
L
s
L
i
o
L
s
s
L
i
L
s
L
i
i
o
y
q
q
y
q
q
y
y
y
y
q
q
y
q
q
q
q
y
q
q
y
y
q
q
y
q
q
y
y
y
x
q
q
x
q
q
x
x
x
x
q
q
x
q
q
q
q
x
q
q
x
x
q
q
x
q
q
x
x
x
σ
θ
σ
θ
σ
σ
σ
σ
θ
σ
θ
θ
σ
θ
σ
σ
θ
σ
θ
σ
σ
σ
σ
θ
σ
θ
σ
σ
σ
σ
θ
σ
θ
θ
σ
θ
σ
σ
θ
σ
θ
σ
σ
σ
+
+
−
+
=
=
+
−
+
+
+
−
+
+
×
−
+
+
−
=
+
−
+
+
+
−
+
+
=
+
+
−
+
=
=
+
+
+
+
+
+
+
+
−
+
+
−
=
+
+
+
+
+
+
+
+
=
Quadrupole Triplet

358
Mahdi Hadi Jasim
Table A2. The Transformation R-Matrix Elements for Different Optical Elements in the Ion Implanter System
Optical elements Transformation R-matrix elements
Drift space
1
R x =
0
S
,
1
Ry
= Rx
Magnet analyzer
Rx
=
1
tanα
m
Ro
0
1
cosk
xl
− kx
sin kxl
sin kxl
kx
cosk
xl
1
tanα
m
Ro
0
1
1
R tan( m )
y = β −ψ
−
R
0
1
cosk
yl
− k sin k l
sin k yl
k y
cosk
l
1
tan( α m −ψ
)
−
R
0
1
Accelerating tube
Quadrupole triplet
Electrostatic deflector
1
R r
x = , Ry
=
R
±
0
o
La
2
( R + 1)
1
R
= 4
θ L
− 2(
)( +
L 3
q
H int : + CDDC
R
x
=
2
2α
−
Ld
0
r
1
( 1−
α )
2
s
Lq
,
0
)
2
α
( 1−
)
2
2
( 1−
α )
y
R
2(
2
x
L
− DCCD
1
The Arabian Journal for Science and Engineering, Volume 33, Number 2A July 2008
q
1
α.
L
2
α
y
+ s).(
1±
θ ( 1+
d
1
2
y
s
L
q
))
o

Table A3. Some of the Parameter Symbols and Definitions Used in Tables A1 and A2
Parameters Symbols definitions
x , ′ Particle position and divergence (mm.mrad) in radial direction
o o x
o o y
y , ′ Particle position and divergence (mm.mrad) in axial direction
z Beam line length (mm)
s Particle displacement (mm)
S Drift space length (mm)
α The magnet analyzer entrance angle (degree)
m
β The magnet analyzer exit angle (degree)
R
m
o
k x , k y
Radius of the magnet analyzer (mm)
The wave number for the radial (
kx
n Field index
l Path length inside the magnet (mm)
L a
The accelerator tube length(mm)
R r Particle energy ratio
α Electric deflection angle (degree)
L Path length along lens (mm)
L Effective length of the lens (mm)
q
REFERENCES
θ The change of particle direction in horizontal plane
CDDC Convergent–divergent–divergent–convergent
DCCD Divergent–convergent–convergent–divergent
Mahdi Hadi Jasim
1
( 1−
n)
2
n
= ) and axial ( k y = ) oscillations
Ro
Ro
[1] G.H. Gillespie and T.A. Brown, “Optics Elements for Modeling Electrostatic Lenses and Accelerator Components I.
Einzel Lenses”, IEEE Tran. Nucl. Sci., NS-45(1998), pp. 2559–2561.
[2] N. Tsoupas, W. Glenn, S. Tepikian, W. MacKay, and L. Ahrens, "A Computer Code to Measure the Beam Emittance
and Beam Parameters of the AIR Line", C-A/AP/42. Collider-Accelerator Department, Brookhaven National
Laboratory, Upton, NY-11973, 2001.
[3] P. Tanedo, "Modeling the Transverse Linear Optics of a Charged Particle Storage Ring", Stanford Linear Accelerator:
Report, 2003, 14 pp.
[4] H. Glawischnig, "Ion Implantation System Concepts" in Ion Implantation Techniques, ed. H. Ryssel and H.
Glawischnig. Springer Series in Electrophysics, vol. 10, 1982, pp. 3–20.
[5] Intesar Hatto Hashim, “A Study of the Main Parameters Effects in Designing the Medium Range Ion Implanter”,
Ph.D. Thesis , Al-Mustansiryah University, College of Science , 2004
[6] H.F. Glavish, “Magnet Optics for Beam Transport”, Nucl. Instr. and Meth., 189(1981), pp. 43–53.
[7] K.L. Brown, “Beam Envelope Matching for Beam Guidance System”, Nucl. Instr. and Meth., 187(1981), pp. 51–65.
[8] W.B. Thompson, I. Honjo, and N. Turner, “Use of Computers for Designing and Testing Beam Systems” in Ion
Implantation: Equipment and Techniques, ed. H. Ryssel and H. Glawischnig. Springer Series in Electrophysics, vol. 11,
1983, pp. 86–96.
[9] D.C. Cary, “High Energy Charged-Particle Optics Computer Programs”, Nucl. Instr. and Meth., 187(1981) pp. 97–102.
July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 359