- Email: [email protected]
Computer modelling for ion-beam system design
521
Nuclear Instruments and Methods in Physics Research B55 (1991) 527-532 North-Holland
Computer modelling for ion-beam system design Hiroyuki Ito and Nicholas R. White Applied Materials
Implant Division, Horsham,
West Sussex RHI3
5PY,
UK
The design of ion-beam transport systems based on computer modelling is discussed and some typical examples are presented. Integrated modelling work involves beam envelope programs to design overall systems, Poisson or Laplace solutions to calculate electric and magnetic fields in the system, ray-trace programs to see the collective movement of charged particles, plasma solutions for the consideration of the target environment and plasma-simulation programs to predict possible microscopic interactions between charged species and the fields. Experimental checks to assure the performance of the beam-line components are also given and explained. These are used as a means of making more accurate predictions in the future.
target region. Fig. 1 shows which design tools are used for which parts of the beam line, and the physics to be considered [3-S]. It is always important to ensure that the modelhng can closely follow the real situation so that design work based on these predictions is sufficiently reliable. Associated experiments should be performed to check the agreement with the theoretical models. The results help determine the conditions under which the programs are valid and can-suggest further improvements in calculation.
1. Introduction Ion-beam transport systems and beam-optics calculations have been developed largely in nuclear physics and other related fields [l]. As semiconductor device structures increase in complexity, tight control of the ion-beam conditions becomes more important in ion implantation doping processes [2]. The main concerns are the beam current extracted and transferred at a certain energy through the system, beam divergence, mass resolution and the beam-plasma conditions in the
Ion Beam Transport System I
Experimentalchecks
I
I
Target Environment (Design Tools) HWVW?l
ODWS l
0
2D Raytrace with Plasma Solutbn 1D Plasma Simulation
0
0
3DBeam Envelopa up to 2nd order 1DPlasma Simulation
0
2DLaplace Solution for magnetic fields
spaca charge, scattering and resolutbn)
bnisation Plasma sheath formation Electric 8 Magnetic field pwletratbn spaccl charge Beam optics
ZDRaytrace 3DBeam Envelope
Beam Optics Optics aberration
0 0 0
i (Physics
Transfer Matrix Method (Overall design considering
0 0
1D Plasma Simulation 1D Plasma Solutbn ‘2D Raytrace
Beam Profile
0 0 0 0
0
Emittance Focus Properties Langmuir Probe Charge neutralization
involved)
&,
SpaCe Charge
Plasma conditions
B~n;~;;xce) Space charge (divergence)
-
Bw&ya
;eam,“p’ics
Space charge
characteristics Space charge
I
_I
Fig. 1. System overview. System devices, computer design tools and the physics involved in the modelling are shown. 0168-583X/91/$03.50
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
V. MACHINES
H. Ito, N.R. White / Computer modelhg for ion-beam system design
528
2. Overall system design
neutralisation is assumed in accelerator tubes, so focussing can be strong. The validity of first-order calculations is limited, second-order aberrations may cause large errors, example in the determination of mass resolution. differences which appear in second order should minimised to achieve performance close to the order (see section 4).
For an ion implantation beam line, as with any ion-beam system, the whole system should first be designed to a first-order approximation according to the desired specification. The main concerns at this stage are: (1) energy range, (2) beam current with species and associated energy range, (3) beam dimensions and divergence, (4) mass resolution and (5) overall system dimensions and interface to other systems. There are some physical limits which might not allow a theoretical model to be realised, such as the minimum gap between acceleration electrodes. These constraints can give a certain conflict with the ideal design and the best possible solution should be sought by considering other changeable parameters of the related devices. A design tool used for this purpose is an interactive 3D first-order beam-envelope program based on the transfer-matrix method [6] called OPTICIAN [7], which calculates the coordinates of the beam envelope through the system. Beam coordinates are composed of spatial coordinates x and y (having z coincide with the central ray), divergence, path-length spread and momentum spread. The first-order FWHM mass-resolving power can be derived from the dispersion element of the transfer matrix. Fig. 2 shows a hypothetical ion-implanter beam line which can bend a 60 keV As+ beam through 90° and accelerate it to 90 keV onto the target. The tightly controlled point-to-point focus between the entrance and the end of the drift element 5 can be seen. One of the additional features implemented into OPTICIAN is that space-charge effects including neutralisation are considered [8]. These give rise to radial electric fields. The potential difference between the beam centre and the plasma sheath is assumed to be T,/2 (T, is the electron temperature) based on stable plasmasheath formation [9], and the resultant electric field can cause positive ions to drift outward. No space-charge
deand for The be first
3. Ion-source and extraction system The ion source and its extraction-system requirements need to be specified as follows: (1) extraction energy range, (2) beam current and density range, (3) ion species, (4) beam dimensions and divergence and (5) optics control over the operation range. There are many important parameters which affect the performance of this system, such as ion mass, electron temperature, ion density in the source chamber, electrode geometry and space charge. The maximum current extracted through the system, for example, is limited by several relations shown below [lo]. The number of ions leaving the plasma cannot exceed the value determined by the product of the Bohm velocity and the ion density given by J
xc
P
n.T’/2m7’/2 i
p,e
)
where JP is the current density at the plasma sheath, cp a constant, ni the ion density at the plasma sheath, T, the electron temperature and mi the mass of the ion. The beam current extracted through the electrodes is also limited by the space-charge effect, expressed by J, = c,d-2m;1/2V3/2~,
(2)
where J, is the current density at extraction, d the extraction sheath distance, c, a constant, V the extraction voltage and f, the space-charge neutralisation factor. For systems in which the extraction energy is high
789
”
Illi
10
Target
i
r L
Fig. 2. Ion-beam transport system of a 300 mm radius 90” bending magnet, with 60 keV extraction and 30 keV post-acceleration using an As+ beam, modelled by the 3D first-order beam envelope program OPTICIAN [7]: (1) Source, (2) lens, (3) drift, (4) magnet, (5,6) drift, (7-9) accelerator and (10) drift.
H. Ito, N.R. White / Computer modelling for ion-beamsystem design
529
Fig. 3. Ion-source and extraction system composed of source chamber, suppression electrode and ground electrode, modelled by the 2D ray-trace program SORCERY [7]. The potential is.20 kV at the source front plate (left), -5 kV at the suppression electrode (middle), 0 V at the ground electrode (right), and the ion species is Ar+.
(2 10 keV), the beam divergence is usually dominated by the optical properties of the extraction system [ll], rather than the thermal motion of the ions which causes momentum spread. The main tool used to design the extraction region is a 2D ray-trace program called SORCERY [7]. The program traces particle trajectories solving Poisson’s equation by the finite-element method, assuming a Boltzmann distribution of electrons inside the plasma. Each particle trajectory is integrated using the RungeKutta method. The plasma boundary adopts a shape satisfying eq. (2). The performance of any ray-trace programs should be equivalent regardless of the differences in trajectory integration as long as the calculation of the field is sufficiently accurate [li]. 2D raytrace programs are extremely useful to display the electrostatic lens formation around the beam extraction area. As can be seen in fig. 3 (double-electrode extraction system: one to suppress the electron backstreaming, and another to define the final energy), the electric field along the plasma sheath converges the ions toward the axis, then the beam passes through a divergent lens formed around the extraction electrodes. The combination of these two lenses determines the beam formation.
4. Mass analyser The first-order design of the(.mass analyser is assumed to have been done in the overall system design
explained in section 2, which would give the first-order parameters such as bending radius, bending angle, magnetic field strength, field index, pole face angles and positions of the foci.’ A 3D second-order beam-envelope program called TRANSPORT from SLAC [13] is then used to check the first-order design and to perform second-order optimisation. The method of second-order calculation is also based on transfer matrices which now contain second-order terms. The results are affected by such variables as the quadratic field coefficient c and the entrance and exit pole-face curvatures. Beam growth caused by the magnet aberration is minimised by changing the second-order variables. If these parameters are not considered, the aberration tends to give a crescent shape to the output of a ribbon beam. The effects of the fringing field are taken into account in terms of field integrals 1, and I, [14] which give corrections to the central ray displacement and the focal power in the non-dispersion plane, respectively. These are zeroth- and first-order constraints, but require accurate calculations to determine the entrance and exit pole geometry. The actual pole shape can be designed by solving the Laplace equations assuming the magnetic scalar potential is valid between the poles. 2D ray-trace programs can be used as a Laplace solver. The pole radial cross section determines the value of z and the entrance and exit pole shapes determine Ii and r2. Fig. 4 shows the equipotential plot in the plane of the magnet pole cross section. The field near the edge of V. MACHINES
H. Ito, N.R. White / Computermodelling for ion-beam system design
530
Fig. 4. Equipotentialplot in the plane of the magnet pole cross section, obtained as a 2D Laplace solution using SORCERY. the pole decreases as the gap between potential lines increases. The field profile along the beam axis showing the effect of the fringing field is plotted in the left half of fig. 5. Similarly the effect of E on the radial profile is shown in the right half of fig. 5.
5. Acceleration tubes To design acceleration (or deceleration) systems, energy range, beam dimensions and optics control, balanc-
ing focal power against space charge, should be considered. The field inside the acceleration tubes forms a convergent lens and the effect is increased as the acceleration energy is increased. If the energy is high, the beam can be focussed to a very small size, making the beam current density high, which may aggravate problems such as charging up on the semiconductor wafers [15]. If, on the other hand, the energy is low, spacecharge blow-up would play. a more dominant role, making the optics”contro1 very difficult. 2D ray-trace programs are again effectively used .,for. this design. The field lens formation is easily seen ,from the equipotential lines. OPTICIAN can also be used to see the macroscopic character since it approximates the space-charge effect in the acceleration tube.
6. Target environment (wafer chamber) The requirements of each beam transport system strongly depend on the actual processes in the target chamber and its environment. The process-related problems, such as “wafer charging” mentioned in the previous section, are getting more and more subtle as complex submicron structures are developed with increasing sensitivity to the environment. In the target chamber the ion beam will collide with neutral gas, creating ions which then form a beam-plasma together with the -1.03
‘1
*
Note
different
scales
1.6
r-7
1.4-
9 8 L
Pole entrance
1.2-
at POOmm
centreof pole
-0 z Y-
/
1 -
\
.$ z
0.8 -
ET
I1 = 0.5. k! = 0.6 0.6
5
-
-_! 0.97
._ Axial
coordinate
[mm]
Radial
distance
[mm]
Fig. 5. Magnetic field profile in the median plane. The left-hand side shows the field along the beam axis. The extended fringing field is clearly seen in the region outside the pole. The right-hand side shows the field along the radial direction. The field is maximum at the centre and decreases outward, as can be seen in fig. 4.
531
H. Ito, N. R. White / Computer modelling for ion-beam system design 9.OE+14
90
7 ion
Beam
0
Electron
8.OE+14 7.OE+14
Species
Ar+
Beam current
10 mA
Beam
a 00
70
energy
Electron temp. 6.OE-tl4
/ -k--x
5.OE-t 14 4.OE-t14
Beam radius
I%I
Wall radius
30 mm
Pressure
1 x 10W4ton
60
nominal
50
B
D s. E?L 3
40
3.OE-!- 14 2.OE+
1.OE-t
0
0.004
I 0.006 Radial
I 0.012 distxtce
I
I 0.016 fran
I
I 0.02
beam
axis
,
,--1--r0.024
0
0.028
Cm1
7
1
!30
b I90
Beam current
IO mA
Beam energy
20 keV
Electron temp. Beam 5.OE+ 14
radius
4 eV 20 mm nominal
Wall radius
30 mm
Pressure
1 x IO5 torr
4.OE+ 14 30
3.OE+14 Z.OE+ 14
20
:
10
l.OE+l4 0 0
0.004
0.006 Radial
0.012 distance
0.016 from
0.02 tieam
axi5
0.024
0.028
EmI
Fig. 6. (a) Radial distribution of the beam plasma at 1 X 10W4 Torr assuming a 4 eV electron temperature, modelled by a 1D plasma solution [16]. The density of each species and the potential are expressed in terms of the number per cubic metre and volts, respectively. A well-defined plasma around the ion beam with a small Debye length is seen. (b) Radial distribution of the beam plasma at 1 X lo-’ Torr at the same electron temperature of 4 eV. The field penetration is much greater than that in (a), reflecting the fact that the Debye length is now large due to the decrease in plasma density. Further data are: 20 keV beam energy, 20 mm nominal beam radius and 30 mm wall radius. V. MACHINES
532
H. Ito, N.R. white / Computer modelling for ion-beam system design
trapped electrons inside its potential well [8,16]. All of these processes need to be understood. In terms of the computer modelling, some simulation programs have been intensively developed by plasma physicists in recent years [17,18]. A 1D plasma solution [16] is one of the tools used to see the radial distribution of each particle species and the potential, electric field and particle flux in the beam-plasma in the steady state. This program solves Poisson’s equation with the contin&ty equation based on the finite difference method. Ionisation and charge-exchange collisions are taken into account, and up to two Maxwellian distributions of electron species can be calculated at different temperatures. A well-collimated cylindrical beam is assumed and cold ion species created from neutrals drift along the field. Figs. 6a and b are examples of the results. The former presents the well-defined plasma around the beam with a small Debye length at a pressure of 10e4 Torr, and the latter shows the relatively large field penetration across the system at the lower pressure of lop5 Torr. A real-time simulation is the 1D plasma simulation program called the PDXl series, developed by the Plasma Theory and Simulation Group at the University of California at Berkeley [19]. This program solves Poisson’s equation together with the external circuit connected to the system boundary based on the particle in cell method, and advances particles in real time by applying the Lorentz force. Particle collisions resulting in excitation, charge exchange and ionisation are also implemented by the Monte Carlo method. By using this program, the effects of a potential applied in a short time (- 1 ps) on one side of the electrodes, for instance, can be evaluated effectively.
7. Experimental checks The main purposes of experimental checks are (1) to check whether the performance of devices is close enough to that predicted by the model, and (2) derive any possible suggestions which can be implemented into the modelling procedure for future improvement. For examnle: (1) Beam profile. Beams are basically better if symmetric and uniformly distributed along the axes in the plane of the cross section. Some commercial beam profilers are available to measure the distribution. (2) Focal point. The focal point must be well defined to ensure high resolution. It can be found by making a beam burn on a tantalum plate placed in the beam at a shallow angle, or by viewing directly through a window near the focus.
(3) Langmuir probe. Electron temperature and plasma densities are important parameters in understanding the plasma character around the beam. Langmuir-probe techniques are widely used to obtain these values [20].
8. Conclusion Ion beam transport systems can be modelled accurately by computer if the physics involved in each component is properly considered. This gives great advantages in speeding up development, reducing costs and understanding the system performance.
References [l] K.L. Brown, R. Belbeoch and P. Bounin, Rev. Sci. Instr. 35 (1964) 481. [2] M.E. Mack, G. Ryding, D.H. Douglas-Hamilton, K. Steeples, M. Farley, V. Gillis, N. White, A. Wittkower and R. Lambracht, Nucl. Instr. and Meth. B6 (1985) 405. [3] K.L. Brown, Advanced Particle Phys. 1 (1967) 71. [4] D.C. Carey, Fermilab Report No. NAL-64 (1971). [S] A.J.T. Holmes, Phys. Rev. Al9 (1979) 389. [6] A.P. Banford, The Transport of Charged Particle Beams, (E. & F.N. Svon. London, 1966). [71 N.R. White,Nucl. Instr. and Meth. B21 (1987) 339. PI N.R. White, these Proceedings (8th Int. Conf. on Ion Implantation Technology, Guildford, UK, 1990) Nucl. Instr. and Meth. B55 (1991) 287. [91 F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, (Plenum, New York 1984). [W .I. Ishikawa, Ion Source Technology (Ionics, Japan, 1986) p. 178. u11 N.R. White and AS. Devaney, Proc. 12th Symp. on ISIAT ‘89, Tokyo, 1989, p. 111. WI P. Spadtke, The Physics and Technology of Ion Sources, (Wiley, New York, 1989) p. 107. D31 K.L. Brown, F. Rothacker, D.C. Carey and Ch. Iselin, CERN Report SO-04 (1980). t141 H.A. Enge, Rev. Sci. Instr. 35 (1964) 278. [I51 M.I. Current, A. Bhattacharyya and M. Khid, Nucl. Instr. and Meth. B37/38 (1989) 555. 1161 H. Ito, Steady-state beam plasma solution, Internal Report, Applied Materials, UK (1990). u71 C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, 1985). [W R.W. Hackney and J.W. Eastwood, Computer Simulation Using Particles (Hilger, 1988). [I91 J.P. Verboncoeur and V. Vahedi, Proc. 13th Numerical Simulation Conference, Santa Fe, NM, USA, 1989. P-01 J.A. Strain, Y. Tanaka, N.R. White and R. Woodward, these Proceedings (8th Int. Conf. on Ion Implantation Technology, Guildford, UK, 1990) Nucl. Instr. and Meth. B55 (1991) 97.
Nuclear Instruments and Methods in Physics Research B55 (1991) 527-532 North-Holland
Computer modelling for ion-beam system design Hiroyuki Ito and Nicholas R. White Applied Materials
Implant Division, Horsham,
West Sussex RHI3
5PY,
UK
The design of ion-beam transport systems based on computer modelling is discussed and some typical examples are presented. Integrated modelling work involves beam envelope programs to design overall systems, Poisson or Laplace solutions to calculate electric and magnetic fields in the system, ray-trace programs to see the collective movement of charged particles, plasma solutions for the consideration of the target environment and plasma-simulation programs to predict possible microscopic interactions between charged species and the fields. Experimental checks to assure the performance of the beam-line components are also given and explained. These are used as a means of making more accurate predictions in the future.
target region. Fig. 1 shows which design tools are used for which parts of the beam line, and the physics to be considered [3-S]. It is always important to ensure that the modelhng can closely follow the real situation so that design work based on these predictions is sufficiently reliable. Associated experiments should be performed to check the agreement with the theoretical models. The results help determine the conditions under which the programs are valid and can-suggest further improvements in calculation.
1. Introduction Ion-beam transport systems and beam-optics calculations have been developed largely in nuclear physics and other related fields [l]. As semiconductor device structures increase in complexity, tight control of the ion-beam conditions becomes more important in ion implantation doping processes [2]. The main concerns are the beam current extracted and transferred at a certain energy through the system, beam divergence, mass resolution and the beam-plasma conditions in the
Ion Beam Transport System I
Experimentalchecks
I
I
Target Environment (Design Tools) HWVW?l
ODWS l
0
2D Raytrace with Plasma Solutbn 1D Plasma Simulation
0
0
3DBeam Envelopa up to 2nd order 1DPlasma Simulation
0
2DLaplace Solution for magnetic fields
spaca charge, scattering and resolutbn)
bnisation Plasma sheath formation Electric 8 Magnetic field pwletratbn spaccl charge Beam optics
ZDRaytrace 3DBeam Envelope
Beam Optics Optics aberration
0 0 0
i (Physics
Transfer Matrix Method (Overall design considering
0 0
1D Plasma Simulation 1D Plasma Solutbn ‘2D Raytrace
Beam Profile
0 0 0 0
0
Emittance Focus Properties Langmuir Probe Charge neutralization
involved)
&,
SpaCe Charge
Plasma conditions
B~n;~;;xce) Space charge (divergence)
-
Bw&ya
;eam,“p’ics
Space charge
characteristics Space charge
I
_I
Fig. 1. System overview. System devices, computer design tools and the physics involved in the modelling are shown. 0168-583X/91/$03.50
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
V. MACHINES
H. Ito, N.R. White / Computer modelhg for ion-beam system design
528
2. Overall system design
neutralisation is assumed in accelerator tubes, so focussing can be strong. The validity of first-order calculations is limited, second-order aberrations may cause large errors, example in the determination of mass resolution. differences which appear in second order should minimised to achieve performance close to the order (see section 4).
For an ion implantation beam line, as with any ion-beam system, the whole system should first be designed to a first-order approximation according to the desired specification. The main concerns at this stage are: (1) energy range, (2) beam current with species and associated energy range, (3) beam dimensions and divergence, (4) mass resolution and (5) overall system dimensions and interface to other systems. There are some physical limits which might not allow a theoretical model to be realised, such as the minimum gap between acceleration electrodes. These constraints can give a certain conflict with the ideal design and the best possible solution should be sought by considering other changeable parameters of the related devices. A design tool used for this purpose is an interactive 3D first-order beam-envelope program based on the transfer-matrix method [6] called OPTICIAN [7], which calculates the coordinates of the beam envelope through the system. Beam coordinates are composed of spatial coordinates x and y (having z coincide with the central ray), divergence, path-length spread and momentum spread. The first-order FWHM mass-resolving power can be derived from the dispersion element of the transfer matrix. Fig. 2 shows a hypothetical ion-implanter beam line which can bend a 60 keV As+ beam through 90° and accelerate it to 90 keV onto the target. The tightly controlled point-to-point focus between the entrance and the end of the drift element 5 can be seen. One of the additional features implemented into OPTICIAN is that space-charge effects including neutralisation are considered [8]. These give rise to radial electric fields. The potential difference between the beam centre and the plasma sheath is assumed to be T,/2 (T, is the electron temperature) based on stable plasmasheath formation [9], and the resultant electric field can cause positive ions to drift outward. No space-charge
deand for The be first
3. Ion-source and extraction system The ion source and its extraction-system requirements need to be specified as follows: (1) extraction energy range, (2) beam current and density range, (3) ion species, (4) beam dimensions and divergence and (5) optics control over the operation range. There are many important parameters which affect the performance of this system, such as ion mass, electron temperature, ion density in the source chamber, electrode geometry and space charge. The maximum current extracted through the system, for example, is limited by several relations shown below [lo]. The number of ions leaving the plasma cannot exceed the value determined by the product of the Bohm velocity and the ion density given by J
xc
P
n.T’/2m7’/2 i
p,e
)
where JP is the current density at the plasma sheath, cp a constant, ni the ion density at the plasma sheath, T, the electron temperature and mi the mass of the ion. The beam current extracted through the electrodes is also limited by the space-charge effect, expressed by J, = c,d-2m;1/2V3/2~,
(2)
where J, is the current density at extraction, d the extraction sheath distance, c, a constant, V the extraction voltage and f, the space-charge neutralisation factor. For systems in which the extraction energy is high
789
”
Illi
10
Target
i
r L
Fig. 2. Ion-beam transport system of a 300 mm radius 90” bending magnet, with 60 keV extraction and 30 keV post-acceleration using an As+ beam, modelled by the 3D first-order beam envelope program OPTICIAN [7]: (1) Source, (2) lens, (3) drift, (4) magnet, (5,6) drift, (7-9) accelerator and (10) drift.
H. Ito, N.R. White / Computer modelling for ion-beamsystem design
529
Fig. 3. Ion-source and extraction system composed of source chamber, suppression electrode and ground electrode, modelled by the 2D ray-trace program SORCERY [7]. The potential is.20 kV at the source front plate (left), -5 kV at the suppression electrode (middle), 0 V at the ground electrode (right), and the ion species is Ar+.
(2 10 keV), the beam divergence is usually dominated by the optical properties of the extraction system [ll], rather than the thermal motion of the ions which causes momentum spread. The main tool used to design the extraction region is a 2D ray-trace program called SORCERY [7]. The program traces particle trajectories solving Poisson’s equation by the finite-element method, assuming a Boltzmann distribution of electrons inside the plasma. Each particle trajectory is integrated using the RungeKutta method. The plasma boundary adopts a shape satisfying eq. (2). The performance of any ray-trace programs should be equivalent regardless of the differences in trajectory integration as long as the calculation of the field is sufficiently accurate [li]. 2D raytrace programs are extremely useful to display the electrostatic lens formation around the beam extraction area. As can be seen in fig. 3 (double-electrode extraction system: one to suppress the electron backstreaming, and another to define the final energy), the electric field along the plasma sheath converges the ions toward the axis, then the beam passes through a divergent lens formed around the extraction electrodes. The combination of these two lenses determines the beam formation.
4. Mass analyser The first-order design of the(.mass analyser is assumed to have been done in the overall system design
explained in section 2, which would give the first-order parameters such as bending radius, bending angle, magnetic field strength, field index, pole face angles and positions of the foci.’ A 3D second-order beam-envelope program called TRANSPORT from SLAC [13] is then used to check the first-order design and to perform second-order optimisation. The method of second-order calculation is also based on transfer matrices which now contain second-order terms. The results are affected by such variables as the quadratic field coefficient c and the entrance and exit pole-face curvatures. Beam growth caused by the magnet aberration is minimised by changing the second-order variables. If these parameters are not considered, the aberration tends to give a crescent shape to the output of a ribbon beam. The effects of the fringing field are taken into account in terms of field integrals 1, and I, [14] which give corrections to the central ray displacement and the focal power in the non-dispersion plane, respectively. These are zeroth- and first-order constraints, but require accurate calculations to determine the entrance and exit pole geometry. The actual pole shape can be designed by solving the Laplace equations assuming the magnetic scalar potential is valid between the poles. 2D ray-trace programs can be used as a Laplace solver. The pole radial cross section determines the value of z and the entrance and exit pole shapes determine Ii and r2. Fig. 4 shows the equipotential plot in the plane of the magnet pole cross section. The field near the edge of V. MACHINES
H. Ito, N.R. White / Computermodelling for ion-beam system design
530
Fig. 4. Equipotentialplot in the plane of the magnet pole cross section, obtained as a 2D Laplace solution using SORCERY. the pole decreases as the gap between potential lines increases. The field profile along the beam axis showing the effect of the fringing field is plotted in the left half of fig. 5. Similarly the effect of E on the radial profile is shown in the right half of fig. 5.
5. Acceleration tubes To design acceleration (or deceleration) systems, energy range, beam dimensions and optics control, balanc-
ing focal power against space charge, should be considered. The field inside the acceleration tubes forms a convergent lens and the effect is increased as the acceleration energy is increased. If the energy is high, the beam can be focussed to a very small size, making the beam current density high, which may aggravate problems such as charging up on the semiconductor wafers [15]. If, on the other hand, the energy is low, spacecharge blow-up would play. a more dominant role, making the optics”contro1 very difficult. 2D ray-trace programs are again effectively used .,for. this design. The field lens formation is easily seen ,from the equipotential lines. OPTICIAN can also be used to see the macroscopic character since it approximates the space-charge effect in the acceleration tube.
6. Target environment (wafer chamber) The requirements of each beam transport system strongly depend on the actual processes in the target chamber and its environment. The process-related problems, such as “wafer charging” mentioned in the previous section, are getting more and more subtle as complex submicron structures are developed with increasing sensitivity to the environment. In the target chamber the ion beam will collide with neutral gas, creating ions which then form a beam-plasma together with the -1.03
‘1
*
Note
different
scales
1.6
r-7
1.4-
9 8 L
Pole entrance
1.2-
at POOmm
centreof pole
-0 z Y-
/
1 -
\
.$ z
0.8 -
ET
I1 = 0.5. k! = 0.6 0.6
5
-
-_! 0.97
._ Axial
coordinate
[mm]
Radial
distance
[mm]
Fig. 5. Magnetic field profile in the median plane. The left-hand side shows the field along the beam axis. The extended fringing field is clearly seen in the region outside the pole. The right-hand side shows the field along the radial direction. The field is maximum at the centre and decreases outward, as can be seen in fig. 4.
531
H. Ito, N. R. White / Computer modelling for ion-beam system design 9.OE+14
90
7 ion
Beam
0
Electron
8.OE+14 7.OE+14
Species
Ar+
Beam current
10 mA
Beam
a 00
70
energy
Electron temp. 6.OE-tl4
/ -k--x
5.OE-t 14 4.OE-t14
Beam radius
I%I
Wall radius
30 mm
Pressure
1 x 10W4ton
60
nominal
50
B
D s. E?L 3
40
3.OE-!- 14 2.OE+
1.OE-t
0
0.004
I 0.006 Radial
I 0.012 distxtce
I
I 0.016 fran
I
I 0.02
beam
axis
,
,--1--r0.024
0
0.028
Cm1
7
1
!30
b I90
Beam current
IO mA
Beam energy
20 keV
Electron temp. Beam 5.OE+ 14
radius
4 eV 20 mm nominal
Wall radius
30 mm
Pressure
1 x IO5 torr
4.OE+ 14 30
3.OE+14 Z.OE+ 14
20
:
10
l.OE+l4 0 0
0.004
0.006 Radial
0.012 distance
0.016 from
0.02 tieam
axi5
0.024
0.028
EmI
Fig. 6. (a) Radial distribution of the beam plasma at 1 X 10W4 Torr assuming a 4 eV electron temperature, modelled by a 1D plasma solution [16]. The density of each species and the potential are expressed in terms of the number per cubic metre and volts, respectively. A well-defined plasma around the ion beam with a small Debye length is seen. (b) Radial distribution of the beam plasma at 1 X lo-’ Torr at the same electron temperature of 4 eV. The field penetration is much greater than that in (a), reflecting the fact that the Debye length is now large due to the decrease in plasma density. Further data are: 20 keV beam energy, 20 mm nominal beam radius and 30 mm wall radius. V. MACHINES
532
H. Ito, N.R. white / Computer modelling for ion-beam system design
trapped electrons inside its potential well [8,16]. All of these processes need to be understood. In terms of the computer modelling, some simulation programs have been intensively developed by plasma physicists in recent years [17,18]. A 1D plasma solution [16] is one of the tools used to see the radial distribution of each particle species and the potential, electric field and particle flux in the beam-plasma in the steady state. This program solves Poisson’s equation with the contin&ty equation based on the finite difference method. Ionisation and charge-exchange collisions are taken into account, and up to two Maxwellian distributions of electron species can be calculated at different temperatures. A well-collimated cylindrical beam is assumed and cold ion species created from neutrals drift along the field. Figs. 6a and b are examples of the results. The former presents the well-defined plasma around the beam with a small Debye length at a pressure of 10e4 Torr, and the latter shows the relatively large field penetration across the system at the lower pressure of lop5 Torr. A real-time simulation is the 1D plasma simulation program called the PDXl series, developed by the Plasma Theory and Simulation Group at the University of California at Berkeley [19]. This program solves Poisson’s equation together with the external circuit connected to the system boundary based on the particle in cell method, and advances particles in real time by applying the Lorentz force. Particle collisions resulting in excitation, charge exchange and ionisation are also implemented by the Monte Carlo method. By using this program, the effects of a potential applied in a short time (- 1 ps) on one side of the electrodes, for instance, can be evaluated effectively.
7. Experimental checks The main purposes of experimental checks are (1) to check whether the performance of devices is close enough to that predicted by the model, and (2) derive any possible suggestions which can be implemented into the modelling procedure for future improvement. For examnle: (1) Beam profile. Beams are basically better if symmetric and uniformly distributed along the axes in the plane of the cross section. Some commercial beam profilers are available to measure the distribution. (2) Focal point. The focal point must be well defined to ensure high resolution. It can be found by making a beam burn on a tantalum plate placed in the beam at a shallow angle, or by viewing directly through a window near the focus.
(3) Langmuir probe. Electron temperature and plasma densities are important parameters in understanding the plasma character around the beam. Langmuir-probe techniques are widely used to obtain these values [20].
8. Conclusion Ion beam transport systems can be modelled accurately by computer if the physics involved in each component is properly considered. This gives great advantages in speeding up development, reducing costs and understanding the system performance.
References [l] K.L. Brown, R. Belbeoch and P. Bounin, Rev. Sci. Instr. 35 (1964) 481. [2] M.E. Mack, G. Ryding, D.H. Douglas-Hamilton, K. Steeples, M. Farley, V. Gillis, N. White, A. Wittkower and R. Lambracht, Nucl. Instr. and Meth. B6 (1985) 405. [3] K.L. Brown, Advanced Particle Phys. 1 (1967) 71. [4] D.C. Carey, Fermilab Report No. NAL-64 (1971). [S] A.J.T. Holmes, Phys. Rev. Al9 (1979) 389. [6] A.P. Banford, The Transport of Charged Particle Beams, (E. & F.N. Svon. London, 1966). [71 N.R. White,Nucl. Instr. and Meth. B21 (1987) 339. PI N.R. White, these Proceedings (8th Int. Conf. on Ion Implantation Technology, Guildford, UK, 1990) Nucl. Instr. and Meth. B55 (1991) 287. [91 F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, (Plenum, New York 1984). [W .I. Ishikawa, Ion Source Technology (Ionics, Japan, 1986) p. 178. u11 N.R. White and AS. Devaney, Proc. 12th Symp. on ISIAT ‘89, Tokyo, 1989, p. 111. WI P. Spadtke, The Physics and Technology of Ion Sources, (Wiley, New York, 1989) p. 107. D31 K.L. Brown, F. Rothacker, D.C. Carey and Ch. Iselin, CERN Report SO-04 (1980). t141 H.A. Enge, Rev. Sci. Instr. 35 (1964) 278. [I51 M.I. Current, A. Bhattacharyya and M. Khid, Nucl. Instr. and Meth. B37/38 (1989) 555. 1161 H. Ito, Steady-state beam plasma solution, Internal Report, Applied Materials, UK (1990). u71 C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, 1985). [W R.W. Hackney and J.W. Eastwood, Computer Simulation Using Particles (Hilger, 1988). [I91 J.P. Verboncoeur and V. Vahedi, Proc. 13th Numerical Simulation Conference, Santa Fe, NM, USA, 1989. P-01 J.A. Strain, Y. Tanaka, N.R. White and R. Woodward, these Proceedings (8th Int. Conf. on Ion Implantation Technology, Guildford, UK, 1990) Nucl. Instr. and Meth. B55 (1991) 97.