- Email: [email protected]
A new spectrometer for Rutherford backscattering spectrometry
Nuclear Instruments and Methods in Physics Research B 229 (2005) 527–532 www.elsevier.com/locate/nimb
A new spectrometer for Rutherford backscattering spectrometry Chikara Ichihara a b
a,*
, Akira Kobayashi a, Ken-ichi Inoue b, Kenji Kimura
c
Electronics Research Laboratory, Kobe Steel Ltd., 1-5-5, Takatsukadai, Nishi-ku, Kobe 651-2271, Japan Production Research Laboratory, Kobe Steel Ltd., 1-5-5, Takatsukadai, Nishi-ku, Kobe 651-2271, Japan c Department of Engineering Physics and Mechanics, Kyoto University, Kyoto 606-8501, Japan Received 18 October 2004; received in revised form 13 December 2004
Abstract A new spectrometer for cyclotron Rutherford backscattering spectrometry (CRBS) is designed, which has a reasonably large solid angle and a high energy resolution compared with those of conventional RBS systems. The system consists of a cryogen-free superconducting magnet that produces a uniform magnetic field, and a two-dimensional position sensitive detector (2D-PSD) that has a small hole for transmittance of incident ions. Both the detector and the specimen are placed in the uniform magnetic field. Probe ions, accelerated by a small accelerator, pass through the hole of the detector and an energy resolving aperture before incident onto the specimen. Since the incident direction is adjusted to be parallel to the magnetic field, the trajectory of the incident beam is not affected by the magnetic field. Ions, backscattered from the specimen, travel along the cyclotron trajectories in the magnetic field, and only ions that satisfy a certain relationship between their energy and scattering angles, pass through the energy resolving aperture. The energy and scattering angle can be determined from the position of the detection in the 2D-PSD. It is shown that this new spectrometer can provide both a large solid angle and a reasonably high energy resolution. 2005 Elsevier B.V. All rights reserved. PACS: 07.81 Keywords: Spectrometer; Rutherford backscattering spectroscopy; Cyclotron trajectory
1. Introduction
*
Corresponding author. Tel.: +81 78 992 5613; fax: +81 78 992 5650. E-mail address: [email protected] (C. Ichihara).
Rutherford backscattering spectrometry (RBS) technique using high-energy ions has been widely used as a means of materials analysis because of its non-destructive, rapid, and quantitative
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.12.132
528
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
features [1]. In recent application of RBS, there is an increasing demand to analyze ultrathin films, for instance, gate dielectric layers in MOS-FET devices whose thicknesses are now a few nanometer. It is thus very difficult to analyze such thin films by conventional RBS systems, because the depth resolution is only about 10 nm using a solidstate detector. Secondary ion mass spectrometry (SIMS), which has a depth resolution of nm, is usually used to analyze such thin films. However, quantitative analysis using SIMS is difficult especially in the very shallow region because of the surface transient effect and the matrix effect [2,3]. For better depth resolution and reliability, we have previously developed a compact high-resolution RBS (HRBS) system with a 90 sector magnetic spectrometer using medium-energy (sub-MeV) helium ions [4]. It is possible to analyze the elemental profiles with high depth resolution of sub-nm level (by experiments), which results from the high energy resolution (0.1%) of the spectrometer, although the solid angle is relatively small (0.4 msr). However since the solid angle is small, a high ion fluence is necessary for measurements, and this sometimes causes serious radiation damages and/or redistribution of elements, especially in the analysis of organic materials. We now propose a new spectrometer to achieve cyclotron RBS (CRBS) measurements with a low ion fluence. The new system provides a large solid angle of about 10 msr together with a relatively high energy resolution of <1%. This allows an elemental depth profiling with a high depth resolution without notable effects by the ion irradiation. In this system, backscattered ions are energy-analyzed by a 2-T uniform magnetic field. In order to generate such a high magnetic field in a large area, a cryogen-free superconducting magnet is employed. CRBS optics provides a large solid angle, because the ion detector simultaneously detects the backscattered ions at any azimuthal angle, when the ion energy and the scattering angle satisfy a certain relationship. This feature can be utilized to analyze ultrathin films with low target damage and high sensitivity. The present paper discusses the basic concept and its characteristics of the new system such as the energy resolution,
and the solid angle. The system is currently under construction.
2. Design of the system Fig. 1 shows a schematic view of the new system. A cryogen-free superconducting magnet is used to generate a vertical uniform magnetic field up to 2 T in the region of /34 cm · 77 cm. A 500-kV accelerator is placed on the top of the magnet. The dimensions of the total system are as compact as about 140 cm of width · 180 cm of depth · 250 cm of height. Helium ions are generated by a PIG (Penning ionization gauge) type ion source, and mass ana(1)
(2)
(3) (4) (5) (7)
(6)
(8)
1m Fig. 1. Schematic drawing of CRBS system using a cylindrical magnetic field: (1) ion source and Wien filter, (2) Cockcroft– Walton type high voltage generator and accelerator tube, (3) objective slit, (4) quadrupole magnet (doublet), (5) ion detector with a hole, (6) energy resolving aperture, (7) cryogen-free superconducting magnet, and (8) specimen.
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
lyzed by a Wien filter, both of which are placed on the high voltage terminal, and accelerated up to 500 keV. The accelerator is installed inside an isolation tank filled with SF6 gas. After acceleration, the ion beam is focused by a quadrupole lens, and vertically led to the spectrometer. Inside the magnet, there are a two-dimensional position-sensitive-detector (2D-PSD) with a center hole for transmittance of the incident beam, an energy resolving aperture, and a goniometer as shown in Fig. 2. The ions pass through the detector hole and the energy resolving aperture, then finally impinge onto the specimen mounted on the goniometer. A part of ions, which are backscattered from the specimen, can go through the energy resolving aperture and are detected by the 2D-PSD. A typical trajectory of the scattered ion in the system is shown by a dashed curve in Fig. 2.
2D-PSD
529
3. Trajectory of ions A typical trajectory of a backscattered ion in a uniform magnetic field B is schematically shown in Fig. 3. All backscattered ions except for those backscattered at 180 move along cyclotron trajectories. The trajectory is given by x ¼ R sinðxc tÞ;
ð1Þ
y ¼ R½1 cosðxc tÞ;
ð2Þ
z ¼ vz t ¼ v cos h t;
ð3Þ
where h is the scattering angle, v is the ion velocity and vz is the vertical velocity (see Fig. 2). The angular frequency xc and the radius R of the cyclotron trajectory are given by the following equations: qe ð4Þ xc ¼ B; m R¼
vr v sin h ¼ ; xc xc
ð5Þ
where qe is the ion charge, m the ion mass, B the magnetic field and vr the horizontal ion velocity.
energy resolving aperture
l
backscattered ion trajectory (4)
(5)
B
incident beam
L
(6)
(1) v
vz
(2)
vr
z
goniometer
θ
y
specimen
Fig. 2. Schematic diagram of the new spectrometer using a cylindrical magnetic field. B is an intensity of a magnetic field, dashed curve is a backscattered ion trajectory, h is a backscattering angle, v is a velocity of the backscattered ion, vz is a vertical velocity, vr is a horizontal velocity, L is the distance between the specimen and the energy resolving aperture, and l is the distance between the aperture and the 2D-PSD.
(3)
x
Fig. 3. Schematic diagram of a backscattered ion trajectory in a magnetic field: (1) incident point, (2) trajectory of backscattered ion, (3)–(5) projections of the trajectory on the x–y, the y–z, the z–x planes, respectively, and (6) direction of the magnetic field.
Using Eqs. (1) and (2), the distance, q, between the ion trajectory and the z-axis is given by x vr xc c t ¼ 2 sin t : ð6Þ q ¼ 2Rsin 2 xc 2 Eq. (6) means that all ions come back to the z-axis at t = 2Np/xc, where N is an integer and will be referred to as a convergence number, hereafter. Thus, the ions backscattered from the specimen can pass through the energy resolving aperture placed at z = L (see Fig. 2) when the following equation is fulfilled: L¼
2N p vz : xc
ð7Þ
Eq. (7) means that vz is resolved by the energy resolving aperture. If the horizontal ion velocity can be measured, both the ion energy and the scattering angle can be obtained. This can be done by measuring the position of the ion detection in the 2D-PSD. The distance between the position of detection and the z-axis, qd, is given by l N p ; ð8Þ qd ¼ 2Rsin L where l is the distance between the aperture and the 2D-PSD. Eq. (8) means that qd has a maximal value when l equals to L/2N. Therefore, a better velocity resolution can be obtained when l = L/ 2N. In the following discussions we employed l = L/2 for simplicity, and in this case the relationship between the horizontal velocity and qd is given by vr ¼
xc q : 2 d
ð9Þ
Thus both the vertical and horizontal velocity of the ion detected by the 2D-PSD is obtained. The energy and the scattering angle of the ion can be calculated from those results, 2 ! m 2 mx2c L 2 2 Eðqd Þ ¼ ðvr þ vz Þ ¼ qd þ ; ð10Þ 2 Np 8
vr hðqd Þ ¼ arctan vz
N pqd ¼ arctan : L
ð11Þ
450 400 350 300 250 200 150 100 50 0 -50 -100 -150 -200 -250 -300 -350 -400
L = 300 mm, N = 1 L = 300 mm, N = 3 L = 200 mm, N = 1 L = 200 mm, N = 3
0
20
40
60
80
100
120
140
290 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 160
θ (deg)
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
E (keV)
530
ρ (mm) d
Fig. 4. The energy and the backscattering angle of the backscattered He+ detected by the 2D-PSD as functions of qd. The intensity of the magnetic field, B, is 2 T, and L is 200 and 300 mm. The ion detector is placed at z = 300 (when L = 200 mm) and 450 mm (when L = 300 mm), and the convergence number N = 1 and 3.
Fig. 4 shows the calculated energy and scattering angle as a function of qd for He+. In the calculation, B = 2 T, L = 200 and 300 mm (l = 100 and 150 mm), and N = 1 and 3 are used. The results for N = 2 are not shown because the ions passing through the aperture converge at qd = 0 when N is an even number. As can be seen, E becomes larger and h becomes smaller with increasing qd. The energy and the angular ranges of the system can also be known from the figure. For instance, in the case of L = 300 mm and N = 1, they are 120–400 keV and 120–180. It should be noted that the energy and the scattering angle cannot be uniquely determined from the observed position qd, because we
(4)
(1)
2R
ρ (3)
(2)
(5)
z L Fig. 5. Schematic view of the z–q projection of the ion trajectories in the magnetic field: (1) ion trajectory when the convergence number N = 1, (2) N = 2, (3) N = 3, (4) energy resolving aperture, and (5) cylindrical obstacle for selecting N = 1 scattering ions.
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
cannot distinguish the convergence number N of the detected ion. However, we can select the ions of particular convergence number by putting cylindrical obstacles along the z-axis (see Fig. 5).
4. Energy resolution and solid angle In this section, the energy resolution and the acceptance solid angle are estimated. If the diameter of the aperture, /a, is infinitely small, the energy resolution is determined by the spatial resolution, dqd, of the 2D-PSD. The energy resolution is obtained from Eq. (10), dEd ¼
mx2c q dq : 4 d d
ð12Þ
If the aperture has a finite size, the energies of the ions detected at the same position qd on the 2DPSD are not unique. Fig. 6 shows the relationship between the ion energy and qd schematically. The thick curve shows the relationship when /a = 0 (given by Eq. (10)) and the hatched area shows the one when the aperture has a finite size. The energy resolution caused by finite size of the aperture is shown as dEa in Fig. 6. In order to estimate dEa we first estimate Dqd, the spread of the detection position for the ions with the same energy caused by the finite size aperture.
E
θ (ρd)+ ∆θ
δ Ea
θ (ρd)
(2) (1)
531
When the aperture is infinitesimal, the ion detected at qd has the energy E(qd) and the scattering angle h(qd) given by Eqs. (10) and (11). If the aperture has a finite size, the ion with the same energy but having a slightly different scattering angle h = h(qd) + Dh can pass through the aperture and detected at slightly different position. The distance between the ion trajectory and the z-axis on the plane of the aperture (at z = L) can be given by 2v sinðhðqd Þ þ DhÞ cos hðqd Þ qL ¼ sin N p xc cosðhðqd Þ þ DhÞ 2v ffi sin hðqd Þ N pjDh tan hðqd Þj ð13Þ xc If qL is smaller than /a, the ion can pass through the aperture. Thus the ion with a scattering angle, hðqd Þ Dh < h < hðqd Þ þ Dh;
ð14Þ
can be detected, where Dh ¼
xc /a : 2vN p sin hðqd Þ tan hðqd Þ
The detection position h = h(qd) + Dh is given by
for
ð15Þ the
ion
with
2v sinðhðqd Þ þ DhÞ cos hðqd Þ 3 sin Np xc cosðhðqd Þ þ DhÞ 2 2v 2v sin hðqd Þ þ Dh cos hðqd Þ ffi xc xc 2v ¼ qd þ Dh cos hðqd Þ: ð16Þ xc
q0d ¼
Thus the spread of the detection position is obtained as
(3) E(ρd)
Dqd ¼
ρd ∆ ρd
4v 2/a Dh cos hðqd Þ ¼ xc N ptan2 hðqd Þ
ð17Þ
and the energy resolution due to the finite size of the aperture is given by ρd
Fig. 6. Schematic diagram for the energy spread when the aperture has a finite size: (1) energy of ion which passes through the center of the energy resolving aperture as a function of qd, (2) and (3) maximum and minimum energies of ions which pass through the aperture, respectively, dEa is the energy resolution, and Dqd is the spread of the detection position for the ions with the same energy.
dEa ¼
dEðqd Þ mx2c qd /a Dqd ¼ : dqd 2N ptan2 hðqd Þ
ð18Þ
The energy resolution including the spatial resolution of the detector is calculated by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ð19Þ DE ¼ ðdEd Þ þ ðdEa Þ :
532
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532 1E7
L =300 mm, N = 1 L =200 mm, N = 1
10 1
1000000 100000
0.1
1000 HRBS
B=2T
φ a = 1 mm δρd = 0.1 mm
0.01
1
HRBS
0
20
40
60
80
100
120
140
160
5. Conclusion
100 10
1E-3 1E-4
angle simultaneously. This allows us to deduce the information of the crystal structure of the specimen from the observed azimuthal angle distribution.
10000
Ω (msr)
dE/E (%)
100
0.1 180
ρd (mm)
Fig. 7. Calculated results of the energy resolution and the solid angle as functions of qd. The intensity of the magnetic field, B, is 2 T, l is L/2, /a is 1 mm, and dqd, the spatial resolution of the detector, is 0.1 mm.
Next, the solid angle X of the spectrometer is estimated. When the ions satisfy Eq. (14), they can pass through the energy resolving aperture and are detected by the detector. Hence, X is given by X ¼ 2p sin h 2Dh ¼
4/a j cos hðqd Þj: N qd
ð20Þ
In Fig. 7, the calculated energy resolution and the solid angle are shown as a function of qd. In the calculation, B = 2 T, /a = 1 mm, dqd = 0.1 mm, L = 200 and 300 mm (l = L/2), and N = 1 are used. The results at qd <10 mm are not shown because the approximation used in Eqs. (13) and (16) cannot be applied in this region. As can be seen, both DE/E and X become smaller with increasing qd. For instance, in the case of L = 300 mm and N = 1, the energy resolution decreases from 11% to 0.23%, and the solid angle decreases from 360 to 13 msr when qd changes from 10 to 160 mm. It should be noted that the present spectrometer can analyze the ions scattered at any azimuthal
A novel type magnetic spectrometer for CRBS is designed and its basic features are discussed. The spectrometer consists of a superconducting magnet, which produces a strong uniform magnetic field, and a 2D-PSD. Choosing proper values for its parameters, the energy resolution of 0.2% and the solid angle of 10 msr are available. Comparing with the commercially available standard type 90 magnetic spectrometer [4], the solid angle is more than 10 times larger while the energy resolution is almost the same.
Acknowledgments This work was supported by the Key Technology Research Promotion Program from New Energy and Industrial Technology Development Organization (NEDO), Japan.
References [1] For example, L.C. Feldman, J.W. Mayer, Fundamentals of Surface and Thin Film Analysis, North-Holland, Amsterdam, 1986. [2] W. Vandervorst, F.R. Shepherd, Appl. Surf. Sci. 21 (1985) 230. [3] G.E. Hammer, J. Vac. Sci. Technol. 20 (3) (1982) 403. [4] K. Kimura, M. Kimura, Y. Mori, M. Maehara, H. Fukuyama, Applications of Accelerators in Research and Industry, The American Institute of Physics, 1999, 500.
A new spectrometer for Rutherford backscattering spectrometry Chikara Ichihara a b
a,*
, Akira Kobayashi a, Ken-ichi Inoue b, Kenji Kimura
c
Electronics Research Laboratory, Kobe Steel Ltd., 1-5-5, Takatsukadai, Nishi-ku, Kobe 651-2271, Japan Production Research Laboratory, Kobe Steel Ltd., 1-5-5, Takatsukadai, Nishi-ku, Kobe 651-2271, Japan c Department of Engineering Physics and Mechanics, Kyoto University, Kyoto 606-8501, Japan Received 18 October 2004; received in revised form 13 December 2004
Abstract A new spectrometer for cyclotron Rutherford backscattering spectrometry (CRBS) is designed, which has a reasonably large solid angle and a high energy resolution compared with those of conventional RBS systems. The system consists of a cryogen-free superconducting magnet that produces a uniform magnetic field, and a two-dimensional position sensitive detector (2D-PSD) that has a small hole for transmittance of incident ions. Both the detector and the specimen are placed in the uniform magnetic field. Probe ions, accelerated by a small accelerator, pass through the hole of the detector and an energy resolving aperture before incident onto the specimen. Since the incident direction is adjusted to be parallel to the magnetic field, the trajectory of the incident beam is not affected by the magnetic field. Ions, backscattered from the specimen, travel along the cyclotron trajectories in the magnetic field, and only ions that satisfy a certain relationship between their energy and scattering angles, pass through the energy resolving aperture. The energy and scattering angle can be determined from the position of the detection in the 2D-PSD. It is shown that this new spectrometer can provide both a large solid angle and a reasonably high energy resolution. 2005 Elsevier B.V. All rights reserved. PACS: 07.81 Keywords: Spectrometer; Rutherford backscattering spectroscopy; Cyclotron trajectory
1. Introduction
*
Corresponding author. Tel.: +81 78 992 5613; fax: +81 78 992 5650. E-mail address: [email protected] (C. Ichihara).
Rutherford backscattering spectrometry (RBS) technique using high-energy ions has been widely used as a means of materials analysis because of its non-destructive, rapid, and quantitative
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.12.132
528
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
features [1]. In recent application of RBS, there is an increasing demand to analyze ultrathin films, for instance, gate dielectric layers in MOS-FET devices whose thicknesses are now a few nanometer. It is thus very difficult to analyze such thin films by conventional RBS systems, because the depth resolution is only about 10 nm using a solidstate detector. Secondary ion mass spectrometry (SIMS), which has a depth resolution of nm, is usually used to analyze such thin films. However, quantitative analysis using SIMS is difficult especially in the very shallow region because of the surface transient effect and the matrix effect [2,3]. For better depth resolution and reliability, we have previously developed a compact high-resolution RBS (HRBS) system with a 90 sector magnetic spectrometer using medium-energy (sub-MeV) helium ions [4]. It is possible to analyze the elemental profiles with high depth resolution of sub-nm level (by experiments), which results from the high energy resolution (0.1%) of the spectrometer, although the solid angle is relatively small (0.4 msr). However since the solid angle is small, a high ion fluence is necessary for measurements, and this sometimes causes serious radiation damages and/or redistribution of elements, especially in the analysis of organic materials. We now propose a new spectrometer to achieve cyclotron RBS (CRBS) measurements with a low ion fluence. The new system provides a large solid angle of about 10 msr together with a relatively high energy resolution of <1%. This allows an elemental depth profiling with a high depth resolution without notable effects by the ion irradiation. In this system, backscattered ions are energy-analyzed by a 2-T uniform magnetic field. In order to generate such a high magnetic field in a large area, a cryogen-free superconducting magnet is employed. CRBS optics provides a large solid angle, because the ion detector simultaneously detects the backscattered ions at any azimuthal angle, when the ion energy and the scattering angle satisfy a certain relationship. This feature can be utilized to analyze ultrathin films with low target damage and high sensitivity. The present paper discusses the basic concept and its characteristics of the new system such as the energy resolution,
and the solid angle. The system is currently under construction.
2. Design of the system Fig. 1 shows a schematic view of the new system. A cryogen-free superconducting magnet is used to generate a vertical uniform magnetic field up to 2 T in the region of /34 cm · 77 cm. A 500-kV accelerator is placed on the top of the magnet. The dimensions of the total system are as compact as about 140 cm of width · 180 cm of depth · 250 cm of height. Helium ions are generated by a PIG (Penning ionization gauge) type ion source, and mass ana(1)
(2)
(3) (4) (5) (7)
(6)
(8)
1m Fig. 1. Schematic drawing of CRBS system using a cylindrical magnetic field: (1) ion source and Wien filter, (2) Cockcroft– Walton type high voltage generator and accelerator tube, (3) objective slit, (4) quadrupole magnet (doublet), (5) ion detector with a hole, (6) energy resolving aperture, (7) cryogen-free superconducting magnet, and (8) specimen.
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
lyzed by a Wien filter, both of which are placed on the high voltage terminal, and accelerated up to 500 keV. The accelerator is installed inside an isolation tank filled with SF6 gas. After acceleration, the ion beam is focused by a quadrupole lens, and vertically led to the spectrometer. Inside the magnet, there are a two-dimensional position-sensitive-detector (2D-PSD) with a center hole for transmittance of the incident beam, an energy resolving aperture, and a goniometer as shown in Fig. 2. The ions pass through the detector hole and the energy resolving aperture, then finally impinge onto the specimen mounted on the goniometer. A part of ions, which are backscattered from the specimen, can go through the energy resolving aperture and are detected by the 2D-PSD. A typical trajectory of the scattered ion in the system is shown by a dashed curve in Fig. 2.
2D-PSD
529
3. Trajectory of ions A typical trajectory of a backscattered ion in a uniform magnetic field B is schematically shown in Fig. 3. All backscattered ions except for those backscattered at 180 move along cyclotron trajectories. The trajectory is given by x ¼ R sinðxc tÞ;
ð1Þ
y ¼ R½1 cosðxc tÞ;
ð2Þ
z ¼ vz t ¼ v cos h t;
ð3Þ
where h is the scattering angle, v is the ion velocity and vz is the vertical velocity (see Fig. 2). The angular frequency xc and the radius R of the cyclotron trajectory are given by the following equations: qe ð4Þ xc ¼ B; m R¼
vr v sin h ¼ ; xc xc
ð5Þ
where qe is the ion charge, m the ion mass, B the magnetic field and vr the horizontal ion velocity.
energy resolving aperture
l
backscattered ion trajectory (4)
(5)
B
incident beam
L
(6)
(1) v
vz
(2)
vr
z
goniometer
θ
y
specimen
Fig. 2. Schematic diagram of the new spectrometer using a cylindrical magnetic field. B is an intensity of a magnetic field, dashed curve is a backscattered ion trajectory, h is a backscattering angle, v is a velocity of the backscattered ion, vz is a vertical velocity, vr is a horizontal velocity, L is the distance between the specimen and the energy resolving aperture, and l is the distance between the aperture and the 2D-PSD.
(3)
x
Fig. 3. Schematic diagram of a backscattered ion trajectory in a magnetic field: (1) incident point, (2) trajectory of backscattered ion, (3)–(5) projections of the trajectory on the x–y, the y–z, the z–x planes, respectively, and (6) direction of the magnetic field.
Using Eqs. (1) and (2), the distance, q, between the ion trajectory and the z-axis is given by x vr xc c t ¼ 2 sin t : ð6Þ q ¼ 2Rsin 2 xc 2 Eq. (6) means that all ions come back to the z-axis at t = 2Np/xc, where N is an integer and will be referred to as a convergence number, hereafter. Thus, the ions backscattered from the specimen can pass through the energy resolving aperture placed at z = L (see Fig. 2) when the following equation is fulfilled: L¼
2N p vz : xc
ð7Þ
Eq. (7) means that vz is resolved by the energy resolving aperture. If the horizontal ion velocity can be measured, both the ion energy and the scattering angle can be obtained. This can be done by measuring the position of the ion detection in the 2D-PSD. The distance between the position of detection and the z-axis, qd, is given by l N p ; ð8Þ qd ¼ 2Rsin L where l is the distance between the aperture and the 2D-PSD. Eq. (8) means that qd has a maximal value when l equals to L/2N. Therefore, a better velocity resolution can be obtained when l = L/ 2N. In the following discussions we employed l = L/2 for simplicity, and in this case the relationship between the horizontal velocity and qd is given by vr ¼
xc q : 2 d
ð9Þ
Thus both the vertical and horizontal velocity of the ion detected by the 2D-PSD is obtained. The energy and the scattering angle of the ion can be calculated from those results, 2 ! m 2 mx2c L 2 2 Eðqd Þ ¼ ðvr þ vz Þ ¼ qd þ ; ð10Þ 2 Np 8
vr hðqd Þ ¼ arctan vz
N pqd ¼ arctan : L
ð11Þ
450 400 350 300 250 200 150 100 50 0 -50 -100 -150 -200 -250 -300 -350 -400
L = 300 mm, N = 1 L = 300 mm, N = 3 L = 200 mm, N = 1 L = 200 mm, N = 3
0
20
40
60
80
100
120
140
290 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 160
θ (deg)
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
E (keV)
530
ρ (mm) d
Fig. 4. The energy and the backscattering angle of the backscattered He+ detected by the 2D-PSD as functions of qd. The intensity of the magnetic field, B, is 2 T, and L is 200 and 300 mm. The ion detector is placed at z = 300 (when L = 200 mm) and 450 mm (when L = 300 mm), and the convergence number N = 1 and 3.
Fig. 4 shows the calculated energy and scattering angle as a function of qd for He+. In the calculation, B = 2 T, L = 200 and 300 mm (l = 100 and 150 mm), and N = 1 and 3 are used. The results for N = 2 are not shown because the ions passing through the aperture converge at qd = 0 when N is an even number. As can be seen, E becomes larger and h becomes smaller with increasing qd. The energy and the angular ranges of the system can also be known from the figure. For instance, in the case of L = 300 mm and N = 1, they are 120–400 keV and 120–180. It should be noted that the energy and the scattering angle cannot be uniquely determined from the observed position qd, because we
(4)
(1)
2R
ρ (3)
(2)
(5)
z L Fig. 5. Schematic view of the z–q projection of the ion trajectories in the magnetic field: (1) ion trajectory when the convergence number N = 1, (2) N = 2, (3) N = 3, (4) energy resolving aperture, and (5) cylindrical obstacle for selecting N = 1 scattering ions.
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532
cannot distinguish the convergence number N of the detected ion. However, we can select the ions of particular convergence number by putting cylindrical obstacles along the z-axis (see Fig. 5).
4. Energy resolution and solid angle In this section, the energy resolution and the acceptance solid angle are estimated. If the diameter of the aperture, /a, is infinitely small, the energy resolution is determined by the spatial resolution, dqd, of the 2D-PSD. The energy resolution is obtained from Eq. (10), dEd ¼
mx2c q dq : 4 d d
ð12Þ
If the aperture has a finite size, the energies of the ions detected at the same position qd on the 2DPSD are not unique. Fig. 6 shows the relationship between the ion energy and qd schematically. The thick curve shows the relationship when /a = 0 (given by Eq. (10)) and the hatched area shows the one when the aperture has a finite size. The energy resolution caused by finite size of the aperture is shown as dEa in Fig. 6. In order to estimate dEa we first estimate Dqd, the spread of the detection position for the ions with the same energy caused by the finite size aperture.
E
θ (ρd)+ ∆θ
δ Ea
θ (ρd)
(2) (1)
531
When the aperture is infinitesimal, the ion detected at qd has the energy E(qd) and the scattering angle h(qd) given by Eqs. (10) and (11). If the aperture has a finite size, the ion with the same energy but having a slightly different scattering angle h = h(qd) + Dh can pass through the aperture and detected at slightly different position. The distance between the ion trajectory and the z-axis on the plane of the aperture (at z = L) can be given by 2v sinðhðqd Þ þ DhÞ cos hðqd Þ qL ¼ sin N p xc cosðhðqd Þ þ DhÞ 2v ffi sin hðqd Þ N pjDh tan hðqd Þj ð13Þ xc If qL is smaller than /a, the ion can pass through the aperture. Thus the ion with a scattering angle, hðqd Þ Dh < h < hðqd Þ þ Dh;
ð14Þ
can be detected, where Dh ¼
xc /a : 2vN p sin hðqd Þ tan hðqd Þ
The detection position h = h(qd) + Dh is given by
for
ð15Þ the
ion
with
2v sinðhðqd Þ þ DhÞ cos hðqd Þ 3 sin Np xc cosðhðqd Þ þ DhÞ 2 2v 2v sin hðqd Þ þ Dh cos hðqd Þ ffi xc xc 2v ¼ qd þ Dh cos hðqd Þ: ð16Þ xc
q0d ¼
Thus the spread of the detection position is obtained as
(3) E(ρd)
Dqd ¼
ρd ∆ ρd
4v 2/a Dh cos hðqd Þ ¼ xc N ptan2 hðqd Þ
ð17Þ
and the energy resolution due to the finite size of the aperture is given by ρd
Fig. 6. Schematic diagram for the energy spread when the aperture has a finite size: (1) energy of ion which passes through the center of the energy resolving aperture as a function of qd, (2) and (3) maximum and minimum energies of ions which pass through the aperture, respectively, dEa is the energy resolution, and Dqd is the spread of the detection position for the ions with the same energy.
dEa ¼
dEðqd Þ mx2c qd /a Dqd ¼ : dqd 2N ptan2 hðqd Þ
ð18Þ
The energy resolution including the spatial resolution of the detector is calculated by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ð19Þ DE ¼ ðdEd Þ þ ðdEa Þ :
532
C. Ichihara et al. / Nucl. Instr. and Meth. in Phys. Res. B 229 (2005) 527–532 1E7
L =300 mm, N = 1 L =200 mm, N = 1
10 1
1000000 100000
0.1
1000 HRBS
B=2T
φ a = 1 mm δρd = 0.1 mm
0.01
1
HRBS
0
20
40
60
80
100
120
140
160
5. Conclusion
100 10
1E-3 1E-4
angle simultaneously. This allows us to deduce the information of the crystal structure of the specimen from the observed azimuthal angle distribution.
10000
Ω (msr)
dE/E (%)
100
0.1 180
ρd (mm)
Fig. 7. Calculated results of the energy resolution and the solid angle as functions of qd. The intensity of the magnetic field, B, is 2 T, l is L/2, /a is 1 mm, and dqd, the spatial resolution of the detector, is 0.1 mm.
Next, the solid angle X of the spectrometer is estimated. When the ions satisfy Eq. (14), they can pass through the energy resolving aperture and are detected by the detector. Hence, X is given by X ¼ 2p sin h 2Dh ¼
4/a j cos hðqd Þj: N qd
ð20Þ
In Fig. 7, the calculated energy resolution and the solid angle are shown as a function of qd. In the calculation, B = 2 T, /a = 1 mm, dqd = 0.1 mm, L = 200 and 300 mm (l = L/2), and N = 1 are used. The results at qd <10 mm are not shown because the approximation used in Eqs. (13) and (16) cannot be applied in this region. As can be seen, both DE/E and X become smaller with increasing qd. For instance, in the case of L = 300 mm and N = 1, the energy resolution decreases from 11% to 0.23%, and the solid angle decreases from 360 to 13 msr when qd changes from 10 to 160 mm. It should be noted that the present spectrometer can analyze the ions scattered at any azimuthal
A novel type magnetic spectrometer for CRBS is designed and its basic features are discussed. The spectrometer consists of a superconducting magnet, which produces a strong uniform magnetic field, and a 2D-PSD. Choosing proper values for its parameters, the energy resolution of 0.2% and the solid angle of 10 msr are available. Comparing with the commercially available standard type 90 magnetic spectrometer [4], the solid angle is more than 10 times larger while the energy resolution is almost the same.
Acknowledgments This work was supported by the Key Technology Research Promotion Program from New Energy and Industrial Technology Development Organization (NEDO), Japan.
References [1] For example, L.C. Feldman, J.W. Mayer, Fundamentals of Surface and Thin Film Analysis, North-Holland, Amsterdam, 1986. [2] W. Vandervorst, F.R. Shepherd, Appl. Surf. Sci. 21 (1985) 230. [3] G.E. Hammer, J. Vac. Sci. Technol. 20 (3) (1982) 403. [4] K. Kimura, M. Kimura, Y. Mori, M. Maehara, H. Fukuyama, Applications of Accelerators in Research and Industry, The American Institute of Physics, 1999, 500.