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The use of a magnetic quadrupole triplet as a high resolution ion energy spectrometer
Nuclear Instruments and Methods in Physics Research B 155 (1999) 153±159
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The use of a magnetic quadrupole triplet as a high resolution ion energy spectrometer M.B.H. Breese a
a,*
, D.N. Jamieson
b
Department of Physics, School of Physical Sciences, University of Surrey, Guildford GU2 5XH, UK b School of Physics, University of Melbourne, Parkville, Vic. 3052, Australia Received 3 November 1998; received in revised form 25 February 1999
Abstract The use of a nuclear microprobe, containing a magnetic quadrupole triplet, as a high resolution energy spectrometer is proposed here. It is calculated that energy dierences of 300 eV can be resolved for 3 MeV protons which are transmitted through thin samples, corresponding to an energy resolution of dE 0:01%. The optics and performance of this energy spectrometer are discussed and compared with other types which are used for ion beam analysis. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 61.80.+p; 07.78.+s; 41.85.Lc Keywords: Energy spectrometry; Quadrupole multiplets; Transmission channeling
1. Introduction In a magnetic or electrostatic energy spectrometer, a backscattered or transmitted ion beam is analysed with high energy resolution in order to improve on that attainable using semiconductor detectors, or other forms of energy measurement. Refs. [1±3] give examples of recently developed energy spectrometers for ion beam analysis, whereas Refs. [4,5] illustrate respectively how long ion and electron spectrometers have been in use. The energy resolution of semiconductor detectors
* Corresponding author. Tel.: +44-1483-876796; fax: +441483-259501; e-mail: [email protected]
is limited to 15 keV, enabling a depth resolution of 10 nm using Rutherford Backscattering Spectrometry. With energy spectrometers, a resolution of 1±2 keV is attainable (i.e. approximately a factor of 10 improvement), enabling a depth resolution of 1 nm or better. This is usually at the expense of a reduced solid angle for collecting the scattered ions and hence a reduced counting rate. Energy spectrometers resolve small dierences in ion energies by passing the backscattered, or transmitted, beam through an electrostatic or magnetic ®eld. The resultant spatial dispersion of the de¯ected ions, due to their momentum (i.e. chromatic) spread, is then measured. The ability to resolve small energy dierences using spectrometers largely depends on their ability to measure
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small spatial dispersions of typically 100±200 lm, which is limited by the resolution of the position sensitive detectors which are commonly used to record the ®nal ion locations in the image plane. The channeling oscillations of ions as they move in regions of dierent electron density between the lattice walls of a crystal result in dierent energy losses as a function of crystal thickness and emergent angle. Another use for energy spectrometers has been to measure small variations in the energy of ions transmitted through thin crystals in channeling alignment, in order to determine the channeled ion stopping power or the oscillation frequency. Such measurements have been carried out using keV protons by Eisen [6] using an electrostatic analyser; higher energies were not be studied owing to insucient ®eld strength. Datz et al. [7,8] measured the energy loss of high-energy heavy ions through thin crystals to observe the dierent planar channeled energy losses of dierent oscillatory groups. The large energy losses made the use of semiconductor detectors to directly measure the transmitted energies possible. The aim of the proposed energy spectrometer described here in this paper is for measurements of the energy loss of MeV light ions, such as protons and helium ions, as a function of emergent angle. These are transmitted in channeling alignment through thin crystals which are located at the object aperture of a microprobe. Ref. [9] describes Monte Carlo simulations of such trajectories, showing the energy losses of ten thousand 3 MeV protons transmitted through the (1 1 0) planes of thin silicon crystals. In simulations through 200 nm thick layers the proton energy loss varied from 2.5 to 5 keV, with variations occurring over small changes of the planar channeling angle of wp 2 mrad. Energy peaks with a width of 100±200 eV were produced when the transmitted beam is collimated in angle to approximately wp =10. An energy resolution of hundreds of eV, with an angular acceptance of 0.2 mrad is thus required from the spectrometer described here. Such a system would also be useful for studies of small energy loss variations due to Ôrainbow channelingÕ eects [10] for MeV protons which are axially channeled through thin crystals.
2. Eect of the chromatic aberration of a quadrupole triplet The use of a multiplet of quadrupole lenses to focus MeV ion beams to spot sizes as small as 100 nm is well established using microprobes [11,12]. The focused beam is ideally mono-energetic, so that the eects of chromatic aberrations cause minimum degradation of the focused beam spot. This causes an ion with a slightly greater momentum to be under-focused in the image plane, and one with slightly less momentum to be over-focused. Whilst the percentage momentum spread, dp, of a charged particle beam, rather than its percentage energy spread, dE, is commonly used to characterise the variation of trajectories through a magnetic ®eld, both de®nitions are used here to best highlight the relationship between the dierent proton energies and their individual trajectories. They are however related by dp dE=2. Since this paper only considers MeV protons, no account is taken of any eects due to dierent charge states. The MeV ion beams used in most microprobes are usually generated by a Van de Graa accelerator, which can give a full-width-at-half-maximum (FWHM) energy spread of 150 eV for a 3 MeV proton beam, i.e. dE 0:005%. During normal microprobe operation, a collimator aperture, which is located symmetrically about the beam axis, is used to de®ne a small acceptance angle into the lens system. This minimises the spatial dispersion in the image plane due to the unwanted eects of chromatic aberrations. The dispersion increases linearly with trajectory angle into the quadrupole triplet. With a focused beam current of approximately 100 pA, the trajectory angles h0 and /0 into the lenses in the horizontal (x) and vertical (y) directions respectively, are typically 0.1 mrad. For the microprobe con®guration using a high-excitation quadrupole triplet shown in Figs. 1 and 2, the chromatic aberration coecients can be expressed as y=/ dp 900 lm/mrad% in the vertical direction, and x=h dp 400 lm/mrad% in the horizontal direction. This gives a total range of vertical displacements in the image plane of 0.5 lm for an energy spread of dE 0:005%. This enables a nuclear microprobe to operate with a
M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
Fig. 1. (a) Plot of proton trajectories in the vertical (upper half) and horizontal (lower half) directions, with trajectory angles of h0 0.25 mrad and /0 0.25 mrad respectively, diverging from the object aperture (xo ,yo ) 0,0 and focused to the microprobe image plane. The proton energies are 2.988, 3.000, 3.012 MeV, i.e. 3.000 MeV dE 4.0%. (b) shows an expanded scale of the trajectories in the vertical direction close to the image plane. (c) shows the same as (b) except with a range of trajectory angles of /0 0.24, 0.25, 0.26 mrad for each beam energy. The outlines of the quadrupole lenses are shown to their correct horizontal scale but their vertical scale is exaggerated.
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typical spatial resolution of 1 lm or better with a beam current of 100 pA, which is used for elemental analysis using a range of ion beam analysis techniques [11]. The best reported spatial resolution with a nuclear microprobe is 100 nm [13], at a very low beam current of 1 fA (i.e. 6000 ions per second), which is used for energy loss imaging using scanning transmission ion microscopy (STIM). This very low beam current is typical of that used in the quadrupole triplet spectrometer described here. In a nuclear microprobe, the eects of chromatic aberrations on the beam which is focused by the quadrupole lenses should be as small as possible, in order to produce the smallest beam spot. However, for use as an energy spectrometer, the opposite eect is required, whereby the spatial dispersion in the image plane due to a small energy spread should be as large as possible, in order to achieve a high measured energy resolution. The eect of an energy spread of a proton beam passing through a high excitation quadrupole triplet can be seen in Fig. 1(a), where the individual quadrupole lenses are numbered 1±3. The trajectories of protons with energies of 2.880, 3.000 and 3.120 MeV (i.e. 3 MeV with dE 4%) are plotted in the horizontal and vertical directions. The proton beam diverges from an object aperture located at 0 on the z axis in Fig. 1(a). These are calculated using the matrix ray-tracing program PRAM [14], with the quadrupole lens strengths remaining the same throughout this paper. This lens system focuses the beam in the image plane, which is 15 cm downstream of the exit face of the last quadrupole. It gives a high demagni®cation of Dx 90 in the horizontal direction and a lower demagni®cation of Dy 25 in the vertical direction. Thus in Fig. 1(a) the beam convergence angle hi in the horizontal direction in the image plane is 3.5 times larger than /i in the vertical direction. However, the dispersion for dierent proton energies is larger in the vertical direction, as indicated by the above chromatic aberration coecients. This eect is shown on an expanded scale in Fig. 1(b), where an energy shift of +4% causes a proton with an angle of /0 0.25 mrad to be displaced by +450 lm in the image plane, compared with a proton with an identical trajectory but with
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Fig. 2. Plot of proton trajectories in the vertical direction, close to the microprobe image plane. The proton energies in each case are 2.997, 3.000, 3.003 MeV, i.e. 3.000 MeV dE 0.1%. (a) With trajectory angles of /0 0.24, 0.25, 0.26 mrad, and object coordinates of yo 0, 4 lm. (b), (c) same as (a) but with object coordinates of yo 0, 40 lm and yo 0, 400 lm, respectively. (d) same as (a) but with trajectory angles of /0 0.20, 0.25, 0.30 mrad.
no energy shift. Similarly a beam energy shift of ÿ4% causes the same trajectory to be over-focused by ÿ450 lm in the image plane. Other quadrupole multiplets, such as a doublet or a quadruplet, could have been chosen here, but since a triplet has the largest chromatic aberration coecients it is best suited for use as an energy spectrometer. During normal microprobe operation, a further reason why the trajectory angles into the lenses are kept as small as possible is to minimise the eects of spherical aberration [11]. This causes a reduction in the lens focal length with increasing trajectory angle. Those protons with a large angle of h0 or /0 are over-focused, as can be seen in Fig. 1(b), where the proton trajectory with no energy shift is displaced from the beam axis in the image plane. Account must therefore be taken of
the eects of both chromatic and spherical aberrations within the quadrupole lenses on the ion trajectories. 3. Use of a quadrupole triplet as an energy spectrometer For the proposed use of a microprobe as an energy spectrometer, the sample is located at the object aperture. The microprobe collimator should be o-set in the vertical direction, as shown in Fig. 1(a), while remaining on the beam axis in the horizontal direction. The vertical direction is chosen because it has the larger chromatic aberration coecient, and since h0 0 the chromatic aberration in the horizontal direction can be
M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
ignored, along with any spherical aberration crossterms which depend on h0 . In this con®guration, ions with dierent energies are dispersed in the image plane, as shown in Fig. 1(b). A dipole ®eld is used to de¯ect a speci®c transmitted beam angle onto the displaced collimator aperture. Consider the required size of the displaced collimator aperture needed to transmit enough beam to carry out the measurement of the spatial dispersion of the transmitted ions in a reasonable time. A geometric spot size in the image plane of 0.1 lm can be achieved with an object aperture full size of xo ,yo 9, 2.5 lm for demagni®cations of Dx 90 and Dy 25. A counting rate of 6000 events per second (equivalent to a beam current of 1 fA), is the maximum available on most microprobe data acquisition systems. A typical beam brightness at the object aperture of B 5 pA/(lm2 mrad2 MeV) for 3 MeV protons may be reduced by a typical factor of 100 [9] after passing through a 1 lm thick silicon crystal. Under these conditions a collimator aperture full size of 0.02 mrad is required for a beam current of 1 fA in the image plane. There are, of course, many combinations of object and collimator aperture sizes which would give the same required current, but this may be taken as a typical example to give the approximate aperture sizes needed. The idealised situation of single trajectories for each separate beam energy shown in Fig. 1(b) is thus replaced in Fig. 1(c) by a beam envelope of width 0.01 mrad which is centred on /0 0.25 mrad, i.e. a range of trajectory angles from /0 0.24 to 0.26 mrad. The focus shifts towards the lenses for lower beam energies. Because of this, the beam broadens out across a given image plane due to the range of trajectory angles, even though each separate proton energy produces a well-focused spot. Fig. 1 gives an example of a large energy shift, resulting in a big dispersion in the image plane. Fig. 2 shows an example of much smaller energy shift, such as might be acquired by MeV protons passing through a silicon crystal <1 lm in thickness. This demonstrates the limitations on the energy resolution due to a large object or collimator aperture in this proposed spectrometer. Fig. 2 shows trajectory plots for proton energies of
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2.997, 3.000 and 3.003 MeV (i.e. 3 MeV with dE 0.1%). Note that the box area shown in Fig. 2 is oset from the beam axis by 60 lm in the vertical direction, owing to the eects of spherical aberration changing the location at which the bunches of trajectories are focused. This cannot be seen in Fig. 1 due to the large area shown. The image plane in Fig. 2 is shown by the vertical line, and it has been moved forward by 30 mm compared with Fig. 1. Fig. 2(a) shows the trajectories for each proton with /0 0.24, 0.25, 0.26 mrad, and an object aperture of yo 0, 4 lm. This shows good spatial resolution of the dierent energy bunches, which are each separated by 11 lm across the image plane. These are, of course, very small spatial separations which would not be detectable in a conventional energy spectrometer where the spatial resolution in the image plane is typically 200 lm. However the method described in Section 4 for recording the spatial distribution of transmitted ions takes advantage of the much higher spatial resolution attainable in a microprobe to distinguish small variations in energy. Fig. 2(b) and (c) show respectively the eect of an object aperture size of yo 0, 40 lm and yo 0, 400 lm, where the collimator aperture size is the same as in Fig. 2(a). The spatial separation of the different energies is degraded in Fig. 2(b) compared with Fig. 2(a) since the demagni®ed geometric object size of yi 1.6 lm increases the focused beam spot size for each separate energy. In Fig. 2(c) the separation of the dierent energies is totally destroyed by the use of a very large object aperture. In Fig. 2(d), the object aperture is the same size as in Fig. 2(a), but the collimator aperture is ®ve times larger, giving trajectory angles of /0 0.20, 0.25, 0.30 mrad. Each separate energy is still focused to a small spot, but since the divergence is so large the separation across the image plane is very poor. The size of both the collimator and the object apertures thus aect the spatial resolution in the image plane and hence the attainable energy resolution. Both should be kept as small as possible. From Fig. 2(a) the energy resolution attainable with this system can be estimated. An energy shift
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M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
of dE 0.1% gives a separation of 11 lm in the image plane. The broadening of the distribution across the image plane, which is proportional to the range of trajectory angles, is 0.8 lm for a range of /0 of 0.01 mrad. Under these conditions an estimate of the minimum resolvable energy dierence can be taken as the beam size divided by the dispersion, i.e. dE (0.8/11 lm) 0.1% 0:01%, which is equivalent to 300 eV for a 3 MeV proton beam. A more optimistic estimate, based on the minimum attainable spot size of 100 nm in a microprobe, would give a minimum energy resolution of dE 0:001%. 4. Measuring the spatial distribution of transmitted ions The method proposed to measure the dispersion of dierent proton energies is to use the microprobe dipole scan coils, shown located between the collimator aperture and the quadrupole lenses in Fig. 1(a), to scan the focused beam distribution over a sharp edge, such as a slit blade located in the image plane. Such a slit blade generally has a surface smoothness of better than 1 lm. The cumulative number of protons which are transmitted past this edge is measured using a semiconductor detector located on the beam axis. Since a position sensitive detector is not used, the spatial resolution is not limited by their minimum resolvable pixel size of 100±200 lm. The semiconductor detector thus only records each ion, not measures its energy, so the minimum resolvable energy does not depend on its resolution. This approach has the advantage that no changes are required to the microprobe data acquisition system, which records the cumulative number of transmitted ions as a function of dipole scan amplitude. The recorded linescan can then be dierentiated as a function of dipole scan amplitude to turn the cumulative measure of transmitted ions into a linescan giving the number of measured counts as a function of spatial displacement in the image plane, i.e. as the energy shift. A drawback of this approach is that it gives sequential energy measurement, unlike a position sensitive detector.
This approach only works if the displacement of the focused protons with dierent energies is approximately linear with dipole ®eld strength. For small displacements in the image plane due to magnetic scanning, pthe error in displacement is proportional to dE. In Fig. 2(a) where there is a separation of 11 lm for an energy shift of dE 0.1%, the displacement error is 5 nm, which is negligible. The performance of this spectrometer can now be compared with that designed by Lanford et al. [3]. The change of image plane for dierent energies passing through the magnetic ®eld of their spectrometer was also noted. This was solved by tilting the position sensitive detector array, so that each energy was in focus across its surface. Their spectrometer has an energy dispersion in the image plane of (x/dE) 1.8 mm/%. In comparison, the spectrometer described here gives a dispersion of (x/dE) 110 lm/%. Their spectrometer is designed to measure a wide range of ion energies (88% of the maximum energy entering the spectrometer). At a proton energy of 3 MeV, the maximum scanning range in the image plane for spectrometer described here is 1 mm, giving the ability to measure a maximum range of incident energies of 10%. It should be pointed out that there have been at least two previous examples of the use of quadrupoles as an energy analyser. Enge used a ÔbrezelÕ con®guration, in which the ions entered at an oblique angle into a single quadrupole, to provide energy dispersion. Larson used a similar idea as presented here to separate dierent ion charge states which had passed through the stripper in a tandem accelerator. 5. Conclusions The use of a nuclear microprobe lens system as a high resolution energy spectrometer has been studied, and the experimental conditions necessary to attain good performance have been described. It is calculated that an energy resolution of dE 0:01% is attainable, which compares well with types of energy spectrometer currently used for ion beam analysis. This spectrometer is based
M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
on a very small acceptance angle in order to produce a small focused beam spot. Its use for backscattering measurements would seem to be prohibited by the much smaller intensities encountered than for transmission measurements. It is interesting to note that a ÔSingletronÕ accelerator has recently been constructed, which reports an energy stability of 50 eV at a terminal voltage of 1.881 MV, and 20 eV under normal laboratory conditions [15]. Such an accelerator would enhance the use of this proposed spectrometer by signi®cantly reducing the energy spread of the beam before transmission through the crystal. The maximum trajectory angle which can be used in this system is 0.37 mrad, limited by the diameter of the vacuum pipe running through the lenses. A slightly larger value of /0 could therefore have been chosen to increase the energy dispersion, so long as care is taken to ensure that the trajectories do not hit the beam pipe. This value could be further increased if an oval beam pipe was used [16], where the pipe was longer in the vertical direction such that it protruded between the pole pieces beyond the lens bore radius. This would allow a larger trajectory angle /0 , and hence a larger dispersion. Acknowledgements The authors wish to thank Prof. H. Wollnik for providing helpful comments on this work.
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References [1] W.M. Arnoldbik, W. Wolfswinkel, D.K. Inia, V.C.G. Verleun, S. Lobner, J.A. Reinders, F. Labohm, D.O. Boerma, Nucl. Instr. and Meth. B 118 (1996) 566. [2] H.D. Carstanjen, Nucl. Instr. and Meth. B 136±138 (1998) 1183. [3] W. Lanford, B. Andersberg, H.A. Enge, B. Hjorvarsson, Nucl. Instr. and Meth. B 136±138 (1998) 1177. [4] H.A. Enge, W.W. Buechner, Phys. Rev. 88 (1952) 963. [5] A. Klemperer, Electron Optics, Cambridge University Press, Cambridge, 1953. [6] F.H. Eisen, M.T. Robinson, Phys. Rev. B 4 (1971) 1457. [7] S. Datz, B.R. Appleton, C.D. Moak, D.V. Morgan, in: D.V. Morgan (Ed.), Channeling, Theory, Observation and Applications, ch. 6, Wiley, London, 1973. [8] S. Datz, C.D. Moak, T.S. Noggle, B.R. Appleton, H.O. Lutz, Phys. Rev. 179 (1966) 315. [9] M.B.H. Breese, P.J.M. Smulders, Nucl. Instr. and Meth. B 145 (1998) 346. [10] H.F. Krause, S. Datz, P.F. Dittner, J. Gomez del Campo, P.D. Miller, C.D. Moak, N. Neskovic, P.L. Pepmiller, Phys. Rev. B 33 (1986) 6036. [11] M.B.H. Breese, D.N. Jamieson, P.J.C. King, Materials Analysis Using a Nuclear Microprobe, Wiley, New York, 1996. [12] G.W. Grime, F. Watt, Beam Optics of Quadrupole Probeforming Systems, Adam Hilger, Bristol, 1984. [13] F. Watt, T.F. Choo, K.K. Lee, T. Osipowicz, I. Orlic, S.M. Tang, Nucl. Instr. and Meth. B 104 (1995) 101. [14] D.N. Jamieson, G.J.F. Legge, Nucl. Instr. and Meth. B 29 (1987) 544. [15] D.J.W. Mous, R.G. Haitsma, T. Butz, R.-H. Flagmeyer, D. Lehmann, J. Vogt, Nucl. Instr. and Meth. B 130 (1997) 31. [16] H. Wollnik, Private communication.
www.elsevier.nl/locate/nimb
The use of a magnetic quadrupole triplet as a high resolution ion energy spectrometer M.B.H. Breese a
a,*
, D.N. Jamieson
b
Department of Physics, School of Physical Sciences, University of Surrey, Guildford GU2 5XH, UK b School of Physics, University of Melbourne, Parkville, Vic. 3052, Australia Received 3 November 1998; received in revised form 25 February 1999
Abstract The use of a nuclear microprobe, containing a magnetic quadrupole triplet, as a high resolution energy spectrometer is proposed here. It is calculated that energy dierences of 300 eV can be resolved for 3 MeV protons which are transmitted through thin samples, corresponding to an energy resolution of dE 0:01%. The optics and performance of this energy spectrometer are discussed and compared with other types which are used for ion beam analysis. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 61.80.+p; 07.78.+s; 41.85.Lc Keywords: Energy spectrometry; Quadrupole multiplets; Transmission channeling
1. Introduction In a magnetic or electrostatic energy spectrometer, a backscattered or transmitted ion beam is analysed with high energy resolution in order to improve on that attainable using semiconductor detectors, or other forms of energy measurement. Refs. [1±3] give examples of recently developed energy spectrometers for ion beam analysis, whereas Refs. [4,5] illustrate respectively how long ion and electron spectrometers have been in use. The energy resolution of semiconductor detectors
* Corresponding author. Tel.: +44-1483-876796; fax: +441483-259501; e-mail: [email protected]
is limited to 15 keV, enabling a depth resolution of 10 nm using Rutherford Backscattering Spectrometry. With energy spectrometers, a resolution of 1±2 keV is attainable (i.e. approximately a factor of 10 improvement), enabling a depth resolution of 1 nm or better. This is usually at the expense of a reduced solid angle for collecting the scattered ions and hence a reduced counting rate. Energy spectrometers resolve small dierences in ion energies by passing the backscattered, or transmitted, beam through an electrostatic or magnetic ®eld. The resultant spatial dispersion of the de¯ected ions, due to their momentum (i.e. chromatic) spread, is then measured. The ability to resolve small energy dierences using spectrometers largely depends on their ability to measure
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 2 3 6 - 0
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M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
small spatial dispersions of typically 100±200 lm, which is limited by the resolution of the position sensitive detectors which are commonly used to record the ®nal ion locations in the image plane. The channeling oscillations of ions as they move in regions of dierent electron density between the lattice walls of a crystal result in dierent energy losses as a function of crystal thickness and emergent angle. Another use for energy spectrometers has been to measure small variations in the energy of ions transmitted through thin crystals in channeling alignment, in order to determine the channeled ion stopping power or the oscillation frequency. Such measurements have been carried out using keV protons by Eisen [6] using an electrostatic analyser; higher energies were not be studied owing to insucient ®eld strength. Datz et al. [7,8] measured the energy loss of high-energy heavy ions through thin crystals to observe the dierent planar channeled energy losses of dierent oscillatory groups. The large energy losses made the use of semiconductor detectors to directly measure the transmitted energies possible. The aim of the proposed energy spectrometer described here in this paper is for measurements of the energy loss of MeV light ions, such as protons and helium ions, as a function of emergent angle. These are transmitted in channeling alignment through thin crystals which are located at the object aperture of a microprobe. Ref. [9] describes Monte Carlo simulations of such trajectories, showing the energy losses of ten thousand 3 MeV protons transmitted through the (1 1 0) planes of thin silicon crystals. In simulations through 200 nm thick layers the proton energy loss varied from 2.5 to 5 keV, with variations occurring over small changes of the planar channeling angle of wp 2 mrad. Energy peaks with a width of 100±200 eV were produced when the transmitted beam is collimated in angle to approximately wp =10. An energy resolution of hundreds of eV, with an angular acceptance of 0.2 mrad is thus required from the spectrometer described here. Such a system would also be useful for studies of small energy loss variations due to Ôrainbow channelingÕ eects [10] for MeV protons which are axially channeled through thin crystals.
2. Eect of the chromatic aberration of a quadrupole triplet The use of a multiplet of quadrupole lenses to focus MeV ion beams to spot sizes as small as 100 nm is well established using microprobes [11,12]. The focused beam is ideally mono-energetic, so that the eects of chromatic aberrations cause minimum degradation of the focused beam spot. This causes an ion with a slightly greater momentum to be under-focused in the image plane, and one with slightly less momentum to be over-focused. Whilst the percentage momentum spread, dp, of a charged particle beam, rather than its percentage energy spread, dE, is commonly used to characterise the variation of trajectories through a magnetic ®eld, both de®nitions are used here to best highlight the relationship between the dierent proton energies and their individual trajectories. They are however related by dp dE=2. Since this paper only considers MeV protons, no account is taken of any eects due to dierent charge states. The MeV ion beams used in most microprobes are usually generated by a Van de Graa accelerator, which can give a full-width-at-half-maximum (FWHM) energy spread of 150 eV for a 3 MeV proton beam, i.e. dE 0:005%. During normal microprobe operation, a collimator aperture, which is located symmetrically about the beam axis, is used to de®ne a small acceptance angle into the lens system. This minimises the spatial dispersion in the image plane due to the unwanted eects of chromatic aberrations. The dispersion increases linearly with trajectory angle into the quadrupole triplet. With a focused beam current of approximately 100 pA, the trajectory angles h0 and /0 into the lenses in the horizontal (x) and vertical (y) directions respectively, are typically 0.1 mrad. For the microprobe con®guration using a high-excitation quadrupole triplet shown in Figs. 1 and 2, the chromatic aberration coecients can be expressed as y=/ dp 900 lm/mrad% in the vertical direction, and x=h dp 400 lm/mrad% in the horizontal direction. This gives a total range of vertical displacements in the image plane of 0.5 lm for an energy spread of dE 0:005%. This enables a nuclear microprobe to operate with a
M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
Fig. 1. (a) Plot of proton trajectories in the vertical (upper half) and horizontal (lower half) directions, with trajectory angles of h0 0.25 mrad and /0 0.25 mrad respectively, diverging from the object aperture (xo ,yo ) 0,0 and focused to the microprobe image plane. The proton energies are 2.988, 3.000, 3.012 MeV, i.e. 3.000 MeV dE 4.0%. (b) shows an expanded scale of the trajectories in the vertical direction close to the image plane. (c) shows the same as (b) except with a range of trajectory angles of /0 0.24, 0.25, 0.26 mrad for each beam energy. The outlines of the quadrupole lenses are shown to their correct horizontal scale but their vertical scale is exaggerated.
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typical spatial resolution of 1 lm or better with a beam current of 100 pA, which is used for elemental analysis using a range of ion beam analysis techniques [11]. The best reported spatial resolution with a nuclear microprobe is 100 nm [13], at a very low beam current of 1 fA (i.e. 6000 ions per second), which is used for energy loss imaging using scanning transmission ion microscopy (STIM). This very low beam current is typical of that used in the quadrupole triplet spectrometer described here. In a nuclear microprobe, the eects of chromatic aberrations on the beam which is focused by the quadrupole lenses should be as small as possible, in order to produce the smallest beam spot. However, for use as an energy spectrometer, the opposite eect is required, whereby the spatial dispersion in the image plane due to a small energy spread should be as large as possible, in order to achieve a high measured energy resolution. The eect of an energy spread of a proton beam passing through a high excitation quadrupole triplet can be seen in Fig. 1(a), where the individual quadrupole lenses are numbered 1±3. The trajectories of protons with energies of 2.880, 3.000 and 3.120 MeV (i.e. 3 MeV with dE 4%) are plotted in the horizontal and vertical directions. The proton beam diverges from an object aperture located at 0 on the z axis in Fig. 1(a). These are calculated using the matrix ray-tracing program PRAM [14], with the quadrupole lens strengths remaining the same throughout this paper. This lens system focuses the beam in the image plane, which is 15 cm downstream of the exit face of the last quadrupole. It gives a high demagni®cation of Dx 90 in the horizontal direction and a lower demagni®cation of Dy 25 in the vertical direction. Thus in Fig. 1(a) the beam convergence angle hi in the horizontal direction in the image plane is 3.5 times larger than /i in the vertical direction. However, the dispersion for dierent proton energies is larger in the vertical direction, as indicated by the above chromatic aberration coecients. This eect is shown on an expanded scale in Fig. 1(b), where an energy shift of +4% causes a proton with an angle of /0 0.25 mrad to be displaced by +450 lm in the image plane, compared with a proton with an identical trajectory but with
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Fig. 2. Plot of proton trajectories in the vertical direction, close to the microprobe image plane. The proton energies in each case are 2.997, 3.000, 3.003 MeV, i.e. 3.000 MeV dE 0.1%. (a) With trajectory angles of /0 0.24, 0.25, 0.26 mrad, and object coordinates of yo 0, 4 lm. (b), (c) same as (a) but with object coordinates of yo 0, 40 lm and yo 0, 400 lm, respectively. (d) same as (a) but with trajectory angles of /0 0.20, 0.25, 0.30 mrad.
no energy shift. Similarly a beam energy shift of ÿ4% causes the same trajectory to be over-focused by ÿ450 lm in the image plane. Other quadrupole multiplets, such as a doublet or a quadruplet, could have been chosen here, but since a triplet has the largest chromatic aberration coecients it is best suited for use as an energy spectrometer. During normal microprobe operation, a further reason why the trajectory angles into the lenses are kept as small as possible is to minimise the eects of spherical aberration [11]. This causes a reduction in the lens focal length with increasing trajectory angle. Those protons with a large angle of h0 or /0 are over-focused, as can be seen in Fig. 1(b), where the proton trajectory with no energy shift is displaced from the beam axis in the image plane. Account must therefore be taken of
the eects of both chromatic and spherical aberrations within the quadrupole lenses on the ion trajectories. 3. Use of a quadrupole triplet as an energy spectrometer For the proposed use of a microprobe as an energy spectrometer, the sample is located at the object aperture. The microprobe collimator should be o-set in the vertical direction, as shown in Fig. 1(a), while remaining on the beam axis in the horizontal direction. The vertical direction is chosen because it has the larger chromatic aberration coecient, and since h0 0 the chromatic aberration in the horizontal direction can be
M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
ignored, along with any spherical aberration crossterms which depend on h0 . In this con®guration, ions with dierent energies are dispersed in the image plane, as shown in Fig. 1(b). A dipole ®eld is used to de¯ect a speci®c transmitted beam angle onto the displaced collimator aperture. Consider the required size of the displaced collimator aperture needed to transmit enough beam to carry out the measurement of the spatial dispersion of the transmitted ions in a reasonable time. A geometric spot size in the image plane of 0.1 lm can be achieved with an object aperture full size of xo ,yo 9, 2.5 lm for demagni®cations of Dx 90 and Dy 25. A counting rate of 6000 events per second (equivalent to a beam current of 1 fA), is the maximum available on most microprobe data acquisition systems. A typical beam brightness at the object aperture of B 5 pA/(lm2 mrad2 MeV) for 3 MeV protons may be reduced by a typical factor of 100 [9] after passing through a 1 lm thick silicon crystal. Under these conditions a collimator aperture full size of 0.02 mrad is required for a beam current of 1 fA in the image plane. There are, of course, many combinations of object and collimator aperture sizes which would give the same required current, but this may be taken as a typical example to give the approximate aperture sizes needed. The idealised situation of single trajectories for each separate beam energy shown in Fig. 1(b) is thus replaced in Fig. 1(c) by a beam envelope of width 0.01 mrad which is centred on /0 0.25 mrad, i.e. a range of trajectory angles from /0 0.24 to 0.26 mrad. The focus shifts towards the lenses for lower beam energies. Because of this, the beam broadens out across a given image plane due to the range of trajectory angles, even though each separate proton energy produces a well-focused spot. Fig. 1 gives an example of a large energy shift, resulting in a big dispersion in the image plane. Fig. 2 shows an example of much smaller energy shift, such as might be acquired by MeV protons passing through a silicon crystal <1 lm in thickness. This demonstrates the limitations on the energy resolution due to a large object or collimator aperture in this proposed spectrometer. Fig. 2 shows trajectory plots for proton energies of
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2.997, 3.000 and 3.003 MeV (i.e. 3 MeV with dE 0.1%). Note that the box area shown in Fig. 2 is oset from the beam axis by 60 lm in the vertical direction, owing to the eects of spherical aberration changing the location at which the bunches of trajectories are focused. This cannot be seen in Fig. 1 due to the large area shown. The image plane in Fig. 2 is shown by the vertical line, and it has been moved forward by 30 mm compared with Fig. 1. Fig. 2(a) shows the trajectories for each proton with /0 0.24, 0.25, 0.26 mrad, and an object aperture of yo 0, 4 lm. This shows good spatial resolution of the dierent energy bunches, which are each separated by 11 lm across the image plane. These are, of course, very small spatial separations which would not be detectable in a conventional energy spectrometer where the spatial resolution in the image plane is typically 200 lm. However the method described in Section 4 for recording the spatial distribution of transmitted ions takes advantage of the much higher spatial resolution attainable in a microprobe to distinguish small variations in energy. Fig. 2(b) and (c) show respectively the eect of an object aperture size of yo 0, 40 lm and yo 0, 400 lm, where the collimator aperture size is the same as in Fig. 2(a). The spatial separation of the different energies is degraded in Fig. 2(b) compared with Fig. 2(a) since the demagni®ed geometric object size of yi 1.6 lm increases the focused beam spot size for each separate energy. In Fig. 2(c) the separation of the dierent energies is totally destroyed by the use of a very large object aperture. In Fig. 2(d), the object aperture is the same size as in Fig. 2(a), but the collimator aperture is ®ve times larger, giving trajectory angles of /0 0.20, 0.25, 0.30 mrad. Each separate energy is still focused to a small spot, but since the divergence is so large the separation across the image plane is very poor. The size of both the collimator and the object apertures thus aect the spatial resolution in the image plane and hence the attainable energy resolution. Both should be kept as small as possible. From Fig. 2(a) the energy resolution attainable with this system can be estimated. An energy shift
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of dE 0.1% gives a separation of 11 lm in the image plane. The broadening of the distribution across the image plane, which is proportional to the range of trajectory angles, is 0.8 lm for a range of /0 of 0.01 mrad. Under these conditions an estimate of the minimum resolvable energy dierence can be taken as the beam size divided by the dispersion, i.e. dE (0.8/11 lm) 0.1% 0:01%, which is equivalent to 300 eV for a 3 MeV proton beam. A more optimistic estimate, based on the minimum attainable spot size of 100 nm in a microprobe, would give a minimum energy resolution of dE 0:001%. 4. Measuring the spatial distribution of transmitted ions The method proposed to measure the dispersion of dierent proton energies is to use the microprobe dipole scan coils, shown located between the collimator aperture and the quadrupole lenses in Fig. 1(a), to scan the focused beam distribution over a sharp edge, such as a slit blade located in the image plane. Such a slit blade generally has a surface smoothness of better than 1 lm. The cumulative number of protons which are transmitted past this edge is measured using a semiconductor detector located on the beam axis. Since a position sensitive detector is not used, the spatial resolution is not limited by their minimum resolvable pixel size of 100±200 lm. The semiconductor detector thus only records each ion, not measures its energy, so the minimum resolvable energy does not depend on its resolution. This approach has the advantage that no changes are required to the microprobe data acquisition system, which records the cumulative number of transmitted ions as a function of dipole scan amplitude. The recorded linescan can then be dierentiated as a function of dipole scan amplitude to turn the cumulative measure of transmitted ions into a linescan giving the number of measured counts as a function of spatial displacement in the image plane, i.e. as the energy shift. A drawback of this approach is that it gives sequential energy measurement, unlike a position sensitive detector.
This approach only works if the displacement of the focused protons with dierent energies is approximately linear with dipole ®eld strength. For small displacements in the image plane due to magnetic scanning, pthe error in displacement is proportional to dE. In Fig. 2(a) where there is a separation of 11 lm for an energy shift of dE 0.1%, the displacement error is 5 nm, which is negligible. The performance of this spectrometer can now be compared with that designed by Lanford et al. [3]. The change of image plane for dierent energies passing through the magnetic ®eld of their spectrometer was also noted. This was solved by tilting the position sensitive detector array, so that each energy was in focus across its surface. Their spectrometer has an energy dispersion in the image plane of (x/dE) 1.8 mm/%. In comparison, the spectrometer described here gives a dispersion of (x/dE) 110 lm/%. Their spectrometer is designed to measure a wide range of ion energies (88% of the maximum energy entering the spectrometer). At a proton energy of 3 MeV, the maximum scanning range in the image plane for spectrometer described here is 1 mm, giving the ability to measure a maximum range of incident energies of 10%. It should be pointed out that there have been at least two previous examples of the use of quadrupoles as an energy analyser. Enge used a ÔbrezelÕ con®guration, in which the ions entered at an oblique angle into a single quadrupole, to provide energy dispersion. Larson used a similar idea as presented here to separate dierent ion charge states which had passed through the stripper in a tandem accelerator. 5. Conclusions The use of a nuclear microprobe lens system as a high resolution energy spectrometer has been studied, and the experimental conditions necessary to attain good performance have been described. It is calculated that an energy resolution of dE 0:01% is attainable, which compares well with types of energy spectrometer currently used for ion beam analysis. This spectrometer is based
M.B.H. Breese, D.N. Jamieson / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 153±159
on a very small acceptance angle in order to produce a small focused beam spot. Its use for backscattering measurements would seem to be prohibited by the much smaller intensities encountered than for transmission measurements. It is interesting to note that a ÔSingletronÕ accelerator has recently been constructed, which reports an energy stability of 50 eV at a terminal voltage of 1.881 MV, and 20 eV under normal laboratory conditions [15]. Such an accelerator would enhance the use of this proposed spectrometer by signi®cantly reducing the energy spread of the beam before transmission through the crystal. The maximum trajectory angle which can be used in this system is 0.37 mrad, limited by the diameter of the vacuum pipe running through the lenses. A slightly larger value of /0 could therefore have been chosen to increase the energy dispersion, so long as care is taken to ensure that the trajectories do not hit the beam pipe. This value could be further increased if an oval beam pipe was used [16], where the pipe was longer in the vertical direction such that it protruded between the pole pieces beyond the lens bore radius. This would allow a larger trajectory angle /0 , and hence a larger dispersion. Acknowledgements The authors wish to thank Prof. H. Wollnik for providing helpful comments on this work.
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