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Parallel beams from nuclear microprobe lens systems
Nuclear Instruments and Methods in Physics Research B 181 (2001) 78±82
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Parallel beams from nuclear microprobe lens systems Jacinta den Besten a, Paul Spizzirri a, David N. Jamieson a
a,*
, Alexander D. Dymnikov
b
Microanalytical Research Centre, School of Physics, University of Melbourne, Victoria, 3010, Australia b RARAF, Columbia University, Irvington, NY 10533, USA
Abstract A nuclear microprobe lens system is normally used to focus a diverging beam into a ®ne probe. It does this by making the astigmatism terms in the ®rst-order transfer matrix: x=h and y=/ zero. Thus the position of a ray vector in the image plane (x; y) in the linear approximation will not depend on the divergence of the ray vector in the object plane (h; /). This is accomplished at the expense of magnifying the object divergence by factors h=h and /=/ in the xoz and yoz planes, respectively, leading to relatively steep convergence angles at the Gaussian image plane where the specimen is located. An alternative operation mode of the nuclear microprobe lens system is possible where the convergence angle of the beam after the lens system in the linear approximation is made independent of the divergence angle of the beam prior to the lens system. In this case the terms h=h and /=/ in the ®rst-order transfer matrix are zero. This mode of the lens system does not produce a focused beam, so is most suitable for crystals without lateral structure. As an example, we present measurements from the h0 0 0 1i a-Al2 O3 axis, which show signi®cant improvement in channeling angular widths for planar channeling mode even when compared to the unfocused mode. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 61.85.+p; 41.85.)p; 82.80.Yc; 91.60.Ed Keywords: Ion channeling; Ion optics; Ion beam analysis; Nuclear microprobe
1. Introduction and motivation Many applications of ion beam analysis require a well-collimated beam. Most common of these is the ion channeling technique [1] where an ion beam is directed along the atomic rows of a crystalline material. From analysis of the signal of
* Corresponding author. Tel.: 61-3-8344-5376; fax: 61-39347-4783. E-mail address: [email protected] (D.N. Jamieson).
transmitted [2] or backscattered [3] ions, information about the structure of the crystal can be obtained. Recent work in our laboratory has been directed towards the modeling of the ion channeling process by means of Bloch wave analysis [4]. To fully test this model, accurate channeling angular yield curves are required because subtle differences from the classical theory can be obscured by the beam convergence angle. In these cases, the incident ion beam needs to be collimated to a divergence (or convergence) angle less than the channeling angular width of the crystal being studied [5] so the ion beam may
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 5 6 3 - 8
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
channel into the crystal axes or planes. Studies involving planar channeling are particularly sensitive to the beam divergence as the channeling angular width is smaller than for the crystal axes. For 2 MeV H ion beam in silicon, the channeling angular half-width, w1=2 of the h1 1 0i axis is 0.36° and for the {1 1 0} planes is 0.12° [6]. Under typical operating conditions of the MP2 system in Melbourne (parameters in Table 1), the full beam convergence angle is 0.2°, which, in this case, is therefore unsuitable for accurate planar channeling analysis. The traditional method for collimating the ion beam so that the divergence angle is less than the channeling angular widths is by means of two or more widely spaced apertures so that the divergence of the beam is suciently reduced [7], but not eliminated. Of necessity, this requires discarding some of the original beam current, which is undesirable as low beam currents may prolong the measurement being performed. Stringent collimation, required for testing the Bloch wave model described earlier for planar channeling, may result in an unacceptably low beam current. 2. Method An alternative approach to production of wellcollimated beams is to employ a lens system con-
79
®gured to produce a ``parallel'' beam. We understand ``parallel'' beam in this context as the beam with minimum divergence spread. One possible con®guration is presented here which employs a lens system normally used as a probe-forming lens in a nuclear microprobe. The ion optical properties of a system of lenses and drift spaces may be represented by a transfer matrix: 2
3 2 xi x=x 6 hi 7 6 h=x 6 76 4 yi 5 4 y=x /=x /i
x=h x=y h=h h=y y=h y=y /=h /=y
T
32 3 x=/ xo 6 ho 7 h=/ 7 76 7; y=/ 54 yo 5 /=/ /o
where x h y / de®nes a ray vector travelling in the z-direction (subscript o in the object plane and i in the image plane) with extent and divergence x; h and y; / in the xoz and yoz planes, respectively. The coecients of the transfer matrix depend on the lens excitations, as well as the other physical parameters of the system. In a nuclear microprobe lens system, the lens excitations are adjusted to set the astigmatism coecients x=h and y=/ to zero. In this situation, the position of all rays in the image plane in the linear approximation does not depend on the initial divergence of the rays and hence the system has produced an image of the object on the image plane. In a nuclear microprobe system, the locus of ray vectors from the object is typically set by an object collimator located in the object plane and an aperture collimator located
Table 1 Ion optical parameters of the Melbourne Nuclear Microprobe system Parameter
Value
Unit
Drift: Object to quadrupole lens 1 Length of quadrupole lenses 1 and 4 Length of quadrupole lenses 2 and 3 Drift: Spacing of the lenses Quadrupole lens bore radius Drift: Quadrupole lens 4 to specimen
7.20 0.030 0.060 0.035 6.0 0.15
m m m m mm m
Normal mode (values for 3 MeV H ) Pole tip ®eld of lenses 1 and 4 Pole tip ®eld of lenses 2 and 3
2.15 2.50
kG kG
Parallel mode (values for 3 MeV H ) Pole tip ®eld of lenses 1 and 4 Pole tip ®eld of lenses 2 and 3
0.33 0.45
kG kG
80
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
just upstream of the probe-forming lens system (see Fig. 1). It is possible to operate the system in a different mode to produce a ``parallel'' beam (see Fig. 2). In this case the lens system is adjusted so
Fig. 1. The optical layout of the MP2 system with ray trajectories for the normal mode of operation where the probe forming lens system produces a focused probe on the specimen. The rays traced here originated from the object diaphragm with coordinates (0, 0.1 mr), (0, 0.3 mr), (250 lm, 0.3 mr) in both the xoz and yoz planes. The paths in the xoz and yoz planes are shown above and below the axis, respectively. The vertical lines across the axis around 8.0 m designate (from left to right) the entrance and exit principle planes as well as the Gaussian image plane. Note that the plot commences 6 m downstream of the object.
Fig. 2. The ray trajectories of the MP2 system for the parallel mode where the probe forming lens system is used to produce a parallel beam on the specimen. The initial ray coordinates are the same as for Fig. 1.
that the divergence at the exit of the system in the linear approximation does not depend on the divergence in the object plane. It is therefore necessary for the lens excitations to be adjusted so that the transfer matrix elements h=h and /=/ are set to zero. This calculation may conveniently be performed by the ion optics computer code PRAM [8]. Strictly, the minimum divergence spread achievable in the ``parallel'' beam mode is de®ned by the beam emittance. To obtain this minimum we need to choose, for a given emittance, an appropriate optimal size of the object collimator. In the case of a given divergence spread at the exit of the parallel system this optimal collimator determines the maximum beam current. This additional step of optimisation is not discussed further since it requires detailed knowledge of the ¯ux distribution within the beam phase space which is a strong function of the accelerator. 3. Experiment As a demonstration of the ``parallel'' beam technique, a series of channeling measurements were performed on the Melbourne Nuclear Microprobe system [9]. The optical parameters of this system appear in Table 1. The transfer matrix for the system in the normal con®guration (probe forming lens system) and the parallel con®guration are shown in Table 2. The specimen was a h0 0 0 1i oriented a-sapphire crystal (purchased from Crystal Systems, USA) sputtered with a 25 nm layer of gold to remove charge build-up. The surface had been polished and the dimensions of the crystal were nominally 10 10 0:5 mm3 . The crystal was mounted on the specimen stage goniometer of the MP2 microprobe system in Melbourne. The goniometer is controlled by an automated control system based on a National Instruments Virtual Instrument called GPAQ [10]. The backscattered particles were detected by an uncollimated silicon surface barrier PIPS detector with an area of 100 mm2 at a scattering angle of 145°. GPAQ allowed automated channeling angular yield maps and scans to be obtained normalised to beam charge. A beam
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
81
Table 2 Transfer matrices for the Melbourne Nuclear Microprobe system (units of m, rad) (x)
(h)
(y)
(/)
Normal mode (x) (h) (y) (/)
)0.038 )3.35 0 0
0 )26.4 0 0
0 0 )0.038 )3.35
0 0 0 )26.4
Parallel mode (x) (h) (y) (/)
0.964 )0.122 0 0
of 3.0 MeV H was employed for the measurements reported here as this beam was used in most of the theoretical simulations described earlier and to be reported separately. Channeling angular yield maps and scans were conducted with the lens system in three modes: o, focused to a probe and set in the parallel mode. Adjustment of the lens system to the focused mode was done with reference to a quartz focusing screen. Adjustment of the lens system to the parallel mode was done by setting the lens excitations to the theoretical values from program PRAM. Previous measurements had already shown that
8.17 0 0 0
0 0 0.964 )0.122
0 0 8.17 0
PRAM provides a very accurate model for lens excitation in the focused mode. The dramatic eect of the beam convergence angle on the channeling yield maps from sapphire is shown by the three channeling angular yield maps in Fig. 3. In the case of the focused beam, channeling is only really possible for the axis because the contrast for the planes is very poor. This technique also in¯icted a large amount of damage on the sample because the beam was so intense on a very small area. In the case of the unfocused beam (with the lenses switched o) the divergence angle of the beam is ®xed by the object and ap-
Fig. 3. Channeling angular yield maps of the h0 0 0 1i axis of a hexagonal sapphire crystal for the system in three modes. The analysis beam was 3 MeV H and the backscattered beam was detected using an uncollimated silicon surface barrier PIPS detector with an area of 100 mm2 at a scattering angle of 145°. The yield from the detector was restricted to a 40 keV wide window centred on the surface energy of aluminium. The convergence angle of the beam on the specimen in the three modes is: 0.04° unfocused mode, 0° parallel mode and 1.0° focused mode. The dierences between the unfocused and parallel mode are subtle and shown in more detail in Fig. 4.
82
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
4. Conclusion We have shown that an alternative operating mode of a nuclear microprobe lens system can be used to produce a ``parallel'' beam on the specimen. In the case of the Melbourne MP2 system this results in a signi®cant increase in the channeling angular yield widths of crystal planes for sapphire crystals. Acknowledgements Fig. 4. Channeling angular yield curves taken with the h0 0 0 1i axis of a hexagonal sapphire crystal tilted 1° o the beam direction for the parallel and unfocused mode for the conditions of Fig. 3.
erture collimators of the system. In this case both axial and low-order planar channeling are possible and such maps can readily be used to identify the order of unknown crystal axes [11]. The channeling angular yield map for the parallel mode of the system is also shown in Fig. 3 and this appears super®cially similar to the map for the unfocused mode. Once again, channeling in the axis and the low-order planes is clearly visible. The resolution of the angular steps used to obtain the images in Fig. 3 was about 0.05°. Differences in images between the unfocused and parallel modes are subtle when viewing the maps, close examination reveals dierences in the widths of the high order planes. However, the dierences become very clear if an azimuthal channeling angular yield curve is obtained with higher angular resolution. This is done by tilting the axis o the beam direction by 1.0° and using the goniometer to rotate the axis around the beam direction by 360° and plotting the yield. Curves for both the unfocused and parallel modes are shown in Fig. 4. These data show that the channeling angular widths of the low-order planar channels in the sapphire crystal are 6.5% wider in the case of the parallel mode and up to 30% for the high-order planes. This con®rms the fact that the parallel mode is in fact producing a superior beam collimation for channeling experiments.
We gratefully acknowledge the assistance of Roland Szymanski for operation of the accelerator used to provide the beam used in these measurements and to Les Allen for fruitful discussions. This work has been supported by grants from the Australian Research Council. References [1] D.S. Gemmel, Rev. Mod. Phys. 46 (1974) 129. [2] D.D. Armstrong, W.M. Gibson, H.E. Wegner, Radiat. E. 11 (1971) 241. [3] D.V. Morgan (Ed.), Channeling; Theory Observation and Applications, Wiley, UK, 1973. [4] J.L. den Besten, L.J. Allen, D.N. Jamieson, Phys. Rev. 60 (5) (1999) 3120. [5] S.T. Picraux, J.U. Andersen, Phys. Rev. 186 (1969) 267. [6] J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, USA, 1995. [7] D.D. Armstrong, H.E. Wegner, Rev. Sci. Instrum. 42 (1971) 40. [8] M.B.H. Breese, D.N. Jamieson, P.J.C. King, Materials Analysis with a Nuclear Microprobe, Wiley, New York, 1996, Chapter 3. [9] D.N. Jamieson, Nucl. Instr. and Meth. B 136±138 (1998) 1. [10] P.G. Spizzirri, J.L. den Besten, D.N. Jamieson, in: Proceedings of the Seventh Australian Conference on Nuclear Techniques of Analysis, Lucas Heights, ISSN 1325-1694, 1999, p. 274. [11] J.L. den Besten, D.N. Jamieson, C.G. Ryan, Nucl. Instr. and Meth. B 152 (1999) 135.
www.elsevier.com/locate/nimb
Parallel beams from nuclear microprobe lens systems Jacinta den Besten a, Paul Spizzirri a, David N. Jamieson a
a,*
, Alexander D. Dymnikov
b
Microanalytical Research Centre, School of Physics, University of Melbourne, Victoria, 3010, Australia b RARAF, Columbia University, Irvington, NY 10533, USA
Abstract A nuclear microprobe lens system is normally used to focus a diverging beam into a ®ne probe. It does this by making the astigmatism terms in the ®rst-order transfer matrix: x=h and y=/ zero. Thus the position of a ray vector in the image plane (x; y) in the linear approximation will not depend on the divergence of the ray vector in the object plane (h; /). This is accomplished at the expense of magnifying the object divergence by factors h=h and /=/ in the xoz and yoz planes, respectively, leading to relatively steep convergence angles at the Gaussian image plane where the specimen is located. An alternative operation mode of the nuclear microprobe lens system is possible where the convergence angle of the beam after the lens system in the linear approximation is made independent of the divergence angle of the beam prior to the lens system. In this case the terms h=h and /=/ in the ®rst-order transfer matrix are zero. This mode of the lens system does not produce a focused beam, so is most suitable for crystals without lateral structure. As an example, we present measurements from the h0 0 0 1i a-Al2 O3 axis, which show signi®cant improvement in channeling angular widths for planar channeling mode even when compared to the unfocused mode. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 61.85.+p; 41.85.)p; 82.80.Yc; 91.60.Ed Keywords: Ion channeling; Ion optics; Ion beam analysis; Nuclear microprobe
1. Introduction and motivation Many applications of ion beam analysis require a well-collimated beam. Most common of these is the ion channeling technique [1] where an ion beam is directed along the atomic rows of a crystalline material. From analysis of the signal of
* Corresponding author. Tel.: 61-3-8344-5376; fax: 61-39347-4783. E-mail address: [email protected] (D.N. Jamieson).
transmitted [2] or backscattered [3] ions, information about the structure of the crystal can be obtained. Recent work in our laboratory has been directed towards the modeling of the ion channeling process by means of Bloch wave analysis [4]. To fully test this model, accurate channeling angular yield curves are required because subtle differences from the classical theory can be obscured by the beam convergence angle. In these cases, the incident ion beam needs to be collimated to a divergence (or convergence) angle less than the channeling angular width of the crystal being studied [5] so the ion beam may
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 5 6 3 - 8
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
channel into the crystal axes or planes. Studies involving planar channeling are particularly sensitive to the beam divergence as the channeling angular width is smaller than for the crystal axes. For 2 MeV H ion beam in silicon, the channeling angular half-width, w1=2 of the h1 1 0i axis is 0.36° and for the {1 1 0} planes is 0.12° [6]. Under typical operating conditions of the MP2 system in Melbourne (parameters in Table 1), the full beam convergence angle is 0.2°, which, in this case, is therefore unsuitable for accurate planar channeling analysis. The traditional method for collimating the ion beam so that the divergence angle is less than the channeling angular widths is by means of two or more widely spaced apertures so that the divergence of the beam is suciently reduced [7], but not eliminated. Of necessity, this requires discarding some of the original beam current, which is undesirable as low beam currents may prolong the measurement being performed. Stringent collimation, required for testing the Bloch wave model described earlier for planar channeling, may result in an unacceptably low beam current. 2. Method An alternative approach to production of wellcollimated beams is to employ a lens system con-
79
®gured to produce a ``parallel'' beam. We understand ``parallel'' beam in this context as the beam with minimum divergence spread. One possible con®guration is presented here which employs a lens system normally used as a probe-forming lens in a nuclear microprobe. The ion optical properties of a system of lenses and drift spaces may be represented by a transfer matrix: 2
3 2 xi x=x 6 hi 7 6 h=x 6 76 4 yi 5 4 y=x /=x /i
x=h x=y h=h h=y y=h y=y /=h /=y
T
32 3 x=/ xo 6 ho 7 h=/ 7 76 7; y=/ 54 yo 5 /=/ /o
where x h y / de®nes a ray vector travelling in the z-direction (subscript o in the object plane and i in the image plane) with extent and divergence x; h and y; / in the xoz and yoz planes, respectively. The coecients of the transfer matrix depend on the lens excitations, as well as the other physical parameters of the system. In a nuclear microprobe lens system, the lens excitations are adjusted to set the astigmatism coecients x=h and y=/ to zero. In this situation, the position of all rays in the image plane in the linear approximation does not depend on the initial divergence of the rays and hence the system has produced an image of the object on the image plane. In a nuclear microprobe system, the locus of ray vectors from the object is typically set by an object collimator located in the object plane and an aperture collimator located
Table 1 Ion optical parameters of the Melbourne Nuclear Microprobe system Parameter
Value
Unit
Drift: Object to quadrupole lens 1 Length of quadrupole lenses 1 and 4 Length of quadrupole lenses 2 and 3 Drift: Spacing of the lenses Quadrupole lens bore radius Drift: Quadrupole lens 4 to specimen
7.20 0.030 0.060 0.035 6.0 0.15
m m m m mm m
Normal mode (values for 3 MeV H ) Pole tip ®eld of lenses 1 and 4 Pole tip ®eld of lenses 2 and 3
2.15 2.50
kG kG
Parallel mode (values for 3 MeV H ) Pole tip ®eld of lenses 1 and 4 Pole tip ®eld of lenses 2 and 3
0.33 0.45
kG kG
80
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
just upstream of the probe-forming lens system (see Fig. 1). It is possible to operate the system in a different mode to produce a ``parallel'' beam (see Fig. 2). In this case the lens system is adjusted so
Fig. 1. The optical layout of the MP2 system with ray trajectories for the normal mode of operation where the probe forming lens system produces a focused probe on the specimen. The rays traced here originated from the object diaphragm with coordinates (0, 0.1 mr), (0, 0.3 mr), (250 lm, 0.3 mr) in both the xoz and yoz planes. The paths in the xoz and yoz planes are shown above and below the axis, respectively. The vertical lines across the axis around 8.0 m designate (from left to right) the entrance and exit principle planes as well as the Gaussian image plane. Note that the plot commences 6 m downstream of the object.
Fig. 2. The ray trajectories of the MP2 system for the parallel mode where the probe forming lens system is used to produce a parallel beam on the specimen. The initial ray coordinates are the same as for Fig. 1.
that the divergence at the exit of the system in the linear approximation does not depend on the divergence in the object plane. It is therefore necessary for the lens excitations to be adjusted so that the transfer matrix elements h=h and /=/ are set to zero. This calculation may conveniently be performed by the ion optics computer code PRAM [8]. Strictly, the minimum divergence spread achievable in the ``parallel'' beam mode is de®ned by the beam emittance. To obtain this minimum we need to choose, for a given emittance, an appropriate optimal size of the object collimator. In the case of a given divergence spread at the exit of the parallel system this optimal collimator determines the maximum beam current. This additional step of optimisation is not discussed further since it requires detailed knowledge of the ¯ux distribution within the beam phase space which is a strong function of the accelerator. 3. Experiment As a demonstration of the ``parallel'' beam technique, a series of channeling measurements were performed on the Melbourne Nuclear Microprobe system [9]. The optical parameters of this system appear in Table 1. The transfer matrix for the system in the normal con®guration (probe forming lens system) and the parallel con®guration are shown in Table 2. The specimen was a h0 0 0 1i oriented a-sapphire crystal (purchased from Crystal Systems, USA) sputtered with a 25 nm layer of gold to remove charge build-up. The surface had been polished and the dimensions of the crystal were nominally 10 10 0:5 mm3 . The crystal was mounted on the specimen stage goniometer of the MP2 microprobe system in Melbourne. The goniometer is controlled by an automated control system based on a National Instruments Virtual Instrument called GPAQ [10]. The backscattered particles were detected by an uncollimated silicon surface barrier PIPS detector with an area of 100 mm2 at a scattering angle of 145°. GPAQ allowed automated channeling angular yield maps and scans to be obtained normalised to beam charge. A beam
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
81
Table 2 Transfer matrices for the Melbourne Nuclear Microprobe system (units of m, rad) (x)
(h)
(y)
(/)
Normal mode (x) (h) (y) (/)
)0.038 )3.35 0 0
0 )26.4 0 0
0 0 )0.038 )3.35
0 0 0 )26.4
Parallel mode (x) (h) (y) (/)
0.964 )0.122 0 0
of 3.0 MeV H was employed for the measurements reported here as this beam was used in most of the theoretical simulations described earlier and to be reported separately. Channeling angular yield maps and scans were conducted with the lens system in three modes: o, focused to a probe and set in the parallel mode. Adjustment of the lens system to the focused mode was done with reference to a quartz focusing screen. Adjustment of the lens system to the parallel mode was done by setting the lens excitations to the theoretical values from program PRAM. Previous measurements had already shown that
8.17 0 0 0
0 0 0.964 )0.122
0 0 8.17 0
PRAM provides a very accurate model for lens excitation in the focused mode. The dramatic eect of the beam convergence angle on the channeling yield maps from sapphire is shown by the three channeling angular yield maps in Fig. 3. In the case of the focused beam, channeling is only really possible for the axis because the contrast for the planes is very poor. This technique also in¯icted a large amount of damage on the sample because the beam was so intense on a very small area. In the case of the unfocused beam (with the lenses switched o) the divergence angle of the beam is ®xed by the object and ap-
Fig. 3. Channeling angular yield maps of the h0 0 0 1i axis of a hexagonal sapphire crystal for the system in three modes. The analysis beam was 3 MeV H and the backscattered beam was detected using an uncollimated silicon surface barrier PIPS detector with an area of 100 mm2 at a scattering angle of 145°. The yield from the detector was restricted to a 40 keV wide window centred on the surface energy of aluminium. The convergence angle of the beam on the specimen in the three modes is: 0.04° unfocused mode, 0° parallel mode and 1.0° focused mode. The dierences between the unfocused and parallel mode are subtle and shown in more detail in Fig. 4.
82
J. den Besten et al. / Nucl. Instr. and Meth. in Phys. Res. B 181 (2001) 78±82
4. Conclusion We have shown that an alternative operating mode of a nuclear microprobe lens system can be used to produce a ``parallel'' beam on the specimen. In the case of the Melbourne MP2 system this results in a signi®cant increase in the channeling angular yield widths of crystal planes for sapphire crystals. Acknowledgements Fig. 4. Channeling angular yield curves taken with the h0 0 0 1i axis of a hexagonal sapphire crystal tilted 1° o the beam direction for the parallel and unfocused mode for the conditions of Fig. 3.
erture collimators of the system. In this case both axial and low-order planar channeling are possible and such maps can readily be used to identify the order of unknown crystal axes [11]. The channeling angular yield map for the parallel mode of the system is also shown in Fig. 3 and this appears super®cially similar to the map for the unfocused mode. Once again, channeling in the axis and the low-order planes is clearly visible. The resolution of the angular steps used to obtain the images in Fig. 3 was about 0.05°. Differences in images between the unfocused and parallel modes are subtle when viewing the maps, close examination reveals dierences in the widths of the high order planes. However, the dierences become very clear if an azimuthal channeling angular yield curve is obtained with higher angular resolution. This is done by tilting the axis o the beam direction by 1.0° and using the goniometer to rotate the axis around the beam direction by 360° and plotting the yield. Curves for both the unfocused and parallel modes are shown in Fig. 4. These data show that the channeling angular widths of the low-order planar channels in the sapphire crystal are 6.5% wider in the case of the parallel mode and up to 30% for the high-order planes. This con®rms the fact that the parallel mode is in fact producing a superior beam collimation for channeling experiments.
We gratefully acknowledge the assistance of Roland Szymanski for operation of the accelerator used to provide the beam used in these measurements and to Les Allen for fruitful discussions. This work has been supported by grants from the Australian Research Council. References [1] D.S. Gemmel, Rev. Mod. Phys. 46 (1974) 129. [2] D.D. Armstrong, W.M. Gibson, H.E. Wegner, Radiat. E. 11 (1971) 241. [3] D.V. Morgan (Ed.), Channeling; Theory Observation and Applications, Wiley, UK, 1973. [4] J.L. den Besten, L.J. Allen, D.N. Jamieson, Phys. Rev. 60 (5) (1999) 3120. [5] S.T. Picraux, J.U. Andersen, Phys. Rev. 186 (1969) 267. [6] J.R. Tesmer, M. Nastasi (Eds.), Handbook of Modern Ion Beam Materials Analysis, Materials Research Society, USA, 1995. [7] D.D. Armstrong, H.E. Wegner, Rev. Sci. Instrum. 42 (1971) 40. [8] M.B.H. Breese, D.N. Jamieson, P.J.C. King, Materials Analysis with a Nuclear Microprobe, Wiley, New York, 1996, Chapter 3. [9] D.N. Jamieson, Nucl. Instr. and Meth. B 136±138 (1998) 1. [10] P.G. Spizzirri, J.L. den Besten, D.N. Jamieson, in: Proceedings of the Seventh Australian Conference on Nuclear Techniques of Analysis, Lucas Heights, ISSN 1325-1694, 1999, p. 274. [11] J.L. den Besten, D.N. Jamieson, C.G. Ryan, Nucl. Instr. and Meth. B 152 (1999) 135.