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Energy loss of channeled protons in Al single crystal
NUCLEAR
INSTRUMENTS
AND
METHODS
I32
(I976)
I03-IO7;
©
NORTH-HOLLAND
PUBLISHING
CO.
ENERGY L O S S OF C H A N N E L E D P R O T O N S IN AI SINGLE CRYSTAL K.G.
PRASAD and R.P. SHARMA
Tata Institute of Fundamental Research, Bombay, lndia T w o s t r o n g resonances in the 27Al(p,~)24Mg reaction at p r o t o n energies 1365 keV a n d 1726 keV respectively are used to investigate the energy loss o f p r o t o n s in an AI single crystal along the channeled direction. T h e incident p r o t o n energy for the 1726 keV resonance has been adjusted at 1735, 1760 a n d 1786 keV respectively, so that the resonance occurs at depths 0.35, 1.0 a n d 1.9/~m respectively. T h e widening o f the observed ~t-peak on the low energy side a n d the e n h a n c e m e n t in the c o u n t i n g rate between the backscattered p r o t o n edge a n d the ~-peak for the aligned incidence as c o m p a r e d to the r a n d o m incidence h a s clearly s h o w n a wide distribution in the energy loss o f p r o t o n s incident along the ( 1 1 0 ) direction. Pile-up effects are suitably taken into account. Quantitative analysis o f the distribution in the energy loss is m a d e to s h o w that it m a y n o t be very appropriate to use an average energy loss for the particles incident along a crystallographic direction.
1. Introduction The charged particle channeling technique has been extensively used in the study of structural defects 1) and impurities 2) in single crystals. In carrying out such studies as a function of depth, Bogh 1) has shown that wide angle scattering of charged particles can be effectively used provided the random and channelled energy loss of incident particles in the target material are known. The random stopping power is well known3), but for the particles incident along a low index direction a straight forward procedure is not applicable. We know that whenever charged particles are incident parallel to a crystallographic direction in a single crystal, the probability of their interaction with lattice atoms is considerably reduced and they travel relatively longer paths in the crystal. However, due to various reasons, some of these particles incident in a channel undergo dechanneling even at or very near the surface, and get scattered from the lattice atoms. The degree of dechanneling increases with increasing depths. It is thus difficult to get a unique value for the energy loss of such particles incident along a channel, even though different values for their energy loss ranging from 0.6 to 1.0 (sometimes even more than unity) times the random value have been reported in the literature4-7). Feldman and Appelton 8) suggest that the stopping power obtained from transmission measurements with thin single crystals can be treated as a lower limit for use in the scattering experiment. They further proceed to obtain an "upper limit" by resonance elastic scattering of protons while treating planar channeling in silicon single crystals. In general an average channeled energy loss has been suggested for analysis of wide angle scattering measurements. On the other hand Bottiger and Eisen 9) from their recent measurements have concluded that the stopping power
to be used in dechanneling experiments and localization studies of substitutional impurities should be the random stopping power. They also say that in the case of a buried damage layer the appropriate stopping power should be about 15 % higher than the peak value, as taken from standard transmission experiments. In the present work it is shown unambiguously that at a particular depth in the crystal there is a wide distribution in the energy loss of the particles incident along a crystallographic direction and this distribution increases with the depth. It is therefore not very appropriate to use an average energy loss for such particles. A1 single crystals have been used for these investigations as the radiation damage caused to these crystals during the measurements are negligibly small at the proton doses involved. Use has been made of two strong resonances in the 27Al(p, 0t)24Mg reaction at proton energies 1365 keV and 1726keV. The resonance nature of the reaction defines the depth at which the reaction takes place and hence the energy of the outgoing ~-particle. 2. Experimental details and results The measurements have been carried out partly at the 2 MeV Van de Graaff machine at the Institute of Physics, Aarhus University, Denmark and partly at the 5.5 MeV machine at BARC, Trombay, India. A well collimated (0.5 ram×0.5 ram) beam of protons of required energy is allowed to fall on an AI single crystal (thickness 3 ram) mounted on a double axis goniometer. The crystal is surrounded by a cold trap cooled to liquid nitrogen temperature to reduce the carbon build-up on its surface during the measurement. A negative voltage ( - 2 0 0 V) applied to the cold trap serves to suppress the secondary electrons. The emerIII. E L E C T R O N I C
STOPPING
104
K. G. P R A S A D A N D R. P. S H A R M A
gent a-particles following the (p, a) resonance reaction in A1, are detected in a surface barrier detector (energy resolution ~ 16 keV for 5 MeV ~-particles) kept in the backward direction at an angle of 150 ° with respect to the incident beam. The pile-up effects have been minimized by keeping the incident beam current small ( ~ 5 hA) and also using an amplifier with a short time constant (0.1/is × 0.1/~s). First the A1 single crystal was aligned along the ( l l 0 ) direction in the usual way by the channeling technique, using a 2 MeV a-beam. In this high purity well polished crystal, a 33-fold dip was observed along the (110) axis for the c~-particles, backscattered from just below the surface. The incident beam was then changed to protons and its energy was adjusted at 1400 keV, i.e. 35 keV above the (p, c0 resonance at 1365 keV proton energy in A1 and the emergent ~particle and scattered proton energy spectra were recorded in a multichannel analyser. The spectra were taken for two orientations of the crystal, one in which the proton beam was aligned with the (110) axis and the other in which it was along a random direction. In the latter case the (p, a) resonance occurred at a depth of 0.93/~m in A1, corresponding to an energy loss of 35 keV for the incident protons. As the Q-value of the reaction is 1600 keV, the emergent ~-particles are well separated in energy from the backscattered proton edge, as seen in fig. I. Here the a-peak resulting from
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Fig. 1. Backscattered proton and c<-particle energy spectra for 1400keV protons incident on an AI single crystal along a r a n d o m direction (o) and parallel to (110> axis ( × ) respectively. The c<-peak corresponds to the ZTAl(p,~)Z4Mg resonance reaction at an energy o f 1365 keV for the incident protons.
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Fig. 2. Backscattered proton and ~-particle energy spectra for (a) 1735 keV, (b) 1760 keV and (c) 1786 keV protons incident on an A1 single crystal along a random direction (o) and parallel to the (110) axis ( × ) respectively. The c~-peak in each case is due to the ~TAl(p, c0~4Mg resonance reaction at an incident proton energy o f 1726 keV. The integrated proton current for the random and aligned incidence respectively is (a) 7.7/~C and 90/~C, (b) 10/~C and 100 # C and (c) 10/~C and 60/~C. The energy calibrations are (a) 4.04 keV per channel, (b) 4.29 keV per channel and (c) 6.38 keV per channel. The backscattered proton edge (150 °) and the c~-peak are at energies (a) 1529 keV, 2494 keV (b) 1551 keV, 2341 keV and (c) 1574 keV, 2129 keV respectively. The increase in the width o f the ~-peak (full width at half maximum) for aligned incidence as compared to the random incidence is (a) 76 keV and (b) 197 keV.
E N E R G Y LOSS OF C H A N N E L E D
the protons incident along the (110) direction is much wider ( ~ 5 0 % ) on the low energy side as compared to the one arising from random incidence. Also in the former case there is considerable enhancement in the counting rate in the region between the e-peak and the backscattered proton edge. This could be due to pileup effects, since the proton beam current in the above two cases was kept approximately the same, 3.5 hA, while the dose was adjusted to get approximately the same intensity at the e-peak. The dechanneling effects at different depths were investigated by carrying out the measurements at three proton energies: Ep=1735, 1760 and 1786keV respectively, each time the proton beam incident successively in the aligned ((110)) and random directions. At these energies, for the protons incident in the random direction the 1726 keV Al(p, e) reso50XIO 4
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nance will correspond to reaction depths of 0.35, 1.0 and 1.9/tm respectively. The e-particle spectra following the resonance along with the backscattered proton edge are shown in fig. 2. It is clearly seen that in the aligned case the e-peak is wider at the low energy side and this width increases with the depth. Similarly the shape of the spectrum in the region between the e-peak and backscattered proton edge is markedly different and sensitive to the incident proton energy, i.e. the depth at which the reaction is taking place in the two cases of random and aligned incidences; the counting rate in that region particularly in the aligned case is enhanced and this increase is depth-dependent. Such an increase in the counting rate could arise due to different pile-up rates because of the difference in the proton dose even though the incident current for the two directions was approximately the same. A separate experiment was carried out at Ep = 1760 keV, keeping the proton dose equal, both for the random as well as aligned incidence. In order to have the same pile-up rates in these two cases the proton current in the random case was correspondingly reduced. This reduction was in the same proportion as that in the minimum scattering yield, Xmi,, when the proton beam was aligned along the (110) axis in the crystal. The resulting spectra are shown in fig. 3. Examining once again that part of the spectrum between the e-peak and scattered proton edge, one finds an enhancement in the counting rate for the aligned case, even though the quality of the Al-crystal used for this purpose (Zm~,~30%) was not as good as the earlier ones (Xml. ~ 3 %). It may be mentioned here that the poorer quality of the crystal turned out to be advantageous; otherwise it would have been necessary to reduce the proton current by a factor of 30, in the case of random incidence, rendering the control of the accelerator difficult.
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Fig. 3. The energy spectra o f backscattered proton and or-particles following 1726 keV (p,~)resonance in Al for the r a n d o m (.) and aligned ( x ) incidence respectively. The incident p r o t o n energy is 1760 keV. The backscattered 0 5 0 °) p r o t o n edge and the ~-peaks are at energies 1533 and 2260 keV. The (p,c¢) resonance occurs at a depth of 1/~m in the Al single crystal when the 1760 keV proton beam is incident along a r a n d o m direction. The ~particle energy at resonance is 2530 keV. The total p r o t o n dose has been kept the same for the two cases o f r a n d o m and aligned incidence.
The comparison of the shapes of the (p, e) resonance spectra in the A1 single crystal for protons incident in a random direction and parallel to the (110) crystallographic direction figs. 1, 2 and 3 have clearly shown in the latter case (a) the enhancement in the width of the e-peak on the low energy side and (b) an increase in the counting rate in the region between the e-peak and the backscattered proton edge. The width of the e-peak for the random incidence is due to detector resolution, natural width of the resonance and the straggling in the energy loss of the incident protons and emergent e-particles in traversing the Al-crystal. The enhanceIlI. ELECTRONIC
STOPPING
106
K. G. P R A S A D
AND
ments (a) and (b) above for the aligned incidence thus clearly indicate that in this case there is a considerable distribution in the energy loss of the incident protons, due to which the (p, ~) resonance reaction occurs at different depths causing a large spread in the energy of the a-particles emerging out of the crystal surface following the resonance. As long as the incident protons remain in the channel they never approach a nucleus sufficiently close so as to interact with it. However for various reasons the particles are lost from the channel, their number increasing with the distance traversed in the crystal, and once lost from the channel they behave in the same manner as the random beam. Hence for a proton beam of finite energy incident parallel to a crystallographic direction, the variation in the energy loss of protons which ultimately causes a large spread in the emergent a-particle energy is due to an increase in the random fraction of the incident aligned beam with increasing penetration into the crystal along that axis as a result of proton escape from the channel. In the figs. 2a and b, it is clearly seen that as the incident proton energy is increased from 1735 keV to 1760 keV for which the corresponding increase in the 1726 keV Al(p, ~) resonance reaction depth is 0.65/~m for random incidence, the increase in the width (fwhm) of the observed a-peaks following the resonance reaction at the two depth, 0.35 and 1/~m respectively is about 76 keV (i.e. 113 keV to 189 keV). However, when the beam is aligned in the ( l l 0 ) direction the same increase is 197 keV, i.e. the fwhm changes from 129 keV to 326 keV. When the incident energy of protons is increased to 1786 keV in which case the (p, ~) resonance will occur at 1.9/~m the observed peak becomes so wide (fig. 2c) that it is difficult to fix any value for the width. In this measurement, in order to compare the widths more accurately, the a-peak intensities are almost kept the same and hence a larger dose of the incident protons has been given in the aligned case. The radiation damage effects are negligible. The analysis of the spectra taken with the incident beam parallel to the (110) axis is done by fitting the a-peak line shape as observed in the corresponding case of random incidence. Apart from the observed widening of the a-peak on the low energy side (figs. 2a, b, c) the enhancement in the counting rate in the region between the backscattered proton edge and a-peak clearly indicates that a sizeable fraction of the incident proton beam remains channeled even at larger depths. In a separate measurement where the uncertainty due to pile-up effects is removed the analysis of the observed spectra shows clearly (fig. 3) the following:
R. P. S H A R M A
a) At a depth of 1 ~m there is 50 % attenuation in the yield of a-particles when the incident beam is aligned along the (110) axis. b) The increase in the width of the a-peak is 73 keV for the aligned incidence (i.e. from 145 keV in the random case to 218 keV in the aligned case). The ~width for the random incidence here (fig. 3, 145 keV) is less than that mentioned in the above measurement (fig. 2b, 189 keV) because of somewhat poorer resolution of the detector used in that case. It should also be noted that the increase in the widths in the two cases (fig. 2b, 137 keV and fig. 3, 73 keV) is almost double even though the incident proton energy is the same (1760keV). This difference arises mainly due to a better crystal used in the measurements given in fig. 2 as compared to the ones given in fig. 3 and hence in the latter case for the same aligned incident proton energy (1760keV) the a-particles following (p,~) resonance will be produced at a greater depth. In the measurements of fig. 2 even though the integrated proton current for aligned incidence was much higher, the radiation damage effects in A1 were found to be negligible for the proton doses used here. c) In the spectra given in fig. 3 the a-peak is clearly separated by about 300 keV from the backscattered proton edge and in this region the increase in the counting rate for the aligned incidence is 20 % of the total random value. The above discussion has very clearly brought out the fact that for the t760 keV proton beam incident parallel to the (110) axis of an A1 single crystal, 50 % of the incident particles remain channeled at a depth of 1/~m, 24 % of these get dechanneled in the immediate neighbourhood after crossing this depth as reflected in the widening of the a-peak, while 20 % get dechanneled gradually beyond this depth. The dechanneling rate is very much depth-dependent and is also affected by the quality of the crystal. It can therefore be said that a large uncertainty is brought in due to the changing fraction of the initially aligned beam, getting deehanneled at different depths in the crystal, and it may not be very correct to use an average value for the energy loss in such cases. Repeating the measurements of fig. 3 at a few more incident proton energies above the resonance will bring out additional quantitative information.
We are grateful to Erik Bogh and J. U. Andersen for many interesting discussions on the subject. One of us (K.G.P.) wishes to acknowledge a grant from D A N I D A during his stay in Aarhus, Denmark.
E N E R G Y LOSS OF C H A N N E L E D P R O T O N S
References 1) E. Bogh, Can. J. Phys. 46 (1968) 653. 2) j. W. Mayer, L. Eriksson and J. A. Davies, Ion implantation in semi-conductors (Academic Press, New York, 1970). a) L. C. Northcliffe and R. F. Schilling, Nucl. Data Tables AT, no. 3 (1970) 4. 4) j. A. Davies, J. Denhartog and J. L. Whitton, Phys. Rev. 165 (1968) 345. 5) R. Hellborg, Physica Scripta 4 (1971) 75; R . D . Edge and R . L . Dixon, Atomic collision phenomena in solids (Eds. D . W . Palmer, M . W . Thompson and P . D . Townsend;
107
North-Holland Publ. Co., Amsterdam, 1970) p. 435. 6) j. A. Davies, L. M. Howe, D. A. Marsden and J. L. Whitton, Atomic collisions in solids (Eds. S. Andersen, K. B. Bjorkquist, K. Domeij and N. G. E. Johansson; Gordon and Breach London, New York and Paris, 1972) p. 208. See also other related works in same reference. 7) G. Gotz, K. D. Kimgl and U. Finger, Proc. 3rd Int. Conf. on Atomic collisions in solids, Gatlinburg, U.S.A. September 1973 (Plenum Press, to be published). 8) L. C. Feldman and B. R. Appleton, Phys. Rev. B8 (1973) 935. 9) j. Bottiger and F. H. Eisen, Thin Solid Films 19 (1973) 239.
III. E L E C T R O N I C S T O P P I N G
INSTRUMENTS
AND
METHODS
I32
(I976)
I03-IO7;
©
NORTH-HOLLAND
PUBLISHING
CO.
ENERGY L O S S OF C H A N N E L E D P R O T O N S IN AI SINGLE CRYSTAL K.G.
PRASAD and R.P. SHARMA
Tata Institute of Fundamental Research, Bombay, lndia T w o s t r o n g resonances in the 27Al(p,~)24Mg reaction at p r o t o n energies 1365 keV a n d 1726 keV respectively are used to investigate the energy loss o f p r o t o n s in an AI single crystal along the channeled direction. T h e incident p r o t o n energy for the 1726 keV resonance has been adjusted at 1735, 1760 a n d 1786 keV respectively, so that the resonance occurs at depths 0.35, 1.0 a n d 1.9/~m respectively. T h e widening o f the observed ~t-peak on the low energy side a n d the e n h a n c e m e n t in the c o u n t i n g rate between the backscattered p r o t o n edge a n d the ~-peak for the aligned incidence as c o m p a r e d to the r a n d o m incidence h a s clearly s h o w n a wide distribution in the energy loss o f p r o t o n s incident along the ( 1 1 0 ) direction. Pile-up effects are suitably taken into account. Quantitative analysis o f the distribution in the energy loss is m a d e to s h o w that it m a y n o t be very appropriate to use an average energy loss for the particles incident along a crystallographic direction.
1. Introduction The charged particle channeling technique has been extensively used in the study of structural defects 1) and impurities 2) in single crystals. In carrying out such studies as a function of depth, Bogh 1) has shown that wide angle scattering of charged particles can be effectively used provided the random and channelled energy loss of incident particles in the target material are known. The random stopping power is well known3), but for the particles incident along a low index direction a straight forward procedure is not applicable. We know that whenever charged particles are incident parallel to a crystallographic direction in a single crystal, the probability of their interaction with lattice atoms is considerably reduced and they travel relatively longer paths in the crystal. However, due to various reasons, some of these particles incident in a channel undergo dechanneling even at or very near the surface, and get scattered from the lattice atoms. The degree of dechanneling increases with increasing depths. It is thus difficult to get a unique value for the energy loss of such particles incident along a channel, even though different values for their energy loss ranging from 0.6 to 1.0 (sometimes even more than unity) times the random value have been reported in the literature4-7). Feldman and Appelton 8) suggest that the stopping power obtained from transmission measurements with thin single crystals can be treated as a lower limit for use in the scattering experiment. They further proceed to obtain an "upper limit" by resonance elastic scattering of protons while treating planar channeling in silicon single crystals. In general an average channeled energy loss has been suggested for analysis of wide angle scattering measurements. On the other hand Bottiger and Eisen 9) from their recent measurements have concluded that the stopping power
to be used in dechanneling experiments and localization studies of substitutional impurities should be the random stopping power. They also say that in the case of a buried damage layer the appropriate stopping power should be about 15 % higher than the peak value, as taken from standard transmission experiments. In the present work it is shown unambiguously that at a particular depth in the crystal there is a wide distribution in the energy loss of the particles incident along a crystallographic direction and this distribution increases with the depth. It is therefore not very appropriate to use an average energy loss for such particles. A1 single crystals have been used for these investigations as the radiation damage caused to these crystals during the measurements are negligibly small at the proton doses involved. Use has been made of two strong resonances in the 27Al(p, 0t)24Mg reaction at proton energies 1365 keV and 1726keV. The resonance nature of the reaction defines the depth at which the reaction takes place and hence the energy of the outgoing ~-particle. 2. Experimental details and results The measurements have been carried out partly at the 2 MeV Van de Graaff machine at the Institute of Physics, Aarhus University, Denmark and partly at the 5.5 MeV machine at BARC, Trombay, India. A well collimated (0.5 ram×0.5 ram) beam of protons of required energy is allowed to fall on an AI single crystal (thickness 3 ram) mounted on a double axis goniometer. The crystal is surrounded by a cold trap cooled to liquid nitrogen temperature to reduce the carbon build-up on its surface during the measurement. A negative voltage ( - 2 0 0 V) applied to the cold trap serves to suppress the secondary electrons. The emerIII. E L E C T R O N I C
STOPPING
104
K. G. P R A S A D A N D R. P. S H A R M A
gent a-particles following the (p, a) resonance reaction in A1, are detected in a surface barrier detector (energy resolution ~ 16 keV for 5 MeV ~-particles) kept in the backward direction at an angle of 150 ° with respect to the incident beam. The pile-up effects have been minimized by keeping the incident beam current small ( ~ 5 hA) and also using an amplifier with a short time constant (0.1/is × 0.1/~s). First the A1 single crystal was aligned along the ( l l 0 ) direction in the usual way by the channeling technique, using a 2 MeV a-beam. In this high purity well polished crystal, a 33-fold dip was observed along the (110) axis for the c~-particles, backscattered from just below the surface. The incident beam was then changed to protons and its energy was adjusted at 1400 keV, i.e. 35 keV above the (p, c0 resonance at 1365 keV proton energy in A1 and the emergent ~particle and scattered proton energy spectra were recorded in a multichannel analyser. The spectra were taken for two orientations of the crystal, one in which the proton beam was aligned with the (110) axis and the other in which it was along a random direction. In the latter case the (p, a) resonance occurred at a depth of 0.93/~m in A1, corresponding to an energy loss of 35 keV for the incident protons. As the Q-value of the reaction is 1600 keV, the emergent ~-particles are well separated in energy from the backscattered proton edge, as seen in fig. I. Here the a-peak resulting from
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Fig. 1. Backscattered proton and c<-particle energy spectra for 1400keV protons incident on an AI single crystal along a r a n d o m direction (o) and parallel to (110> axis ( × ) respectively. The c<-peak corresponds to the ZTAl(p,~)Z4Mg resonance reaction at an energy o f 1365 keV for the incident protons.
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Fig. 2. Backscattered proton and ~-particle energy spectra for (a) 1735 keV, (b) 1760 keV and (c) 1786 keV protons incident on an A1 single crystal along a random direction (o) and parallel to the (110) axis ( × ) respectively. The c~-peak in each case is due to the ~TAl(p, c0~4Mg resonance reaction at an incident proton energy o f 1726 keV. The integrated proton current for the random and aligned incidence respectively is (a) 7.7/~C and 90/~C, (b) 10/~C and 100 # C and (c) 10/~C and 60/~C. The energy calibrations are (a) 4.04 keV per channel, (b) 4.29 keV per channel and (c) 6.38 keV per channel. The backscattered proton edge (150 °) and the c~-peak are at energies (a) 1529 keV, 2494 keV (b) 1551 keV, 2341 keV and (c) 1574 keV, 2129 keV respectively. The increase in the width o f the ~-peak (full width at half maximum) for aligned incidence as compared to the random incidence is (a) 76 keV and (b) 197 keV.
E N E R G Y LOSS OF C H A N N E L E D
the protons incident along the (110) direction is much wider ( ~ 5 0 % ) on the low energy side as compared to the one arising from random incidence. Also in the former case there is considerable enhancement in the counting rate in the region between the e-peak and the backscattered proton edge. This could be due to pileup effects, since the proton beam current in the above two cases was kept approximately the same, 3.5 hA, while the dose was adjusted to get approximately the same intensity at the e-peak. The dechanneling effects at different depths were investigated by carrying out the measurements at three proton energies: Ep=1735, 1760 and 1786keV respectively, each time the proton beam incident successively in the aligned ((110)) and random directions. At these energies, for the protons incident in the random direction the 1726 keV Al(p, e) reso50XIO 4
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105
PROTONS
nance will correspond to reaction depths of 0.35, 1.0 and 1.9/tm respectively. The e-particle spectra following the resonance along with the backscattered proton edge are shown in fig. 2. It is clearly seen that in the aligned case the e-peak is wider at the low energy side and this width increases with the depth. Similarly the shape of the spectrum in the region between the e-peak and backscattered proton edge is markedly different and sensitive to the incident proton energy, i.e. the depth at which the reaction is taking place in the two cases of random and aligned incidences; the counting rate in that region particularly in the aligned case is enhanced and this increase is depth-dependent. Such an increase in the counting rate could arise due to different pile-up rates because of the difference in the proton dose even though the incident current for the two directions was approximately the same. A separate experiment was carried out at Ep = 1760 keV, keeping the proton dose equal, both for the random as well as aligned incidence. In order to have the same pile-up rates in these two cases the proton current in the random case was correspondingly reduced. This reduction was in the same proportion as that in the minimum scattering yield, Xmi,, when the proton beam was aligned along the (110) axis in the crystal. The resulting spectra are shown in fig. 3. Examining once again that part of the spectrum between the e-peak and scattered proton edge, one finds an enhancement in the counting rate for the aligned case, even though the quality of the Al-crystal used for this purpose (Zm~,~30%) was not as good as the earlier ones (Xml. ~ 3 %). It may be mentioned here that the poorer quality of the crystal turned out to be advantageous; otherwise it would have been necessary to reduce the proton current by a factor of 30, in the case of random incidence, rendering the control of the accelerator difficult.
,/g
3. Discussion 0 160
I 180
I 200
i 220
240
CHANNEL
260
280
300
i 320
"~q 340
NUMBER
Fig. 3. The energy spectra o f backscattered proton and or-particles following 1726 keV (p,~)resonance in Al for the r a n d o m (.) and aligned ( x ) incidence respectively. The incident p r o t o n energy is 1760 keV. The backscattered 0 5 0 °) p r o t o n edge and the ~-peaks are at energies 1533 and 2260 keV. The (p,c¢) resonance occurs at a depth of 1/~m in the Al single crystal when the 1760 keV proton beam is incident along a r a n d o m direction. The ~particle energy at resonance is 2530 keV. The total p r o t o n dose has been kept the same for the two cases o f r a n d o m and aligned incidence.
The comparison of the shapes of the (p, e) resonance spectra in the A1 single crystal for protons incident in a random direction and parallel to the (110) crystallographic direction figs. 1, 2 and 3 have clearly shown in the latter case (a) the enhancement in the width of the e-peak on the low energy side and (b) an increase in the counting rate in the region between the e-peak and the backscattered proton edge. The width of the e-peak for the random incidence is due to detector resolution, natural width of the resonance and the straggling in the energy loss of the incident protons and emergent e-particles in traversing the Al-crystal. The enhanceIlI. ELECTRONIC
STOPPING
106
K. G. P R A S A D
AND
ments (a) and (b) above for the aligned incidence thus clearly indicate that in this case there is a considerable distribution in the energy loss of the incident protons, due to which the (p, ~) resonance reaction occurs at different depths causing a large spread in the energy of the a-particles emerging out of the crystal surface following the resonance. As long as the incident protons remain in the channel they never approach a nucleus sufficiently close so as to interact with it. However for various reasons the particles are lost from the channel, their number increasing with the distance traversed in the crystal, and once lost from the channel they behave in the same manner as the random beam. Hence for a proton beam of finite energy incident parallel to a crystallographic direction, the variation in the energy loss of protons which ultimately causes a large spread in the emergent a-particle energy is due to an increase in the random fraction of the incident aligned beam with increasing penetration into the crystal along that axis as a result of proton escape from the channel. In the figs. 2a and b, it is clearly seen that as the incident proton energy is increased from 1735 keV to 1760 keV for which the corresponding increase in the 1726 keV Al(p, ~) resonance reaction depth is 0.65/~m for random incidence, the increase in the width (fwhm) of the observed a-peaks following the resonance reaction at the two depth, 0.35 and 1/~m respectively is about 76 keV (i.e. 113 keV to 189 keV). However, when the beam is aligned in the ( l l 0 ) direction the same increase is 197 keV, i.e. the fwhm changes from 129 keV to 326 keV. When the incident energy of protons is increased to 1786 keV in which case the (p, ~) resonance will occur at 1.9/~m the observed peak becomes so wide (fig. 2c) that it is difficult to fix any value for the width. In this measurement, in order to compare the widths more accurately, the a-peak intensities are almost kept the same and hence a larger dose of the incident protons has been given in the aligned case. The radiation damage effects are negligible. The analysis of the spectra taken with the incident beam parallel to the (110) axis is done by fitting the a-peak line shape as observed in the corresponding case of random incidence. Apart from the observed widening of the a-peak on the low energy side (figs. 2a, b, c) the enhancement in the counting rate in the region between the backscattered proton edge and a-peak clearly indicates that a sizeable fraction of the incident proton beam remains channeled even at larger depths. In a separate measurement where the uncertainty due to pile-up effects is removed the analysis of the observed spectra shows clearly (fig. 3) the following:
R. P. S H A R M A
a) At a depth of 1 ~m there is 50 % attenuation in the yield of a-particles when the incident beam is aligned along the (110) axis. b) The increase in the width of the a-peak is 73 keV for the aligned incidence (i.e. from 145 keV in the random case to 218 keV in the aligned case). The ~width for the random incidence here (fig. 3, 145 keV) is less than that mentioned in the above measurement (fig. 2b, 189 keV) because of somewhat poorer resolution of the detector used in that case. It should also be noted that the increase in the widths in the two cases (fig. 2b, 137 keV and fig. 3, 73 keV) is almost double even though the incident proton energy is the same (1760keV). This difference arises mainly due to a better crystal used in the measurements given in fig. 2 as compared to the ones given in fig. 3 and hence in the latter case for the same aligned incident proton energy (1760keV) the a-particles following (p,~) resonance will be produced at a greater depth. In the measurements of fig. 2 even though the integrated proton current for aligned incidence was much higher, the radiation damage effects in A1 were found to be negligible for the proton doses used here. c) In the spectra given in fig. 3 the a-peak is clearly separated by about 300 keV from the backscattered proton edge and in this region the increase in the counting rate for the aligned incidence is 20 % of the total random value. The above discussion has very clearly brought out the fact that for the t760 keV proton beam incident parallel to the (110) axis of an A1 single crystal, 50 % of the incident particles remain channeled at a depth of 1/~m, 24 % of these get dechanneled in the immediate neighbourhood after crossing this depth as reflected in the widening of the a-peak, while 20 % get dechanneled gradually beyond this depth. The dechanneling rate is very much depth-dependent and is also affected by the quality of the crystal. It can therefore be said that a large uncertainty is brought in due to the changing fraction of the initially aligned beam, getting deehanneled at different depths in the crystal, and it may not be very correct to use an average value for the energy loss in such cases. Repeating the measurements of fig. 3 at a few more incident proton energies above the resonance will bring out additional quantitative information.
We are grateful to Erik Bogh and J. U. Andersen for many interesting discussions on the subject. One of us (K.G.P.) wishes to acknowledge a grant from D A N I D A during his stay in Aarhus, Denmark.
E N E R G Y LOSS OF C H A N N E L E D P R O T O N S
References 1) E. Bogh, Can. J. Phys. 46 (1968) 653. 2) j. W. Mayer, L. Eriksson and J. A. Davies, Ion implantation in semi-conductors (Academic Press, New York, 1970). a) L. C. Northcliffe and R. F. Schilling, Nucl. Data Tables AT, no. 3 (1970) 4. 4) j. A. Davies, J. Denhartog and J. L. Whitton, Phys. Rev. 165 (1968) 345. 5) R. Hellborg, Physica Scripta 4 (1971) 75; R . D . Edge and R . L . Dixon, Atomic collision phenomena in solids (Eds. D . W . Palmer, M . W . Thompson and P . D . Townsend;
107
North-Holland Publ. Co., Amsterdam, 1970) p. 435. 6) j. A. Davies, L. M. Howe, D. A. Marsden and J. L. Whitton, Atomic collisions in solids (Eds. S. Andersen, K. B. Bjorkquist, K. Domeij and N. G. E. Johansson; Gordon and Breach London, New York and Paris, 1972) p. 208. See also other related works in same reference. 7) G. Gotz, K. D. Kimgl and U. Finger, Proc. 3rd Int. Conf. on Atomic collisions in solids, Gatlinburg, U.S.A. September 1973 (Plenum Press, to be published). 8) L. C. Feldman and B. R. Appleton, Phys. Rev. B8 (1973) 935. 9) j. Bottiger and F. H. Eisen, Thin Solid Films 19 (1973) 239.
III. E L E C T R O N I C S T O P P I N G