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Structure dependence of radiation damage depths after ion implantation
Nuclear Instruments
and Methods
in Physics Research
Nuclear Instruments & Methods in Physics Research SectIon B
B64 (1992) 242-245
North-Holland
Structure dependence after ion implantation
of radiation
E. Friedland and M. Fletcher of Physics, Unil,er.sifyof Pretoria,
Department
damage
depths
Preforia 0002, Soufll Africa
Single crystals of palladium, platinum and cobalt were implanted with 1.50 keV argon ions at temperatures of 77, 300 and 573 K. Damage depths were analyzed by a-particle channeling in a backscattering geometry for different lattice orientations. The observed damage depths exceeded the projected ion ranges significantly in all cases. For palladium this effect was nearly independent of the implantation temperature. whilst an appreciable reduction of the damage depth was found for platinum at 573 K. For cobalt a dependence on implantation direction was observed, indicating a structure dependence of damage depths.
1. Introduction Implantation of ions into solids generally leads to radiation damage, which in many cases modifies surface properties much more severely than the implanted impurity atoms. As ion implantation becomes increasingly important in modern technology, the analysis of damage profiles is not only of academic interest but is of considerable importance for many applications in industry. In general radiation damage is an unwanted phenomenon, which necessitates expensive and in many cases complicated annealing procedures. However, some applications can be envisaged, where radiation damage may create new and useful surface properties. For example, the corrosive and elastic properties of the surface region may in some cases be changed in such a manner that wear resistance is strongly enhanced. In such an application the depth of the damage would of course be of vital importance. Damage depths, which exceed projected ion ranges by up to an order of magnitude, have been observed in many metals [l-.5]. Computer simulations based on binary collision models cannot easily explain this phenomenon [6,7]. In metals the primary damage is produced by atomic collisions only, leading to defects with an expected distribution closely related to the projected range of the implanted ions. The maximum of the distribution of point defects as obtained from Monte Carlo calculations is usually found slightly nearer to the surface than the maximum of the implantation profile. This shift towards the surface becomes more apparent for larger ion masses. Contrary to this theoretical expectation, experimental damage depths in most metals are deeper than the projected ion 0168-583X/92/$05.00
0 1992 - Elsevier
Science
Publishers
ranges and this enhancement increases for a given material with increasing ion mass [S]. To explain this effect by migration of interstitial atoms as proposed by some workers [3] is not very convincing. This would lead to similar damage depths in all solids with comparable migration energies, which is not observed. Furthermore, computations using molecular dynamic simulations [Y], which also include nonlinear processes, rcveal that very few of the interstitial atoms created during the primary collisional phase survive the subscquent thermal spike phase. The same computations also show that replacement collision sequences cannot be responsible for the observed deep damage depths, as the calculated average lengths of such focusons are much too short. The fact that very large damage depths were often found in metals with face centered cubic lattices makes a structure-dependent mechanism more likely [lb]. A possible mechanism could be a dislocation propagation process due to large stress field gradients near ion tracks. The efficiency of such a process would sensitively depend on the Peicrls force, which has to be surmounted in order to move a dislocation. It is generally assumed that this force is relatively small in fee structures and quite high in diamond type lattices. If dislocation dynamics is indeed responsible for the enhanced damage depths, one would furthermore expect that the implantation direction relative to the lattice orientation should have an influence on the final damage depth because of the anisotropy of the Peierls force. In order to get a clear picture of the mechanisms responsible for the final damage distribution, a systematic study of the influences of all relevant parameters is currently undertaken in our laboratory. In this work
B.V. All rights reserved
243
E. Friedland, M. Fletcher / Structure dependence of radiation damage depths
results for platinum, tals arc reported.
2. Experimental
palladium
and cobalt
single crys-
method
Samples were cut by spark erosion from singlecrystal rods of platinum, palladium and cobalt. In the case of platinum and palladium all samples were cut perpendicular to the (111) direction, whilst cobalt samples were prepared with (0001) and (0011) orientations respectively. After mechanical lapping, electrolytical polishing and vacuum furnace annealing, the samples were implanted with 1.50 keV argon ions at a fluence of 10lh cmm7 and a dose rate of 10” cm-* s-‘. To prevent ion channeling, the surface normal was tilted by 7 o relative to the implantation direction. The platinum and palladium samples were implanted at temperatures of 77, 300 and 573 K. Cobalt specimens were only implanted at room temperature. Samples were analyzed before and after ion bombardment by a-particle channeling in a backscattering geometry. For this purpose crystals were mounted on a three-axis goniometer in a scattering chamber which was pumped down to 10eh Torr. The goniometer was equipped with electronically read digitizers rigidly fixed to its axes, which allowed an angular accuracy of better than 0.05 O. The analyzing beam of cu-particles was obtained from the 2.5 MV Van de Graaff accelerator of the University of Pretoria. Collimation of the beam was obtained by a system of apertures without any active focussing elements. Beam divergence was less than 0.04 ’ with a spot size of approximately 1 mm and a beam current of about 30 nA, which was measured directly on the target holder. In order to suppress secondary electrons, a negative voltage of 300 V was applied to a ring-shaped electrode in front of the target. Scattered particles were detected by a surface barrier detector at an angle of 165’ with an acceptance angle of 2 O. The energy resolution of the system was approximately 13 keV. For the fee metals platinum and palladium aligned backscattering spectra were taken for the (11 l), (1 lo), (100) and (211) orientations. However, for the hexagonal cobalt only alignments along either the (0001) or the (0011) direction could be obtained. These spectra were normalized to the random spectra obtained by rotating the target during data acquisition about an axis tilted by 5” with respect to the aligned orientation. Energy calibration was obtained by means of the scattering contributions from the surface for beam energies of 1.5 and 1.8 MeV. The energy was converted to a depth scale by using the elemental stopping power data of Ziegler [ll], assuming the surface approximation. These stopping power data are strictly valid for unchanneled particles only and consequently slightly
overestimate energy losses for aligned particles. This will lead to a slight underestimation of the depths.
3. Results and discussion Fig. 1 shows aligned backscattering spectra after implantation of 10lh Ar+ cm-’ into platinum with an energy of 150 keV at temperatures of 77 and 573 K respectively. Also given are the aligned and random spectra before implantation. Striking differences between the shapes of the low and high temperature implantations are quite obvious. Apart from the much higher damage level, the disturbed surface zone is appreciably deeper for the low temperature implantation. Furthermore a damage peak is visible at the surface after the 77 K implantation, whilst the same region seems to be relatively free of defects after implantation at 573 K. The existence of a damage peak indicates severe short range defects like a partial amorphization or polycrystalline region in the immediate vicinity of the surface. The thickness of this region is approximately 50% of the projected ion range as calculated with the Monte Carlo simulation code TRIM [7]. A similar damage peak is not observed after room temperature implantation, although the depth of the disturbed region, which is characterized by an increased slope of the dechanneling spectrum, agrees within experimental uncertainties with that observed at 77 K. The enhanced slope of the dechanneling spcctrum beyond the damage peak points to extended defects like dislocation networks, typically found in metals after ion implantation. During passage through such an extended defect, a-particles are gradually
Energy 3000
._
0.5 ,
(MeV)
1.0 I
1.5 I
360
460
2.0 I
560
660
Channel
Fig. 1. Aligned and random backscattering spectra before and after implantation of lOI Ar’ cm-’ into Pt (111) at temperatures of 573 and 77 K: (1) Unimplanted; (2) implanted at 573 K; (3) implanted at 77 K; (4) random. E, = 1.8 MeV; 0 = 165 O.
V. LATTICE SITES/STRUCTURE
244
E. Friedlund,
Table 1 Depths of damage Sample
M. Fletcher
/ Structure
dependence
8 peaks and disturbed
Temperature
Damage peak
[Kl
[nml
damage depths
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
regions
Disturbed
region [nml
R, (TRIM)
[nml
Pt (111)
77 300 573
26k5 _
232k41 211k27 126+ 9
49
Pd (Ill)
77 300 573
32+5 33_+5 _
166i17 lhh_+ 17 142+20
57
co (0001) co (001 I)
300
108k44 160+40
64
_ _
ofradiution
Fig. 2. Temperature dependence of the ratios of experimental damage depths and projected ion ranges for some metals. Lines are drawn to guide the eye.
steered away from the aligned direction by correlated small angle scattering, leading to an increasing dechanWing cross section. The end of the disturbed lattice region is marked by a decrease in slope, forming a typical knee in the normalized backscattering spectrum. The depth of the disturbed region, which is determined from the position of this knee, exceeds the calculated projected range in all samples quite significantly as is obvious from table 1. The quoted errors are obtained from a statistical analysis of the experimental values found for different sample orientations and analyzing ion beam energies. Backscattering spectra for the implanted palladium samples at temperatures of 77 and 573 K are similar to those shown for platinum. Again a damage peak with a total width of approximately 50% of the expected projected range is observed after low temperature implantation However, a surface damage peak is also observed after room temperature implantation. At high temperature the damage peak is absent, but the dcchanncling cross section is significantly higher near the surface than for the unimplanted sample. Also for palladium damage depths are determined, which are much larger than expected from the calculated projected ranges. However, the enhancement is appreciably smaller than in platinum. As in platinum, a somewhat smaller damage depth is also found after the 573 K implantation. However, as the difference is barely outside the experimental error, it is not clear whether this is a significant effect. The temperature dependence of damage depths in platinum and palladium is compared in fig. 2 with that for copper, nickel and iron from ref. [12]. With the exception of platinum, a relatively weak dcpendcnce on temperature is observed. This is expected, if the final damage is mainly determined by a dislocation propagation mechanism. Although the Peierls force is
expected to bc temperature dependent, the temperatures encountered in collision cascades during the thermal spike phase are an order of magnitude higher than the employed substrate temperatures. The unexpected behaviour of platinum is difficult to understand, but is possibly an indication of an ion-beam-induced anncaling process at elevated temperatures. Such a process may play a more prominent role in platinum than in the other four metals because of its appreciably higher cascade energy density [13]. The damage depths in cobalt after implantation into samples with surface orientations normal to the (0001) and (0011) directions respectively arc also given in table 1. The room temperature results for these two orientations, which are perpendicular to each other, differ by approximately 50%. Unfortunately the experimental uncertainties are almost as large, making it difficult to express a convincing opinion about a struc-
Table 2 Relative damage temperature
depths
after
argon
implantation
Material
Lattice structure
Relative damage depth
Copper (111) Nickel (100) Palladium (111) Platinum (I 11)
fee
4.2 2.4 2.9 4.3
Cobalt (0001) Rhenium (0001)
hcp
1.7 1.1
Iron (111)
bee
1.5
at room
E. Friedland, h4. Fletcher / Structure dependence
ture dependence of the final damage depth. However, the Peierls force is expected to be significantly higher in the (0001) direction than in any orientation perpendicular to it. The observed difference is therefore at lcast in the right direction. A more convincing argument for structure dependence can be extracted from table 2, listing the relative damage depths after argon implantation for some metals, which have been determined so far in this laboratory. The numbers in the last column are the energy-independent ratios of the experimental damage depths at room temperature and the projected ion ranges as determined by TRIM. These ratios are relatively large for the fee materials and significantly smaller for the hcp and bee structures. This general trend certainly points to a structure dependent dislocation propagation mechanism, as the glide opposing Peierls force should be smaller in fee lattices.
The authors would like to thank Dr. J.F. Prins for the implantations done at the Wits-CSIR Schonland Research Centre for Nuclear Sciences. We are also grateful to the Foundation of Research Development for partially funding this work.
245
damage depths
References [l] G. Linker, M. Gettings and 0. Meyer, in: Ion Implanta-
[2] [3] [4] [5] [6] [7]
[8] [9]
Acknowledgements
ofradiation
[lo] [ll] [12] [13]
tion in Semiconductors and Other Materials, ed. B.L. Crowder (Plenum, New York, 1973) p. 465. D.K. Sood and G. Dearnaley, J. Vat. Sci. Technol. 12 (1975) 463. M. Vos and D.M. Boerma, Nucl. Instr. and Meth. B15 (1986) 337. E. Friedland, J.B. Malherbe, H.W. Alberts, R.E. Vorster and J.F. Prim, S. Afr. J. Phys. 9 (1986) 135. E. Friedland, H. Ie Roux and J.B. Malherbe, Radiat. Eff. Lett. 87 (1986) 281. M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008. J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985). E. Friedland and H.W. Alberts, Nucl. Instr. and Meth. B33 (1988) 710. R.S. Averback, T. Diaz de la Rubia and R. Benedek, Nucl. Instr. and Meth. B33 (1988) 693. E. Friedland and H.W. Alberts, Nucl. Instr. and Meth. B35 (1988) 244. J.F. Ziegler, Helium Stopping Powers and Ranges in All Elemental Matter (Pergamon, New York, 1977). E. Friedland, H.W. Alberts and M. Fletcher, Nucl. Instr. and Meth. B45 (1990) 492. S.-J. Kim, M.-A. Nicolet, R.S. Averback and D. Peak, Phys. Rev. B37 (1988) 38.
V. LATTICE
SITES/STRUCTURE
and Methods
in Physics Research
Nuclear Instruments & Methods in Physics Research SectIon B
B64 (1992) 242-245
North-Holland
Structure dependence after ion implantation
of radiation
E. Friedland and M. Fletcher of Physics, Unil,er.sifyof Pretoria,
Department
damage
depths
Preforia 0002, Soufll Africa
Single crystals of palladium, platinum and cobalt were implanted with 1.50 keV argon ions at temperatures of 77, 300 and 573 K. Damage depths were analyzed by a-particle channeling in a backscattering geometry for different lattice orientations. The observed damage depths exceeded the projected ion ranges significantly in all cases. For palladium this effect was nearly independent of the implantation temperature. whilst an appreciable reduction of the damage depth was found for platinum at 573 K. For cobalt a dependence on implantation direction was observed, indicating a structure dependence of damage depths.
1. Introduction Implantation of ions into solids generally leads to radiation damage, which in many cases modifies surface properties much more severely than the implanted impurity atoms. As ion implantation becomes increasingly important in modern technology, the analysis of damage profiles is not only of academic interest but is of considerable importance for many applications in industry. In general radiation damage is an unwanted phenomenon, which necessitates expensive and in many cases complicated annealing procedures. However, some applications can be envisaged, where radiation damage may create new and useful surface properties. For example, the corrosive and elastic properties of the surface region may in some cases be changed in such a manner that wear resistance is strongly enhanced. In such an application the depth of the damage would of course be of vital importance. Damage depths, which exceed projected ion ranges by up to an order of magnitude, have been observed in many metals [l-.5]. Computer simulations based on binary collision models cannot easily explain this phenomenon [6,7]. In metals the primary damage is produced by atomic collisions only, leading to defects with an expected distribution closely related to the projected range of the implanted ions. The maximum of the distribution of point defects as obtained from Monte Carlo calculations is usually found slightly nearer to the surface than the maximum of the implantation profile. This shift towards the surface becomes more apparent for larger ion masses. Contrary to this theoretical expectation, experimental damage depths in most metals are deeper than the projected ion 0168-583X/92/$05.00
0 1992 - Elsevier
Science
Publishers
ranges and this enhancement increases for a given material with increasing ion mass [S]. To explain this effect by migration of interstitial atoms as proposed by some workers [3] is not very convincing. This would lead to similar damage depths in all solids with comparable migration energies, which is not observed. Furthermore, computations using molecular dynamic simulations [Y], which also include nonlinear processes, rcveal that very few of the interstitial atoms created during the primary collisional phase survive the subscquent thermal spike phase. The same computations also show that replacement collision sequences cannot be responsible for the observed deep damage depths, as the calculated average lengths of such focusons are much too short. The fact that very large damage depths were often found in metals with face centered cubic lattices makes a structure-dependent mechanism more likely [lb]. A possible mechanism could be a dislocation propagation process due to large stress field gradients near ion tracks. The efficiency of such a process would sensitively depend on the Peicrls force, which has to be surmounted in order to move a dislocation. It is generally assumed that this force is relatively small in fee structures and quite high in diamond type lattices. If dislocation dynamics is indeed responsible for the enhanced damage depths, one would furthermore expect that the implantation direction relative to the lattice orientation should have an influence on the final damage depth because of the anisotropy of the Peierls force. In order to get a clear picture of the mechanisms responsible for the final damage distribution, a systematic study of the influences of all relevant parameters is currently undertaken in our laboratory. In this work
B.V. All rights reserved
243
E. Friedland, M. Fletcher / Structure dependence of radiation damage depths
results for platinum, tals arc reported.
2. Experimental
palladium
and cobalt
single crys-
method
Samples were cut by spark erosion from singlecrystal rods of platinum, palladium and cobalt. In the case of platinum and palladium all samples were cut perpendicular to the (111) direction, whilst cobalt samples were prepared with (0001) and (0011) orientations respectively. After mechanical lapping, electrolytical polishing and vacuum furnace annealing, the samples were implanted with 1.50 keV argon ions at a fluence of 10lh cmm7 and a dose rate of 10” cm-* s-‘. To prevent ion channeling, the surface normal was tilted by 7 o relative to the implantation direction. The platinum and palladium samples were implanted at temperatures of 77, 300 and 573 K. Cobalt specimens were only implanted at room temperature. Samples were analyzed before and after ion bombardment by a-particle channeling in a backscattering geometry. For this purpose crystals were mounted on a three-axis goniometer in a scattering chamber which was pumped down to 10eh Torr. The goniometer was equipped with electronically read digitizers rigidly fixed to its axes, which allowed an angular accuracy of better than 0.05 O. The analyzing beam of cu-particles was obtained from the 2.5 MV Van de Graaff accelerator of the University of Pretoria. Collimation of the beam was obtained by a system of apertures without any active focussing elements. Beam divergence was less than 0.04 ’ with a spot size of approximately 1 mm and a beam current of about 30 nA, which was measured directly on the target holder. In order to suppress secondary electrons, a negative voltage of 300 V was applied to a ring-shaped electrode in front of the target. Scattered particles were detected by a surface barrier detector at an angle of 165’ with an acceptance angle of 2 O. The energy resolution of the system was approximately 13 keV. For the fee metals platinum and palladium aligned backscattering spectra were taken for the (11 l), (1 lo), (100) and (211) orientations. However, for the hexagonal cobalt only alignments along either the (0001) or the (0011) direction could be obtained. These spectra were normalized to the random spectra obtained by rotating the target during data acquisition about an axis tilted by 5” with respect to the aligned orientation. Energy calibration was obtained by means of the scattering contributions from the surface for beam energies of 1.5 and 1.8 MeV. The energy was converted to a depth scale by using the elemental stopping power data of Ziegler [ll], assuming the surface approximation. These stopping power data are strictly valid for unchanneled particles only and consequently slightly
overestimate energy losses for aligned particles. This will lead to a slight underestimation of the depths.
3. Results and discussion Fig. 1 shows aligned backscattering spectra after implantation of 10lh Ar+ cm-’ into platinum with an energy of 150 keV at temperatures of 77 and 573 K respectively. Also given are the aligned and random spectra before implantation. Striking differences between the shapes of the low and high temperature implantations are quite obvious. Apart from the much higher damage level, the disturbed surface zone is appreciably deeper for the low temperature implantation. Furthermore a damage peak is visible at the surface after the 77 K implantation, whilst the same region seems to be relatively free of defects after implantation at 573 K. The existence of a damage peak indicates severe short range defects like a partial amorphization or polycrystalline region in the immediate vicinity of the surface. The thickness of this region is approximately 50% of the projected ion range as calculated with the Monte Carlo simulation code TRIM [7]. A similar damage peak is not observed after room temperature implantation, although the depth of the disturbed region, which is characterized by an increased slope of the dechanneling spectrum, agrees within experimental uncertainties with that observed at 77 K. The enhanced slope of the dechanneling spcctrum beyond the damage peak points to extended defects like dislocation networks, typically found in metals after ion implantation. During passage through such an extended defect, a-particles are gradually
Energy 3000
._
0.5 ,
(MeV)
1.0 I
1.5 I
360
460
2.0 I
560
660
Channel
Fig. 1. Aligned and random backscattering spectra before and after implantation of lOI Ar’ cm-’ into Pt (111) at temperatures of 573 and 77 K: (1) Unimplanted; (2) implanted at 573 K; (3) implanted at 77 K; (4) random. E, = 1.8 MeV; 0 = 165 O.
V. LATTICE SITES/STRUCTURE
244
E. Friedlund,
Table 1 Depths of damage Sample
M. Fletcher
/ Structure
dependence
8 peaks and disturbed
Temperature
Damage peak
[Kl
[nml
damage depths
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
regions
Disturbed
region [nml
R, (TRIM)
[nml
Pt (111)
77 300 573
26k5 _
232k41 211k27 126+ 9
49
Pd (Ill)
77 300 573
32+5 33_+5 _
166i17 lhh_+ 17 142+20
57
co (0001) co (001 I)
300
108k44 160+40
64
_ _
ofradiution
Fig. 2. Temperature dependence of the ratios of experimental damage depths and projected ion ranges for some metals. Lines are drawn to guide the eye.
steered away from the aligned direction by correlated small angle scattering, leading to an increasing dechanWing cross section. The end of the disturbed lattice region is marked by a decrease in slope, forming a typical knee in the normalized backscattering spectrum. The depth of the disturbed region, which is determined from the position of this knee, exceeds the calculated projected range in all samples quite significantly as is obvious from table 1. The quoted errors are obtained from a statistical analysis of the experimental values found for different sample orientations and analyzing ion beam energies. Backscattering spectra for the implanted palladium samples at temperatures of 77 and 573 K are similar to those shown for platinum. Again a damage peak with a total width of approximately 50% of the expected projected range is observed after low temperature implantation However, a surface damage peak is also observed after room temperature implantation. At high temperature the damage peak is absent, but the dcchanncling cross section is significantly higher near the surface than for the unimplanted sample. Also for palladium damage depths are determined, which are much larger than expected from the calculated projected ranges. However, the enhancement is appreciably smaller than in platinum. As in platinum, a somewhat smaller damage depth is also found after the 573 K implantation. However, as the difference is barely outside the experimental error, it is not clear whether this is a significant effect. The temperature dependence of damage depths in platinum and palladium is compared in fig. 2 with that for copper, nickel and iron from ref. [12]. With the exception of platinum, a relatively weak dcpendcnce on temperature is observed. This is expected, if the final damage is mainly determined by a dislocation propagation mechanism. Although the Peierls force is
expected to bc temperature dependent, the temperatures encountered in collision cascades during the thermal spike phase are an order of magnitude higher than the employed substrate temperatures. The unexpected behaviour of platinum is difficult to understand, but is possibly an indication of an ion-beam-induced anncaling process at elevated temperatures. Such a process may play a more prominent role in platinum than in the other four metals because of its appreciably higher cascade energy density [13]. The damage depths in cobalt after implantation into samples with surface orientations normal to the (0001) and (0011) directions respectively arc also given in table 1. The room temperature results for these two orientations, which are perpendicular to each other, differ by approximately 50%. Unfortunately the experimental uncertainties are almost as large, making it difficult to express a convincing opinion about a struc-
Table 2 Relative damage temperature
depths
after
argon
implantation
Material
Lattice structure
Relative damage depth
Copper (111) Nickel (100) Palladium (111) Platinum (I 11)
fee
4.2 2.4 2.9 4.3
Cobalt (0001) Rhenium (0001)
hcp
1.7 1.1
Iron (111)
bee
1.5
at room
E. Friedland, h4. Fletcher / Structure dependence
ture dependence of the final damage depth. However, the Peierls force is expected to be significantly higher in the (0001) direction than in any orientation perpendicular to it. The observed difference is therefore at lcast in the right direction. A more convincing argument for structure dependence can be extracted from table 2, listing the relative damage depths after argon implantation for some metals, which have been determined so far in this laboratory. The numbers in the last column are the energy-independent ratios of the experimental damage depths at room temperature and the projected ion ranges as determined by TRIM. These ratios are relatively large for the fee materials and significantly smaller for the hcp and bee structures. This general trend certainly points to a structure dependent dislocation propagation mechanism, as the glide opposing Peierls force should be smaller in fee lattices.
The authors would like to thank Dr. J.F. Prins for the implantations done at the Wits-CSIR Schonland Research Centre for Nuclear Sciences. We are also grateful to the Foundation of Research Development for partially funding this work.
245
damage depths
References [l] G. Linker, M. Gettings and 0. Meyer, in: Ion Implanta-
[2] [3] [4] [5] [6] [7]
[8] [9]
Acknowledgements
ofradiation
[lo] [ll] [12] [13]
tion in Semiconductors and Other Materials, ed. B.L. Crowder (Plenum, New York, 1973) p. 465. D.K. Sood and G. Dearnaley, J. Vat. Sci. Technol. 12 (1975) 463. M. Vos and D.M. Boerma, Nucl. Instr. and Meth. B15 (1986) 337. E. Friedland, J.B. Malherbe, H.W. Alberts, R.E. Vorster and J.F. Prim, S. Afr. J. Phys. 9 (1986) 135. E. Friedland, H. Ie Roux and J.B. Malherbe, Radiat. Eff. Lett. 87 (1986) 281. M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008. J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985). E. Friedland and H.W. Alberts, Nucl. Instr. and Meth. B33 (1988) 710. R.S. Averback, T. Diaz de la Rubia and R. Benedek, Nucl. Instr. and Meth. B33 (1988) 693. E. Friedland and H.W. Alberts, Nucl. Instr. and Meth. B35 (1988) 244. J.F. Ziegler, Helium Stopping Powers and Ranges in All Elemental Matter (Pergamon, New York, 1977). E. Friedland, H.W. Alberts and M. Fletcher, Nucl. Instr. and Meth. B45 (1990) 492. S.-J. Kim, M.-A. Nicolet, R.S. Averback and D. Peak, Phys. Rev. B37 (1988) 38.
V. LATTICE
SITES/STRUCTURE