- Email: [email protected]
Computer simulations of slowing down of heavy ions in polycrystalline materials
Volume 95A, number 8
PIlYSICS LETTERS
23 May 1983
COMPUTER SIMULATIONS OF SLOWING DOWN OF HEAVY IONS IN POLYCRYSTALLINE MATERIALS M. HAUTALA Department o f Physics, University o f ttelsinki, Siltavuorenpenger 20 C, SF-O0170 Helsinki 17, Finland
Received 8 February 1983 Revised manuscript received 22 March 1983
A fast computer code is constructed to simulate the slowing down of ions in crystalline materials. The programme is used to study the range distributions of 120 keV Pb in polycrystalline A1 and 60 keV A1 in polycrystalline Ta. Good agreement with experiment is found, when partial preferred orientation of the microcrystals is assumed.
The slowing down of low-energy ions in amorphous materials can be calculated quite reliably. When the potential between colliding atoms is calculated assuming the total electron density to be the sum of the two atomic densities [ 1], the nuclear stopping power and ranges agree to 10% with experiment (e.g. refs. [2,31). To date, however, very little has been done on comparing quantitatively theoretical and experimental range distributions in crystalline materials. In the 1960's the potential was not well enough known and the comparisons were only qualitative. In the 1970's MARLOWE [4] has primarily been used in fusionrelated problems. There is an obvious need to know more about the slowing-down process in polycrystalline materials, e.g., when measuring nuclear lifetimes using the Doppler-shift-attenuation (DSA) method, because the target materials are usually polycrystalline. The main goal in constructing the computer code was to make it as fast as possible without any serious loss of accuracy. The main features of the programme are: (1) The incident particle is assumed to make only binary collisions with the atoms of the target. (2) The scatterer is chosen from the nearest and second-nearest neighbours to be the one with the smallest impact parameter. (3) The scattering angle is evaluated from the standard scattering integral. 5000 scattering angles for 100 impact parameters and 50 energies are calcu436
lated at the beginning of the simulation. The angle used in the simulation is found from interpolation. (4) Thermal vibrations are included, assuming the displacements to be gaussian distributed and uncorrelated (tins-vibration amplitudes for Ta and AI were 0.066 A ( T = 300 K) and 0.064 A ( T = 77 K) [51, respectively). In the calculations, the electronic stopping according to the LSS theory [6] was used and the potentials were those described above, i.e. the Gordon Kim method [1] was used. The points (2) and (3) above, which are intended to make the simulation fast, are the main differences from MARLOWE. The accuracy of the approximations and a comparison with other calculations will be presented in a separate paper. The calculations should most accurately simulate experiment, when low-energy heavy ions slow down in polycrystalline stopping materials consisting of lighter atoms. Then the scattering angles in the laboratory coordinates are small, but in tile cm system they are noticeable, so that there is rapid slowing down. The effect of the electronic stopping, which is not well known, is small in this case. Heavy ion ranges in A1 have shown wide scatter and many possible reasons for the discrepancies have been given [7,8]. Therefore, we first calculate the range distributions of 120 keV Pb in polycrystalline A1. As a second example, the slowing down of 60 keV A1 in polycrystalline Ta is calculated. Ta is a very important backing material
0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
Volume 95A, n u m b e r 8
PHYSICS LETTERS
o I0° w
R>-
,,m10-1 IE g._ b_ 0 z
~10-; b-
AM/ORPHOUS"".... /
"~
(J00).0.
120 keY P b ~ A [
160
260 DEPTH(nm)
3oo
Fig. 1. The integral range distributions o f 120 keV Pb in AI, for various orientations. The measured curve is reproduced from the m e a s u r e m e n t s o f ref. [ 8]. The implantation temperature was 77 K.
in the DSA measurements and, in addition, the experimental and theoretical mean ranges differ from each other by a factor of 1.47 -+ 0.06 [9]. In the calculations, various degrees of polycrystallinity are allowed. The polar angle 0 of the incident ion is chosen randomly between some minimum and maximum angles with respect to a selected direction. The azimuthal angle ¢ is random between 0 ° and 360 °. The ions slow down in a single crystal. So the calculations are valid when the ranges of the ions are small with respect to the grain size. The calculations are compared with theory in figs. 1 and 2. It is seen
oI0° [JJ
Ro
~ E A
03
" (I00) 'SURED (100).0"<0<13"
>Z
,m10-' , IE
z
_o
~ 10-2 u_
6 0 keY At ~ T a
sb
,~0
DEPTH(nm)
,s0
Fig. 2. The integral range distributions o f 60 keV A1 in Ta, for various orientations. The measured curve is reproduced from the m e a s u r e m e n t s o f ref. [9]. The angle o f incidence in the implantation was 0 = 6 ° away from the normal.
23 May 1983
that the theoretical distributions, with the assumption o f amorphous stopping material, differ appreciably from both the calculated and experimental distributions, when the backing material is polycrystalline. On the other hand, if some orientation of microcrystals is supposed, e.g., so that the { 100) plane has a tendency to be parallel to the surface, the experimental results are well produced. When the limit of the polar angle is chosen so that the theoretical curve agrees with the experimental curve, the effect of the surface oxide layer and damage, which is to spread out the beam, is also partly taken into account in the calculations. It is natural that the (100) direction is preferred in the A1 case, because the microcrystals tend to orient in this way, when the A1 plate is rolled. Further proof against complete isotropy in the orientation of the microcrystals can be achieved by comparing the most probable ranges. The theoretical top is at 35 -+ 3 nm, whereas experimentally it is found at 43.5 -+ 3.0 nm [8] and, if in the calculation the polar angle is between 0 ° and 7 ° with respect to the <100) direction, the top is at 4 0 -+ 5 nm. In both cases studied, the experimental concentration near the surface is larger than the calculated value. This is probably due to diffusion and oxidation at the surface [7,8]. Further calculations indicate that a small change in the potential or in the inelastic energy loss does not affect these conclusions. However, the sensitivity o f the distributions to the rms-vibration amplitudes indicates a definite sensitivity to temperature. From the above results we can make a few remarks to be kept in mind in future applications. When measuring the stopping values in polycrystalline materials, the type of material used should be def']ned with care. At least in the Pb ~ AI case, some dependence of the concentration distribution on the implantation angle and temperature can probably be measured. The potentials seem to be adequate also for studies on slowing down in the well channeled cases, where the inelastic energy loss is more important than the elastic energy loss. The computer simulations presented indicate that even in the case of polycrystalline materials with very strong preferential orientation, the effect on the most probable range is small. The main effect of crystaUinity is to produce long tails in the distributions, leading to important asymmetries and consequently to higher mean ranges. 437
Volume 95A, number 8
PHYSICS LETTERS
References [1] R.G. Gordon and Y.S. Kim, J. Chem. Phys. 56 (1972) 3122. [2] W.D. Wilson, L.G. Haggmark and J.P. Biersack, Phys. Rev. B15 (1977) 2488. [3] M. Bister, M. Hautala and M. Jgntti, Radiat. Eff. 42 (1979) 201. [4] M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008.
438
23 May 1983
[5] International tables for X-ray crystallography, Vol. I11 (Kynoch Press, Birmingham, 1962). [6] J. Lindhard, M. Scharff and H.B. Schffptt, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 33 (1963) no. 14. 171 J.L. Gombasson, B.W. Farmery, D. McCulloch, G.W. Neilson and M.W. Thompson,Radiat. Eff. 36 (1978) 149. [8] M. Bister, J. Keinonen and A. Anttila, Phys. Lett. 74A (1979) 357. [9] J. Keinonen, M. Hautala, M. Luomaj~rvi, A. Anttila and M. Bister, Radiat. Eff. 39 (1978) 189.
PIlYSICS LETTERS
23 May 1983
COMPUTER SIMULATIONS OF SLOWING DOWN OF HEAVY IONS IN POLYCRYSTALLINE MATERIALS M. HAUTALA Department o f Physics, University o f ttelsinki, Siltavuorenpenger 20 C, SF-O0170 Helsinki 17, Finland
Received 8 February 1983 Revised manuscript received 22 March 1983
A fast computer code is constructed to simulate the slowing down of ions in crystalline materials. The programme is used to study the range distributions of 120 keV Pb in polycrystalline A1 and 60 keV A1 in polycrystalline Ta. Good agreement with experiment is found, when partial preferred orientation of the microcrystals is assumed.
The slowing down of low-energy ions in amorphous materials can be calculated quite reliably. When the potential between colliding atoms is calculated assuming the total electron density to be the sum of the two atomic densities [ 1], the nuclear stopping power and ranges agree to 10% with experiment (e.g. refs. [2,31). To date, however, very little has been done on comparing quantitatively theoretical and experimental range distributions in crystalline materials. In the 1960's the potential was not well enough known and the comparisons were only qualitative. In the 1970's MARLOWE [4] has primarily been used in fusionrelated problems. There is an obvious need to know more about the slowing-down process in polycrystalline materials, e.g., when measuring nuclear lifetimes using the Doppler-shift-attenuation (DSA) method, because the target materials are usually polycrystalline. The main goal in constructing the computer code was to make it as fast as possible without any serious loss of accuracy. The main features of the programme are: (1) The incident particle is assumed to make only binary collisions with the atoms of the target. (2) The scatterer is chosen from the nearest and second-nearest neighbours to be the one with the smallest impact parameter. (3) The scattering angle is evaluated from the standard scattering integral. 5000 scattering angles for 100 impact parameters and 50 energies are calcu436
lated at the beginning of the simulation. The angle used in the simulation is found from interpolation. (4) Thermal vibrations are included, assuming the displacements to be gaussian distributed and uncorrelated (tins-vibration amplitudes for Ta and AI were 0.066 A ( T = 300 K) and 0.064 A ( T = 77 K) [51, respectively). In the calculations, the electronic stopping according to the LSS theory [6] was used and the potentials were those described above, i.e. the Gordon Kim method [1] was used. The points (2) and (3) above, which are intended to make the simulation fast, are the main differences from MARLOWE. The accuracy of the approximations and a comparison with other calculations will be presented in a separate paper. The calculations should most accurately simulate experiment, when low-energy heavy ions slow down in polycrystalline stopping materials consisting of lighter atoms. Then the scattering angles in the laboratory coordinates are small, but in tile cm system they are noticeable, so that there is rapid slowing down. The effect of the electronic stopping, which is not well known, is small in this case. Heavy ion ranges in A1 have shown wide scatter and many possible reasons for the discrepancies have been given [7,8]. Therefore, we first calculate the range distributions of 120 keV Pb in polycrystalline A1. As a second example, the slowing down of 60 keV A1 in polycrystalline Ta is calculated. Ta is a very important backing material
0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
Volume 95A, n u m b e r 8
PHYSICS LETTERS
o I0° w
R>-
,,m10-1 IE g._ b_ 0 z
~10-; b-
AM/ORPHOUS"".... /
"~
(J00).0.
120 keY P b ~ A [
160
260 DEPTH(nm)
3oo
Fig. 1. The integral range distributions o f 120 keV Pb in AI, for various orientations. The measured curve is reproduced from the m e a s u r e m e n t s o f ref. [ 8]. The implantation temperature was 77 K.
in the DSA measurements and, in addition, the experimental and theoretical mean ranges differ from each other by a factor of 1.47 -+ 0.06 [9]. In the calculations, various degrees of polycrystallinity are allowed. The polar angle 0 of the incident ion is chosen randomly between some minimum and maximum angles with respect to a selected direction. The azimuthal angle ¢ is random between 0 ° and 360 °. The ions slow down in a single crystal. So the calculations are valid when the ranges of the ions are small with respect to the grain size. The calculations are compared with theory in figs. 1 and 2. It is seen
oI0° [JJ
Ro
~ E A
03
" (I00) 'SURED (100).0"<0<13"
>Z
,m10-' , IE
z
_o
~ 10-2 u_
6 0 keY At ~ T a
sb
,~0
DEPTH(nm)
,s0
Fig. 2. The integral range distributions o f 60 keV A1 in Ta, for various orientations. The measured curve is reproduced from the m e a s u r e m e n t s o f ref. [9]. The angle o f incidence in the implantation was 0 = 6 ° away from the normal.
23 May 1983
that the theoretical distributions, with the assumption o f amorphous stopping material, differ appreciably from both the calculated and experimental distributions, when the backing material is polycrystalline. On the other hand, if some orientation of microcrystals is supposed, e.g., so that the { 100) plane has a tendency to be parallel to the surface, the experimental results are well produced. When the limit of the polar angle is chosen so that the theoretical curve agrees with the experimental curve, the effect of the surface oxide layer and damage, which is to spread out the beam, is also partly taken into account in the calculations. It is natural that the (100) direction is preferred in the A1 case, because the microcrystals tend to orient in this way, when the A1 plate is rolled. Further proof against complete isotropy in the orientation of the microcrystals can be achieved by comparing the most probable ranges. The theoretical top is at 35 -+ 3 nm, whereas experimentally it is found at 43.5 -+ 3.0 nm [8] and, if in the calculation the polar angle is between 0 ° and 7 ° with respect to the <100) direction, the top is at 4 0 -+ 5 nm. In both cases studied, the experimental concentration near the surface is larger than the calculated value. This is probably due to diffusion and oxidation at the surface [7,8]. Further calculations indicate that a small change in the potential or in the inelastic energy loss does not affect these conclusions. However, the sensitivity o f the distributions to the rms-vibration amplitudes indicates a definite sensitivity to temperature. From the above results we can make a few remarks to be kept in mind in future applications. When measuring the stopping values in polycrystalline materials, the type of material used should be def']ned with care. At least in the Pb ~ AI case, some dependence of the concentration distribution on the implantation angle and temperature can probably be measured. The potentials seem to be adequate also for studies on slowing down in the well channeled cases, where the inelastic energy loss is more important than the elastic energy loss. The computer simulations presented indicate that even in the case of polycrystalline materials with very strong preferential orientation, the effect on the most probable range is small. The main effect of crystaUinity is to produce long tails in the distributions, leading to important asymmetries and consequently to higher mean ranges. 437
Volume 95A, number 8
PHYSICS LETTERS
References [1] R.G. Gordon and Y.S. Kim, J. Chem. Phys. 56 (1972) 3122. [2] W.D. Wilson, L.G. Haggmark and J.P. Biersack, Phys. Rev. B15 (1977) 2488. [3] M. Bister, M. Hautala and M. Jgntti, Radiat. Eff. 42 (1979) 201. [4] M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008.
438
23 May 1983
[5] International tables for X-ray crystallography, Vol. I11 (Kynoch Press, Birmingham, 1962). [6] J. Lindhard, M. Scharff and H.B. Schffptt, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 33 (1963) no. 14. 171 J.L. Gombasson, B.W. Farmery, D. McCulloch, G.W. Neilson and M.W. Thompson,Radiat. Eff. 36 (1978) 149. [8] M. Bister, J. Keinonen and A. Anttila, Phys. Lett. 74A (1979) 357. [9] J. Keinonen, M. Hautala, M. Luomaj~rvi, A. Anttila and M. Bister, Radiat. Eff. 39 (1978) 189.