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A note on neutron-sputtering measurements
Journal of Nuclear Materials 76 & 77 (1978) 190-192 0 North-Holland Publishing Company
ANOTEONNEUTRON-SPUTTERINGMEASUREMENTS Hans Hen& ANDERSEN
sputtering from 14.MeV neutrons originate from recoils from inelastic neutron-interaction events. This has been shown to be the case for copper and niobium fo] and for gold [IO,1 11. The momentum of the recoil after the decay of the resulting compound nucleaus is strongly forward-peaked, for niobium, for example, within a cone with an opening angle of approximately 15”. The energy is peaked narrowly around EJA, where En is the energy of the incoming neutron and A is the target mass number. The above situation permits an extremely simple estimate of the forward-to-backward sputtering-yield ratio. Let f&x) be the depositied-energy depth distribution of the target-atom recoils, with the origin of the x-axis at the starting point of the recoils, and
After some years of considerable controversy over the sputtering yields of energetic neutrons, these yields now seem to be converging [l-5] to values of appro~ately a few times lo-‘, in reasonable agreement with theoretical predictions. Two facts catch the eye when more recent measurements are contemplated: only upper limits are given for the sputtering yields, and very small amounts of material, i.e., considerably less than one monolayer, are sputtered away during measurements. It is well established that sputtering yields may be orders of magnitude lower than the equilibrium value until at least one monolayer has been sputtered away [6]; hence considerable doubt as to the magnitude of the expe~ent~ results still persists. Also the theoretical results [7] may to some extent be dubious. In particular, a large number of neutron-sputtering experiments have been performed on a low-yield material, i.e., niobium, and sputtering theory has been found systematically to overestimate the yields of low-yield materials [S] , and the present a~eement between experiment and theory for neutron-sputtering yields may be fortuitous and should not be used as an argument for closing the case. It is the purpose of the present note to present a very simple calculation of the ratio between forward and backward neutron-sputte~ng yields. The result of the calculation, the assumption of which has otherwise been tested experimentally, will be found to disagree strongly with experiment. The method used differs from a direct calculation of sputtering yields but gives a very similar answer. Hence, it apparently disproves the remark in ref. [3 f that the disagreement between experimental and theoretical values of the ratio between forward and backward neutron-sputtering yields might stem from a basic weakness in the sputtering theory. The main fraction of radiation damage as well as
(1) -(10
and Y(E) is the amount of recoil energy E remaking in atomic motion in the fully developed cascade. For 150.keV niobium in niobium, vQ is approximately [ 121 0.9E. We shall now use a basic result of sputtering theory 171, viz. that for a given material, the sputtering yield is proportional to f&) at the surface. As the foils used for neutron-sputte~g experiments are substantially thicker than the recoil ranges in question, we have
Sbac!ward = k x s ’ fd@)
-00
190
do .
(3)
191
H.H. Andersen /Neutron-sputtering measurements
recoils, of course, will give approximately the same forward and backward sputtering and hence make the ratio of eq. (6) less extreme. Thus it is necessary to estimate the influence also of elastic collisions. Let us divide the recoils into groups indexed by i. The recoils originating from inelastic neutron reactions may be counted as one group. In accordance with eqs. (2) and (3) we have
We assume now that Sr >> S, (which will be found to be consistent with the result of our calculation) and have
sb/sf
= sb/@f
+ k s”
_m
fd(x)
+ sb) = k s” fd@) -m
h)
= j
fd(x)
W(k
oh’@?)
1 0
fd(x)
do
.
(4)
_-oD
The energy-reflection coefficient (also called the sputtering efficiency) is given by
sf=k CPi j?d,i(x) i
do >
Sb = k CPi
do P
0
i
_/
fd,i(x)
(7)
_m
and hence and was predicted to be energy-independent and to depend on the ratio between target mass and projectile only [ 131. For the equal-mass case, y was calculated to be 2.4 X 10m2.It was found experimentally that to some extent, y depended on energy but could be depicted as a function of mass ratio and reduced Thomas-Fermi energy E [ 14,151. For the equal-mass case, the theoretical result was very well corroborated at low energies. For 150-keV niobium, y is inferred to be [ 141 2.0 X 10m2,which is in perfect agreement with recent, numerical estimates [ 161. From eqs. (4) and (S), we have (6)
at low energies. For higher energies, T(J?) decreases, but E/(u(&)) increases at approximately the same rate. For 150-keV niobium, the ratio will have decreased to l/45. Hence the result in eq. (6) holds with reasonable precision for all neutron-sputtering experiments, independent of neutron-energy spectrum and target material provided all the sputtering is caused by inelastic neutron events. Experiments [2,3,5] yield Sb and Sr of approximately the same magnitude, in strong disagreement with eq. (6). At energies where inelastic neutron scattering becomes less dominant, they occur mainly at the expense of hard elastic collisions. Hence, the remaining elastic collisions are mainly soft ones with recoils nearly perpendicular to the neutron trajectory. These
sb/sf
= sb/(sb
+ sf)
= &i~i’Yik~
i
i
W’j(Ti)>
3
03)
where pi is the relative population of the individual recoil groups with energy Tj. Evaluation of eq. (8) is complicated by the fact that the recoils do not start in directions perpendicular to the surface. In ref. [ 141, however, it was found that Y(cp)= -Y(O)+ ($ - Y(0)) (1 - cos (P)23
(9)
where cpis the angle between the recoil direction and the target-surface normal and, further, the angle between the incidence direction of the neutrons and the recoil direction; hence, through application of elementary kinematics, r(r) = C,,)
+ (; - r(T-))
(1 - G);;>’
> (10)
which may be inserted into eq. (8), using the recoil-probability densities of ref. [9]. For 15-MeV neutrons incident on niobium, numerical evaluation yields St& = 1122 .
(11)
This ratio rapidly becomes more extreme with increasing neutron energy. The general shape of the recoil spectra as well as
192
H.H. Andersen
/Neutron-sputtering
the ratio between elastic and inelastic neutron collisions do not differ appreciably from niobium to copper and gold [9,1 l] ; hence the yield ratio will not differ much form eq. (11) for these materials, We conclude that simple estimates such as eqs. (6) and (11) predict the forward- and backward-sputtering yield of neutron sputtering to differ by between one and two orders of magnitude. It is not possible to infer whether the discrepancy between these estimates and experimental-yield ratios is due to uncertainties in the measured forward or backward yield or, possibly, to both. Hence, in spite of the reservations made in the opening paragraph concerning theoretical estimates of neutron-sputtering yields [ 1,7], such estimates may still be more reliable than existing experimental data. A clarification may first be available when experiments have been performed on targets sputter-cleaned inside the UHV target chamber or through measurements of synenergistic effects under simultaneous irradiation with charged-particle beams.
References [l] R. Behrisch, Nucl. Instrum. Methods 132 (1976) 293. [2] O.K. Harling, M.T. Thomas, R.L. Brodzinski, and L.A.
measurements
Ranticelli, J. Nucl. Mat. 63 (1976) 422. [3] L.H. Jenkins, G.J. Smith, J.F. Wendelken, and M.J. Saltmarsh, J. Nucl. Mat. 63 (1976) 438. [4] R. Behrisch, O.K. Harling, M.T. Thomas, R.L. Brodzinski, L.H. Jenkins, G.J. Smith, J.F. Wendelken, M.J. Saltmarsh, M. Kaminsky, S.K. Das, C.M. Logan, R. R. Meisenheimer, J.E. Robinson, M. Shimotomai, and D.A. Thompson, J. Appl. Phys. 48 (1977) 3914. [5] O.K. Harling, M.T. Thomas, R.L. Brodzinski, and L.A. Ranticelli, J. Appl. Phys. 48 (1977) 4315. [6] J.S. Colligon, C.M. Hicks, and A.P. Neokleous, Radiat. Eff. 18 (1973) 119. [7] P. Sigmund, Phys. Rev. 184 (1969) 383. [S] H.H. Andersen and H.L. Bay (to be published). (91 J.B. Roberto and M.T. Robinson, J. Nucl. Mat. 61 (1976) 149. [lo] R. Behrisch, R. Gahler, and J. Kalus, J. Nucl. Mater. 53 (1974) 183. [ 111 J.B. Roberto, M.T. Robinson, and C.Y. Fu, J. Nucl. Mat. 63 (1976) 460. [ 121 M.T. Robinson, in: Radiation-Induced Voids in Metals, eds. J.W. Corbett and I.C. Janiello (USAEC Office of Information Service Series, 1972) p. 397. [13] P. Sigmund, Can. J. Phys. 46 (1968) 731. [ 141 H.H. Andersen, Radiat. Eff. 7 (1971) 179. [ 151 H.H. Andersen, Radiat. Eff. 3 (1970) 51. [ 161 K.B. Winterbon, Ion Implantation Range and Energy Deposition Distributions, vol. 2 (Plenum Press, New York, 1975).
ANOTEONNEUTRON-SPUTTERINGMEASUREMENTS Hans Hen& ANDERSEN
sputtering from 14.MeV neutrons originate from recoils from inelastic neutron-interaction events. This has been shown to be the case for copper and niobium fo] and for gold [IO,1 11. The momentum of the recoil after the decay of the resulting compound nucleaus is strongly forward-peaked, for niobium, for example, within a cone with an opening angle of approximately 15”. The energy is peaked narrowly around EJA, where En is the energy of the incoming neutron and A is the target mass number. The above situation permits an extremely simple estimate of the forward-to-backward sputtering-yield ratio. Let f&x) be the depositied-energy depth distribution of the target-atom recoils, with the origin of the x-axis at the starting point of the recoils, and
After some years of considerable controversy over the sputtering yields of energetic neutrons, these yields now seem to be converging [l-5] to values of appro~ately a few times lo-‘, in reasonable agreement with theoretical predictions. Two facts catch the eye when more recent measurements are contemplated: only upper limits are given for the sputtering yields, and very small amounts of material, i.e., considerably less than one monolayer, are sputtered away during measurements. It is well established that sputtering yields may be orders of magnitude lower than the equilibrium value until at least one monolayer has been sputtered away [6]; hence considerable doubt as to the magnitude of the expe~ent~ results still persists. Also the theoretical results [7] may to some extent be dubious. In particular, a large number of neutron-sputtering experiments have been performed on a low-yield material, i.e., niobium, and sputtering theory has been found systematically to overestimate the yields of low-yield materials [S] , and the present a~eement between experiment and theory for neutron-sputtering yields may be fortuitous and should not be used as an argument for closing the case. It is the purpose of the present note to present a very simple calculation of the ratio between forward and backward neutron-sputte~ng yields. The result of the calculation, the assumption of which has otherwise been tested experimentally, will be found to disagree strongly with experiment. The method used differs from a direct calculation of sputtering yields but gives a very similar answer. Hence, it apparently disproves the remark in ref. [3 f that the disagreement between experimental and theoretical values of the ratio between forward and backward neutron-sputtering yields might stem from a basic weakness in the sputtering theory. The main fraction of radiation damage as well as
(1) -(10
and Y(E) is the amount of recoil energy E remaking in atomic motion in the fully developed cascade. For 150.keV niobium in niobium, vQ is approximately [ 121 0.9E. We shall now use a basic result of sputtering theory 171, viz. that for a given material, the sputtering yield is proportional to f&) at the surface. As the foils used for neutron-sputte~g experiments are substantially thicker than the recoil ranges in question, we have
Sbac!ward = k x s ’ fd@)
-00
190
do .
(3)
191
H.H. Andersen /Neutron-sputtering measurements
recoils, of course, will give approximately the same forward and backward sputtering and hence make the ratio of eq. (6) less extreme. Thus it is necessary to estimate the influence also of elastic collisions. Let us divide the recoils into groups indexed by i. The recoils originating from inelastic neutron reactions may be counted as one group. In accordance with eqs. (2) and (3) we have
We assume now that Sr >> S, (which will be found to be consistent with the result of our calculation) and have
sb/sf
= sb/@f
+ k s”
_m
fd(x)
+ sb) = k s” fd@) -m
h)
= j
fd(x)
W(k
oh’@?)
1 0
fd(x)
do
.
(4)
_-oD
The energy-reflection coefficient (also called the sputtering efficiency) is given by
sf=k CPi j?d,i(x) i
do >
Sb = k CPi
do P
0
i
_/
fd,i(x)
(7)
_m
and hence and was predicted to be energy-independent and to depend on the ratio between target mass and projectile only [ 131. For the equal-mass case, y was calculated to be 2.4 X 10m2.It was found experimentally that to some extent, y depended on energy but could be depicted as a function of mass ratio and reduced Thomas-Fermi energy E [ 14,151. For the equal-mass case, the theoretical result was very well corroborated at low energies. For 150-keV niobium, y is inferred to be [ 141 2.0 X 10m2,which is in perfect agreement with recent, numerical estimates [ 161. From eqs. (4) and (S), we have (6)
at low energies. For higher energies, T(J?) decreases, but E/(u(&)) increases at approximately the same rate. For 150-keV niobium, the ratio will have decreased to l/45. Hence the result in eq. (6) holds with reasonable precision for all neutron-sputtering experiments, independent of neutron-energy spectrum and target material provided all the sputtering is caused by inelastic neutron events. Experiments [2,3,5] yield Sb and Sr of approximately the same magnitude, in strong disagreement with eq. (6). At energies where inelastic neutron scattering becomes less dominant, they occur mainly at the expense of hard elastic collisions. Hence, the remaining elastic collisions are mainly soft ones with recoils nearly perpendicular to the neutron trajectory. These
sb/sf
= sb/(sb
+ sf)
= &i~i’Yik~
i
i
W’j(Ti)>
3
03)
where pi is the relative population of the individual recoil groups with energy Tj. Evaluation of eq. (8) is complicated by the fact that the recoils do not start in directions perpendicular to the surface. In ref. [ 141, however, it was found that Y(cp)= -Y(O)+ ($ - Y(0)) (1 - cos (P)23
(9)
where cpis the angle between the recoil direction and the target-surface normal and, further, the angle between the incidence direction of the neutrons and the recoil direction; hence, through application of elementary kinematics, r(r) = C,,)
+ (; - r(T-))
(1 - G);;>’
> (10)
which may be inserted into eq. (8), using the recoil-probability densities of ref. [9]. For 15-MeV neutrons incident on niobium, numerical evaluation yields St& = 1122 .
(11)
This ratio rapidly becomes more extreme with increasing neutron energy. The general shape of the recoil spectra as well as
192
H.H. Andersen
/Neutron-sputtering
the ratio between elastic and inelastic neutron collisions do not differ appreciably from niobium to copper and gold [9,1 l] ; hence the yield ratio will not differ much form eq. (11) for these materials, We conclude that simple estimates such as eqs. (6) and (11) predict the forward- and backward-sputtering yield of neutron sputtering to differ by between one and two orders of magnitude. It is not possible to infer whether the discrepancy between these estimates and experimental-yield ratios is due to uncertainties in the measured forward or backward yield or, possibly, to both. Hence, in spite of the reservations made in the opening paragraph concerning theoretical estimates of neutron-sputtering yields [ 1,7], such estimates may still be more reliable than existing experimental data. A clarification may first be available when experiments have been performed on targets sputter-cleaned inside the UHV target chamber or through measurements of synenergistic effects under simultaneous irradiation with charged-particle beams.
References [l] R. Behrisch, Nucl. Instrum. Methods 132 (1976) 293. [2] O.K. Harling, M.T. Thomas, R.L. Brodzinski, and L.A.
measurements
Ranticelli, J. Nucl. Mat. 63 (1976) 422. [3] L.H. Jenkins, G.J. Smith, J.F. Wendelken, and M.J. Saltmarsh, J. Nucl. Mat. 63 (1976) 438. [4] R. Behrisch, O.K. Harling, M.T. Thomas, R.L. Brodzinski, L.H. Jenkins, G.J. Smith, J.F. Wendelken, M.J. Saltmarsh, M. Kaminsky, S.K. Das, C.M. Logan, R. R. Meisenheimer, J.E. Robinson, M. Shimotomai, and D.A. Thompson, J. Appl. Phys. 48 (1977) 3914. [5] O.K. Harling, M.T. Thomas, R.L. Brodzinski, and L.A. Ranticelli, J. Appl. Phys. 48 (1977) 4315. [6] J.S. Colligon, C.M. Hicks, and A.P. Neokleous, Radiat. Eff. 18 (1973) 119. [7] P. Sigmund, Phys. Rev. 184 (1969) 383. [S] H.H. Andersen and H.L. Bay (to be published). (91 J.B. Roberto and M.T. Robinson, J. Nucl. Mat. 61 (1976) 149. [lo] R. Behrisch, R. Gahler, and J. Kalus, J. Nucl. Mater. 53 (1974) 183. [ 111 J.B. Roberto, M.T. Robinson, and C.Y. Fu, J. Nucl. Mat. 63 (1976) 460. [ 121 M.T. Robinson, in: Radiation-Induced Voids in Metals, eds. J.W. Corbett and I.C. Janiello (USAEC Office of Information Service Series, 1972) p. 397. [13] P. Sigmund, Can. J. Phys. 46 (1968) 731. [ 141 H.H. Andersen, Radiat. Eff. 7 (1971) 179. [ 151 H.H. Andersen, Radiat. Eff. 3 (1970) 51. [ 161 K.B. Winterbon, Ion Implantation Range and Energy Deposition Distributions, vol. 2 (Plenum Press, New York, 1975).