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Surface layer destruction during ion beam analysis
Nuclear Instruments and Methods in Physics Research B 155 (1999) 440±446
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Surface layer destruction during ion beam analysis R. Behrisch
a,*
, W. von der Linden b, U. von Toussaint a, D. Grambole
c
a
c
Max Planck Institut f ur Plasmaphysik, EURATOM Association, Boltzmannstrasse 2, D-85748 Garching, Germany b Institut f ur theoretische Physik, Technische Universit at Graz, A-8010 Graz, Austria Forschungszentrum Rossendorf e.V., Institut f ur Ionenstrahlphysik und Materialforschung, P.F. 510119, D-01314 Dresden, Germany Received 13 April 1999; received in revised form 1 June 1999
Abstract In ion beam analysis the decrease of the measuring signal with a number of incident ions, due to a destruction of the surface layer being analysed, depends critically on the lateral intensity distribution in the analysing ion beam. For the assumption of destruction in one step, the decrease was calculated and the obtained analytical formulae was ®tted to the decrease as measured in ERDA and PIXE analyses. This allows to obtain values for the destruction cross sections for the ions and the samples in the analysis, as well as information about the lateral intensity distribution in the analysing ion beam. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction During ion bombardment of solids the surface layers are eroded by sputtering and ion-induced desorption. If surface layers are analysed by MeV ion beam techniques, such as RBS, NRA, PIXE or ERDA, the signals generally decrease with the number of ions incident during the analyses. This is especially critical for surface layer analysis with ion micro beams [1], when a high incident ion current density is needed in the micro-spot for getting a spectrum with suciently small statistical errors. The observed decrease has mostly been ®tted by one or two exponentially decreasing
* Corresponding author. Tel.: +89-3299-1250; fax: +893299-1149; e-mail: [email protected]
functions [2±6] or even more complex empirical ®tting curves [7]. In the following, based on a single step destruction process and Poisson statistics for the incident analysing ions, a model is derived for the decrease of the measuring signal with the number of incident ions for dierent distributions of the analysing ion beam current. 2. The model An ion beam with a rectangular or a bellshaped current distribution, where the wings may be cut by passing the beam through a diaphragm, is incident onto the surface to be analysed. For calculating the destruction of the surface layer with analysing the number of incident ions, resulting in the decrease of the measured signal, we will assume
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 4 9 1 - 7
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
that every incident ion may damage around its point of incidence xn in one step, a volume with an eective surface area of about pq2 and a depth d of the order of the range of the analysing ions, i.e., up to the depth from which the analysis signal originates. In this volume the atoms are removed by an ion hitting the surface at a point xi , depending on the distance between xi and xn . We will calculate the `survival probability' PS xn ; U, i.e., the probability that an area centred around the position xn is still present after a number of incident ions U, with the incident ion beam having an intensity distribution F xi ; x0 around the centre of the ion beam impact at x0 . We will assume a Gaussian distribution for the incoming ion beam intensity with a 1/e half width of R and a total radius of a which may be determined by a diaphragm. 2
F xi ; x0 C exp ÿ xi ÿ x0 =R2 ÿ1 2 2 : with C pR2 1 ÿ eÿa =R
1
The constant C is a normalisation factor, which simpli®es to 1/(pa2 ) for a constant rectangular current density, i.e., the case a R and to 1/(pR2 ) for a peaked Gaussian distribution i.e., the case a R. 2.1. The survival probability The survival probability PS xn ; U for an area around a position xn after analysing with a number of incident ions U may also be looked at as the fraction of the original surface area which is not destructed after analysing with U incident ions. The dierential change dPS xn ; U for an incident number of ions dU is given by dPS xn ; U ÿdU PS xn ; U Z Pr jxi ÿ xn jF xi ; x0 d2 xi :
2
With Pr jxi ÿ xn j being the probability that an ion incident at xi will damage an area around xn , for an ion beam pro®le F xi ; x0 around the centre of
441
the ion beam impact at x0 . The integral over all possible impact positions gives the change in the area density at xn . Since Pr jxi ÿ xn j is peaked around zero, the eective area of destruction pq2 is given by Z 3 Pr jxi ÿ xn jF xi ; x0 d2 xi pq2 F xn ; x0 : The solution of the dierential equation (2) for the survival probability PS xn ; U gives PS xn ; U PS xn ; 0 exp ÿpq2 UF xn ; x0 :
4
This means that the survival probability PS xn ; U for an area around a position xn decreases exponentially with the number of ions U incident onto the area 1/F(xn ,x0 ) being analysed and with the eective area pq2 destructed by each impinging ion. The intensity of the analysing ion beam is generally not uniformly distributed on the bombarded area pa2 , but may spatially vary, and will be given by the distribution function F xi ; x0 around the centre at x0 of the ion beam, such as by Eq. (1). 2.2. Signal in ion beam analysis In ion beam analysis the signal YM (scattered ions, recoiled target atoms, products from a nuclear reaction, or X-ray intensity) measured with an incident number of ions DU after analysing with a number of incident ions U RDU will be given by: Z Z PS xn ; Uf jxi ÿ xn j YM U; DU DU F xi ; x0 d2 xi d2 xn : Similar to Eq. (3) we will put Z f jxi ÿ xn j F xi ; x0 d2 xi r F xn ; x0
5
6
with r being the dierential cross section for the reaction used in the analysis, times the acceptance angle of the detector. By inserting Eqs. (1), (4) and (6) in Eq. (5) we get for the decrease of the measured signal with total number of incident ions U
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R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
Z YM U; DU r DU
exp ÿpq2 UC 2
exp ÿ xn ÿ x0 =R2 C exp ÿ xn ÿ x0 2 =R2 2p xn dxn : 7 Integration within the boundaries 0 and a (for convenience we may put x0 0) gives the decrease of the measuring signal with the number of incident ions, for the general current distribution as given by Eq. (1): 2 R2 h YM U; DU rDU 2 exp ÿ pq2 UC eÿ a=R a i. ÿ exp ÿpq2 UC pq2 U: 8 Two special cases of Eq. (8) with Eq. (1) can be regarded for the incident current distribution. For a R, resulting in C 1/pa2 , i.e., a uniform rectangular current density distribution across the beam spot we get r 9 YM U; DU DU 2 exp ÿpq2 U=pa2 pa corresponding to an exponential decrease with the analysing ion ¯uence U/pa2 . For a R, resulting in C 1/pR2 corresponding to a Gaussian distribution we ®nally get the decrease of the signal with the number of analysing ions U R DU or an analysing ¯uence U/pR2 YM U; DU DU
2
2
r 1 ÿ exp ÿpq U=pR : pa2 pq2 U=pR2
10
For the rectangular current density distribution (a R) of the analysing ion beam we get an exponential decrease of the analyses signals, while for the Gaussian distribution (a R) the decrease of the signal is dierent, depending on the values for R and a. For a small number of analysing ions (U ® 0) Eqs. (9) and (10) show that the initial signals are the same, i.e., independent of the current density distribution. 2.3. Determination of the destruction area pq2 From the measured decrease of the analysis signal YM with the number of incident ions U, such
as observed in this work for the hydrogen isotope recoils in micro beam ERDA measurements and the Au PIXE signals in micro beam PIXE measurements, it is possible to get information both about the ion current distribution on the measured spot and to determine the destruction areas. We will de®ne the parameters Pv by P2 q=R2
P1 r=pa2 ;
and
2
P3 exp ÿ a=R : The expected analytical decrease of the analysis signals with the number of incident ions (Eqs. (8)± (10) with Eq. (1)) may be written as YM U; DU DU P1 exp ÿ P2 UP3 = 1 ÿ P3 ÿ exp ÿ P2 U= 1 ÿ P3 =P2 U:
8a
We will again consider the two limiting cases, i.e. a R and a R. For a R, i.e., a uniform rectangular current density distribution we have P3 ® 1 and, similar to Eq. (9), we get YM U; DU DU P1 exp P2 = ln P3 U:
9a
For a R, i.e., a Gaussian distribution, we have P3 ® 0 and similar to Eq. (10) we get YM U; DU DU P1
1 ÿ eÿP2 U : P2 U
10a
By ®tting the calculated analytical dependence of the signal decrease with the number of incident ions U (Eq. (8a)) to the measured decrease of signals, the coecients Pv , and thus the ion current distribution on the measured spot, and the destruction areas pq2 can be determined. The values for r/pa2 P1 , are the initial yield for the nondestructed target as obtained from the ®rst analysis with an incremental number of incident ions DU (see Eqs. (8a)±(10a)).
3. Experiments The sample analysed was a carbon layer which had been deposited during plasma discharges together with hydrogen and deuterium onto the tungsten-coated divertor plates of the fusion ex-
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
periment ASDEX Upgrade in the Max-PlanckInstitut f ur Plasmaphysik, Garching [8]: For measuring the depth distribution of the hydrogen isotopes in the deposit a wedge was cut at the carbon layer and the slope was analysed with micro ion beam ERDA using a 10 MeV Si beam at an angle of incidence of 75° relative to the surface normal [1]. Before cutting the wedge an Au layer, 75 nm thick, had been evaporated onto the carbon ®lm to mark the surface. This Au layer was also analysed with 10 MeV Si ions at an angle of incidence of 75°, by micro beam PIXE. The decrease of the PIXE signals with the number of incident ions is shown in Fig. 2. During the ERDA analyses of the H and D in the carbon layer, the signals, each measured with an incremental number of ions DU 4:7 1010 Si ions, were stored. The signals for the amount of H and D present in the target decrease with total number of ions U RDU in units of 1010 Si ions, as shown in Fig. 1. The decreases of the ERDA signals as well as of the PIXE signals (see Fig. 2) were ®tted to the calculated general analytical dependence on the number of incident ions Eq. (8a) using the ®tting routine of Microcal, Origin, version 5.0, to determine the values for the Pv . Another non-linear least squares ®t with the programme XMGR, version 4.1.2. [9] con®rmed the results for the Pv . For good ®tting, a back-
Fig. 1. Measured decrease of the H and D ERDA signals for analysing H and D in a carbon ®lm [1]. The measured points are ®tted with a decrease corresponding to a Gauû current density distribution, shown by solid lines, and with an exponential decrease, corresponding to a uniform current distribution, shown by dashed lines.
443
Fig. 2. Measured decrease of the Au PIXE signal for analysing an Au layer with 10 MeV Si ions. The measured points are ®tted with an exponential decrease, corresponding to a uniform current distribution. The good agreement indicates a rectangular current density distribution in this measurement.
ground had to be subtracted from the measured data. This was performed ®rst by a four parameter ®t with the background as the additional parameter P4 . The values obtained for the background P4 agreed within the uncertainties with the values obtained for the background by extrapolation of the measured data to U ® 1. Finally the measured decrease in the ERDA measurements of the H and D in the carbon layer was also ®tted by a simple exponential decrease (see Eq. (9a)). This ®t, shown by dashed lines in Fig. 1 is worse than the general ®t shown by the continuous lines. The values obtained for the Pv by the dierent ®tting programmes agreed to better than 5%, they are summarized in Table 1. The parameter P1 times DU gives the signal at the start of the analysis. This is determined by the cross section for the analysis reaction, the geometry and the opening angle of the detector. P2 gives the destruction area relative to the half width pR2 of the analysing ion beam, and P3 gives information about the shape of the incident ion beam. For a Gaussian distribution i.e. R a we get very small values for P3 , such as that obtained for the ERDA measurements of the H and D. In this case the ®t using Eq. (8a) was the same as using Eq. (10a), however the ®t using the simple exponential decrease in Eq. (9a) did not give a good agreement, as shown in Fig. 1. For the Au PIXE measurements, the general ®t gave a value for P3 of the order of 1, indicating a constant rectangular
444
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
Table 1 Values for the parameters Pv as obtained by ®tting the predicted analytical dependence of the signal yield YM U; DU) Eq. (8a) with analysing the number of incident ions U to the measured values (see Figs. 1 and 2) Sample
P1 r=pa2
P2 pq2 =pR2
P3 expÿ a=R2
Background, P4
ERDA, H release from C ERDA, D release from C PIXE sputtering of Au on C
1.4 ´ 10ÿ8 3 ´ 10ÿ9 6 ´ 10ÿ7
8.1 ´ 10ÿ12 8.1 ´ 10ÿ12 3.5 ´ 10ÿ12
3 ´ 10ÿ6 3 ´ 10ÿ6 0.3
209 73 11 600
current distribution i.e. R a. This is in agreement with the current distribution used in the measurements. In the case of the Au PIXE analysis, the ®t to Eq. (9a) was the same as the ®t to the general Eq. (8a). The values calculated from the data of Table 1 for the half width of the ion beam area pR2 pa2 = ÿ ln P3 and for the destruction areas pq2 P2 pR2 are summarised in Table 2. We may further calculate average sputtering yields with
analysed was about 5±6 at.% of the atomic density of C (NV;C 102 nmÿ3 ), resulting in NVH NVD 3 nmÿ3 , while the atomic density for Au is NV;Au 59 nmÿ3 . This gives a volume which is destroyed in the ERDA analyses of H, D of about 75±150 nm3 , corresponding to about 2.3 ´ 102 H and 5 ´ 102 D atoms released per incident 10 MeV Si ion. For Au the total thickness is 290 nm giving a volume which is destroyed of about 2.3 nm3 corresponding to about 80 Au atoms removed per incident 10 MeV Si ion.
YS pq2 dNV : Here pq2 dNV is the number of atoms in the eective volume which is eroded at the impact of one analysing ion, with d the depth of the destructed cylinder and NV the number density of the atoms in the solid, which is analysed. The values for pq2 are given in Table 2. For d the mean depth analysed by the ions has been taken. In the Au PIXE measurements the depth analysed is the thickness of the Au layer being 75 nm. This layer is penetrated by the analysing ion beam at an angle of 75° to the surface normal, resulting in a depth d 75/cos 75 290 nm, while for the geometry and 10 MeV Si ions used in the ERDA measurements the analysed depths for H is about 100 nm, while it is about 200 nm for D. For H and D the atomic density (D + H in C) in the deposits
4. Discussion The measured decrease of the ERDA and PIXE signals with the number of incident ions in ion beam analysis could be ®tted, within the statistical errors of the measurements, to the analytical decrease expected for dierent lateral current distributions. The lateral current distributions derived from the ®tting to the measurements agreed qualitatively with the current distributions used in the measurements. For the assumption of destruction in one step eective areas of ion bombardment-induced desorption and sputtering, giving the yields per incident ion have been derived, which do not depend on the current distribution used for the measurements.
Table 2 Total ion beam area pa2 which was used in the experiments, the half width area of the ion beam pR2 as calculated from the values for P3 and the destruction area pq2 as calculated from the values P2 of Table 1
ERDA (H release from C) ERDA (D release from C) PIXE (sputtering of Au on C)
pa2 (nm)2
pR2 (nm)2 estim.
pq2 (nm)2
1.19 ´ 1012 1.19 ´ 1012 2.7 ´ 109
9.3 ´ 1010 9.3 ´ 1010 2.24 ´ 109
0.75 0.75 7.84 ´ 10ÿ3
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
In the model used here, it has been assumed that destruction of an eective cylinder around the point of impact of the analysing ions takes place in one step and that the destruction depends only on the total number of incident ions on the analysed spot. This model may have to be re®ned. Experimentally, ®rst, at the very beginning of the analysis, i.e., for a very low number of incident ions no measurable destruction has been reported [10]. Further, in some experiments particularly the bombardment-induced desorption of gases was found to depend also on the local current density of the analysing ion beam [11]. Finally for the ion bombardment-induced release of hydrogen from carbon materials a two-step process has been proposed. In a ®rst step free hydrogen atoms may be created by release from binding sites at carbon atoms. The hydrogen atoms may subsequently be bound again to carbon atoms or they may combine with another hydrogen atom to a molecule, which may diuse to and leave the carbon surface [12]. Depending on the time scales for the processes of these two steps and the current densities applied in the analyses, this may also have an in¯uence on the decrease of the measuring signal with the number of analysing ions. These two eects have to be investigated in more detail, so that the contribution of each eect to the signal decrease can be separated and controlled. 5. Summary and conclusion In ion beam analysis, especially with a microbeam, a decrease of the detected signal with the number of incident ions is found, due to a destruction, i.e., ion bombardment-induced desorption of trapped gases or sputtering of solids. This decrease has generally been ®tted by two exponentially decreasing functions. In this work it was shown, that the decrease depends on the lateral current distribution of the analysing ion beam. For a simple model, i.e., every incident ion destructs an eective area pq2 around its point of incidence, analytical formulae have been derived for the decrease of the signal with the number of incident ions and its dependence on the shape of the ion
445
current distribution on the area to be analysed. This has to be taken into account in the analyses of destruction measurements and the conclusions in respect to destruction models. By ®tting the analytical formulae to the signal decrease obtained in measurements, information about the current distribution and the cross section for ion bombardment desorption or sputtering can be obtained, which allow us further to derive desorption and sputtering yields. For bombardment with 10 MeV Si ions, at an angle of incidence 75° to the normal, the desorption yields for H and D in carbon are found to be in the range of 102 H and D per incident 10 MeV Si ion, while the sputtering yield for Au is about 80 Au atoms per incident 10 MeV Si ion. These large yields are much higher than the sputtering yields measured for 230 MeV Au ion bombardment on Au [13,14], and higher than predicted for cascade sputtering. This indicates that the destruction is not only caused by collision cascade processes, but some larger removal due to insucient sticking of the Au layer on the carbon substrate may also contribute. The formalism described here is well suited for a fast measurement of the destruction cross sections and the yields for dierent bombardment conditions for comparing the destruction of surface layers during the analysis with dierent ions and energies, in order to obtain destruction cross sections and optimal analysis conditions. Acknowledgements We would like to thank our colleagues W. Eckstein, R. Gr otzschel and F. Herrman for many helpful comments and discussions.
References [1] D. Grambole, F. Herrmann, R. Behrisch, W. Haue, Nucl. Instr. and Meth. B, (in press). [2] B.M.U. Scherzer, R.S. Blewer, R. Behrisch, R. Schulz, J. Roth, J. Borders, R. Langley, J. Nucl. Mater. 85 (1979) 102. [3] J. Roth, B.M.U. Scherzer, R.S. Blewer, D.K. Brice, S.T. Picraux, W.R. Wampler, J. Nucl. Mater. 93/94 (1980) 601.
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[4] R. Behrisch, V.M. Prozesky, H. Huber, W. Assmann, Nucl. Instr. and Meth. B 118 (1996) 262. [5] S. Nagata, S. Yamaguchi, H. Bergs aker, B. Emmoth, Nucl. Instr. and Meth. B 33 (1988) 739. [6] B.M.U. Scherzer, M. Wielunski, W. M oller, A. Turos, J. Roth, Nucl. Instr. and Meth. B 33 (1988) 714. [7] S. Turgeon, R.W. Paynter, Nucl. Instr. and Meth. B 118 (1996) 322. [8] K. Krieger, H. Maier, R. Neu, J. Nucl. Mater. 266 (1999) 207.
[9] http:// plasma-gate.weizmann.ac.il/xmgr. [10] GT. Dollinger, Private communication. [11] D. Grambole, F. Herrmann, U. Kreissig, R. Behrisch, to be published. [12] M.P. de Joung, A.J.H. Maas, L.J. van IJzendoorn, S.S Klein, M.A.J de Voigt, J. Appl. Phys. 82 (3) (1997) 1058. [13] H.D. Miskes, W. Assmann, M. Brodale, M. Dobler, H. Gl uckler, P. Hartung, P. Stenzel, Nucl. Instr. and Meth. B 146 (1998) 162. [14] W. Eckstein, Private communication.
www.elsevier.nl/locate/nimb
Surface layer destruction during ion beam analysis R. Behrisch
a,*
, W. von der Linden b, U. von Toussaint a, D. Grambole
c
a
c
Max Planck Institut f ur Plasmaphysik, EURATOM Association, Boltzmannstrasse 2, D-85748 Garching, Germany b Institut f ur theoretische Physik, Technische Universit at Graz, A-8010 Graz, Austria Forschungszentrum Rossendorf e.V., Institut f ur Ionenstrahlphysik und Materialforschung, P.F. 510119, D-01314 Dresden, Germany Received 13 April 1999; received in revised form 1 June 1999
Abstract In ion beam analysis the decrease of the measuring signal with a number of incident ions, due to a destruction of the surface layer being analysed, depends critically on the lateral intensity distribution in the analysing ion beam. For the assumption of destruction in one step, the decrease was calculated and the obtained analytical formulae was ®tted to the decrease as measured in ERDA and PIXE analyses. This allows to obtain values for the destruction cross sections for the ions and the samples in the analysis, as well as information about the lateral intensity distribution in the analysing ion beam. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction During ion bombardment of solids the surface layers are eroded by sputtering and ion-induced desorption. If surface layers are analysed by MeV ion beam techniques, such as RBS, NRA, PIXE or ERDA, the signals generally decrease with the number of ions incident during the analyses. This is especially critical for surface layer analysis with ion micro beams [1], when a high incident ion current density is needed in the micro-spot for getting a spectrum with suciently small statistical errors. The observed decrease has mostly been ®tted by one or two exponentially decreasing
* Corresponding author. Tel.: +89-3299-1250; fax: +893299-1149; e-mail: [email protected]
functions [2±6] or even more complex empirical ®tting curves [7]. In the following, based on a single step destruction process and Poisson statistics for the incident analysing ions, a model is derived for the decrease of the measuring signal with the number of incident ions for dierent distributions of the analysing ion beam current. 2. The model An ion beam with a rectangular or a bellshaped current distribution, where the wings may be cut by passing the beam through a diaphragm, is incident onto the surface to be analysed. For calculating the destruction of the surface layer with analysing the number of incident ions, resulting in the decrease of the measured signal, we will assume
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 4 9 1 - 7
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
that every incident ion may damage around its point of incidence xn in one step, a volume with an eective surface area of about pq2 and a depth d of the order of the range of the analysing ions, i.e., up to the depth from which the analysis signal originates. In this volume the atoms are removed by an ion hitting the surface at a point xi , depending on the distance between xi and xn . We will calculate the `survival probability' PS xn ; U, i.e., the probability that an area centred around the position xn is still present after a number of incident ions U, with the incident ion beam having an intensity distribution F xi ; x0 around the centre of the ion beam impact at x0 . We will assume a Gaussian distribution for the incoming ion beam intensity with a 1/e half width of R and a total radius of a which may be determined by a diaphragm. 2
F xi ; x0 C exp ÿ xi ÿ x0 =R2 ÿ1 2 2 : with C pR2 1 ÿ eÿa =R
1
The constant C is a normalisation factor, which simpli®es to 1/(pa2 ) for a constant rectangular current density, i.e., the case a R and to 1/(pR2 ) for a peaked Gaussian distribution i.e., the case a R. 2.1. The survival probability The survival probability PS xn ; U for an area around a position xn after analysing with a number of incident ions U may also be looked at as the fraction of the original surface area which is not destructed after analysing with U incident ions. The dierential change dPS xn ; U for an incident number of ions dU is given by dPS xn ; U ÿdU PS xn ; U Z Pr jxi ÿ xn jF xi ; x0 d2 xi :
2
With Pr jxi ÿ xn j being the probability that an ion incident at xi will damage an area around xn , for an ion beam pro®le F xi ; x0 around the centre of
441
the ion beam impact at x0 . The integral over all possible impact positions gives the change in the area density at xn . Since Pr jxi ÿ xn j is peaked around zero, the eective area of destruction pq2 is given by Z 3 Pr jxi ÿ xn jF xi ; x0 d2 xi pq2 F xn ; x0 : The solution of the dierential equation (2) for the survival probability PS xn ; U gives PS xn ; U PS xn ; 0 exp ÿpq2 UF xn ; x0 :
4
This means that the survival probability PS xn ; U for an area around a position xn decreases exponentially with the number of ions U incident onto the area 1/F(xn ,x0 ) being analysed and with the eective area pq2 destructed by each impinging ion. The intensity of the analysing ion beam is generally not uniformly distributed on the bombarded area pa2 , but may spatially vary, and will be given by the distribution function F xi ; x0 around the centre at x0 of the ion beam, such as by Eq. (1). 2.2. Signal in ion beam analysis In ion beam analysis the signal YM (scattered ions, recoiled target atoms, products from a nuclear reaction, or X-ray intensity) measured with an incident number of ions DU after analysing with a number of incident ions U RDU will be given by: Z Z PS xn ; Uf jxi ÿ xn j YM U; DU DU F xi ; x0 d2 xi d2 xn : Similar to Eq. (3) we will put Z f jxi ÿ xn j F xi ; x0 d2 xi r F xn ; x0
5
6
with r being the dierential cross section for the reaction used in the analysis, times the acceptance angle of the detector. By inserting Eqs. (1), (4) and (6) in Eq. (5) we get for the decrease of the measured signal with total number of incident ions U
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R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
Z YM U; DU r DU
exp ÿpq2 UC 2
exp ÿ xn ÿ x0 =R2 C exp ÿ xn ÿ x0 2 =R2 2p xn dxn : 7 Integration within the boundaries 0 and a (for convenience we may put x0 0) gives the decrease of the measuring signal with the number of incident ions, for the general current distribution as given by Eq. (1): 2 R2 h YM U; DU rDU 2 exp ÿ pq2 UC eÿ a=R a i. ÿ exp ÿpq2 UC pq2 U: 8 Two special cases of Eq. (8) with Eq. (1) can be regarded for the incident current distribution. For a R, resulting in C 1/pa2 , i.e., a uniform rectangular current density distribution across the beam spot we get r 9 YM U; DU DU 2 exp ÿpq2 U=pa2 pa corresponding to an exponential decrease with the analysing ion ¯uence U/pa2 . For a R, resulting in C 1/pR2 corresponding to a Gaussian distribution we ®nally get the decrease of the signal with the number of analysing ions U R DU or an analysing ¯uence U/pR2 YM U; DU DU
2
2
r 1 ÿ exp ÿpq U=pR : pa2 pq2 U=pR2
10
For the rectangular current density distribution (a R) of the analysing ion beam we get an exponential decrease of the analyses signals, while for the Gaussian distribution (a R) the decrease of the signal is dierent, depending on the values for R and a. For a small number of analysing ions (U ® 0) Eqs. (9) and (10) show that the initial signals are the same, i.e., independent of the current density distribution. 2.3. Determination of the destruction area pq2 From the measured decrease of the analysis signal YM with the number of incident ions U, such
as observed in this work for the hydrogen isotope recoils in micro beam ERDA measurements and the Au PIXE signals in micro beam PIXE measurements, it is possible to get information both about the ion current distribution on the measured spot and to determine the destruction areas. We will de®ne the parameters Pv by P2 q=R2
P1 r=pa2 ;
and
2
P3 exp ÿ a=R : The expected analytical decrease of the analysis signals with the number of incident ions (Eqs. (8)± (10) with Eq. (1)) may be written as YM U; DU DU P1 exp ÿ P2 UP3 = 1 ÿ P3 ÿ exp ÿ P2 U= 1 ÿ P3 =P2 U:
8a
We will again consider the two limiting cases, i.e. a R and a R. For a R, i.e., a uniform rectangular current density distribution we have P3 ® 1 and, similar to Eq. (9), we get YM U; DU DU P1 exp P2 = ln P3 U:
9a
For a R, i.e., a Gaussian distribution, we have P3 ® 0 and similar to Eq. (10) we get YM U; DU DU P1
1 ÿ eÿP2 U : P2 U
10a
By ®tting the calculated analytical dependence of the signal decrease with the number of incident ions U (Eq. (8a)) to the measured decrease of signals, the coecients Pv , and thus the ion current distribution on the measured spot, and the destruction areas pq2 can be determined. The values for r/pa2 P1 , are the initial yield for the nondestructed target as obtained from the ®rst analysis with an incremental number of incident ions DU (see Eqs. (8a)±(10a)).
3. Experiments The sample analysed was a carbon layer which had been deposited during plasma discharges together with hydrogen and deuterium onto the tungsten-coated divertor plates of the fusion ex-
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
periment ASDEX Upgrade in the Max-PlanckInstitut f ur Plasmaphysik, Garching [8]: For measuring the depth distribution of the hydrogen isotopes in the deposit a wedge was cut at the carbon layer and the slope was analysed with micro ion beam ERDA using a 10 MeV Si beam at an angle of incidence of 75° relative to the surface normal [1]. Before cutting the wedge an Au layer, 75 nm thick, had been evaporated onto the carbon ®lm to mark the surface. This Au layer was also analysed with 10 MeV Si ions at an angle of incidence of 75°, by micro beam PIXE. The decrease of the PIXE signals with the number of incident ions is shown in Fig. 2. During the ERDA analyses of the H and D in the carbon layer, the signals, each measured with an incremental number of ions DU 4:7 1010 Si ions, were stored. The signals for the amount of H and D present in the target decrease with total number of ions U RDU in units of 1010 Si ions, as shown in Fig. 1. The decreases of the ERDA signals as well as of the PIXE signals (see Fig. 2) were ®tted to the calculated general analytical dependence on the number of incident ions Eq. (8a) using the ®tting routine of Microcal, Origin, version 5.0, to determine the values for the Pv . Another non-linear least squares ®t with the programme XMGR, version 4.1.2. [9] con®rmed the results for the Pv . For good ®tting, a back-
Fig. 1. Measured decrease of the H and D ERDA signals for analysing H and D in a carbon ®lm [1]. The measured points are ®tted with a decrease corresponding to a Gauû current density distribution, shown by solid lines, and with an exponential decrease, corresponding to a uniform current distribution, shown by dashed lines.
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Fig. 2. Measured decrease of the Au PIXE signal for analysing an Au layer with 10 MeV Si ions. The measured points are ®tted with an exponential decrease, corresponding to a uniform current distribution. The good agreement indicates a rectangular current density distribution in this measurement.
ground had to be subtracted from the measured data. This was performed ®rst by a four parameter ®t with the background as the additional parameter P4 . The values obtained for the background P4 agreed within the uncertainties with the values obtained for the background by extrapolation of the measured data to U ® 1. Finally the measured decrease in the ERDA measurements of the H and D in the carbon layer was also ®tted by a simple exponential decrease (see Eq. (9a)). This ®t, shown by dashed lines in Fig. 1 is worse than the general ®t shown by the continuous lines. The values obtained for the Pv by the dierent ®tting programmes agreed to better than 5%, they are summarized in Table 1. The parameter P1 times DU gives the signal at the start of the analysis. This is determined by the cross section for the analysis reaction, the geometry and the opening angle of the detector. P2 gives the destruction area relative to the half width pR2 of the analysing ion beam, and P3 gives information about the shape of the incident ion beam. For a Gaussian distribution i.e. R a we get very small values for P3 , such as that obtained for the ERDA measurements of the H and D. In this case the ®t using Eq. (8a) was the same as using Eq. (10a), however the ®t using the simple exponential decrease in Eq. (9a) did not give a good agreement, as shown in Fig. 1. For the Au PIXE measurements, the general ®t gave a value for P3 of the order of 1, indicating a constant rectangular
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Table 1 Values for the parameters Pv as obtained by ®tting the predicted analytical dependence of the signal yield YM U; DU) Eq. (8a) with analysing the number of incident ions U to the measured values (see Figs. 1 and 2) Sample
P1 r=pa2
P2 pq2 =pR2
P3 expÿ a=R2
Background, P4
ERDA, H release from C ERDA, D release from C PIXE sputtering of Au on C
1.4 ´ 10ÿ8 3 ´ 10ÿ9 6 ´ 10ÿ7
8.1 ´ 10ÿ12 8.1 ´ 10ÿ12 3.5 ´ 10ÿ12
3 ´ 10ÿ6 3 ´ 10ÿ6 0.3
209 73 11 600
current distribution i.e. R a. This is in agreement with the current distribution used in the measurements. In the case of the Au PIXE analysis, the ®t to Eq. (9a) was the same as the ®t to the general Eq. (8a). The values calculated from the data of Table 1 for the half width of the ion beam area pR2 pa2 = ÿ ln P3 and for the destruction areas pq2 P2 pR2 are summarised in Table 2. We may further calculate average sputtering yields with
analysed was about 5±6 at.% of the atomic density of C (NV;C 102 nmÿ3 ), resulting in NVH NVD 3 nmÿ3 , while the atomic density for Au is NV;Au 59 nmÿ3 . This gives a volume which is destroyed in the ERDA analyses of H, D of about 75±150 nm3 , corresponding to about 2.3 ´ 102 H and 5 ´ 102 D atoms released per incident 10 MeV Si ion. For Au the total thickness is 290 nm giving a volume which is destroyed of about 2.3 nm3 corresponding to about 80 Au atoms removed per incident 10 MeV Si ion.
YS pq2 dNV : Here pq2 dNV is the number of atoms in the eective volume which is eroded at the impact of one analysing ion, with d the depth of the destructed cylinder and NV the number density of the atoms in the solid, which is analysed. The values for pq2 are given in Table 2. For d the mean depth analysed by the ions has been taken. In the Au PIXE measurements the depth analysed is the thickness of the Au layer being 75 nm. This layer is penetrated by the analysing ion beam at an angle of 75° to the surface normal, resulting in a depth d 75/cos 75 290 nm, while for the geometry and 10 MeV Si ions used in the ERDA measurements the analysed depths for H is about 100 nm, while it is about 200 nm for D. For H and D the atomic density (D + H in C) in the deposits
4. Discussion The measured decrease of the ERDA and PIXE signals with the number of incident ions in ion beam analysis could be ®tted, within the statistical errors of the measurements, to the analytical decrease expected for dierent lateral current distributions. The lateral current distributions derived from the ®tting to the measurements agreed qualitatively with the current distributions used in the measurements. For the assumption of destruction in one step eective areas of ion bombardment-induced desorption and sputtering, giving the yields per incident ion have been derived, which do not depend on the current distribution used for the measurements.
Table 2 Total ion beam area pa2 which was used in the experiments, the half width area of the ion beam pR2 as calculated from the values for P3 and the destruction area pq2 as calculated from the values P2 of Table 1
ERDA (H release from C) ERDA (D release from C) PIXE (sputtering of Au on C)
pa2 (nm)2
pR2 (nm)2 estim.
pq2 (nm)2
1.19 ´ 1012 1.19 ´ 1012 2.7 ´ 109
9.3 ´ 1010 9.3 ´ 1010 2.24 ´ 109
0.75 0.75 7.84 ´ 10ÿ3
R. Behrisch et al. / Nucl. Instr. and Meth. in Phys. Res. B 155 (1999) 440±446
In the model used here, it has been assumed that destruction of an eective cylinder around the point of impact of the analysing ions takes place in one step and that the destruction depends only on the total number of incident ions on the analysed spot. This model may have to be re®ned. Experimentally, ®rst, at the very beginning of the analysis, i.e., for a very low number of incident ions no measurable destruction has been reported [10]. Further, in some experiments particularly the bombardment-induced desorption of gases was found to depend also on the local current density of the analysing ion beam [11]. Finally for the ion bombardment-induced release of hydrogen from carbon materials a two-step process has been proposed. In a ®rst step free hydrogen atoms may be created by release from binding sites at carbon atoms. The hydrogen atoms may subsequently be bound again to carbon atoms or they may combine with another hydrogen atom to a molecule, which may diuse to and leave the carbon surface [12]. Depending on the time scales for the processes of these two steps and the current densities applied in the analyses, this may also have an in¯uence on the decrease of the measuring signal with the number of analysing ions. These two eects have to be investigated in more detail, so that the contribution of each eect to the signal decrease can be separated and controlled. 5. Summary and conclusion In ion beam analysis, especially with a microbeam, a decrease of the detected signal with the number of incident ions is found, due to a destruction, i.e., ion bombardment-induced desorption of trapped gases or sputtering of solids. This decrease has generally been ®tted by two exponentially decreasing functions. In this work it was shown, that the decrease depends on the lateral current distribution of the analysing ion beam. For a simple model, i.e., every incident ion destructs an eective area pq2 around its point of incidence, analytical formulae have been derived for the decrease of the signal with the number of incident ions and its dependence on the shape of the ion
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current distribution on the area to be analysed. This has to be taken into account in the analyses of destruction measurements and the conclusions in respect to destruction models. By ®tting the analytical formulae to the signal decrease obtained in measurements, information about the current distribution and the cross section for ion bombardment desorption or sputtering can be obtained, which allow us further to derive desorption and sputtering yields. For bombardment with 10 MeV Si ions, at an angle of incidence 75° to the normal, the desorption yields for H and D in carbon are found to be in the range of 102 H and D per incident 10 MeV Si ion, while the sputtering yield for Au is about 80 Au atoms per incident 10 MeV Si ion. These large yields are much higher than the sputtering yields measured for 230 MeV Au ion bombardment on Au [13,14], and higher than predicted for cascade sputtering. This indicates that the destruction is not only caused by collision cascade processes, but some larger removal due to insucient sticking of the Au layer on the carbon substrate may also contribute. The formalism described here is well suited for a fast measurement of the destruction cross sections and the yields for dierent bombardment conditions for comparing the destruction of surface layers during the analysis with dierent ions and energies, in order to obtain destruction cross sections and optimal analysis conditions. Acknowledgements We would like to thank our colleagues W. Eckstein, R. Gr otzschel and F. Herrman for many helpful comments and discussions.
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