INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 39 (2006) 2876–2880
doi:10.1088/0022-3727/39/13/037
Unfolding procedure for AMS depth profiling Mihaela Enachescu1,3 , V Lazarev2 and C Stan-Sion1 1 2
National Institute of Physics and Nuclear Engineering, NIPNE, MG-6, Bucharest, Romania Technische Universit¨at M¨unchen, Fakult¨at f¨ur Physik E15, D-85748 Garching, Germany
E-mail:
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Received 14 March 2006 Published 16 June 2006 Online at stacks.iop.org/JPhysD/39/2876 Abstract Accelerator mass spectrometry measures the depth profiles of material concentration in solid samples. Crater edge effects affect the experimental data when the secondary ions are sputtered from the sidewalls of the produced crater. We present a simple mathematical unfolding procedure that removes the perturbing contribution from the measured depth profile data. Application of this procedure to experimental data is also presented.
1. Introduction Depth profiling of the material concentration in samples is commonly performed with secondary ion mass spectrometry (SIMS). Recently, it has also been performed with accelerator mass spectrometry (AMS) [1–5]. Independently of the employed method, the depth resolution depends on flat bottom craters produced by the sputter ion beam. Modern instruments provide uniform sputter currents, by sweeping a finely focused primary beam in a raster pattern over a square area [6]. In other instruments, apertures select secondary ions from the crater bottoms but not the edges [2, 3]. Alternatively, when the primary beam is at the ends of its raster pattern, the data processing system ignores all secondary ions produced. In AMS, the applied solutions are moving the target or the target holder in front of the Cs+ -sputter ion beam [5]. Similar to SIMS, in order to avoid crater edge effects, when the Cs+ ion beam is sputtering on the crater walls, the data acquisition system ignores the secondary ions. In comparison to a static ion bombardment, both the target movement and the beam sweeping produce a tremendous increase in the measurement time. This is especially important in AMS, where an accelerator is used and supplementary costs have to be taken into account. In this paper, we present in section 2.1 a depth profiling experiment using the raster method by the target movement and compare the result with that obtained after a static ion bombardment. Applying a simple unfolding procedure, presented in section 2.2, the depth profile distribution can be corrected for the perturbing contribution from the secondary 3
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ions sputtered from the the sidewalls of the produced crater. This procedure uses the crater dimensions provided by the optic profilometry measurement, which is performed at the end of the in-beam experiment. Conclusions are presented in section 3.
2. Experiments, data processing and results 2.1. Experiments using target scanning The AMS facility used in our investigations is characterized by the use of an ultra clean ion injector (UCI) as described in [7]. It permits the movement of the target holder by two stepper motors, in two directions, in front of the Cs+ -sputter ion beam produced by a Cs-gun. Figure 1 presents the scanning system that supports up to 16 targets. The total movement of each target was performed stepwise with a resolution of 4 µm and with a typical step length of 400 µm in front of the Cs+ -sputter ion beam. The lateral resolution of our scanning method is 1.2 mm. Data was recorded by the computer in list mode, as an array of nine parameters: energy E1 , E2 , E3 , E4 , E5 (the system was constructed to permit detection of all hydrogen isotopes. For the tritium measurements two energy detectors are sufficient), the position coordinates x and y, the cycle number and time. For every complete cycle, a matrix of 81 data register was recorded. The cycle number determines the depth of the crater in the sample. Using the optic profilometry measurement performed at the end of the experiment, the cycle number is converted to depth. In order to be able to avoid crater edge effects by setting digital windows, the beam scanned area was chosen to be about nine times larger than the area of the beam spot.
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Unfolding procedure for AMS depth profiling
Figure 1. Target sputter chamber of the UCS, showing the target holder placed on the x-y scanning unit, the trajectory of the Cs+ sputtering beam and the extracted negative ions.
2.2. Experiments using stationary target followed by data unfolding Alternatively, in order to correct the crater edge effects in stationary performed experiments (without target movement), a mathematical unfolding procedure can be applied. It uses the crater dimensions provided by the optic profilometry measurement. The sputtering of a sample is performed without
2.0E+14
1.5E+14 3
T (atoms/cm )
After the UCI, the selected negative ion beam is preaccelerated and injected into the tandem accelerator. Atomic and molecular species having the same mass are accelerated and pass the stripper foil placed in the tandem terminal. The stripping process at high energies causes the molecular ions to break apart. At the exit of the tandem accelerator, the high energy particles are analysed according to their velocity by the Wien velocity filter and according to their momentum by the 90◦ magnet. Finally, these ions are identified and counted in a particle detector. Figure 2 shows an example of measurements for depth profiling of tritium in a graphite sample performed with our AMS facility. Two tritium (T) depth distributions are shown. One depth distribution was measured employing the target movement (raster) followed by digital correction and the other one was measured stationary. In the latest case, crater edge effects hide the T depth distribution peak at about 1.8 µm depth. In the raster method the digital gating, applied on the registered experimental data, selects only the flat region of the crater bottom, revealing the true depth profile of the T concentration. At larger depth, the background tailing is eliminated. Thus, the ‘true’ concentration depth profile is provided by the raster method. However, this method is very time consuming since a desirable operating condition is that the raster size should be at least three beam diameters [8].
1.0E+14 stationary sputtering raster distribution
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Figure 2. Tritium depth distribution in a carbon sample from the ASDEX-Upgrade fusion experiment measured by stationary sputtering and by the raster method.
target movement and is followed by the analysis of the recorded data. As shown in figure 1 the + Cs sputter beam is strongly collimated by two apertures (cup and entrance-aperture) before reaching the target surface. The strong electric field, acting between the extraction electrode and the entrance aperture, produces a 90◦ incidence angle of the beam on the target. The optic profilometry measurement, performed off line for each analysed sample-target, confirmed that the produced craters are axially symmetric and have similar shapes. This is illustrated in figure 3, where some results of the optic profilometry measurement are shown. Measurements were performed along two arbitrary perpendicular directions x and y. Typically, the difference between the profilometry performed (surface integral) on each of the two perpendicular axes is not more than 10%. Therefore, the shape of the produced crater can be approximated with that of a truncated cone having the 2877
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Figure 3. Results of the optic profilometry measurement performed on sputtered craters. The beam profile is shown along two arbitrary perpendicular directions x and y. A lateral shift was introduced to make more visible each profile.
Figure 4. Schematic representation of the + Cs beam sputtered crater.
radii R and r (see figure 4). The height H (crater depth) is determined by the intensity of the Cs+ beam and by the time of the sputtering process. Since only the sample material sputtered from the central cylinder volume gives the correct depth distribution, the crater sidewall contributions have to be subtracted. For this reason, as shown in figure 4, we divide the excavated (sputtered) volume in N discrete volume segments of height δ = H /N. The depth of each volume is given by hi = i·δ. Typically, δ is 1 nm for a total depth profiling of about 10 µm. Thus, in the layer i we have volumes Vi containing the ‘true’ concentration Ci and a sum of side volumes Vij contributing with different concentrations Cj from the above layers j = 1, 2, . . . , i − 1. Then, for the volume of the layer i, one can write
hi−1
Since the ratio (R − r)/H represents the slope of the side correction, the form of the unfolded spectra is sensitive to the r and R radii of the truncated cone. The rest of the sputtered material in layer i originates from the walls of the crater, from the layers j = 1, 2, . . . , i − 1. The volume of the material extracted from the layer j can be 2878
calculated as hi [(ri (h))2 − (ri−1 (h))2 ]dh Vi,j = π hi−1 2j − 1 = π(R − r) · δ R i · (i − 1) (2i − 1)(j 2 − j + 1/3) . (3) −(R − r) i 2 (i − 1)2 The corresponding number of the sputtered tritium atoms can be found performing the multiplication of the tritium concentration Cj by the volume Vij . Thus, the total number of the extracted T atoms within the layer i is given by X i = Ci · V i +
i−1
Vi,j · Cj .
(4)
j =1
hi
r 1 (R − r)2 ], πri (h)2 dh = πδ[r 2 + (R − r) + 3 · i2 i (1) where ri (h) is the radius to the crater wall given by the relation R−r ri (h) = R − · h. (2) i·δ Vi =
Figure 5. Comparison of unfolded and raster T-depth profiles performed by AMS on the same carbon sample as presented in figure 2.
Finally, the corrected T concentration in every layer i can be calculated according to the recursive formula i−1 Ci = Xi − Vi . Vi,j · Cj (5) j =1
Using this simple recursive formula, the unfolding procedure is straightforward. It starts at the beginning of the depth profile, calculates the new layer concentration and corrects the concentration distribution up to a depth equal to the division interval. Then, the procedure continues stepwise, each further correction using the previous corrected depth distribution concentrations. Finally, the unfolded spectrum is obtained. Figure 5 presents the comparison of two T-depth
Unfolding procedure for AMS depth profiling
Figure 6. T-depth distributions measurement stationary by AMS (upper curves) and unfolded-crater edge effect corrected distributions (lower curves).
distributions measured on the same sample as in figure 2, but this time employing the unfolding correction in a static-mode analysis and using the target raster movement. The differences of the two distributions are less than 10% for the integrated concentration values. The differences occur most due to errors in the optic profilometry measurement and due to the unavoidable differences in the sputter optics (beam profile). Moreover, the approximation of the beam profile with a truncated cone is not always optimal. Whenever small material displacements take place due to the ion beam bombardment these cannot be taken into account by the unfolding procedure but are eliminated by the digital gating of the raster size in the alternative experimental method. The mathematical unfolding correction can be easily implemented and fast executed. It only requires a normalization of the calculated distribution using adequate standards [7] and the results of the optic profilometry measurement. Finally, we present in figure 6 some experimental tritium (T) depth profiling distributions corrected by the described unfolding procedure. The registered T ions steam from D–D reactions in a tokamak experiment at ASDEX-Upgrade. Tritium (T) is predominately generated from the fusion reaction in the centre of the good confined plasma with an initial energy of 1.01 MeV. Then, it is slowed down by drifting on orbits in the magnetic cage and released with an energy below 30 keV at the end of the discharge period. It corresponds to a peaking of the depth profile at about 0.5 µm or less. The surface deposition is due to tritium ions having energies in the 100 eV range. Scattering of the T ions by interaction with 100 keV Deuterons, injected into the plasma for supplementary heating, produces the widening of the peaks in the depth distribution. Some of these physical aspects were used to verify the sensitivity of the unfolding method. Figure 6(a) shows a depth distribution having only a surface peak corresponding to the 100 eV surface deposition of tritium. Since the tritium atoms are located mostly on the surface, the unfolding correction is linear. The next plot, in figure 6(b), shows a wide peak distribution produced by scattering effects. The unfolding procedure deals in this case with a correction over a large depth interval and even small oscillations in the experimental data could affect the
result. In the next two depth distributions (figures 6(c) and (d)), performed with a 10 times lower depth resolution, the unfolding procedure reveals the hidden peaks of the T released at the end of the discharge period. These plots demonstrate the sensitivity of the unfolding procedure even at a lower depth resolution. In the last plot a disturbance effect in the confinement of fusion experiment can be observed. It produces a faster release of T before the end of the discharge period. Therefore the T peak is at a higher energy and a widening of the entire spectrum can be observed. The peak is situated at a larger depth and due to the recurrent computing mode the previous concentrations of the depth profile must be accurately calculated. Without the unfolding procedure these peaks would have remained hidden in the static depth profile.
3. Conclusions In order to correct the depth profiling distributions for crater edge effects in the case of a static ion bombardment a simple mathematical unfolding procedure was developed and applied in AMS experiments. If the optic profilometry measurement of the sputtered crater can be performed and the beam profile can be well approximated by a truncated cone then the unfolding procedure is efficient and useful. It provides the correct concentration distribution and it also reduces the measuring time by a factor of ten. However, if host material displacements occur during the ion bombardment or the host material has a loose structure (e.g. CFC carbon fibre composite) the alternative raster methods remain the valid solutions for eliminating crater edge effects. The method was applied successfully in our experiments of material depth profiling on pirolytic graphite using the AMS facility in Garching [4]. The concentration depth profiling of T and D in protection tiles from the reaction vessel of the tokamak experiments, ASDEX-Upgrade (Germany) and JET (Great Britain), was measured.
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