Sputtering Yields for Gold Using Argon Gas Cluster Ion Beams - The

Oct 11, 2012 - The measured Aut– signals for 1 ≤ t ≤ 6 show an enhancement of ... with Sigmund and Claussen's thermal spike model valid here for...
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Sputtering Yields for Gold Using Argon Gas Cluster Ion Beams Li Yang,* Martin P. Seah, and Ian S. Gilmore Analytical Science Division, National Physical Laboratory, Teddington, Middlesex TW11 0LW, U.K. ABSTRACT: Measurements are reported of the sputtering yields of gold using Arn+ gas cluster ion beams of energies E of 5, 10, and 20 keV with 100 ≤ n ≤ 5000. In measuring the sputtering yields for 30 nm gold layers on silicon wafers with a thin thermal oxide, the analysis is conducted using SIMS with 25 keV Bi3+ primary ions. The measured Aut− signals for 1 ≤ t ≤ 6 show an enhancement of intensity beyond the Au/SiO2 interface arising from the presence of the oxide on the Si wafer, but this intensity enhancement is reduced by a factor t−1.38 between the secondary ions so that it may be removed to establish the sputtering dose at the interface. The sputtering yield, Y, so determined, exhibits a consistent dependence of Y/n on E/n for all beam energies showing that their effects are linearly additive in this regime (i.e., doubling the number of atoms in the cluster at the same energy per atom doubles the total yield). An empirical description of these sputtering yields is provided for 100 ≤ n ≤ 5000. The trend at low n values is consistent with Sigmund and Claussen’s thermal spike model valid here for 1 ≤ n ≤ 10. This confirms that the maximum yields occur for 10 ≤ n ≤ 200. No indication of a threshold below which sputtering ceases was found.

1. INTRODUCTION Gas cluster ion beams (GCIBs) containing between hundreds and thousands of atoms or molecules have two important properties: low particle velocity and high particle numbers compared with atomic or molecular (monomer) ion beams. An atom in a gas cluster carries only a small energy, Eatom, and this may be comparable to, or only a small multiple of, the interatomic bond energies. For example, in GCIBs with 2000 atoms accelerated to 20 keV, each atom has 10 eV/atom, which is typically only 2−4 times that of metallic or covalent bonds. This leads to low levels of damage in the sputtered layer. In addition, the GCIBs can transport thousands of times larger numbers of atoms at the same ion current compared with monomer ion beams, and this can lead to the high sputtering yields required for some depth profiles. A recent review by Toyoda and Yamada1 has summarized the history of argon GCIB developments, the instrumentation, the fundamentals of gas cluster impacts, and the applications of GCIBs. Argon GCIBs were initially developed for surface smoothing, shallow doping, trimming, and low-damage etching among other aspects. The successful applications of argon GCIBs have been demonstrated in the manufacturing of semiconductor devices,2 the surface polishing to obtain a uniform polycrystalline SiC or CVD diamond film,3 the surface modification of magnetic materials,4 and the assistance of optical thin film5 and ultrahard diamond-like carbon thin film6 formation. In 2001, Matsuo and co-workers7 pioneered the introduction of argon GCIBs into secondary-ion mass spectrometry (SIMS) for use as the primary analytical beam. In their early work, the authors show many benefits of using Ar clusters, including a high secondary ion signal, high sputtering yields, and minimal induced surface damage and topography. This opens up many new capabilities for SIMS analysis. Already, promising results Published 2012 by the American Chemical Society

have been demonstrated with argon GCIBs for SIMS studies of organic and biological materials. Moritani et al.8 have reported a ToF-SIMS study of polystyrene thin film using size-selected argon GCIBs with Eatom 1−22 eV. The Eatom dependence suggests a threshold of Eatom for specific chemical bond breaking. The secondary ion spectra of GlyGlyGly and arginine with strongly reduced molecular fragmentation have also been obtained using Ar cluster ions.9 Lee et al.10 used 20 keV Ar500+ and Ar1000+ to study the well-characterized Irganox 3114 multiple delta layer in Irganox 1010 reference material11 and found approximately constant sputtering rates with increasing dose. A very recent paper12 has used an extended range of Ar cluster sizes (300−2000) to examine the influence of the cluster size on ion formation by studying the yields of molecular ion species from four amino acid specimens (arginine, glycine, phenylalanine, and tyrosine). Rabbani and co-workers13 have conducted a direct comparison between Arn+ and C60+ ions in the same instrument on polymer, polymer additive, and bimolecular lipids and peptides. They also reported an approximately constant sputtering rates as a function of the Arn+ dose with n = 60, 200, 500, 1000 and 2000, a significantly reduced damage accumulation, and a more gentle ejection mechanism compared with C60+. Most of the studies so far have shown excellent potential for organic depth profiling. However, few results can be found for inorganic materials using Ar gas cluster ion beams. Although it is unlikely that the above benefits will also be found in elemental and inorganic materials, nevertheless, it is important to understand the sputtering behavior since these materials are Received: July 20, 2012 Revised: October 9, 2012 Published: October 11, 2012 23735

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nozzle, generating Arn+ clusters ranging from 100 to 20000 atoms in size. The neutral Ar beam is ionized by electron impact and accelerated to energies in the range from 2.5 to 50 keV. This ion beam contains various sizes of cluster ions with the same energy. The ion clusters of interest here are selected by a Wien filter and a 90° pulsing system. This selects a significantly narrower range of cluster sizes (typically, Δn/n ∼20%) than the system described by Ninomiya et al.24 (∼75%) and is reduced further (Δn/n < 2%) to allow high mass resolution in the time-of-flight mass analyzer for the singlebeam mode. The size-selected Ar cluster ions are then passed through the ion optical column for focusing and raster-scanning on the sample in a vacuum environment of ∼10−9 mbar. In this study, six mean cluster sizes (Ar100+, Ar200+, Ar500+, Ar1000+, Ar2000+, and Ar5000+) and three impact energies (5, 10, and 20 keV) are used. Depth-profiling experiments were conducted using both the single-beam and dual-beam methods. The single-beam method was generated using the “noninterlaced” mode by repeating a 2 s pulsed beam analysis and a 2 s continuous beam sputtering cycle during which the analyzer extraction potential was switched off. A batch processing program, available in the instrumental software, was used to control this sputtering and acquisition cycle. The Arn+ ion beam with a spot size of ∼30 μm diameter was typically rastered over a 300 μm × 300 μm area. The beam diameter for the Arn+ ion beam varied a little with each ion beam setting, and so only the central 100 μm × 100 μm area was analyzed. In contrast, the dual-beam method (the two beams were aligned before any profiling) was conducted in the “interlaced” mode, consisting of cycles of a short pulse of 25 keV Bi3+ primary ions for SIMS analysis followed by a longer period of continuous Arn+ sputtering during which the analyzer extraction potential was switched off. In this case, again, the Arn+ beam was rastered over a 300 μm × 300 μm area, and the central 100 μm × 100 μm area was analyzed but with the Bi3+ primary ion beam. The Bi3+ beam had a spot size of ∼5 μm diameter and was rastered in a 128 × 128 array. The time for each cycle (∼0.2 ms) determines the maximum detectable mass (∼3597 Da) during the experiment. Beam currents were measured using a Faraday cup on the sample holder both before and after each depth profile. For Arn+, these ranged from 7 pA for 5 keV clusters with n = 100 to 2.4 nA for 20 keV clusters with n = 2000. For n ≥ 200, the current was >0.4 nA for all energies used. Depth profiles were also reconstructed using the data from the central 25 μm × 25 μm area to check for any crater edge effect. In this instrument, the sample stage could be rotated with a specially designed sample holder (ION-TOF GmbH, Münster, Germany). Two ion beam settings were repeated with rotation for the dual beam mode depth profiling. 2.3. AFM Measurements. The thickness of the gold film was measured by line traces at a scribed edge using an Asylum MFP-3D atomic force microscope (AFM) in tapping mode. Clear steps were observed that could be measured with high accuracy. The thickness of the film used for most of the studies was found to be 29.5 nm with the standard deviation of repeat measurements being 0.26 nm as described elsewhere.26 The thickness of the film used for extra tests was found to be 25.28 nm with a standard deviation of 0.29 nm. The calibration of the AFM height scale was better than 2%. The roughnesses at the crater bottom of selective etching craters were measured by AFM to check for roughness development during sputtering.

often the support systems or framework on which organic molecules are located. These materials therefore appear in profiles of devices, particularly nanofabricated devices, incorporating organic materials. Additionally, the sputtering properties of many elemental or inorganic materials are well characterized for many monatomic and small cluster primary ion beams, and so it is useful to assess the extent to which experience with small clusters informs the behavior for large clusters. Indeed, one of the most studied materials using monatomic14−18 and small cluster primary ion beams is gold with yields measured for Aun+ primary ions for 1 ≤ n ≤ 13 being well established.19,20 A comparison with the results for Arn+ therefore provides an essential part of the GCIB knowledge base. In the present work, we provide the first extensive characterization of sputtering yields for gold using Arn+, at 45° incidence, with n = 100, 200, 500, 1000, 2000, and 5000 for 5 ≤ E ≤ 20 keV impact energies. Results for n = 2000, 3000, 5000, and 10000 at 20 keV have previously been published by Matsuo et al.21 and also data for n = 2000 at 10, 20, and 40 keV by Seki et al.22 These limited data have been interpreted to show a clear threshold at an E/n value corresponding to the interatomic binding energy, U, of 3.8 eV, below which the sputtering yield is zero. Sputtering yields have been measured here from profiles at 45° incidence for 5, 10, and 20 keV Arn+ at room temperature in both single-beam and dual-beam SIMS modes for pure gold films of known thicknesses deposited on a Si wafer substrate. The film thickness was measured by atomic force microscopy (AFM), and the sputtering yield was then determined as a function of the sputtering beam energy and Arn+ cluster size for 100 ≤ n ≤ 5000.

2. EXPERIMENTAL DETAILS 2.1. Preparation of the Flat Au Thin Film. For most of the data, a gold film, 29.5 nm thick, was prepared by thermal evaporation in a Tectra coater system (GmbH, Physikalische Instrumente) with the thickness monitored approximately by a calibrated quartz crystal microbalance (QCM) during deposition. A (100) silicon wafer sample, approximately 10 mm × 10 mm square, was cleaved from a full wafer with a surface silicon oxide of 7.86 nm thickness, as measured directly by spectroscopic ellipsometry (M2000, Woollam, NE), to form the substrate. Before the deposition, the wafer sample had been carefully cleaned23 by soaking overnight in isopropanol (IPA) and then agitating ultrasonically in IPA solution for 2 min, followed by rinsing with copious amounts of distilled water and then by drying with an argon gas jet. After final cleaning with ultraviolet light and ozone for 30 min, the silicon wafer was rapidly inserted into the Tectra vacuum chamber and a pressure below 1 × 10−5 Pa achieved before deposition. For extra tests, a film 25.28 nm thick was deposited on a second (100) wafer but with only ∼0.7 nm of surface oxide. 2.2. TOF-SIMS Depth Profiling. SIMS spectra and depth profiles were measured using a ToF-SIMS IV (IONTOF GmbH, Münster, Germany) time-of-flight secondary ion mass spectrometer. The instrument was equipped with a Bi liquid metal ion gun and also a size-selected Ar gas cluster ion gun mounted in orthogonal azimuths and each at 45° to the sample surface. Details of the early Ar cluster SIMS instrumentation are given by Ninomiya et al.24 and, for this system, by Kayser et al.25 Briefly, the Ar gas is introduced at high pressure, and clusters are formed in an expansion chamber through a small 23736

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3. RESULTS AND DISCUSSION A depth profile of a gold film using 20 keV C602+ sputtering ions with analysis using 25 keV Bi3+ ions has been shown as Figure 1 in the study of Yang et al.26 In that work it was shown

Figure 2. Aut− profiles for Figure 1 after subtracting the integral SiO2− profile together with the (+) SiO2− data.

dose. To do this, we simulate the profile of an integral of a Gaussian function from the relevant dose to infinity. The standard deviation of this Gaussian represents the profile resolution arising, inter alia, from the roughness caused by the Ar500+ sputtering. This first function is designed to represent the real Au profile, and a similar convolution of a square topped function with this and another Gaussian will represent the SiO2 profile. The doses of the relevant interfaces then depend on the sputtering yields of these two materials, neither of which are yet known. The SiO2 profile is shown in Figure 3 together with the fit for the convolution of the Gaussian with the square topped

Figure 1. Profiles for 29.5 nm gold on a Si wafer with 7.86 nm of thermal oxide, sputtered with 20 keV Ar500+ and analyzed with 25 keV Bi3+. The profiles for Aut− secondary ions are shown with thick lines for odd values of t and thin lines for even values.

that the 7.86 nm thick oxide on the Si wafer surface under the gold enhanced the Au− signal at the interface leading to a slight shift of the apparent interface to a higher sputtering dose. The shift for the Au2− secondary ions was much smaller and was very close to the profiles for Au3−, Au4−, Au5−, and Au6−. The sputtering yields in that work were therefore determined using the Au2− profiles. A similar, but much stronger effect, is seen in the present work using Arn+ sputtering ions. Figure 1 shows the whole profile for sputtering by 20 keV Ar500+ primary ions and analysis with 25 keV Bi3+ ions. The data have all been normalized for convenience of presentation, and in all of this work, it is these normalized intensities that will be used. It is clear that now we have a much greater enhancement of the Au− signal by the SiO2 than occurred with 20 keV C602+ primary sputtering ions, also with analysis by 25 keV Bi3+ ions, where the enhancement for Au− was closer to that exhibited here by Au3−. Presumably, the carbon implanted in the Au layer by the C602+ had reduced the oxygen enhancement. We may start to inspect these profiles to decide what dose reflects the correct interfacial position from which to deduce the sputtering yield as follows. The integral of the SiO2− signal from a given dose to infinite dose, hereinafter called the “integral SiO2 profile” (for that dose), generates a very good profile that follows very closely that of Au6− in Figure 1 but with much superior signal quality. We therefore first consider the excess intensity for Aut− from this integral SiO2− profile for 1 ≤ t ≤ 6. This is shown in Figure 2. The excess intensities all have similar shapes and decay rapidly in total intensity, one Aut− secondary ion with respect to another. It is clear in Figure 2 that the SiO2− peak is symmetric and that, for the Aut− ions, after subtracting the integral SiO2 profile, the remaining intensities are asymmetric with a bias to higher doses. This asymmetry is caused by the integral SiO2− profile not quite reflecting the original Au profile, but a profile whose interface was located a little deeper at the center of the SiO2 film on the Si wafer surface at a dose of 18.7 ions/nm2, i.e., at 3.93 nm greater equivalent depth than the true interface. We therefore need a reference curve showing the true interface

Figure 3. SiO2− profile from Figure 1 (+) and the description with a step function with edges at 17.4 and 19.8 ions/nm2 convolved with Gaussians with standard deviations of 1.8 and 1.9 ions/nm2 (), respectively. The vertical lines show the interfaces at 17.4 and 19.8 ions/nm2.

function. The fit is excellent and gives the Au/SiO2 and SiO2/Si interfaces at doses of 17.4 and 19.8 ions/nm2 with standard deviations of 1.8 and 1.9 ions/nm2, respectively. The fit is excellent but the shape is not too sensitive to the precise positions of the two interfaces. In this case, the full width at half-maximum (fwhm) resolution at the Au/SiO2 interface is 7.2 nm. Measurements by AFM at the base of a crater in a similarly sputtered sample gave an Rq of 1.85 nm. The Rq is equivalent to the standard deviation of the heights measured, and this gives a fwhm contribution of only 4.4 nm, rather less than the sputter depth resolution. 23737

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If, as we have seen, this oxide enhances the Aut− yields, then one may expect the Aut− profiles to be a sum of the gold neutral profile and some factor kt times the SiO2− profile. Thus, the gold profile should be the Aut− profile minus kt times the SiO2− profile. This is shown in Figure 4 for the data of Figure 1 for

what is actually observed is a convolution of this nonlinear result with a Gaussian function describing the roughening, and it is this convolution that linearizes the result. The data are indeed described very closely with a linear proportionality. As before,26 the sputtering yield YAu(45°) measured in atoms per primary ion is given by YAu(45°) =

(2)

where x is the film thickness and aAu is the size of the gold atom, 0.2569 nm, computed from the gold bulk density with atomic volume aAu3. Here, we do not take x as 29.5 nm but reduce this value to allow for the sputtering caused by the 25 keV Bi3+ analytical beam. At the interface, the Bi3+ dose is 0.26 ions/nm2. We do not know the sputtering yield for gold by 25 keV Bi3+ ions, and indeed, it has never been measured. However, the similar result for gold sputtered by Au3+ and for many other Au clusters over a wide energy range has been measured for normal incidence.19 The results for Bi3+ may be slightly different from those for Au3+ since, for example, the momentum exchange is no longer so closely matched. These issues are covered in Sigmund and Claussen’s27 thermal spike model which is an excellent description for Au sputtering of Aun+ for 1 ≤ n ≤ 13 and E < 1 MeV.20 Using the same values of the parameters αA and B for Bi3+ sputtering of Au as were found for Aun+ sputtering of Au,20 the yield for 25 keV Bi3+ is found to be 82 atoms/ion for normal incidence. We do not know how much this changes with angle of incidence, θ, but it will be less than sec θ. At a sec θ dependence the yield will, with θ = 45°, be 116. We use an average of the results for yields of 82 and 116 to allow for the amount of material sputtered by the Bi3+. In this instance it is only 0.4 nm. This small loss of material needs to be included in x for applying eq 2. Thus, for 20 keV Ar500+, YAu(45°) = 99 atoms/ion. The correction above for the Bi3+ sputtering may appear to be trivial since, in this case the relative Arn+ and Bi3+ doses are in the ratio 70:1. In many of our profiles this ratio rises to above 200 so that the effect of the Bi3+ is even smaller, but in a few cases where the Arn+ yield or beam current was low, the effect of the Bi3+ sputtering could lead to significant corrections. The ratio of the Au and SiO2 sputtering yields, YAu/YSiO2, for the 20 keV Ar500+ in Figure 1 is ∼0.5. This is deduced from the doses shown in Figure 3 and the thicknesses of 29.5 and 7.86 nm for the Au and SiO2, respectively. As the beam energy falls and the cluster size increases, the total sputtering yields fall, and as the impact energy per atom approaches the target bond energy, one would expect this ratio to change significantly. This is what is observed, as shown in Figure 5a for 5 keV Ar2000+. Here the SiO2 sputtering yield has fallen significantly, and the ratio is now above unity, a relative change of over 3 times. The sputtering yields are now very low. The above correction for the effect of the oxide, applied as in eq 1 for this case of a very low sputtering rate for the SiO2, is shown in Figure 5b. Here k0 = 0.8 whereas, in Figure 4, k0 was 2.1. The correction to Au6− here is a reduction in dose of 4% whereas in Figure 4 it is 9%. Tests were also conducted by evaluating the sputtering yield for the central 25 μm × 25 μm zone of the analyzed area to ensure that there was consistency and no significant alignment problems. These data showed slight improvements in depth resolution but are not used here since the analytical signal was significantly poorer (generally down by a factor of 16).

Figure 4. Profiles, from Figure 1, for Aut−-ktSiO2− and (●) a calculated profile for a step function ending at 17.4 ions/nm2 convolved with a Gaussian of standard deviation 1.8 ions/nm2. The vertical line shows the interface at 17.4 ions/nm2.

t = 1−6. Thus, by using the gold profile terminating at 17.4 ions/nm2 instead of the integral SiO2− profile, the leading edges of the new Aut− excesses, originally shown in Figure 2, now match the SiO2− profile and, for t > 2, match it at both leading and trailing edges. For Au− and Au2− we see some extra enhancement at the trailing edge that may be caused by the Si substrate. This enhancement is interesting but not of importance in the present work. It is clear that this gives a very consistent profile for the Au/SiO2 interface, as shown by the dotted curve which represents the integral of a Gaussian centered at 17.4 ions/nm2 with a standard deviation of 1.8 ions/nm2. Thus, we conclude that the sputtering yield should be deduced for a dose, D, of 17.4 ions/nm2, ∼1.3 ions/nm2 less than if the center of the SiO2− profile had been used. Additionally, the fwhm of the depth resolution is 4.3 ions/nm2, equivalent to 7.2 nm. The kt values for the above subtractions are found empirically to follow the relation kt = k 0t −1.38

x DaAu 3

(1)

where, since the effect arises from the use of the 25 keV Bi3+ analytical beam, k0 and the power of 1.38 should apply to all profiles. The value of k0, while being intrinsically the same before the Gaussian broadening, will in practice depend on the resolution of the depth profile, and this will depend on E and n. Hence, in deriving the interface position as in Figure 4, the value of k0 is found in each profile by fitting to give profile consistency as shown in Figure 4. AFM studies of the crater floor of a similar sample sputtered by 20 keV Ar500+ gives Rq = 1.85 nm. The standard deviation here, of 1.8 ions/nm2 converts, using the thickness of 29.5 nm to a standard deviation of 3.1 nm, rather higher than the Rq value, as noted above. It may be that some churn of the material at the crater edges causes this increase in profile width. In general, one would not expect that the ionization probability of the Au− secondary ions would depend linearly on the oxygen level. However, even if it is highly nonlinear, 23738

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just discernible. The final result for the sputtering rate is marginally improved. The measured sputtering yields are shown in Figure 6. These are all for 45° incidence angle. The overall results are well

Figure 6. (color online) Measured sputtering yield, Y, as a function of n for gold using Arn+ on the 7.87 nm oxide (●) 5 keV, (▲) 10 keV, (■) 20 keV and, on the 0.7 nm oxide, (□) 20 keV.

behaved, but yields below unity exhibit a significant experimental scatter. This probably arises from the concomitantly long sputtering times and hence higher corrections needed for any Bi3+ sputtering as mentioned earlier. The whole set of sputtering yield data ranges more than 2 orders of magnitude for these energies and cluster sizes. The values to the left at n = 100 are similar to the yields measured using 10 and 20 keV C60+ at 45° incidence for gold at 53 and 120 atoms per ion by Goacher and Gardella28 and at 40° incidence for silver at 47 and 144 atoms per ion by Sun et al.29 In Figure 6, the points are all plotted at the nominal n values although, as noted in section 2.2, a range of cluster sizes impact the sample with n values ranging 20% either side of the nominal value. Depending on the shape of the yield curve with n, this causes the effective value of n to be raised or lowered. In Figure 6, the maximum shift is less than 1.5%, or less than half the radius of the plotted points, and is ignored. There is one exception to this, and that is for n = 100 where the current was very small. For n = 100, the distribution is broader and the error could be as high as 20% so that 80 < n < 120, but since Y is much less dependent on n in this range, the effect is small. We may rearrange the data in Figure 6 by plotting the yield, Y, per cluster atom, n, versus the impact energy per atom as shown in Figure 7. The solid line is for the function

Figure 5. Profiles for 29.5 nm gold as in Figure 1 but for 5 keV Ar2000+ and analyzed with 25 keV Bi3+: (a) original normalized profiles and (b) profiles for Aut−-ktSiO2− for 1 ≤ t ≤ 6.

Several other checks were made. First, the 25 keV Bi3+ analysis beam was replaced by analysis using the Ar cluster sputtering beam for selected 20 keV samples using n = 500, 1000, and 2000 (the single-beam SIMS mode). This was the single-beam setting that gave the highest intensities for the Au− and SiO2− secondary ions, and while these intensities were comparable to those for 25 keV Bi3+, the intensities for Au2− were weak and those for larger clusters not visible at all. It was then difficult to apply the above procedure to remove any oxygen enhancement, but that enhancement was, anyway, much weaker for both the Au− and Au2− secondary ions. In the single-beam mode, no removal of intensities was therefore made, and the doses were measured from the Au2− profiles. Within the general uncertainties shown later, these data were consistent with the data derived from the 25 keV Bi3+ analyzed profiles. Two profiles for 5 and 20 keV Ar500+ were repeated using sample rotation. The dose at the interface was within 2% of the dose with no rotation. Six more profiles were analyzed for the gold film 25.28 ± 0.29 nm thick deposited on the wafer with a much lower thickness of oxide. This oxide thickness was ∼0.7 nm. For 20 keV Arn+ with 100 ≤ n ≤ 5000, the SiO2 peak is slightly narrower than found for the 7.86 nm oxide. The reason for this small improvement can be seen from Figure 3 when we have Gaussians of fwhm 4.2−4.5 ions/nm2 convolved with, and dominating, the square topped function with a width of 2.44 ions/nm2, giving an observed fwhm of 4.6 ions/nm2. Removing the contribution of the square-topped width is thus small but is

(E /63n)2.6 Y = n 1 + (E /63n)1.6

(3)

where E is in eV. The Y/n data typically scatter about the line by only 3% of the full range of Y/n data. That a single function describes Y/n in terms of E/n implies that if the number of atoms in the primary cluster is doubled at the same incident velocity (i.e., both E and n are doubled), the yield per incident atom is unchanged. This indicates that, in this range of E−n space, the sputtering is linearly additive. We see no threshold here since a threshold would be manifest by the yield falling to zero at some low E/n value. This value is often quoted as U0, the binding energy of the target atoms. The values here, at E/n ∼U0, would then be well below the solid line rather than above it. If there is a threshold here, it would appear to be below E/n = 1, but this is in a regime in which Y/n < 23739

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with Arn+ and analyzing with 25 keV Bi3+; this enhancement falling as t−1.38. The enhancement is much weaker for analysis with the 20 keV cluster Ar500+, Ar1000+, and Ar2000+ beams in the single-beam SIMS mode and, in earlier work,26 was also weaker for sputtering with 20 keV C602+ and analyzing with 25 keV Bi3+. After this enhancement was removed, the sputtering yields of gold, for Arn+ with 100 ≤ n ≤ 5000 and for 5, 10, and 20 keV beam energies, were determined. These yields fall rapidly as n rises to 5000 and appear to saturate at high levels as n falls to 100. All data on a plot of Y/n versus E/n follow the same curve independent of energy showing that, in this region of E−n space, the yields are approximately linearly additive; i.e., if more atoms are added into the primary ion cluster at the same energy per atom, then the yield simply increases proportionately to the number of argon atoms added to the primary cluster. The yields follow the relation of eq 3 for 100 ≤ n ≤ 5000. No evidence of any threshold, below which sputtering ceases, was found in this regime of E−n space.

Figure 7. (color online) Replot of the Figure 6 data for Y/n vs E/n.

10−5, and at such low values, a value of zero could be wrongly assigned. The function of eq 3 may be added to the data of Figure 6 as shown in Figure 8. Added to the left are computed yields using

■

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work forms part of the Chemical and Biological programme of the National Measurement System of the UK Department of Business, Innovation and Skills and with funding by the European Metrology Research Programme (EMRP) and with funding by the European Union. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.

■

Figure 8. (color online) Data from Figure 6 together with the curves for eq 3 shown by solid lines. Also shown at low values of n are dotted lines for the predictions for Sigmund and Claussen’s thermal spike model.20,27

REFERENCES

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Sigmund’s theory for sputtering of n separate incident atoms of energy (E/n).30−32 This is excellent for n = 1 and for the present range of energies. To this has been added Sigmund and Claussen’s thermal spike contribution20,27 but with the spike temperature defined by a fixed primary ion track radius as described by Seah20 for low n but allowing the diameter of the impacted area to increase as n increases at higher values of n. It is really unlikely that such a model would be accurate once E/n falls to low values since Sigmund and Claussen’s theory analyses the thermal evaporation based on a cylindrical spike of heat generated through the surface layer to significant depth. At low E/n values this will not be the case. Nevertheless, for n ≤ 13 the model is a fair description. What these curves usefully show is that the curvature shown in the solid lines of the function given in eq 3 is quite reasonable and that the maximum sputtering yield will occur in the range n = 10−100.

4. CONCLUSIONS In measuring the amount of gold present in sputter depth profiles where oxides are present, the intensity of the Aut− signals will be enhanced by the presence of oxygen. The enhancement of the signal may be up to a factor of 5 for Au− but weakens for Aut− as t increases from 1 to 6 for sputtering 23740

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