Sampling Depths, Depth Shifts, and Depth Resolutions for Bin+ Ion

Feb 17, 2016 - Analysis in Argon Gas Cluster Depth Profiles. R. Havelund ... that effects of the sampling depth leads to apparent shifts in depth prof...
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Sampling Depths, Depth Shifts, and Depth Resolutions for Bin+ Ion Analysis in Argon Gas Cluster Depth Profiles R. Havelund,* M. P. Seah, and I. S. Gilmore Analytical Science Division, National Physical Laboratory, Teddington, Middlesex TW11 0LW, U.K. ABSTRACT: Gas cluster sputter depth profiling is increasingly used for the spatially resolved chemical analysis and imaging of organic materials. Here, a study is reported of the sampling depth in secondary ion mass spectrometry depth profiling. It is shown that effects of the sampling depth leads to apparent shifts in depth profiles of Irganox 3114 delta layers in Irganox 1010 sputtered, in the dual beam mode, using 5 keV Ar2000+ ions and analyzed with Biq+, Bi3q+ and Bi5q+ ions (q = 1 or 2) with energies between 13 and 50 keV. The profiles show sharp delta layers, broadened from their intrinsic 1 nm thickness to full widths at half-maxima (fwhm’s) of 8−12 nm. For different secondary ions, the centroids of the measured delta layers are shifted deeper or shallower by up to 3 nm from the position measured for the large, 564.36 Da (C33H46N3O5−) characteristic ion for Irganox 3114 used to define a reference position. The shifts are linear with the Binq+ beam energy and are greatest for Bi3q+, slightly less for Bi5q+ with its wider or less deep craters, and significantly less for Biq+ where the sputtering yield is very low and the primary ion penetrates more deeply. The shifts increase the fwhm’s of the delta layers in a manner consistent with a linearly falling generation and escape depth distribution function (GEDDF) for the emitted secondary ions, relevant for a paraboloid shaped crater. The total depth of this GEDDF is 3.7 times the delta layer shifts. The greatest effect is for the peaks with the greatest shifts, i.e. Bi3q+ at the highest energy, and for the smaller fragments. It is recommended that low energies be used for the analysis beam and that carefully selected, large, secondary ion fragments are used for measuring depth distributions, or that the analysis be made in the single beam mode using the sputtering Ar cluster ions also for analysis.

1. INTRODUCTION The sampling depth of any analytical technique in sputter depth profiling is important for two reasons: (i) by using a signal that exists over a greater depth, the signal quality may increase but (ii) the depth resolution may then degrade. In our choice of operating conditions, it is usually the depth resolution that is critical. In Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS), the depth resolution involves the sampling depth through the electron attenuation length1,2 which is described by an exponential decay of information along the electron detection direction. This sampling depth is separate from the sputtering and involves the AES or XPS signals and the analysis geometry used. It ranges from 0.5 to 8 nm with a typical value of 3 nm.2 In secondary ion mass spectrometry (SIMS), particularly when depth profiling at the highest depth resolution in inorganic systems, a similar behavior is seen for monatomic secondary ions with an exponential decay that may be either an information depth or a sample-related phenomenon.3,4 This sampling depth has been reported to be as low as zero5 and is often around 1−2 nm. In the present work, we are concerned with the effects, if any, of such sampling or information depths in the SIMS depth profiling of organic layers using argon gas cluster sputtering ion beams. This is important for the three-dimensional (3D) analysis of organic materials, including organic electronic Published XXXX by the American Chemical Society

devices, and biological specimens where the distribution of materials such as lipids and pharmaceutical molecules can be imaged with submicrometer resolution using SIMS.6−12 In the profiling of delta layers, Shard et al.13,14 show that the delta layers, with full width at half maxima (fwhm’s) as low as 5 nm, may be described by the same asymmetric function3 that was developed by Dowsett et al. for the profiling of inorganic materials.3−5 That function involves an exponential growth term, a Gaussian broadening term, and an exponential decay term, convolved together. They are often thought to represent the information depth, the surface roughening caused by sputtering, and the effects of recoil mixing, respectively. Although, algebraically, the analytical functions were the same as those used for inorganic materials, crucially, Shard et al.13 show that, for organic materials, the profile response actually describes the height distribution of the sputtered surface, as measured with an atomic force microscope, i.e. the roughness heights that define the fwhm are described by Dowsett et al.’s function. These height distributions are often assumed to be Gaussian but, for organic materials, are clearly not. Hence, it is not clear if an information depth is associated with organic Received: December 29, 2015 Revised: February 10, 2016

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DOI: 10.1021/acs.jpcb.5b12697 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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thick Irganox 3114 delta layers separated by 50 or 100 nm Irganox 1010 layers13,14 sputter depth profiled using argon cluster ions. This thin delta layer is chosen so that the Irganox 3114 is dilute in the profile to minimize matrix effects21 that may change the profile. For an exponential effect, the sampling depth may be characterized by the mean escape depth and this is equal to the characteristic of the exponential. For other distributions, and we do not yet know the appropriate distribution relevant here, these relations change and the relevant resolution functions may be readily calculated.

profiling using cluster ions and, if that parameter exists, it can be extracted from the data. The molecular dynamics simulations of Paruch et al.15 and Garrison et al.16 show how in sputtering the Ag(111) surface by 20 keV C60+, the depth resolution is around 7 nm but becomes skewed as described by Dowsett et al.’s3−5 function as a result of the roughening formed by multiple impacts. This agrees with the approach of Shard et al.13 Extracting the exponential growth parameter from the delta layer shape may thus tell us something about the sputtering process and not directly about the information depth of the analyzing ion. This is important since two different primary ions may be involved for the sputtering and analysis and either may be optimized, as we see later, to obtain the most relevant data. Brison et al.17 conducted a time-of-flight SIMS (ToF-SIMS) study of the depth profiling of the model organic system of a plasma polymerized tetraglyme film using 10 keV C60+ for sputtering and either Bi+ or Bi3+ for analysis. They illustrated an effect of the analysis beam crater in terms of the cleanup efficiency. In sputtering using argon cluster beams, the issue of, and need for, cleanup, important for C60+, is reduced significantly. In later work, Muramoto et al.18 consider the escape depth to be the characteristic length for an exponential escape of substrate signals through an organic overlayer. This layer was tetraglyme that overlaid, in turn, a protein layer on mica. By using several overlayer thicknesses, they measure the escape depths for K+, CH4N+, and C4H8N+ ions for 25 keV Bi+, 25 keV Bi3+, 50 keV Bi32+, 50 keV Bi52+, and 20 keV C602+ primary ions. The data are too poor to examine the actual shape of the decay profile and whether it is exponential, so the escape depth is taken as the thickness at which the underlying material is just discernible. The results for Bi+ primary ions show a small increase with energy, and a larger increase with a number of atoms in the primary ion cluster. Typical escape depths are 2−4 nm. It is noted that these are significantly greater than the impact crater depths that are cited by Muramoto et al.18 and the mechanism is, thus, unclear. For an escape depth for secondary ions as an analogy to the escape of electrons in AES or XPS, there must, therefore, be emission of material from below the crater floor and through the overlying material. This escape could be through the hot material in the crater base before the thermal spike cools. In earlier work, Delcorte et al.19 show, through three decades of intensity reduction and up to 11 nm of polyelectrolyte coating, that the Si+ secondary ion intensity is, indeed, well described by an exponential for sputtering using 15 keV Ga+ primary ions. The characteristic length of 1.5 nm was reduced to 0.8 nm for SiOH+ and 0.5 nm for SiO3H+ secondary ions. Thus, the largest fragments are the most surface sensitive. Exponential decays were also observed for the Ag+ secondary ions from an Ag substrate with overlayers of H2O up to 23 nm thick.20 The decay length depended on the primary ion, rising from 0.7 nm for 20 keV C60+ to 2.8 nm for 25 keV Au3+, 2.0 nm for 25 keV Au2+, and 2.4 nm for 25 keV Au+. These decays, for Ag+ secondary ions, were also observed over three decades. The decay length is thus not just a samplerelated parameter but also depends on the sputtering ion. The results of Muramoto et al.18 show a significant reduction with increase in the number of ions in the primary ion cluster, in contradiction to the results of Brison et al.17 In the present work, therefore, to investigate the escape depth, we shall measure the depths from which the secondary ions are obtained and evaluate the effect for different analytical ions and their energy in the system studied previously of 1 nm

2. SIMPLE MODELS In the present study we do not have the signal level or data density to evaluate very precise functions, so we shall use very simple models. It will be seen that these models are, in fact, very powerful and allow the important conclusions to be made with some clarity. In the study, depth profiles are made using 5 keV Ar2000+ sputtering ions. These sputtering ions remove a portion of material in each event and leave, it is thought, negligible damaged material behind. In studying the sampling depth of the analytical beams, Biq+, Bi3q+, and Bi5q+ with energies E from 13 000 to 50 000 eV (q = 1 for E ≤ 25 000 eV and q = 2 for E > 25 000 eV), we shall therefore at first ignore the 5 keV Ar2000+ sputtering except to note that it generates a roughness that may be described by a Gaussian fwhm around 8 nm. The models will be detailed in association with the results later since the rationale for the way they are set up depends on the results themselves. 3. EXPERIMENTAL SECTION The sample materials were generated as described by Shard et al.14 for a VAMAS Interlaboratory Study to improve the interlaboratory consistency in SIMS depth profiling of organic systems. Briefly, Irganox 1010 (pentaerythritol tetrakis(3-(3,5di-tert-butyl-4-hydroxyphenyl)propionate), C73H108O12, Mr = 1177.6) and Irganox 3114 (1,3,5-triazine-2,4,6(1H,3H,5H)trione, 1,3,5-tris[[3,5-bis(1,1-dimethylethyl)-4-hydroxyphenyl]methyl]-), C48H69N3O6, Mr = 783.52) from CIBA-Geigy were each sublimed in a Qbox 450 (Mantis Deposition Ltd., Thame, U.K.) with relevant monitoring, shuttering, and sample rotation to create the delta layer structures already shown in Figure 1 of Shard et al.14 The evaporators were controlled by the outputs of quartz crystal oscillators (QCOs) to deposit three layers of Irganox 1010 of 100 nm and then two final layers of 50 nm thickness. Each layer was separated by a 1 nm layer of Irganox 3114. The QCOs were calibrated to relate their outputs to the thicknesses of each material deposited on the wafer substrates by ellipsometry using an M2000DI spectroscopic ellipsometer (Woollam, Lincoln, NE, USA). The above multilayer sample was depth profiled by SIMS using 5 keV Ar2000+ gas cluster primary ions in an ION-TOF SIMS IV instrument (ION-TOF GmbH) with the incident ions at 45° to the surface normal and the cluster size distribution selected with a width of ∼30%. Negative secondary ions were measured using Biq+, Bi3q+, and Bi5q+ ions of 13−50 keV energy, also at 45° incidence angle, but in an azimuth at 90° to the argon gas cluster sputtering beam. The sputtering beam was rastered, in interlaced mode, over an area of 500 μm by 500 μm, and the analysis was in a central zone of 200 μm by 200 μm. The relative Binq+ dose was 25 keV. The solid lines are least-squares straight line fits passing through separate shift values at E = 0 for each secondary ion. (b) The shift for the CNO− peak for different Bi3+ ion energies relative to the C33H46N3O5− peak at 564.36 Da, the 25 keV example of which is shown fitted with a Gaussian peak.

Y=B CNO− at 42.00 Da, C16H22O− at 230.17 Da, and C18H24N3O4− at 346.18 Da. Each peak has a different symbol: circles, squares, triangles, and crosses, respectively. The Biq+ data are shown in black, Bi3q+ data are in red, and Bi5q+ data are in blue, where q = 1 for E ≤ 25 keV and q = 2 for E > 25 keV. The solid lines are least-squares fits to the data for each primary ion which are, here, constrained so that each secondary ion has its own offset at zero energy that is the same for all of the analysis sputtering ion species on the basis that, at zero energy, none have any effect. The overall root-mean-square deviation is 0.12 nm. Measurements for 20 characteristic peaks for 25 keV Bi3+ analysis ions show that the 42.0 and 346.2 Da secondary ions represent the extremes of the shifts and that the average shift for these 20 for the four delta layers is −0.3 nm with a standard deviation of 0.8 nm.

E A

(1)

where B = 0.0176 nm3.26 At 50 keV, this gives a volume of 550 nm3 which, to give an approximate size, is equivalent to a hemispherical volume of radius 6.4 nm. This sputtering yield is smaller than but related to the impact crater volume. In one impact, material is both ejected and thrown to the crater rim. In subsequent impacts, further material is ejected as well as some of the deposited material and so on. Delcorte and Garrison27 show how, for C60+ in the energy range 1−10 keV, the sputtering yield volume may be between 12 and 41% of the material removed from the crater with the remainder deposited on the crater rim and that the fraction may be energy dependent. The deposit on the rim, for both normal incidence and with sputtering cluster ions incident at 45°, is shown in many molecular dynamics calculations.28−32 These show craters D

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fragment differs from that of the reference secondary ion, C33H46N3O5−, in that the latter is the whole molecule stripped of one of its three legs whereas C18H24N3O4− has lost two legs and acquired a hydrogen atom; i.e. they are similar parts of the fragmentation process, but the C18H24N3O4− is half the size and, being more reactive, is more likely to be strongly bonded to the substrate leading to a lower average sputtering yield.25 We would not expect the data for this secondary ion in Figure 4a to exhibit a significant gradient with energy, but the source of the average shift of 0.77 ± 0.15 nm merits further investigation. Observation of the profile of this sample, analyzed with either 50 keV Bi3+ or 20 keV Ar5000+, using sample rotation to avoid any differences in the local surface during analysis, gives a shift of 0.59 nm for the Bi3+ and 1.25 nm for the Ar5000+ using the Gaussian fits. This shows that the shift for C18H24N3O5− has already occurred in the 5 keV Ar2000+ sputtering and is reduced for the Bin+ analysis. A similar but smaller positive shift occurs for the less intense C3H2N3O3− secondary ion at 128.01 Da. This ion represents the reactive core of the molecule. For most of the other ions studied, there is no significant shift in the 5 keV Ar2000+ sputtering and the shift occurs through the analysis ion. The shift for the C18H24N3O4− secondary ion fragment at 346.18 Da to greater depth implies that it takes more sputtering to remove it. This may arise from a reduced sputtering yield for this damaged material and that it is the remainder after the rest of the sputtered volume has been removed. It may be stickier and so requires a second and further hits. The 5 keV Ar2000+ sputtering yield for Irganox 101022,26 is 37.6 nm3 which, for a hemispherical volume, has a depth (i.e., radius, r) of 2.62 nm. If after each 2.62 nm of material is removed a fraction x of the material remains, this leads to an exponential decay with characteristic length, λx, related to r and x by r λx = − ln(x) (4)

that range in shape from approximately cylindrical to approximately conical with most ellipsoidal or paraboloid. Aoki et al.,33 for Ar2000+ between 10 and 100 keV, show results where the rim fraction is fairly independent of energy and is less at 45° compared with 0°. The secondary ion emission volume may be larger or smaller than the sputtering yield volume and may or may not have the same energy dependence. It depends sensitively on the secondary ion fragment used. Here, we reference the shifts to the 564 Da fragment since that shows a narrow peak that does not broaden with the analysis beam energy and is therefore assumed to be unshifted. For this fragment, the depth range of emission is small. We may estimate the depth range of emission from the shifts using simple models. If the emission zone is a cylinder of radius r nm and depth d nm, at 45° to the normal, as illustrated by Brison et al.,17 then the shift s, in nm, of the delta layer secondary ion centroid will be approximately 0.5d cos(45°). Since the shift is proportional to E, as shown in Figure 4a, then (2)

s = mE

where s and d vary with the secondary ion species depending on where in the crater they are generated. Thus, from Figure 4a, for CNO− at m/z = 42.0 using Bi3+ d = (1.535 × 10−4)E

(nm)

(3) −

where E is in eV. At 50 keV, for the CNO fragment, d is 7.7 nm for Bi3+ and 5.7 nm for Bi5+. The depth for Bi3+ is slightly greater than that for Bi5+, as expected. The depth of the emission zone for CN− is lower than that for CNO−; presumably the CN− is restricted to the hotter core. The above numbers all seem reasonable and are well within the depths of the sputtered craters of molecular dynamics calculations.27−36 We may take a different shape for the emission volume such as a paraboloid. This is not tilted over at 45°.29,30,33 The centroid is now slightly closer to the surface and d becomes 1.06 times larger, i.e. 8.1 nm for Bi3+ and 6.1 nm for Bi5+ for the CNO− fragment at 50 keV, extrapolating to 1.2 nm for 10 keV Bi5+. This is significantly less than the crater depth calculated by Delcorte et al.31 indicating that the ions do not come from the full crater depth. However, we cannot tell from these depths if the paraboloid emission volume is more relevant than the cylinder, or some other shape, since the emission depth appears to be significantly smaller than the volume of the crater. For now, we note the important result that the shift increases linearly with E to an extent dependent on the secondary ion fragment and consider the emission volume profile later using a different measurement approach. The results for Bi+ show little shift, and this arises from the very small sputtered volume. The Bi+ ions penetrate much more than the cluster ions but generate a significantly lower yield. There are three further issues with the results of Figure 4a: (i) the large and positive offset at zero analysis beam energy for the secondary ion C18H24N3O4− at 346.18 Da, (ii) the escape depth, and (iii) the implications for the depth resolution. 4.2. Offset for C18H24N3O5− at 346.18 Da. The positive offset for the depth of the peak for the C18H24N3O4− secondary ion is important. The model used so far concerns the Bin+ analysis and cause information to be obtained as or before the 5 keV Ar2000+ has reached any given depth (negative offsets), rather than after it. It is worth noting that the structure of this

The length λx is thus generated by the continual partitioning of the material generating the C18H24N3O4− secondary ion fragment at 346.18 Da rather than the recoil mixing relevant to the atomic profiling of inorganic materials. In the profiling we therefore have some intensity for C18H24N3O4− secondary ions that come from the core of pure material sputtered by the analysis ion and some from a crater rim deposit and redeposit generated by the 5 keV Ar2000+ profiling ion. This latter lasts longer than the signal from the pure material and constitutes a greater fraction for the shallower 20 keV Ar5000+ analysis than that for the 50 keV Bi3+ analysis discussed above. By comparison of the profile for the 564 Da reference ion, convolved with the above exponential decay function, we may closely match the profile for the 346 Da ion and deduce λx as shown for 13 keV Bi3+ analysis in Figure 5. Such computation shows no significant change of λx with the Bi3+ analysis energy in the range 13−50 keV and gives a value 1.88 ± 0.28 nm. This would fit the above estimate for r, using 5 keV Ar2000+ sputtering, with x = 0.25 ± 0.03, i.e., not a large residue but enough to broaden the peak on the high-depth side. In the remainder of this study, we shall consider this secondary ion no further. The sampling or escape depth issue and the depth resolution are related and are dealt with together in section 4.3. 4.3. Sampling or Escape Depth and the fwhm’s. Above, we have illustrated effects using a model of a uniform cylinder or paraboloid of emission and escape of secondary ions E

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In the four examples of GEDDFs in Figure 6, we may consider the constant distribution as the emission of the whole of a cylindrical volume. The exponential could be a combination of, say, an exponential creation and exponential emission with depth. The linear distribution could be the total emission from our paraboloid volume (almost hemispherical at its apex), and the two deltas could be the emission from the surface and the base of the analysis beam crater. The latter is an extreme example but one that could, say arise from the high sputtering in the crater with a low ionization coefficient combined with a lower yield for that fragment from the surface but with a high ionization coefficient. All these very different scenarios are plausible. The GEDDF from a hemispherical volume would be between that for the constant and that for the linear distributions. The convolution of these four analysis-ion GEDDFs with the original profile formed by the sputtering ion in each case causes the measured fwhm to increase as the shift increases. Of course, the best resolution should be, and is, achieved by the unshifted, large, C33H46N3O5− secondary ion assumed to be emitted from the surface region. For these data, we cannot distinguish the four GEDDFs simply from the measured centroid shifts; unfortunately, neither have we the data accuracy to be able to distinguish them from their effect on the fwhm. To clarify the behavior, it is necessary to evaluate the precise peak shapes and this is possible for the conditions giving the strongest effect using 50 keV Bi3q+. Figure 7 shows selected secondary ion intensities for the first delta layer using 50 keV Bi3q+. The 564.46 Da peak has been fitted with Dowsett’s function (the Gaussian is also a good fit but the small errors would be significant for this part of the analysis) and, in (a) and (c) of Figure 7 the data are also shown for secondary ions of mass 42.00 and 230.16 Da, respectively. In both (a) and (c) the fitting of these peaks is shown with the 564.46 Da data convolved with each of the four GEDDFs of Figure 6 adjusted, each time, for minimum residuals. For the 564.46 Da secondary ion, the fit for 42.00 Da using the linear function is excellent. The root-mean-square residuals for the constant, exponential, and two-delta functions are factors of 5, 4, and 3 times worse than for the linear function, respectively. The residuals, shown in Figure 7b, indicate the clear shape differences for the exponential, constant, and two-delta GEDDFs. For the weaker 230.16 Da secondary ion shown in Figure 7c, the ranking remains the same with the linear function best and the constant function worst. In Figure 7a,c it is clear that the constant function gives intensity that is too low in the approach to the delta layer whereas for the exponential function it is too high. The function for two deltas, while matching the two tails to the peak, is significantly in error at the peak. Only the linear function gives a good description over the full depth. The GEDDF is thus shown to be consistent with a linear function, falling with depth. This is what would be expected from sputtering where the emitted ions come from a paraboloid shaped zone within the crater. This is more reasonable than an exponential function since it is difficult to see how any significant signal could be obtained from much below the crater floor except for the monatomic Bi+ primary ion. The GEDDF total depths, for the 42.00 and 230.16 Da secondary ions for 50 keV Bi3+, are 11 and 10 nm, respectively. These total depths are 3.7 times the shift in depth for the peaks associated with each secondary ion and are close to the 3.0 times from the simple considerations in section 4.1 based on Gaussian structures. These total depths are not inconsistent with the sputtering

Figure 5. The 564 Da reference peak, that peak convolved with an exponential decay with characteristic λx, and the 346 Da peak analyzed with 13 keV Bi3+.

by the Bin+ analytical ions. There are many simple models that one can take for the generation and escape depth distribution functions (GEDDFs), as shown in Figure 6, that are (i)

Figure 6. Four generation and emission depth distribution functions (GEDDFs).

constant to a defined small depth as was used for our cylindrical sputtered volume, (ii) an exponential decay, (iii) a linear reduction with depth to zero, (iv) emission from the surface and a point in the crater as we saw for the 346.18 Da ion, and so on. In all cases, convolution of such a GEDDF with the initial Gaussian depth resolution function generated by the argon gas cluster sputtering that has an intrinsic fwhm greater than the shift, provides a set of very similar final profiles. Unfortunately, for most of the conditions, the different models cannot be distinguished by their profile shapes without very much greater signal levels and greater data densities required to improve the measurement precision. Greater signal levels or data densities would require analytical ion dose levels that start to contribute to the sputter removal in the profiling. We avoid the terms “sampling” or “information depth” which already have a general meaning and are associated with a characteristic value, in favor of the GEDDF which has both a defined shape (yet to be determined) and characteristic value. Escape depths are often associated with one main phenomenon (e.g., escape of secondary electrons of particular energies in AES or XPS), but here they involve both the emission behavior of the characteristic secondary ion and also the generating energy of the primary analytical ion. F

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5. CONCLUSIONS A study is presented of the shifts in the apparent centroid depths and the depth resolutions of delta layers of Irganox 3114 when sputtered by argon gas cluster ions and analyzed by Bin+ ions. These effects depend on the primary sputtering ion beam species and energy, the analysis ion beam species and energy, and the emitted secondary ion species. The shifts increase linearly with the energy of the analyzing ions and, for the 42 and 230 Da ions, reach a shift toward the surface of 3 nm for 50 keV Bi3q+. The shifts for Bi5q+ are slightly less as the craters are thought to be slightly wider and therefore less deep for the same sputtering yield or beam energy. The shifts for Bi+ are much lower since the sputtered volume by monatomic ions for organics is very low. The shifts toward the surface for the largest fragments are very small since they arise from the outer edge of the crater rather than the hot core. A shift toward the substrate occurs for the 346.2 Da fragment which arises mainly from the 5 keV Ar2000+ sputtering and less strongly from the effects of the analysis beam. The shifts toward the surface are shown to be consistent with a linearly falling generation and escape depth distribution function whose total depth is 3.7 times the shift in centroid depth caused by the analysis beam. This distribution is associated with a paraboloid crater shape. The GEDDF is convolved with the intrinsic depth resolution caused by the 5 keV Ar2000+ beam such that the measured depth resolution degrades and is most degraded for the most shifted secondary ion depth profiles. The intensity as a function of depth for the largest secondary ion fragment, at 564.34 Da, is well described by Dowsett’s function.3,4 The depth profiles for other secondary ions result from the convolution of this function with a linear generation and emission depth distribution function whose total depth depends on the analysis ion and its energy. The final results are also often well described by Dowsett’s3,4 function. For measuring depth distributions it is recommended that low energies be used for the analysis beam and that carefully selected, large, secondary ion fragments are used, or that the analysis be made in the single beam mode using the sputtering Ar cluster ions also for analysis. For the truest profile, the secondary ion intensity should be for ions showing no significant matrix effect, or those effects should be removed by computation, and the analysis beam energy should be as low as is consistent with adequate signal quality.

Figure 7. Normalized secondary ion intensities measured for the first delta layer using 50 keV Bi3+, (a) the 42.00 Da and (c) the 230.16 Da secondary ions, both with the 564.36 Da reference secondary ion. In (b), the residual errors of the fits in (a) are shown with the same color lines. The 564.36 Da data (black circles) are well fitted with Dowsett’s function3,4 as shown by the black line. The 42.00 and 230.16 Da data (gray circles) in (a) and (c) are then fitted with the Dowsett function for the 564.36 Da data convolved with the four GEDDFs as shown by the green (exponential), blue (constant), orange (linear), and pink (two deltas) lines.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +442089436202. Notes

The authors declare no competing financial interest.

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yield volumes noted earlier, and for instance, from the sputtering yield of eq 1 for 50 keV Bi3+, a paraboloidal crater with a depth of 11 nm is consistent with a crater rim diameter also of diameter 11 nm. Therefore these two ions may come from much of the crater, whereas other ions come predominantly from the surface. Other GEDDFs could be considered such as a hemispherical emission zone. In that case, it is seen that the results come in between those for the constant and the linear GEDDFs with, in Figure 7b, a rootmean-square scatter halfway between those for the constant and the linear GEDDFs.

ACKNOWLEDGMENTS

The authors would like to thank Alex Shard, Steve Spencer, and Steve Smith for the preparation of the samples. This work forms part of the 3D NanoSIMS project in the Chemical and Biological program of the National Measurement System of the U.K. Department of Business, Innovation and Skills and with funding by the European Metrology Research Programme (EMRP) Project NEW01-TReND. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. G

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DOI: 10.1021/acs.jpcb.5b12697 J. Phys. Chem. B XXXX, XXX, XXX−XXX