Universal Equation for Argon Gas Cluster ... - ACS Publications

Article pubs.acs.org/JPCC

Universal Equation for Argon Gas Cluster Sputtering Yields M. P. Seah* Analytical Science Division, National Physical Laboratory, Teddington TW11 0LW, U.K. ABSTRACT: An analysis is made of the sputtering yields of materials for argon gas cluster ion beams used in SIMS and XPS as a function of the beam energy, E, and the cluster size, n. The analysis is based on the yield data for the elements Si and Au, the inorganic compound SiO2, and the organic materials Irganox 1010, the OLED HTM-1, poly(styrene), poly(carbonate), and poly(methyl methacrylate). The argon primary ions have cluster sizes, n, in the range 100−16 000 and beam energies, E, from 2.5 to 80 keV. It is found that the elemental and compound data expressed as the yields, Y, of atoms sputtered per primary ion may all be described by a simple universal equation: Y/n = (E/An)q/[1 + (E/An)q−1] where the parameters A and q are established by fitting. The sputtering yields of the three organic materials are given as yield volumes expressed in nm3. For these, an extra parameter B is included multiplying the right-hand side of the equation where B is found by fitting to be of the order (0.18 nm)3 to (0.26 nm)3. This universal equation exhibits no threshold energy, and no deviation was observed from the equation, indicating that any threshold energy would have to be significantly below E/n = 1 eV per atom. The equation also shows that doubling the cluster size at the same energy per atom simply doubles the sputtering yield so that in this sense, and probably this sense alone, the sputtering effects are linearly additive. The parameter A is related, inversely, to the mean sputtered fragment size, and the low A values for organic materials are indicative of high yield volumes. For materials with low A values, the universal equation is close to a linear dependence on energy, and if that linear dependence is assumed, an apparent threshold energy is predicted and observed experimentally.

1. INTRODUCTION

The quality of argon GCIB depth profiles is very good, and developments in the ion beams and the operating procedures are leading to improved depth resolutions that generally supersede those achieved by other primary ion beams for organic materials.17 There appears to be little inclusion of the argon atoms, and the lack of reactivity means that, at room temperature, most argon atoms will be lost from the surface to the vacuum. This means that there is no need for the argon beam to sputter its own deposit, as is required for C60,18 and so the lower beam energies, associated with higher depth resolutions, may be used. In most argon GCIB sources, both the energy E and number of atoms n in the primary beam may be selected. This choice of E and n affects four important parameters for the analyst: (i) the sputtering yield and hence the rate of sputtering and duration of the experiment, (ii) the depth resolution, (iii) the fragmentation and secondary ion yields,19 and (iv), through the available instrumentation, the available beam current. All of these parameters are vital, but here we shall consider how the sputtering yields are related to E and n through data for eight materialsAu, SiO2, Si, Irganox 1010, the model organic lightemitting diode (OLED) material HTM-1, poly(styrene), poly(carbonate), and poly(methyl methacrylate) (PMMA)in order to arrive at a predictive and general equation. These results are taken from our own and other published data.

The sputtering yield of solids using monatomic primary ions has been the focus of an extended body of work over a significant period, leading to detailed descriptions of the absolute yield, the angular distribution of emitted secondary particles, their energy distribution, and many other factors, such as the effects of the primary ion angle of incidence and the sample temperature.1−3 That body of work is for single particle primary ions and mainly for single element targets. Studies have been extended to selected important binary compounds such as oxides and semiconductors.2,4,5 Predictive equations6,7 or easily accessible software programs allow the yields to be calculated to an accuracy of some 10%.8 This is particularly important for the sputter-depth profiling of layered materials using secondary ion mass spectrometry (SIMS) or X-ray photoelectron spectroscopy (XPS) when studying layers less than some 500 nm in thickness. For sputter-depth profiling, to reduce the inclusion of primary ions, generally the rare gas primary ions Ar or Xe have been used9 although in SIMS, O2 and Cs primary ions have powerful application.10,11 For the study of organic materials, cluster ion beams have been shown to be important in permitting good signal levels. Initially, SF5 and C60 beams were used,12,13 but later, argon gas cluster ion beams (GCIBs), pioneered by Jiro Matsuo and his team, were found to provide the most constant sputtering rates during profiling and the least damage to organic materials.14 This paved the way for their use for both SIMS15 and XPS depth profiles.16 Published XXXX by the American Chemical Society

Received: March 18, 2013 Revised: May 29, 2013

A

dx.doi.org/10.1021/jp402684c | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Y (2000, E) = 0.0000268(E − Eth)1.5

2. BACKGROUND EQUATIONS Early work by Matsuo et al.20 demonstrated many of the important properties of GCIBs and, in particular, showed two effects. In the first, across seven elemental solids, Si, Ti, Cu, Zr, Ag, W, and Au, they determined the sputtering yield for 20 keV beams with an average cluster size of 3000 atoms. These yields, in the range 10−100 atoms/ion, were ∼10 times the yields for the same elements as calculated for 20 keV Ar monomer ions. It was deduced that the yields depended on 1/U, where U is the binding energy of the target atoms, in the same way as for monomer primary ion yields in this energy range.1−7 The second effect shown20 was a linear dependence on energy observed when using the same average argon gas cluster size of 3000 for Ag and Cu targets for 10 000 ≤ E ≤ 25 000 eV. This linearity indicated a threshold energy of 6 keV in both materials. Below this threshold energy, sputtering appeared to cease. In Matsuo et al.’s studies, the argon ions were incident normally to the sample surface and exhibited a broad range of cluster sizes. With the average argon cluster size of 3000, the above threshold energy was converted to 2 eV per incident atom in the cluster. Later studies for Si and Au21 again showed a linear relation of the yield on energy for 5000 ≤ E ≤ 20 000 eV using argon gas clusters with a peak of the primary ion cluster distribution, n, at 2000. The cluster distribution was broad. Size-selected, narrower distributions were used by Matsuo and his colleagues later and also by those using commercial instruments. As n was increased, for 20 keV and for 2000 ≤ n ≤ 10 000, the yield fell and the yields were fitted to the relation ⎛E ⎞ Y (n , E) = kn p⎜ − Eth⎟ ⎝n ⎠

(2)

where the form of the equation is given by Ichiki et al.23 and where Eth is given as 6000 eV. This gives Eth/n close to U but well below the threshold energy calculated for monatomic sputtering. The above equations are very limited for general use, and so, below, more extensive data are analyzed to provide a generic equation.

3. ANALYSIS OF EXTANT DATA USING A SINGLE EQUATION 3.1. Gold. In our laboratory, sputtering yields have been measured for gold using various argon gas cluster sizes by SIMS in a ToF-SIMS IV (IONTOF GmbH, Munster, Germany) instrument using depth profiles in both the single- and dual-beam modes for films with thicknesses measured using an atomic force microscope (AFM).24 In the SIMS instrument, the size-selected primary argon GCIB is incident at 45° to the surface normal. In the dual-beam mode, the analysis is made with 25 keV Bi3+ ions also incident at 45° but in an azimuth at 90° to that for the argon GCIB. The argon GCIB for sputtering is at a significantly different angle of incidence from the 0° used by Matsuo and his colleagues. Conversion of sputtering yields from one angle to another is problematic as there are no generic angular equations. General sputtering yield equations are provided by Yang et al.25 that may be used for describing the angular dependencies, but these have not been tested. For angles between 0° and 45°, it is likely that the effect could be close to secp θ with 0 ≤ p ≤ 1, but in addition p will be both E and n dependent. The yield at 45° could, therefore, be between 1.0 and 1.4 times that at 0°. We shall revisit this issue later. In the gold study,24 films ∼30 nm thick are deposited on Si wafers in vacuum. The yields are deduced from the measured dose to profile to the Au/Si interface. The sputtering yields are shown in Figures 1a,b with Figure 1a showing the yield data, Y, and Figure 1b the yield per cluster atom, Y/n. These data have been fitted to the equation

(1)

where Eth is a threshold energy for sputtering, p is a coefficient of size effects, and k is a constant.21 Eth was correlated with the surface binding energy, U, of the targets, 4.7 and 3.8 eV for Si and Au, respectively. In eq 1, the threshold energy is assumed to operate for each impacting atom of the GCIB separately, i.e., that an impacting atom needs an energy greater than U to break a bond of energy U. By fitting, the values were found to be k(Si) = 0.0013 eV−1, Eth(Si) = 4.7 eV, p(Si) = 1.1, k(Au) = 0.0016 eV−1, Eth(Au) = 3.8 eV, and p(Au) = 1.1. Experimental data for the yields for n = 10 000 were deemed to be in error as the beam current was low. The method for determining the sputtering yield is not given, but in the earlier work,20 stylus profilometry had been used to measure the material sputtered for sputtered depths in the range 5−80 nm. In this early work, the cluster distribution is broad and not sizeselected. In very recent work, Ichiki et al.22 show by calculation that the use of size-selected clusters gives essentially the same sputtering yield values as without size selection in the primary ion energy range 10−30 keV with n = 2000. In that study,22 more data are provided for Si, and the same linear dependence is seen for the yield dependence on E with the threshold energy for n = 2000 observed at ∼7500 or 3.5 eV per cluster atom. It is noted, however, that the yield is nonzero for 20 keV Ar8000 with E/n = 2.5 eV and that, as this is below U, multiple collisions are important. Again, in a very recent study23 of the yield for a mean cluster size of 2000 incident at 0° to the surface normal, the sputtering yields, Y (atoms per ion), for Si have been measured more carefully for 10 000 ≤ E ≤ 80 000 eV and were found no longer to be linear with energy but can be fitted with the very nonlinear equation

[E /(An)]q Y = n 1 + (E /(An))q − 1

(3)

where A = 63 eV, q = 2.6, and E, the primary ion impact energy, is in eV. The quality of the fit in Figure 1a is poorest for n = 5000 at 5 keV, and this is because the sputtering yield is very low, leading to profiles of long duration and possible concomitant sputtering contributions from the 25 keV Bi3+ analysis beam used for this condition (a correction was included for this but each correction adds uncertainty). Figure 1b shows how the results for all cluster sizes for the same E/n value fall on the same curve for Y/n such that doubling the cluster size at the same E/n leads to a doubling of the yield. In this sense, and probably in this sense alone, the effects are linearly additive. At high values of E/n, eq 3 reduces to Y = E/A; i.e., at low n values the yield has become invariant with n. If it is assumed that the majority of sputtered particles are monatomic, a fixed fraction of the energy given by U0/A is consumed in delivering sputtered particles. This simple estimate ignores both the kinetic energy of the sputtered particles and the size distribution of emitted fragments and is therefore an upper estimate. Here, this fraction is 6%, which is very high. At low values of E/n, Y = n(E/An)q and Y has a simple power dependence on E. Unlike eqs 1 and 2, eq 3 has no threshold energy. There clearly must be a threshold energy below which sputtering does not B



Article

Figure 2. Sputtering yield calculations for condensed argon using Arn+ at 0° incidence and various energies as Y/n versus ε/n, after Anders et al.26 The thin curve is for eq 4, and the red curve is for eq 3.

In terms of simple equations, eq 3 is a good description with surprisingly few degrees of freedom. It is useful, therefore, to evaluate the universality of eq 3 and to determine the values of A and q relevant to other systems. 3.2. Silicon Dioxide. The sputtering yields for SiO2 were measured as for gold above, except that the films were of a thermal oxide with its thickness measured by ellipsometry and not by AFM.27 The results for SiO2 are shown in Figures 3a,b in the same format as the results for Au. Again we see that eq 3 is an excellent description over the whole range, and certainly there is no deviation indicating any onset of a threshold energy even down to E/n = 2.

Figure 1. Sputtering yield for gold using Arn+ at 5, 10, and 20 keV at 45° incidence, presented (a) Y versus n and (b) Y/n versus E/n in eV/atom units using the same symbols as in (a), after Yang et al.24 The solid curves are for eq 3.

occur, but the absolute minimum for E could be ∼U, which would be orders of magnitude to the left of the E−n space presented in Figure 1b. It is important to note that at very low E/n values the kinetic energy of the supersonic gas in the GCIB source provides an energy of 0.065 eV per atom.22 If this were to be ignored, the lowest point in Figure 1b would be plotted 2/3 of a point diameter to the left of its current position. This correction is included in the IONTOF GCIB system. A similar but significantly different empirical equation to eq 3 has been proposed by Anders et al.26 based on molecular dynamics calculations (MDC) of argon cluster sputtering of frozen argon solid. This is a very weakly bonded solid and very different from the solids studied here; nevertheless, a comparison is informative. The yield, Y/n, is measured as the number of atoms liberated from the target per incident projectile of cluster size n and impact energy E at normal incidence. The results for n ≥ 100 are shown in Figure 2 where the abscissa involves the reduced energy ε where ε = E/U0 and U0 is the cohesive energy. Further data points for 10 ≤ n ≤ 100 exist in the energy range 10 ≤ ε/n ≤ 100, and all show no significant divergence from those shown but are not included here since we are only concerned with n ≥ 100. Also shown in Figure 2 by the thin line is the function proposed by Anders et al.:26 Y ε1 + b =α n (εc + ε)b

(4)

Anders et al. fit the data for n = 100 to give values for the fitting parameters α = 0.065, εc = 3160, and b = 0.54. Equation 3 is shown by a thick line for A = 15U0 and q = 2.4. Not only does eq 3 fit the data at low ε/n values rather better than eq 4, but there is one fewer variable to fit. 26

Figure 3. As in Figure 1 but for SiO2 at 45° incidence, after Yang et al.27 The solid curves are for eq 3. C



Article

Table 1. Summary of Parameters material

q

A (eV)

angle of incidence (deg)

U (eV)

B (nm3)

a (nm)

max fractional energy U/(tA)

Au SiO2 Irganox 1010a HTM-1a polystyrenea polycarbonatea PMMAa Si

2.6 3.1 2.76 3.2 3.4 3.0 2.8 2.25

63 39.5 1.6 0.78 2.36 4.2 2.34 57

45 45 45 45 45 45 0 0

3.82 3.3028 4.3b 5.1b 4.7b 4.7b 4.7b 4.66

0.0170 0.0143 0.0176 0.0060 0.0111 0.0170 0.0156 0.0200

0.26 0.24 0.26 0.18 0.22 0.26 0.25 0.27

0.06 0.08 0.2c 0.5c 0.15c 0.15c 0.15c 0.08

a

Y evaluated per nm3 bAverage of C, O, and N bonds, excluding H bonds. ct = 13 for the organic materials and 1 for the elements and inorganic materials.

In eq 3, A = 39.5 eV and q = 3.1. In the 1 ≤ E/n ≤ 10 range, the yield in atoms of SiO2 per particle is approximately that of Au, but as E/n increases, eventually the yield is ∼1.6 times higher. The values of A and q for SiO2 are listed in Table 1 together with the data for Au. In this case, at high E/n values, a fixed fraction near 8% of the incident GCIB energy is used to sputter Si and O atoms, assuming that the primary form of the emitted particles is monatomic. 3.3. Irganox 1010. The sputtering yields here were partly determined from a recent interlaboratory study for depth profiling Irganox 1010 reference samples with delta layers of Irganox 3114 at defined depths29 and also from the work of Niehuis et al.30 using the same material. Irganox 1010 is an antioxidant molecule used as an additive in polymers with the formula C73H108O12 and molecular mass 1176.78 Da. It is a molecule with four equal arms attached to a central carbon atom, has a density of 1.15 g cm−3, and is stable at room temperature. The samples are fabricated by thermal evaporation in vacuum and are deposited as thin layers on a Si wafer with the thicknesses determined by the frequency shift of a quartz crystal oscillator. The sputtering yields are derived from the measured doses to sputter to each interface and are given as sputtering yield volumes in nm3 since it is often thought that the sputtering yield volumes for different organic materials are more consistent and useful than sputtering yields in terms of numbers of atoms. The sputtering yields from the interlaboratory study29 are all measured in SIMS depth profiles for primary ion clusters of different sizes and different energies, incident at 45° to the surface normal, each by a different analyst in a different instrument. The only items in common are the samples and interpretation. Further results given separately by Niehuis et al.30 using the same samples. The combined results are shown in Figures 4a,b in the format of the earlier plots. Here, however, Y is in nm3 units rather than atoms per incident particle and the fit has been made with BIrg (E /1.6n)2.76 Y (nm 3) = n 1 + (E /1.6n)1.76

Figure 4. As in Figure 1 but for Irganox 1010 at 45° incidence from Shard et al.29 and Niehuis et al.30 and in which Y is not measured as atoms/ion but in nm3. The solid curves are for eq 5.

The value of A is now much smaller than for Au or SiO2, and if it is assumed that the sputtering mainly generates C and O atoms with or without added protons, the fraction of the GCIB energy consumed by the emitted particles is U/A, which, if U = 4.3 eV, gives U/A = 2.7, i.e., greater than unity. The assumption that the sputtering generates mainly atomic species is, of course, wrong for organic materials. If, typically, we have t such atoms in an average emitted secondary ion fragment, then the fraction of the GCIB energy consumed by the emitted particles is U/(tA). Irganox 1010 spectra using CGIBs have not been published, but Seah and Gilmore31 provide data from which it can be shown that for Bin+ clusters the average value of t is around 13 C and O atoms with or without added protons. The value of U/(tA) is ∼20%, which is high but a practicable value. What this shows is that the parameter A is inversely related to the mean sputtered fragment size and that high sputtered volumes for organic materials arise since many atoms may be emitted by breaking few bonds. In the

(5)

This fit exhibits a root-mean-square deviation of 7% for the 22 results. The parameter values are compiled in Table 1. Note that relatively large volumes of organics are readily sputtered. The coefficient BIrg has been inserted in eq 5 since Y is now measured in nm3. If the earlier results had been measured as volumes, BAu would be 0.0170 nm3 and BSiO2 would be 0.0143 nm3, both derived using the respective bulk densities. In terms of an atomic volume defined by a cube of side a (i.e., Bx = ax3), aAu = 0.26 nm and aSiO2 = 0.24 nm. Here, we find empirically BIrg = 0.0176 nm3, i.e., aIrg = 0.26 nm, very similar to the results for Au and SiO2. D



Article

away from the minimum to see if parameter values closer to those of Irganox are also consistent with the data. As BHTM is raised from 0.0060 (aHTM = 0.18 nm) to 0.01 nm3 (aHTM = 0.215 nm), A rises to 1.10 and q falls to 2.17 with the rms scatter rising to 12%. These give BHTM and A values closer to those for Irganox 1010, but q remains much lower. In forcing these fits, the predicted results are above the data points at both low and high values of E/n with the fit for BHTM = 0.01 nm3 being just about acceptable. It is clear that the parameter values are significantly different from those for Irganox 1010. 3.5. Polystyrene and Polycarbonate. Sputtering yields here are taken from Rading et al.32 from crater depths with the primary ions incident at 45° with 2500 ≤ E ≤ 20 000 and with n = 500, 2000, and 5000 for polystyrene but with only n = 2000 for polycarbonate. The compiled results for polystyrene in the form of Figure 5b are given in Figure 6. The fit is for

ultimate case of the full molecule being emitted, the energy adsorbed in the intermolecular bond breaking is very low since these molecules are made into films by thermal evaporation involving very weak intermolecular forces. 3.4. HTM-1. Sputtering yields here are taken from the study of Niehuis et al.30 in measuring SIMS depth profiles of model organic light-emitting (OLED) structures supplied by Merck AG. These included a 60 nm layer of 2,2′,7,7′-tetra(N,Nditolyl)amino-9,9-spirobifluorene, C81H68N4, with molecular mass 1096.54 Da. Like Irganox 1010, this is a molecule with four equal parts attached to a central carbon atom and is stable at room temperature. The material is called HTM-1 by Niehuis et al., and elsewhere it is called Spiro-TTB.

B (E /2.36n)3.4 Y (nm 3) = PS n 1 + (E /2.36n)2.4

(7)

Figure 6. As Figure 5b but for polystyrene at 45° incidence from Rading et al.32 The solid curve is for eq 7. The symbols are for the same energies as in Figure 5a.

with BPS = 0.0111 nm3 (i.e., aPS = 0.22 nm) to a relative standard deviation of 9%. The parameter values are compiled in Table 1. The fit shows, again, the excellent description of eq 7. The results for polycarbonate32 are similar to polystyrene and give BPC = 0.0170 nm3 (i.e., aPC = 0.26 nm), APC = 4.2, and qPC = 3.0 with a fit consistent to a relative standard deviation of 7%. 3.6. PMMA. Sputtering yield data for PMMA, (C5H8O2)y, are provided by Ichiki,33 in his PhD thesis for normal incidence using non-size-selected argon gas clusters. The films are 100−300 nm thick, spun cast onto a silicon wafer with the yield volume measured from raster craters using a stylus profilometer. The results are given as the yield per repeat unit of 100.08 Da. The density for the material is given as 1.2 g cm−3 to convert the volume sputtered to the yield per repeat unit. Using the same density, we may recalculate the volume of the repeat unit used as 0.138 nm3 and hence derive, consistently, the original yield volumes. The compiled data in the form of Figure 1b are shown in Figure 7 with the curve shown given by

Figure 5. As Figure 4 but for the OLED material HTM-1 at 45° incidence from Niehuis et al.30 The solid curves are for eq 6.

The results for the yield volumes, again at 45° incidence, are similar to those for Irganox 1010 and are given in Figures 5a,b. The fit is for B (E /0.78n)3.2 Y (nm 3) = HTM n 1 + (E /0.78n)2.2

(6)

3

with BHTM = 0.0060 nm (i.e., aHTM = 0.18 nm) to a relative standard deviation of 8%. These data are compiled in Table 1. This value of BHTM is somewhat smaller than for Irganox 1010 but offsets the lower A value here. The fit shows, again, the excellent description of eq 6. Since the curvature in the line in Figure 5b is defined by only a few points, it is interesting to evaluate the effect of forcing the fit

B (E /2.34n)2.8 Y (nm 3) = PMMA n 1 + (E /2.34n)1.8 E

(8)



Article

Figure 7. As Figure 5b but for PMMA at 0° incidence from Ichiki.33 The solid curve is for eq 8. The symbols show the rainbow colors with red at the lowest energy (5 keV) and violet as the highest (60 keV). The open square symbols show the data of Rading et al.32 for 45° incidence at n = 2000.

Figure 8. Model size distributions for non size-selected GCIBs to match the data of Matsuo et al.34 The noted size values are the curve labels as in Figure 1 of Matsuo et al.34 and indicate the approximate peak values.

size-selected beam with n = n0. If it is assumed that the sputtering follows the behavior shown in eq 3, we may evaluate n0 from n

Here, BPMMA = 0.0156 nm3 (i.e., aPMMA = 0.25 nm). These data are compiled in Table 1 and are similar to polystyrene. Here the scatter is significantly poorer than for polystyrene, being nearer 30% rather than below 10%. The data are recorded in two plots by Ichiki:33 one for the yield versus E/n for E = 5000, 10000, 20 000, and 30 000 eV and one for the yield versus E/n for n = 1000 and 4000 with energies in the range 5000−60 000 eV. These two sets of data may have been recorded at different times since data that are for the same E and n values in the two plots are not the same and show an RMS scatter of 26%. This variability may be the source of the scatter observable in Figure 7. Nevertheless, these results are useful confirmation that polymers, with their long chains, follow the same behavior as for all the other materials. A small set of measurements are independently supplied by Rading et al.32 for n = 2000 and at 45° incidence. These are included in Figure 7 as the large open squares, and it is very clear that they are very consistent with eq 8 and are well within the scatter of Ichiki’s data. These results would indicate an increase at 45° of ∼13% but an increase that has no significant dependence on E/n. The 13% is, of course, much less than the scatter of the data in Figure 7. Rading et al.32 give a greater increase at 45° for polystyrene, but it is not clear if this is a general increase that may be transferred to PMMA. 3.6. Silicon. The Si sputtering data are also taken from the publications of Matsuo’s group in which sputtering yields are generally measured at normal incidence with nonselected GCIBs. It is worth checking at first the effects of the size selection, and in Figure 8, we show the argon cluster distributions of Matsuo et al.34 These curves are not their experimental curves but are computed Gaussian population distributions in log(n) space that closely fit the data shown in Figure 1 of Matsuo et al.34 There are two parameters that are significant to determine. The first is the ratio of the mean of the population, nmean, to the value of n for the peak of that population, npeak. In all the cases shown in Figure 8, nmean/npeak is 1.23; i.e., the average n value is 1.23 times that of the peak n value. This ratio depends, of course, on the shape and width of the distribution, and it is assumed that this shape remains constant in all the nonselected GCIB studies from Matsuo’s group although the width of the Gaussian may vary. A second parameter that is important is the effective n value, n0, for this population that gives the same sputtering yield as for a

n0 =

∑nmax nY (n)P(n) min

n

∑nmax Y (n)P(n) min

(9)

where P(n) is the population of the cluster distribution. If the power dependence of Y on n is known, n0/npeak may be determined. Figures 1 and 3−5 show how the power dependence changes from near zero at low values of n to −2 at high values of n. Figure 9 shows a plot for n0/npeak versus q* where it is assumed

Figure 9. Ratio of n0/npeak versus q*. Solid line: for the GCIB distribution data in Figure 7 with a width standard deviation factor of 0.16 in log(n) or a multiplying and dividing factor of 1.45 in n. Dashed line: a size-selected narrower distribution with a width standard deviation factor of 1.24.

that Y(n) ∝ n1−q*; i.e., q* may run from 1 to 3. For this calculation, the curve labeled “1.45” is for the distribution shown in Figure 8 with a standard deviation of 0.16 in log(n) space, equivalent to a multiplying and dividing factor of 1.45 in n space. Also shown in Figure 9, by the dashed line, is the much weaker effect for size-selected clusters with a standard deviation equivalent to a factor of 1.24 in n space. In these figures, the values of nmin and nmax are set at 0 and ∞ (using limits of 0.25npeak and 4npeak gives the same result), and the summation is easily evaluated by integration as though n were continuous. This amount of size selection almost removes the difference between F



Article

n0 and npeak. In the IONTOF instrument used for the gold and SiO2 measurements, the cluster distribution may be reduced at both higher and lower n values than npeak. The system allows the distribution to be measured. In that work, this standard deviation factor is even lower at 1.17,24,27 producing a negligible difference between n0 and npeak. In eq 3, for the lower E/n values, q ≈ q*. For q* > 2.5, the effect of the high yield at low n values dominates, and the effective n0 value for sputtering is lower than npeak. In the Au, SiO2 and Irganox 1010 data cited earlier, if size-selected clusters had not been used (as in Figure 8), this would have led to n0/npeak being 0.99, 0.92, and 0.97, respectively, with negligible effect. In Si, Ichiki et al.22 observe experimentally that using nonselected and size-selected GCIBs have very similar sputtering yields as Figure 9 would indicate. This may not always be the case, especially for very low n values. The sputtering yield data for Si are taken from the recent papers of Ichiki et al.22,23 in which the incident beam was either size-selected22 or not size-selected.23 In the first of these studies,23 yields are measured from craters for 10 and 20 keV ion beam energies with 1000 ≤ n ≤ 4000 and 1000 ≤ n ≤ 16 000, respectively, and for 30 keV at n = 2000. In the second study,23 the yields are measured for n = 2000 with 10 000 ≤ E ≤ 80 000 eV. In this case it is stated that “the mean cluster size was about 2000”, but a plot of the distribution shows that the value intended is, indeed, the more relevant npeak and not nmean. In both of these cases, the sputtering is normal to the surface. Figures 10a,b show these data together with the plots for eq 3 with A = 57 eV and q = 2.25. These data are compiled in Table 1. The fit is excellent, as previously. It is often thought that the yields increase linearly with energy after an initial threshold energy. Figure 10c shows the plot of data for all energies for n = 2000 and the description of eq 3. The fit here is similar to that of Ichiki et al.23 in that it is not linear but differs in that no threshold energy is observed at 6 keV and the closeness of the fit over the full range is somewhat improved. Ichiki et al.’s23 threshold at 6 keV has an E/n value of 3, but in Figure 10b, we see two data points fitting the thresholdless eq 3 below this for E/n = 2.5 using 20 keV at n = 8000 and using 10 keV at n = 4000. There are a number of other sets of Si sputtering yield data from Matsuo’s group20,21,33,34 which scatter generally about these data, and so the above values of A and q for Si should only be considered approximate. Furthermore, for comparison with the rest of the data, it should be remembered that these data are for normal incidence and also that, at least for monatomic primary ions, there are strong yield dependencies for ions incident close to crystal low index directions.35,36 Nevertheless, Si wafers are used as the substrates for many materials and so these data are important.

Figure 10. As in Figure 1 for (a) and (b) but for Si at 0° incidence. The solid curves are for eq 3. In (a) the successive curves are for beam energies of 10, 20, 30, 40, 50, 60, 70, and 80 keV from bottom to top. In (b) the symbols match those given in (a). In (c), the data are from Figure 3 in ref 23.

is a function of the atomic number of the target, Z2, and of the atomic number and energy of the projectile, Z1 and E. However, it is not known how different the results for cluster primary ions should be. Here, we shall analyze the available specific data sets32,37−42 for cluster primary ions, some of which are calculations using molecular dynamics and some of which are experimental data, to see if any general patterns emerge. The primary ions, samples, and other data are compiled in Table 2. The experimental data are probably for microscopically rough surfaces, whereas the molecular dynamics calculations are all for ideally flat surfaces except one set of data42 where both ideal and rough surfaces are considered. The rough surface shows a much flatter response42 up to 45°, instead of a rapid decline, and indicates, that for practical purposes, most of the molecular dynamics calculations for angular effects may not be too relevant. The results for

4. ANGLE DEPENDENCE OF THE YIELD In the above, the data for PMMA and Si are both for primary ion beam angles of incidence of 0°, but the remainder are for the 45° commonly used in surface analysis studies. There is currently no simple way of converting data for one angle of incidence to another although there are several sets of data32,37−42 for specific cluster ions impacting specific targets at given impact energies. For monatomic primary ions, a general analysis exists based on Sigmund’s43 theory and given by Seah44 with all the relevant parameters simply described. That angular dependence follows a function that generally increases faster than sec θ at first but then reaching a peak at θ = θmax and finally falling to zero. Here θ is the primary ion angle of incidence from the surface normal and θmax G



Article

Table 2. Source of Angle-Dependent Cluster Sputtering Yields

a density of 1.15 g cm−3, the average volume of a C or O atom, ignoring the H, is (0.27 nm)3, as used in Figure 11. Similarly, the molecular weights of HTM-1, polystyrene, polycarbonate, and PMMA, C81H68N4, (C8H8)y, (C16H14O3)y, and (C5H8O2)y, are 1097, 104y, 254y, and 100y with densities of 1.15, 1.06, 1.2, and 1.18 g cm−3, the average volumes of a C, N, or O atom, ignoring the H, are all (0.27 nm)3. This value, with a relative standard deviation of 7%, is also the average for many polymers. Figure 11 shows two essential aspects. First, the sputtering rate for organics, where argon GCIBs have real application, can be 2−4 orders of magnitude higher than the rate for elements or compounds and second that the relative rates of sputtering of, for example, Irganox 1010 and SiO2 can change over 100 times in the range 1 ≤ E/n ≤ 100. The high sputtering yield volumes for the organic materials arise from the low values for A driven, in turn, by the possibility of sputtering t atoms at a time whilst breaking a few bonds. The A value for elements and inorganic materials is ∼50, whereas that for organics is ∼2.5. In Table 1, the final column, U/(tA) gives, approximately, the maximum fraction of the total GCIB energy used in sputtering the emitted atoms at high values of E/n. Such a high sputtering yield may not always occur for polymers if they are very highly cross-linked. With a high degree of cross-linking, more strong bonds need to be broken for a t value of, say, 13, and this will cause the sputtering yield to fall and A increase. This lower sputtering yield for cross-linked material may cause the overall sputtering yield to fall when profiling polymers with primary ions other than argon gas clusters in which there is a significant amount of damaged material remaining on the surface by each impacting primary ion. In none of the data analyzed so far is there any indication of a threshold energy. Observation of a likely effect in E/n would be data points falling below the curves for eqs 3 and 5−8 in Figures 1b, 3b, 4b, 5b, 6, 7, and 10b. The lowest E/n data points involve the greatest relative error, but at E/n = 1, no offset is seen. For monatomic Ar beams, Eth ranges from 4U for Au to 7U for Si.20,21 For cluster beams, the threshold energy for E/n could then be between this upper limit of 7U and a lower limit of 4U/n. Thus,

(C2H5OH)n primary ions may be strongly affected, in practice, by carbon deposits.18 All that can be seen from this is that, for Si, the yield at 45° may be more or less than that at 0°, but the change will not be a dramatic one compared with the ordinate scale of Figure 10b.

5. GENERAL COMMENTS Figure 11 shows a combined plot for all the materials analyzed, and Table 1 summarizes the relevant parameters. The average

Figure 11. Combined plot for Y/n for the seven materials: Au (− −), SiO2 (), Si (---), Irganox 1010 (− −), HTM-1 (), polystyrene (−○−○−), polycarbonate (− −), and PMMA (---). For consistency, the data for Irganox 1010, HTM-1, polystyrene, polycarbonate, and PMMA are the yields per volume using a cube of side 0.27 nm. The solid curves are for eq 3. The data are for 45° incidence except for PMMA and Si which are at 0°.

scatter of the data points about the fitted curves for all materials is equal to the radius of the plotted “O”s for polystyrene. In Figure 11, the data for Irganox 1010, HTD-1, polystyrene, polycarbonate, and PMMA are not plotted as Y in nm3 but as Y per (0.27 nm)3 for consistency so that eq 3 applies universally. The molecular weight of Irganox 1010, C73H108O12, is 1177 and, with H



Article

eV/atom. The curves for eq 5 are shown, and they only differ from straight lines significantly for Y < 20 nm3. This is not a region with significant data in practice, and this explains why an apparent offset may sometimes be used effectively with the linear assumption for energy dependence. If eq 5 is used and is fitted with straight lines in the region shown in the plot for Y > 20 nm3, a good fit is obtained with the apparent offset independent of n at ∼0.7 eV/atom. Using a straight line fit to all the Irganox 1010 data with the slopes proportional to n and with a single threshold energy value, the rms deviation of the ratio of the fit to the data is 8%, slightly worse than the universal equation given above of 7%. The most significant difference appears at low energies where, at 2.5 keV, the maximum relative deviations between the straight line approximation and eq 5 occur. Figure 12b places this in the more generic context of Figure 11 but where the data for the organic materials are plotted as Y/n in nm3 per atom, divided by B. The regimes over which data have been recorded are shown and nonlinear results are expected in the few cases for organics where E/An is less than unity. In the E/An < 1 region in Figure 12b, the yield exhibits a power dependence on E, but for E/An > 1, the fraction of the energy removed by the emitted fragments is so high that this cannot be maintained, and a saturation of the yield occurs such that Y/E cannot increase further and Y ∝ E.

for the elemental and inorganic materials a threshold energy may possibly exist somewhere below E/n = 1 but would be difficult to observe in practice. Molecular dynamics calculations for polyethylene by Delcorte et al.45 give results close to those for HTM-1. Those calculations are for a series of cluster primary ions with sizes as low as for C60 and coronene (C24H12) primary ions and show the same form as that described in eqs 3 and 5−8. On the log/log plot, there is a clear departure from the unity gradient to a new gradient, as observable in Figure 11 for E/n < 10. This new gradient is maintained for Delcorte et al.’s45 data for E/n values as low as 0.2; i.e., these equations are valid over a wider E/n range than used so far with no visible threshold. Additionally, as noted in relation to Figure 2, the description may well be valid for clusters as small as n = 24 for the results of Delcorte et al.45 and as small as n = 12 for those of Anders et al.26 Similarly, in the molecular dynamics calculations for the sputtering of solid benzene by Ar clusters, Postawa et al.46 present results for 1 ≤ E/n ≤ 250 that are well described by eq 3 where consistency occurs for primary ion clusters as small as C60, Ne60, and Ar60. A linear energy dependence with a threshold energy may appear to exist, particularly for data recorded for E/n > 1.5A. As shown in Table 1, this will not generally apply to the elemental or inorganic materials but will generally apply to the organics. For example, Figure 12a shows the Irganox 1010 data from Niehuis et al.30 in the format of their Figure 2a. The data may be fitted with straight lines that give abscissa intercepts in the range 0.6−1.1

6. CONCLUSIONS The sputtering yield of the elements Si and Au, the compound SiO2, and the organic materials Irganox 1010, the OLED material HTM-1, polystyrene, polycarbonate, and PMMA have been analyzed for argon gas cluster primary ions in the energy range 2.5−80 keV for cluster sizes between 100 and 16 000. For all the materials analyzed, the sputtering yield for a given beam energy falls as n increases, slowly at first and then more rapidly. In all cases the yield per atom follows the relation given in eq 3 with two unknown parameters currently determined by fitting and, for organics, a yield volume in nm3 that includes a third parameter as in eqs 5−8. This relation allows the yield to be deduced for many operating conditions from a small set of data so that measurements may be optimized. Figure 11 gives a compiled description for all the materials analyzed. Equations 3 and 5−8 describing the yields include no threshold energy term but do show how an approximately linear dependence on E occurs with an apparent threshold energy for organic materials at E/n values below 1 eV. This apparent threshold energy may be useful in practice for specific materials but reducing E/n leads to a deviation from the linear result and may not cause the cessation of sputtering until impracticably low E/n values are attained.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Tel +44 20 8943 6634. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The author thanks I. S. Gilmore for encouragement in this work and for pointing him in the direction of ref 30, Li Yang for all the Au and SiO2 data and many discussions, Alex Shard for an early view of the data in ref 29, and Kazuya Ichiki for refs 22 and 23 and a copy of his thesis, ref 33. 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

Figure 12. (a) Plot of the yield volumes for Irganox 1010 versus E/n in the format of Figure 2a of ref 30 with the fits of eq 5. (b) Replot of the fitted curves for all materials as a function of E/An with the data ranges of measured data shown (the “○” show the ranges of the organics). The fitted curves for the organics overlay in this plot. I



Article

(20) Matsuo, J.; Toyoda, N.; Akizuki, M.; Yamada, I. Sputtering of Elemental Metals by Ar Cluster Ions. Nucl. Instrum. Methods Phys. Res., Sect. B 1997, 121, 459−463. (21) Seki, T.; Murase, T.; Matsuo, J. Cluster Size Dependence of Sputtering Yield by Cluster Ion Beam Irradiation. Nucl. Instrum. Methods Phys. Res., Sect. B 2006, 242, 179−181. (22) Ichiki, K.; Ninomiya, S.; Seki, T.; Aoki, T.; Matsuo, J. Sputtering Yield Measurements with Size-Selected Gas Cluster Ion Beams. Mater. Res. Soc. Symp. Proc. 2010, 1181, 135−140. (23) Ichiki, K.; Ninomiya, S.; Seki, T.; Aoki, T.; Matsuo, J. Energy Effects on the Sputtering Yield of Si Bombarded with Gas Cluster Ion Beams. AIP Conf. Proc. 2011, 1321, 294−297. (24) Yang, L.; Seah, M. P.; Gilmore, I. S. Sputtering Yields for Gold Using Argon Gas Cluster Ion Beams. J. Phys. Chem. C 2012, 116, 23735−23741. (25) Yang, L.; Seah, M. P.; Lee, J. L. S.; Gilmore, I. S. Sputtering Yields of Gold Nanoparticles by C60 Ions. J. Phys. Chem. C 2012, 116, 9311− 9318. (26) Anders, C.; Urbassek, H. M.; Johnson, R. E. Linearity and Additivity in Cluster-Induced Sputtering: A Molecular-Dynamics Study of Van Der Waals Bonded Systems. Phys. Rev. B 2004, 70, 155404. (27) Yang, L.; Seah, M. P.; Gilmore, I. S.; Morris, R. H.; Dowsett, M. G.; Boarino, L.; Sparnacci, K.; Laus, M. Studies of Nanoparticles by Secondary Ion Mass Spectrometry (SIMS). To be published. (28) Seah, M. P.; Nunney, T. S. Sputtering Yields of Compounds Using Argon. J. Phys. D: Appl. Phys. 2010, 43, 253001 (13 pages). (29) Shard, A. G.; Havelund, R.; Seah, M. P.; Spencer, S. J.; Gilmore, I. S.; Winograd, N.; Miyayama, T.; Niehuis, E.; Rading, D.; Möllers, R. Argon Cluster Ion Beams for Organic Depth Profiling: Results from a VAMAS Interlaboratory Study. Anal. Chem. 2012, 84, 7865−7873. (30) Niehuis, E.; Möllers, R.; Rading, D.; Cramer, H.-G.; Kersting, R. Analysis of Organic Multilayers and 3D Structures Using Ar Cluster Ions. Surf. Interface Anal. 2013, 45, 158−162. (31) Seah, M. P.; Gilmore, I. S. Cluster Primary Ion Sputtering: Correlations in Secondary Ion Intensities in TOF SIMS. Surf. Interface Anal. 2010, 43, 228−235. (32) Rading, D.; Moellers, R.; Cramer, H.-G.; Niehuis, E. Dual Beam Depth Profiling of Polymer Materials: Comparison of C60 and Ar Cluster Ion Beams for Sputtering. Surf. Interface Anal. 2013, 45, 171− 174. (33) Ichiki, K. Study on Size Effect of Cluster Ion Beam Irradiation. PhD Thesis, Kyoto University, 2012. (34) Matsuo, J.; Ninomiya, S.; Nakata, Y.; Ichiki, K.; Aoki, T.; Seki, T. Size Effect in Cluster Collision on Solid Surfaces. Nucl. Instrum. Methods, Sect. B 2007, 257, 627−631. (35) Andersen, H. H.; Bay, H. L. Sputtering Yield Measurements. Sputtering by Particle Bombardment I Physical Sputtering of Single-Element Solids; Topics in Applied Physics Vol. 47; Behrisch, R., Ed.; Springer: Berlin, 1981; Chapter 4, pp 145−218. (36) Roosendaal, H. E. Sputtering Yields of Single Crystalline Targets. Sputtering by Particle Bombardment I Physical Sputtering of Single-Element Solids; Topics in Applied Physics Vol. 47; Behrisch, R., Ed.; Springer: Berlin, 1981; Chapter 5, pp 219−256. (37) Kitani, H.; Toyoda, N.; Matsuo, J.; Yamada, I. Incident Angle Dependence of the Sputtering Effect of Ar-Cluster-Ion Bombardment. Nucl. Instrum. Methods, Sect. B 1997, 121, 489−492. (38) Postawa, Z.; Czerwinski, B.; Szewczyk, M.; Smiley, E. J.; Winograd, N.; Garrison, B. J. Microscopic Insights into the Sputtering of Ag{111} Induced by C60 and Ga Bombardment. J. Phys. Chem. B 2004, 108, 7831−7838. (39) Ryan, K. E.; Smiley, E. J.; Winograd, N.; Garrison, B. J. Angle of Incidence Effects in a Molecular Solid. Appl. Surf. Sci. 2008, 255, 844− 846. (40) Takaoka, G. H.; Kawashita, M.; Okada, T. Physical and Chemical Sputterings of Solid Surfaces Irradiated by Ethanol Cluster Ion Beams. Rev. Sci. Instrum. 2008, 79, 02C503−1−3. (41) Czerwinski, B.; Rzeznik, L.; Paruch, R.; Garrison, B. J.; Postawa, Z. Effect of Impact Angle and Projectile Size on Sputtering Efficiency of

project NEW01 TReND of the European Metrology Research Programme (EMRP). The EMRP is jointly funded by the EMRP participating countries within EURAMET and by the European Union.

■

REFERENCES

(1) Sputtering by Particle Bombardment I Physical Sputtering of SingleElement Solids; Topics in Applied Physics Vol. 47; Behrisch, R., Ed.; Springer: Berlin, 1981; pp 1−256. (2) Sputtering by Particle Bombardment II Sputtering of Alloys and Compounds, Electron and Neutron Sputtering, Surface Topography; Topics in Applied Physics Vol. 52; Behrisch, R., Ed.; Springer: Berlin, 1983; pp 1−355. (3) Sputtering by Particle Bombardment Experiments and Computer Calculations from Threshold to MeV Energies; Topics in Applied Physics Vol. 110; Behrisch, R., Eckstein, W., Eds.; Springer: Berlin, 2007; pp 1− 449. (4) Malherbe, J. B. Sputtering of Compound Semiconductor Surfaces. I. Ion-Solid Interactions and Sputtering Yields. Crit. Rev. Solid State Mater. Sci. 1994, 19, 55−127. (5) Malherbe, J. B. Sputtering of Compound Semiconductor Surfaces. II. Compositional Changes and Radiation-Induced Topography and Damage. Crit. Rev. Solid State Mater. Sci. 1994, 19, 129−195. (6) Seah, M. P.; Clifford, C. A.; Green, F. M.; Gilmore, I. S. An Accurate Semi-Empirical Equation for Sputtering Yields, I: for Argon Ions. Surf. Interface Anal. 2005, 37, 444−458. (7) Seah, M. P. An Accurate Semi-Empirical Equation for Sputtering Yields, II: for Neon, Argon and Xenon Ions. Nucl. Instrum. Methods, Sect. B 2005, 229, 348−358. (8) SRIM 2006 available free from www.srim.org/SRIM/SRIM2006. htm. (9) Hofmann, S. Depth Profiling in AES and XPS. Practical Surface Analysis, 2nd ed.; Briggs, D., Seah, M. P., Eds.; Wiley: Chichester, 1990; Vol. 1, Chapter 4, pp 143−199. (10) Wittmaack, K. Basic Aspects of Sputter Depth Profiling, 2nd ed.; Briggs, D., Seah, M. P., Eds.; Wiley: Chichester, 1992; Vol. 2, Chapter 3, pp 105−175. (11) Dowsett, M.; Clark, E. A. Dynamic SIMS and Its Applications in Microelectronics. Practical Surface Analysis, 2nd ed.; Briggs, D., Seah, M. P., Eds.; Wiley: Chichester, 1992; Vol. 2, Chapter 5, pp 229−301. (12) Vickerman, J. C. Molecular Surface Mass Spectrometry by SIMS. Surface Analysis The Principal Techniques, 2nd ed.; Vickerman, J. C., Gilmore, I. S., Eds.; Wiley: Chichester, 2009; Chapter 4, pp 113−205. (13) Mahoney, C. M. Cluster Secondary Ion Mass Spectrometry of Polymers and Related Materials. Mass Spectrom. Rev. 2010, 29, 247− 293. (14) Yamada, I.; Matsuo, J.; Toyoda, N.; Kirkpatrick, A. Materials Processing by Gas Cluster Ion Beams. Mater. Sci. Eng., R 2001, 34, 231− 295. (15) Matsuo, J.; Ninomiya, S.; Yamada, H.; Ichiki, K.; Wakamatsu, Y.; Hada, M.; Seki, T.; Aoki, T. SIMS with Highly Excited Primary Beams for Molecular Depth Profiling and Imaging of Organic and Biological Materials. Surf. Interface Anal. 2010, 42, 1612−1615. (16) Miyayama, T.; Sanada, N.; Bryan, S. R.; Hammond, J. S.; Suzuki, M. Removal of Ar+ Beam-Induced Damaged Layers from Polyimide Surfaces with Argon Gas Cluster Ion Beams. Surf. Interface Anal. 2010, 42, 1453−1457. (17) Lee, J. L. S.; Ninomiya, S.; Matsuo, J.; Gilmore, I. S.; Seah, M. P.; Shard, A. G. Organic Depth Profiling of a Nanostructured Delta Layer Reference Material using Large Argon Cluster Ions. Anal. Chem. 2010, 82, 98−105. (18) Lee, J. L. S.; Seah, M. P.; Gilmore, I. S. Artifacts in the Sputtering of Inorganics by C60n+. Appl. Surf. Sci. 2008, 255, 934−937. (19) Ninomiya, S.; Nakata, Y.; Honda, Y.; Ichiki, K.; Seki, T.; Aoki, T.; Matsuo, J. A Fragment-Free Ionization Technique for Organic Mass Spectrometry with Large Ar Cluster Ions. Appl. Surf. Sci. 2008, 255, 1588−1590. J



Article

Solid Benzene Investigated by Molecular Dynamics Simulations. Nucl. Instrum. Methods, Sect. B 2011, 269, 1578−1581. (42) Rzeznik, L.; Paruch, R.; Garrison, B. J.; Postawa, Z. Erosion of Ag Surface by Continuous Irradiation with Slow, Large Ar Clusters. Nucl. Instrum. Methods, Sect. B 2011, 269, 1586−1590. (43) Sigmund, P. Theory of Sputtering. I. Sputtering Yield of Amorphous and Polycrystalline Targets. Phys. Rev. 1969, 184, 383−416. (44) Seah, M. P. Topography Effects and Monatomic Ion Sputtering of Undulating Surfaces, Particles and Large Nanoparticles: Sputtering Yields, Effective Sputter Rates and Topography Evolution. Surf. Interface Anal. 2012, 44, 208−218. (45) Delcorte, A.; Garrison, B. J.; Hamraoul, K. Dynamics of Molecular Impacts on Soft Materials: From Fullerenes to Organic Nanodrops. Anal. Chem. 2009, 81, 6676−6686. (46) Postawa, Z.; Paruch, R.; Rzeznik, L.; Garrison, B. J. Dynamics of Large Ar Cluster Bombardment of Organic Solids. Surf. Interface Anal. 2013, 45, 35−38.

K


Universal Equation for Argon Gas Cluster ... - ACS Publications

Recommend Documents