Cluster Size Dependence and Yield Linearity in Cluster Bombardment

Aug 8, 2008 - to investigate the effect of projectile cluster size and incident energy on the resulting yield. Using the mesos- cale energy deposition...
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Anal. Chem. 2008, 80, 6666–6670

Cluster Size Dependence and Yield Linearity in Cluster Bombardment Simulations of Benzene Kathleen E. Ryan and Barbara J. Garrison* 104 Chemistry Building, Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802 Cluster bombardment of a molecular solid, benzene, is modeled using molecular dynamics simulations in order to investigate the effect of projectile cluster size and incident energy on the resulting yield. Using the mesoscale energy deposition footprint (MEDF) model, we are able to model large projectiles with incident energies from 5 to 140 keV and predict trends in ejection yield. The highest ejection yield at 5 keV was observed at C20 and C60, but shifts toward larger clusters for higher energies. These trends are explained in terms of the MEDF model. For these projectiles, all of the incident energy is deposited in the near-surface region, which is optimal for the projectile energy to contribute to the ejection yield. Because the energy is deposited in the optimal position for contributing to the ejection process, the yields increase linearly with incident energy with a slope that is nearly independent of the cluster size. Energetic cluster bombardment has afforded improvements in the ability of secondary ion mass spectrometry (SIMS) to image organic and biological samples due to its unique features from atomic bombardment including an enhancement of ejection yields and a decrease in damage accumulation.1 The range of projectiles used in experiments may vary from atomic projectiles to clusters containing two to millions of particles, which are used to desorb molecules intact to be detected via a mass spectrometer.2–6 The commercial cluster beams developed to date have been chosen based on experimental properties such as ease of ionization, ability to focus, or cost. The obvious question is whether better choices could be made. Molecular dynamics (MD) simulations have been used to describe a variety of phenomena associated with cluster bombardment including elucidating the mesoscopic physical processes that occur during the bombardment event such as projectile energy deposition to the substrate, ejection mechanisms and yields, sample mixing, and crater formation. Thus, we will use MD simulations to explore possible different clusters that could be * To whom correspondence should be addressed. E-mail: [email protected]. (1) Winograd, N. Anal. Chem. 2005, 77, 142A. (2) Davies, N.; Weibel, D. E.; Blenkinsopp, P.; Lockyer, N.; Hill, R.; Vickerman, J. C. Appl. Surf. Sci. 2003, 203, 223. (3) Weibel, D.; Wong, S.; Lockyer, N.; Blenkinsopp, P.; Hill, R.; Vickerman, J. C. Anal. Chem. 2003, 75, 1754. (4) Wong, S. C. C.; Hill, R.; Blenkinsopp, P.; Lockyer, N. P.; Weibel, D. E.; Vickerman, J. C. Appl. Surf. Sci. 2003, 203, 219. (5) Rickman, R. D.; Verkhoturov, S. V.; Hager, G. J.; Schweikert, E. A. Int. J. Mass Spectrom. 2005, 245, 48. (6) Takats, Z.; Wiseman, J. M.; Gologan, B.; Cooks, R. G. Science 2004, 306, 471.

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used for SIMS experiments. The substrates of interest are organic and biological solids. Previous simulations have shown that the optimal mass of the atoms in the cluster is the same as the mass of the atoms in the target.7,8 Thus, we confine ourselves to clusters containing predominately carbon atoms. One of the challenges faced when performing MD simulations of energetic particle bombardment of a surface is computation time. Although computing power has surely grown, the sophistication of the systems we would like to model increases at an even faster rate. The inclusion of cluster projectiles such as C60 and an increase in incident projectile kinetic energy have led to systems composed of millions of atoms in order to contain all of the motion of the bombardment event. Therefore, models that allow us to gain insight into the bombardment event by running short-time simulations are necessary to allow us to model systems of relevant interest, such as low mass/binding energy organic surfaces bombarded by projectiles with high incident energies. To overcome the huge computing cost, the mesoscale energy deposition footprint (MEDF) model9–11 uses similarities to fluid dynamics calculations12 to describe the projectile energy deposition as an energized track within the sample. By analyzing the size and intensity of this track when 90% of the projectile energy is deposited to the sample, one may predict trends in yield as a function of properties such as incident particle energy and size. In this paper, we investigate the yield trends as a function of incident energy and cluster size. In a previous study, simulations of 5-keV carbon cluster bombardment of benzene exhibit the highest yield at C20 and C60 projectile cluster sizes.8 However, for higher energies, experimentalists observed a significant increase in yield of several organic molecules when C84+ was used as a projectile compared to C60+, Au3+, Au+, and coronene.13 Still others found that the choice of projectile for maximizing ejection yield is dependent on the projectile energy, size, and nature.14 We present a detailed mechanistic analysis to explain the various features of cluster bombardment, in particular the effect of cluster (7) Anders, C.; Urbassek, H. M. Nucl. Instrum. Methods Phys. Res., Sect. B 2005, 228, 84. (8) Smiley, E. J.; Winograd, N.; Garrison, B. J. Anal. Chem. 2007, 79, 494. (9) Russo, M. F., Jr.; Garrison, B. J. Anal. Chem. 2006, 78, 7206. (10) Russo, M. F., Jr.; Szakal, C.; Kozole, J.; Winograd, N.; Garrison, B. J. Anal. Chem. 2007, 79, 4493. (11) Russo, M. F., Jr.; Ryan, K. E.; Czerwinski, B.; Smiley, E. J.; Postawa, Z.; Garrison, B. J. Appl. Surf. Sci. In press. (12) Jakas, M. M.; Bringa, E. M.; Johnson, R. E. Phys. Rev. B 2002, 65, 165– 425. (13) Biddulph, G. X.; Piwowar, A. M.; Fletcher, J. S.; Lockyer, N. P.; Vickerman, J. C. Anal. Chem. 2007, 79, 7259. (14) Guillermier, C.; Della Negra, S.; Rickman, R. D.; Pinnick, V.; Schweikert, E. A. Appl. Surf. Sci. 2006, 252, 6529. 10.1021/ac800995w CCC: $40.75  2008 American Chemical Society Published on Web 08/08/2008

size and incident energy on the resulting ejection yield. Our analysis utilizes MD simulations and MEDF calculations of Cn (n ) 6, 10, 20, 60, 120, or 180) bombardment of benzene. COMPUTATIONAL DETAILS MD simulations are performed to model cluster bombardment of a benzene system. The projectiles include four fullerene projectiles, C20, C60, C120, and C180, as well as benzene and naphthalene projectiles. Incident projectile energies range from 833 eV to 135 keV and were chosen in order to have a range of incident kinetic energies and several isovelocity series. Only one trajectory was performed for each projectile at each energy as previous simulations have shown that the essence of motion is captured in each trajectory.15 The MD methods used have been described in detail elsewhere.16 In short, Hamilton’s equations of motion are integrated to determine the positions and velocities of each atom as a function of time. The coarse-grained benzene system, described previously,17 combines the carbon and hydrogen atoms in benzene into single CH particles each with a mass of 13 u. The projectile atoms are not coarse-grained, however, and therefore contain both explicit carbon and hydrogen atoms. Lennard-Jones potentials are used to describe the CH-CH interactions between different molecules as well as the C-CH potential between atoms from the projectile and atoms in the sample. A Morse potential is used to describe CH-CH interactions within one molecule allowing the molecule to dissociate yet still possess some internal energy. The REBO potential of Brenner is used to describe the C-C, C-H, and H-H interactions of the cluster projectiles.18 The sample contains ∼1.2 million CH particles, or ∼200 000 benzene molecules, in an orthorhombic structure, and measures 20 nm deep and 34 nm in each lateral direction. For projectiles given 5 keV of incident kinetic energy, full simulations were run until ∼26 ps when approximately all of the sputtered material has been ejected.8 The additional simulations were run only until 90% of the projectile energy was deposited to the sample as this has been defined as the critical time for simulations according to the MEDF9–11 and friction models.19,20 RESULTS AND DISCUSSION The objective of this study is to investigate the trends in ejection yield as a function of incident energy and size of the incident particle. We start by presenting the yields calculated by MD simulations at 5 keV along with yields at higher energies determined by the MEDF model. We then interpret the results in terms of the MEDF model. The yields from the simulations for 5 keV incident energy and the predictions of the MEDF model for yields at 5-20 keV are (15) Postawa, Z.; Czerwinski, B.; Szewczyk, M.; Smiley, E. J.; Winograd, N.; Garrison, B. J. Anal. Chem. 2003, 75, 4402. (16) Garrison, B. J. In ToF-SIMS: Surface Analysis by Mass Spectrometry; Vickerman, J. C., Briggs, D., Eds.; Surface Spectra: Manchester, 2001; pp 223-257. (17) Smiley, E. J.; Postawa, Z.; Wojciechowski, I. A.; Winograd, N.; Garrison, B. J. Appl. Surf. Sci. 2006, 252, 6436. (18) Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S. J.; Ni, B.; Sinnott, S. B. J. Phys.: Condens. Matter 2002, 14, 783. (19) Garrison, B. J.; Ryan, K. E.; Russo, M. F.; Smiley, E. J.; Postawa, Z. J. Phys. Chem. C 2007, 111, 10135. (20) Ryan, K. E.; Russo, M. F., Jr.; Smiley, E. J.; Postawa, Z.; Garrison, B. J. Appl. Surf. Sci. In press.

Figure 1. Ejection yield vs the incident cluster size for 5-keV simulation data as well as MEDF predicted yields for 5-, 10-, 15-, and 20-keV incident energies. Error bars represent yield values obtained using Rcyl ( 3 Å.

shown in Figure 1 as a function of cluster size. The yield is measured in benzene molecule equivalents, which does not take into account which molecules are fragments. The MEDF yields are predicted by analyzing contour plots of the energy deposition at the time when 90% (also labeled) of the projectile energy is deposited to the sample, shown in Figure 2. In general, the larger clusters deposit energy slower than the small clusters but still require no more than several hundred femtoseconds to deposit 90% of the projectile energy. The energy is deposited in an approximate cylinder with a radius of Rcyl. The average excitation energy within the cylinder is measured with respect to the ˜ = Eexc/ cohesive energy of the sample and is represented by E U0. The ejection yield is predicted to originate in a cone at the ˜ 1/2 and surface with a depth of Rcyl and a base radius of Rs = RcylE can be estimated, then, by applying the MEDF equation, Y = n0(π/ ˜ , where n0 is the number density of the sample. The error 3)Rcyl3E bars in Figure 1 represent values of yield that are obtained for Rcyl ± 3 Å. The trends predicted by using the MEDF model agree well with the yields observed from simulation as shown for the 5-keV projectile data shown in Figure 1. As reported previously, the highest ejection yield for 5-keV cluster bombardment of benzene was seen for the C20 and C60 projectiles.8 However, as the incident energy increases, the highest yield shifts to a larger cluster size as seen in Figure 1 so that, at 10 keV, C120 exhibits the highest yield and, at 15 and 20 keV, there is no discernible difference between the yields produce by C60, C120, and C180 projectiles. Experimentally, it was also observed that, as the incident energy of a projectile is increased, larger clusters produce the larger yields. In the case of Ar clusters bombarding Si, using 100-keV incident energy, the highest yield is observed for a cluster containing 2000 atoms. Larger argon clusters at 100 keV resulted in a decrease in yield.21 Biddulph et al. saw that, using a comparison of C24H12+, C60+, and C84+ each with 40 keV of incident energy, C84+ consistently resulted in the highest yield and the lowest amount of damage when used on (21) Seki, T.; Murase, T.; Matsuo, J. Nucl. Instrum. Methods Phys. Res. Sect. B. 2006, 242, 179.

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Figure 2. MEDF plots for all projectiles, C6H6, C10H8, C20, C60, C120, and C180, for 5-keV incident energy. Rcyl is determined from the width of the energized track. The energy is plotted in terms of E˜ ) Eexc/U0 so that blue represents the most intensely energized molecules and yellow represents slightly energized molecules. Gray represents molecules left unaltered. Each plot represents the time when 90% of the projectile energy was deposited to the sample which is labeled in fs.

cyclosporin A, haloperidol, dipalmitoyl phosphatidylcholid, cholesterol, and silver samples.13 Simulations of fullerene bombardment of a clean Ag{111} surface produced the highest yield using a C60 cluster and an incident energy of 15 keV. Lower incident energies resulted in higher yields at smaller clusters.22 The behavior of yield versus cluster size and incident energy can be explained by analyzing the energy deposition rate for each of the projectiles. Figure 2 shows the MEDF plots for all projectiles at 5 keV of incident energy. These plots exemplify the competing ˜ in the MEDF equation. Although Rcyl increases terms of Rcyl and E with increasing projectile size, the energy dissipates throughout the sample faster than it is deposited for the larger projectiles, ˜ is decreased. Therefore, the overall C120 and C180, so that E predicted yield is reduced. As the incident energy is increased, however, the larger projectile can deposit energy more efficiently ˜ is high enough to contribute to a higher into the sample so that E ejection yield. The information in Figure 1 is replotted versus the incident kinetic energy in Figure 3. The error bars have been omitted from Figure 3 for clarity. The incident kinetic energy is represented in terms of energy per cluster atom (E/n), and likewise, the yield is represented as benzene molecule equivalents per cluster atom (22) Czerwinski, B.; Rzeznik, L.; Stachura, K.; Paruch, R.; Garrison, B. J.; Postawa, Z. Vacuum 2008, 82, 1120.

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Figure 3. Y/n vs E/n, where Y is the yield in benzene molecule equivalents, E is the incident kinetic energy, and n is the number of atoms in the projectile cluster.

(Y/n). Since all of the projectiles are composed of the same types of atoms, carbon, projectiles with the same incident energy per number of atoms in the cluster have the same velocity. The yield shows a near-linear trend regardless of projectile. Experimentally,

it has been shown that Au atomic beams of clusters containing just a few Au atoms bombarding Au or Ag exhibit a peak in yield with increasing velocity, rather than the steady increase that we have observed. However, for Au clusters containing more than five atoms, the increase is quite linear with the velocity of the cluster, as we also observe.23 Seki et al. also observed linear trends in yield for Ar2000 bombardment of both silicon and gold. They proposed a model that indicates the yield for any given cluster is proportional to both the cluster size and the total energy of the cluster.21 Simulations of cluster bombardment of water ice by Russo et al. produced a linear increase in yield for both C60 and Au3 projectiles; however, the increase for C60 bombardment was much more rapid than observed for Au3 bombardment,10 which was very similar to the results of Le Beyec et al. for SIMS detection of a phenylalanine target using C60+ and Au4+ ion beams.24 Anders et al. also saw a linear trend for multiple cluster sizes falling on the same line when plotted on a log-log scale for Ar projectiles containing 1-10 000 atoms bombarding a solid argon sample. They hypothesized that the velocity of the cluster is a greater factor in determining ejection yield than the cluster size.25 The key to understanding, however, is to be able to determine the slope of the linear trend. In order to determine why the yield exhibits linearity with incident energy, we examine the various ˜ . The only two components of the MEDF model, Y = n0(π/3)Rcyl3E variables, Rcyl and E, will be presented and discussed separately. The values of Rcyl are determined by making MEDF plots similar to Figure 2 for each projectile at each incident energy. In general, the values of Rcyl are constant for each projectile independent of energy, are larger for the larger projectiles, and are larger than the radius of the incident cluster. The concept of a size for a projectile also occurs in the friction model, which likens the projectile to a single bead with the size of an intact fullerene cluster.19,20 In the friction model, the extended radius of the bead was determined to be the projectile radius plus an interaction radius between the projectile atoms and the sample atoms of 1.95 Å. Figure 4 shows the calculated Rcyl values from the simulation divided by this extended radius (a) and then plotted against the number of carbon atoms in the incident cluster. From this plot, we can estimate that Rcyl for a given cluster is ∼3.5 times the extended radius of the projectile. The largest deviations from this approximation are observed for the nonfullerene projectiles, benzene and naphthalene, and for the slow-moving large clusters, C120 and C180. The slow-moving clusters will be discussed below. The nonspherical structure of benzene and naphthalene means that there is not a unique radius. Even though the concept of radius is not completely appropriate, their values of Rcyl appear to follow a similar trend to the values of Rcyl observed for spherical fullerene projectiles. For these simulations, the impact orientation was chosen randomly, and the projectile was given a slight tilt with respect to the normal. For a more accurate estimate of Rcyl for these projectiles, data from several simulations over all impact orientations would have to be averaged. At this time, the significance of the value of 3.5 is not understood although the (23) Bouneau, S.; Brunelle, A.; Della-Negra, S.; Depauw, J.; Jacquet, D.; Le Beyec, Y.; Pautrat, M.; Fallavier, M.; Poizat, J. C.; Andersen, H. H. Phys. Rev. B 2002, 65, 144106. (24) Le Beyec, Y.; Baudin, K.; Brunelle, A.; DellaNegra, S.; Jacquet, D.; Pautrat, M. Braz. J. Phys. 1999, 29, 428. (25) Anders, C.; Urbassek, H. M.; Johnson, R. E. Phys. Rev. B 2004, 70.

Figure 4. Cylinder radius (Rcyl) divided by the extended radius (a ) radius of the projectile + 1.95 Å) of the projectile vs the cluster size of the projectile.

correlation is remarkably consistent. The energized track size includes not only the size of the incident particle but also the amount of compression of the sample around the projectile due to energy transfer. The question we still have not addressed is why our data and the work of Anders et al.25 indicate that the yield is independent of cluster size while other studies10,21,23,24 show a clear dependence on cluster size. The MEDF model provides insight into why the increase in yields might be appear to be independent of projectile type/size when, in reality, there is still a dependence. For our system, Rcyl increases with increasing projectile size. The fullerene projectiles deposit all of their energy within a depth of ˜ Rcyl so that all of the energy may contribute to ejection. Since E ˜ Rcyl3 is approximately proportional is on a per molecule basis, E to the total energy of the incident particle. Thus, the slope in Figure 3 is almost independent of cluster size. This analysis points out that the linear dependence of yield versus energy is independent of cluster size for these projectiles and target systems. In cases such as Au3 bombardment of water,9,10 the projectile travels much deeper than Rcyl so that considerable incident energy is wasted in terms of ejection. These projectiles would in turn produce yields that increase at a slower rate with respect to the incident energy than the fullerene projectiles. The MEDF model makes predictions about the shapes of the ejected volumes. For a given energy if the total yield is the same, then the larger clusters will have particles that eject from a deeper volume and narrower cone than the smaller clusters. Shown in Figure 5 are approximate ejection cones (red) and energized tracks (yellow) for 20-keV C20, C60, and C180 as predicted by the MEDF model. As the size of the projectile increases, the value of Rcyl increases from 1.5 nm for C20 and 2 nm for C60 to 2.4 nm for ˜ decreases slightly with C120 and 2.8 nm for C180. However, E increasing projectile size. The base of the ejection cone is Rs ) ˜ 1/2Rcyl, so for C20, Rs ) 8 nm, for C60, Rs ) 8.1 nm, for C120, Rs ) E 7.6 nm, and for C180, Rs ) 7 nm. We see, then, how even though C180 penetrates deeper into the sample, it produces an ejection yield similar to C60 because the base of the ejection cone is smaller than that of C60. Since Rcyl is approximately constant for a given Analytical Chemistry, Vol. 80, No. 17, September 1, 2008

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of the ejection volume shown in Figure 5 they arise. One scenario might be that the ions are representative of the entire ejection volume and thus almost independent of the cluster size. On the other hand, they might arise near the region where reactions occur26,29 in which case there would be a dependence on Rcyl, thus depending on cluster size. For the specific SIMS application of depth profiling with multiple impacts at one point on the substrate, there is also the issue of damage accumulation and these simulations do not address how much damage is created with the various projectiles as a function of energy. Figure 5. Diagram of the MEDF model developed as applied to 20keV C20, C60, and C180 simulations. The yellow regions represent the energized cylindrical tracks, which for these projectiles only extend as deep as Rcyl, and the red regions represent the approximate ejection cones.

projectile cluster, the effect of changing the energy is to change the size (Rs) of the base of the cone. Although most of the data follow the general trends discussed above, there are exceptions that should be noted, namely, the cases of 5-keV C120 and C180 shown in Figure 2 and 10-keV C180 (not shown). These projectiles, at 5 keV, deposit energy at a slow rate into the sample. The energy is able to dissipate into the rest of the sample before 90% of the energy is deposited within Rcyl. The visual indication of this phenomenon is apparent in Figure 2, where there is no blue in the plots for C120 and C180. Therefore, the average excitation energy of the cylinder is reduced while Rcyl remains constant, so the overall ejection yield is less. This physics is similar to the concepts of energy confinement discussed in laser ablation.28 For the cluster bombardment to be effective in ejecting material, the energy deposition must be sufficiently fast that 90% of the energy is deposited in the track region (Rcyl) so that fluid flow can be initiated before a significant amount of energy dissipates into the remainder of the system. The predominant fullerene projectile used by experimentalists is C60+ although C84+ and coronene (C24H12)+ have also been investigated.13 The question naturally arises as to whether a different projectile size would give better SIMS signals. The simulations presented here clearly show that changing the projectile size (Figure 1) has minimal influence on the total ejection yield compared to changing the incident energy (Figure 3). The quality of the SIMS signal is only partially related to the total ejection yield however. There is the question of ionization, and it is not clear how the ions are formed or from which portion (26) Garrison, B. J., unpublished data. (27) Szakal, C.; Kozole, J.; RussoJr, M. F.; Garrison, B. J.; Winograd, N. Phys. Rev. Lett. 2006, 96, 216104. (28) Zhigilei, L. V.; Garrison, B. J. J. Appl. Phys. 2000, 88, 1281.

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CONCLUSIONS The ejection yields as a function of incident energy and size for cluster bombardment of a molecular solid, benzene, have been calculated with molecular dynamics simulations and the MEDF model. We find that varying the incident energy over the range of 5-140 keV has more influence on the yield than varying the mass over the range of C6H6-C180. The yields as a function of energy increase at the same rate almost independent of incident cluster size. This apparent similarity is because all of the clusters deposit the same proportion of their incident energy in the critical depth to contribute to the ejection process. We expect the basic conclusions of this study to be applicable to the general class of molecular solids consisting of elements with a similar mass as carbon. ACKNOWLEDGMENT The authors thank the Chemistry Division of the National Science Foundation Grant CHE-0456514 for their financial support of this research. The necessity of conceptual and analytical models evolved from fruitful discussions with Arnaud Delcorte, Zbigniew Postawa, Mike Russo, Ed Smiley, John Vickerman, Roger Webb, and Nick Winograd. We also acknowledge the support provided by the UK Engineering and Physical Sciences Research Council (EPSRC) under its Collaborating for Success through People initiative for a three-month research visit with John Vickerman at the University of Manchester and Roger Webb at the University of Surrey, during which some of the ideas underlying this work were developed. Computational support was provided by the Graduate Education and Research Services (GEaRS) group of Academic Services and Emerging Technologies (ASET) at Pennsylvania State University. Received for review May 15, 2008. Accepted July 1, 2008. AC800995W (29) Ryan, K. E.; Wojciechowski, I. A.; Garrison, B. J. J. Phys. Chem. C 2007, 111, 12822.