Letter pubs.acs.org/NanoLett
Folding Sheets with Ion Beams Cheng-Lun Wu,† Fang-Cheng Li,† Chun-Wei Pao,*,† and David J. Srolovitz*,‡ †
Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan Department of Materials Science and Engineering, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
‡
S Supporting Information *
ABSTRACT: Focused ion beams (FIBs) are versatile tools with cross-disciplinary applications from the physical and life sciences to archeology. Nevertheless, the nanoscale patterning precision of FIBs is often accompanied by defect formation and sample deformation. In this study, the fundamental mechanisms governing the large-scale plastic deformation of nanostructures undergoing FIB processes are revealed by a series of molecular dynamic simulations. A surprisingly simple linear correlation between atomic volume removed from the film bulk and film deflection angle, regardless of incident ion energy and current, is revealed, demonstrating that the mass transport to the surface of material caused by energetic ion bombardment is the primary cause leading to nanostructure deformation. Hence, by controlling mass transport by manipulation of the incident ion energy and flux, it is possible to control the plastic deformation of nanostructures, thereby fabricating nanostructures with complex three-dimensional geometries. KEYWORDS: Focused ion beam, ion irradiation, defects, molecular dynamics, GPU, nanostructure deformation
F
ocused ion beams (FIBs)1−3 are versatile tools for applications ranging from the fabrication of patterned nanostructures including nanophotonic, nanoelectronic, and plasmonic devices,4−6 carbon-based nanomaterials,7−9 microelectromechanical systems,10−13 to materials characterization,14−16 to imaging on the cellular level,17,18 and even to the analysis of the chemical composition of impressionist paintings.19 In most common FIB processes, an energetic ion beam (usually Ga+ ions) bombards a material cutting through, or eroding it, leaving a pattern behind with nanoscale precision.3 Such high-precision patterning from ion beam milling inevitably comes at a price; the ion irradiation introduces defects into the material as a result of the displacement cascades caused by knock-on events. As a result, the nanoscale precision of patterning of FIB is often accompanied by damage within the material as well as structural distortion, which remains a critical issue since the introduction of FIB in the late 1970s.1 The large FIB-induced distortions of thin films/nanowires have been reported in nanostructures over a wide range of both structural dimensionalities and chemical compositions, for example, carbon nanotubes,20 semiconductor/superconducting nanowires, 21−23 free-standing thin films,4,6,24−27 and even in peptide nanotubes.28 While the plastic distortions from FIB are often undesirable, by manipulating the macroscopic FIB-induced shape changes of films or wires, complex, three-dimensional origami-like nanostructures can be fabricated for applications in biomedical devices or metamaterials.6,26,27 Hence, understanding the underlying mechanism of plastic deformation from FIB is the key toward patterning with desirable structures/shapes. The © XXXX American Chemical Society
radiation damage of materials has been of wide interest for well over a half century; nevertheless, the magnitude of the radiation damage induced internal stresses and the shape changes they induce has not been systematically investigated or widely applied to generate prescribed distortions. The goal of this study is to develop both a mechanistic understanding of radiation-damage induced plastic deformation and quantitatively predict the resultant shape change. More specifically, our aim is to understand the relationship between FIB conditions and the shape changes they produce. We approach these questions through large-scale molecular dynamics (MD) simulations of FIB-induced shape change in thin Al films. Figure 1 depicts the MD simulation geometry employed here. The sample was a thin cantilever, as shown in Figure 1. The atoms shown in red were fixed in space, and the simulation cell was periodic in the x-direction and of finite length in y. In order to mimic a polycrystal, the Al cantilever consists of three grains (orientations shown in Figure 1. The two grain boundaries (GBs) are of the same type (bicrystallography) and were chosen to represent “general” (not high symmetry) GBs, that is, nonsymmetric 18° tilt boundaries about a common [111] axis. During the FIB simulation, incoming Ga+ ions bombarded the surface at normal incidence in random locations within a thin (100 × 10 Å2) strip (shown in orange in Figure 1) at fixed kinetic energy (KE) between 7.5 and 20 keV. Table 1 Received: September 23, 2016 Revised: December 4, 2016 Published: December 5, 2016 A
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KE and boundary conditions, hence leading to slightly different ion currents (3.4, 6.6, 6.3, and 5.7 nA for systems A, B, C, and D). Note that simulations were performed at 450 K rather than room temperature (at which most FIB experiments are performed) in order to allow significant defect migration on time scales accessible to MD simulations. The simulations were run until 600−1000 Ga+ ions were introduced, corresponding to doses of 6 × 1015 ions/cm−2 (600 Ga+ ions) or 1016 ions/ cm−2 (1000 Ga+ ions) in this strip. The MD time step was adjusted on-the-fly to ensure that the largest atomic displacement resulting from the implantation did not exceed 0.02 Å in any time step. We employed the embedded atom method (EAM) potential developed by Nam and Srolovitz for the Al− Ga binary system.29,30 In order to account for the nuclear collisions we incorporated the Ziegler−Biersack−Littmark universal screening function (ZBL) potential31 into the Nam−Srolovitz potential by modifying the pair interaction potential: U(rij) = [1 − f(rij)]VZBL(rij) + f(rij)VNS(rij), where VZBL(rij) and VNS(rij) denote the ZBL pair potential and the pairwise term in the Nam−Srolovitz EAM potential, respectively. The Fermi-like function f(rij) = (1 + exp[−A(rij − rc)])−1 is employed to interpolate between the ZBL potential and NS potential, where the parameter A = 14 and the ZBL cutoff rc = 0.95 Å were chosen to yield an appropriately smooth transition. The MD simulations were performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) with GPU acceleration.32,33 Figure 2a shows the evolution of system A during a 7.5 keV FIB simulation. The tricrystal film underwent large-scale film deflection toward the incoming Ga+ ions. Deflection of the Al film toward the Ga+ ion beam is also seen in the plane strain systems B (7.5 keV) and C (10 keV), as seen in Figure 2b,c. This is consistent with the experimental observations that nanostructures bend toward the direction of incoming ion beam.6,21,22,26,27 However, when the Ga+ ion kinetic energy in the ion beam was raised to 20 keV (system D), the Al film deflected away from the beam (i.e., in the negative z-direction). This demonstrates that the Ga+ ion beam can cause the Al film to deflect up or down, depending on the incoming ion energy. This widens the range of bending conformations accessible using a FIB.
Figure 1. Schematic of the Al cantilever simulation cell. Only nonperfect fcc atoms are shown (as determined using the central symmetry parameter) in order to highlight grain boundaries and surfaces.
Table 1. Tricrystal FIB Simulation Conditions system
ion energy (keV)
A B C D
7.5 7.5 10 20
boundary conditions plane plane plane plane
stress strain strain strain
(σxx (εxx (εxx (εxx
= = = =
0) 0) 0) 0)
shows the FIB ion kinetic energies and elastic boundary conditions employed. We investigated both plane stress and plane strain boundary conditions in the x-direction. Plane stress implies that on average σxx = 0 on any plane with normal x (appropriate for cantilevers that are narrow in x), while plane strain implies that on average εxx = 0 (appropriate for cantilevers that are wide in x). The MD simulation of FIB processes were performed by (i) implanting one Ga+ ion at a time, (ii) dissipating the kinetic energy of each incoming Ga+ ion in the Al cantilever in a microcanonical (NVE) (systems B, C, and D) or an isoenthalpic−isobaric (NPH) ensemble (system A) MD simulation until the maximum kinetic energy of any atom in the system drops to below 50% of the cohesive energy of Al, and (iii) thermalizing the system in a canonical (NVT) (systems B, C, and D) or an isothermal−isobaric (NPT) ensemble (system A) MD simulation at 450 K. The times required for each system to cool to 450 K depends on Ga+ ion
Figure 2. Evolution of Al film during FIB simulations. (a) Evolution of system A at several Ga+ ion dose ions; (b−d) images of the plane strain systems B, C, and D (KEs of 7.5, 10, and 20 keV) after a dose of 1000 Ga+ ions (b and c) and 600 Ga+ ions. Note that all atoms with a central symmetry parameter smaller than 6.0 are not displayed to highlight defects and surfaces/interfaces. Animations showing the evolution of the atomic structures of systems A−D can be found in Movies M1−M4 in the Supporting Information. B
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position of the same painted Al atoms at different doses. We also show the atomistic displacement fields, projected in the y− z plane, for systems A and D at NGa = 200 in Figure 4. These images demonstrate that the atoms under the irradiated strip tend to undergo substantial displacements in the +z-direction (with much smaller displacements in y). These images also show that the mound near the irradiated strip on the upper surface is largely associated with these displacement +z displacements. Similarly, the mound that forms on the lower surface, opposite the irradiated strip, at high ion energy, is from the motion of Al atoms from the interior in the direction parallel to the ion beam (−z). An examination of the displacement fields in Figure 4a,d shows that the right half of the film underwent a near rigid-body rotation that accompanies the ±z atomic displacement that create the mounds on the two surfaces in the z-direction. This suggests that mound formation and film deflection are coupled. Most of the atoms transported to the surface to form mounds and leading to film deflection are found to be Al rather than Ga, despite the fact that Ga diffusion in Al is very rapid (Ga was used in the present simulations simply because it is the most common ion using in commercial FIBs). This is not surprising in light of the fact that the maximum Ga concentration is ∼0.1% in the Al and most of the matter transport occurs via plastic deformation. The rapid atomic mass transport in the direction antiparallel with the ion velocity has also been reported in an MD simulation of Si nanopore formation under FIB conditions.34 Blister formation on the surfaces of irradiated materials has also been reported under high displacement cascade conditions in metals and alloys over the past 50 years.35 In the present study, we observe the expansion of the material in the Ga+ collision cascade; we can describe this as thermal pressure resulting from the transfer of the kinetic energy from the incident Ga+ ions to the Al atoms. This kinetic energy both raises the temperature (and the pressure through anharmonic effects) but more directly through the atom velocities.36 Thermal-spike-induced pressures have been reported in recent MD simulations of ion irradiation.37 Thermal pressure induces mass flux out of the cascade region. This happens predominantly through plastic flow, since diffusional transport is too slow to be important on this time scale. The direction of the atomic mass transport is clearly correlated with incident ion energy (and momentum). Figure 4a−c shows that the ion damage cascade is primarily in the upper half of the film at low ion KE; hence, the plastic expulsion of material out the upper surface predominates in these systems (A, B, and C). SRIM calculations38 of the distribution of displaced atoms also indicate that most of the displaced atoms are located in the upper half of the film for KE = 7.5 and 10 keV (Figure S1, Supporting Information). In contrast, in system D (Figure 4d) where the incident Ga+ ion has much higher KE, the damage cascade extends into the lower half of the film, which can also be seen from displaced atom distribution from SRIM calculations (Figure S1, Supporting Information). As a result, material is plastically expelled out of both the upper and lower surfaces, thereby creating mounds on both film surfaces. These results suggest that the primary mechanism of Al film deflection during FIB is atomic mass transport is in the ±zdirection, and the direction of atom transport controls the sense of the film deflection (toward or away from the direction of ion incidence). This is indicated schematically in Figure 5a, in low Ga+ ion energy regime (system A, B, and C), most of the displaced atoms escape out the upper surface of the film,
During the FIB simulation, a mound is formed on the bombarded surface along the strip where ion implantation occurred at low ion beam energy (systems A and B). At larger ion beam kinetic energy (systems C and D), mounds also form on the surface opposite the irradiated strip. These mounds were not reported in the experiments.6,21,22,26,27 We do note, however, that with increasing mounds dose (Figure 2a), at fixed KE, the amplitude of the bending increases and the mound becomes less pronounced. This suggests that these bumps will vanish under large deflection angles. We also suspect that the mounds may be less pronounced under lower current/longer time experiments (the simulation only access nanosecond time scales). It is also interesting to note that ion bombardment leads to grain boundary migration; the central grain in the Al tricrystal shrinks and disappears during the course of the FIB simulation at a large ion dose and/or higher ion KE. This may be a recyrstallization phenomena, where the grain boundary migrates in order to absorb defects created in the ion-induced displacement cascade. The film deflection angle θ is shown as a function of the ion dose (number of incoming Ga+ ions, NGa) in Figure 3. This plot
Figure 3. Al film deflection angle θ as the function of the number of incident Ga+ ions, NGa.
confirms the observations above; the magnitude of the deflection angle increases with ion dose and changes sign at large ion KE. The evolution of film deflection angle with ion doses displayed in Figure 3 (systems A, B, and C) is similar to those measured in FIB experiments.21 Surprisingly, the slope dθ/dNGa shows a maximum at intermediate ion KE for the same boundary conditions (plane strain). By comparing the deflection angles of systems A and B (identical ion energy but distinct boundary conditions in x-direction), we see that the ion beam induced beam deflection is larger in plane stress than in plane strain at the same dose. Note, however, that Figure 3 only shows the “consequences” of ion beam irradiation-induced deflection, but not the mechanisms that cause it. To elucidate the deflection mechanisms, we now look into the atomistic processes occurring during deflection in the MD simulations. To examine the mechanism behind the FIB-induced film deflection, we first focus on how the Al atoms move during the FIB simulation. We visualize this by tracking atom trajectories during the simulation. We paint atoms in three different 10 Å thick flat x−y slabs of Al atoms in the initial tricrystal (see Figure 4a); these slabs are painted simply to identify where atoms at different z move during irradiation. Figure 4 shows the C
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Figure 4. Illustration of Al atomic mass transport during the FIB simulations of systems (a) A, (b) B (c) C, and (d) D. The overlapped images in the middle and upper panels of a and d display the respective atomic displacement fields. The evolution of mass transport can also be seen in Movies M5−M8 in the Supporting Information.
Based on the linear relation between the film deflection angle θ and volume removed, ΔV, we can derive a simple model to predict the deflection. From the atomic displacement field in Figures 4a,d, we can represent the “net” removed volume as a wedge (inset in Figure 5b). If such a wedge of opening angle θ is removed from the film, a rigid-body rotation of the right side of the film about the vertex by the angle θ closes the gap created by the expulsion of material from the film. Note that, for a film undergoing net volume removal from the bottom surface (system D), the wedge is simply the inverse of the one shown in the inset of Figure 5b. We can express the correlation between the volume removed from the bulk of the film (ΔV), the volume of the wedge, and the film deflection angle θ as
leading to a mound on the top surface. The free side of the cantilever rotates toward the ion damage cascade region to eliminate the free volume created by the expulsion of material from the cascade region. This lead to counterclockwise rotation (θ > 0) in systems A, B, and C where material is expelled out the upper surface (red in Figure 5a) and clockwise rotation (θ < 0) in system D when more material is expelled out the lower surface (green in Figure 5a). These considerations suggest that the rigid-body film rotation in response to the atomic mass transport in the ±zdirections is the primary mechanism leading to film deflection. Figure 5b displays the net volume of material expelled from the film to form the mounds, ΔV, as the function of film deflection angle θ for systems A−D (the method estimating ΔV is discussed in the Supporting Information). Surprisingly, all four cases collapse onto a single straight line regardless of incident ion energies and current. This suggests that films subjected to different incident ion energy, ion current, and boundary conditions yield identical deflections for the same amount of volume removed from the bulk to form the mounds. Since the data for all four systems collapse onto a single straight line, we suspect that the slope of that line (Figure 5b) is determined by geometric considerations. Note that, in systems A, B, and C, ΔV > 0 (more atoms flows out the top surface than from the bottom), while for system D ΔV < 0 (more atoms flows out of the bottom surface). This is consistent with the atomic slab displacement images shown in Figure 4. It is clear that the sign of ΔV depends not only on the incident ion energy; rather, it depends on the ion beam energy relative to the film thickness since higher energy leads to deeper implantation. In the high ion energy/small film thickness regime, ions penetrate to near the bottom film surface, thereby contributing to atomic mass transport out of the bottom surface (leading to downward deflection). On the other hand, in the low ion energy/large film thickness regime, the ions penetrate only near the top of the film, leading to transport to the top surface (and upward deflection). Hence, the sign of ΔV and the direction of deflection depend on both the ion energy and film thickness.
ΔV =
g 2 h Lxθ 2
(1)
where g is a constant and h and Lx are the film thickness and simulation cell length in the x-direction (see Figure 1). We introduce the constant g because not all of the volume removed (the area of the wedge) contributes to film deflection. For example, part of the volume removed from the film makes the film shorter in the y-direction, or film microstructures consisting of arrays of grain boundaries or dislocations can result in enhanced point defect recombination thereby reducing the net free volume generated by the collision cascade (hence, g will depend on the microstructure). Note that g = 1 corresponds to the ideal situation that all of the volume removed causes film deflection while retaining a defect-free film structure. Rearranging terms in eq 1 gives g dΔV = h2Lx dθ 2
(2)
This suggests that dΔV/dθ depends only on the film microstructure (through g) and sample geometry (i.e., film thickness h)consistent with Figure 5b. By measuring the slope of the fitted straight line in Figure 5b (15.5 nm3/deg) and substituting the film thickness h and cell length Lx into eq 2, we D
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microstructure (grain size, dislocation density) will affect the rate of point defect annihilation and/or point defect diffusion rates within the material; this should only change the proportionality constant g in the ΔV−θ relationship in eq 1 (note, g was the only free parameter in this equation and was determined here via simulation for our sample geometry and microstructure). Changing the film thickness will change the deflection angle for a given ion energy and flux, as seen from eq 1 which can be rewritten as θ = (ΔV/h2)(gLx)−1; that is, thicker samples will deflect less than thinner onesconsistent with experimental nanowire deflection data (Figure 2b in ref 21). These results yield a clear picture of film deflection during FIB processes. The FIB produces displacement cascades which is accompanied by a thermal-spike-induced stress field. This stress field produces atomic mass transport via plastic deformation that expels material from the film onto the surface(s) and forms surface mounds. The resulting volume deficit in the film is compensated by the rotation of the film around a plastic hinge. The Al film deflects toward the incoming ion flux (namely, upward deflection) at low ion energies, consistent with experimental observations, and deflection in the opposite direction at higher energies. The magnitude of the deflection angle scales approximately linearly with the ion dose. The film deflection angle is found to be proportional to the total volume expelled from the bulk through a simple linear relationship, with the slope depending only on film geometry. The volume of the film expelled into surface mounds (and, hence, the amplitude of the film deflection) for a given ion dose is a complex function that depends on incident ion energies, ion current, ion mass, film material, and sample geometry (boundary conditions). This volume can, however, be determined directly from molecular dynamics simulations. In addition, standard approaches for modeling radiation damage effects, such as SRIM,38 can provide a quick, qualitative prediction of the direction and magnitude of the deflection by examining the distribution of displaced atoms (see Figure S1 in the Supporting Information). Controlling the incident ion energy in the FIB can be used to switch the film deflection direction and controlling the total ion dose can be used to deflect the film to different angles. The ability to predict film deflection as a function of FIB conditions (ion current and energy) opens the door to designing complex, folded 3D shapes that can be produced routinely using commercially available instrumentation (a FIB).
Figure 5. Atomic mass transport and film deflection. (a) Schematic illustration of the atomic mass transport in the z-direction that induces film deflection for both (left panel) low ion energies (systems A, B, and C) and (right panel) high ion energies (system D). (b) The net volume of material removed from the film (ΔV) to form mounds as a function of the measured deflection angle θ. The inset shows the wedge-filling rotation model correlating the volume removed ΔV and the wedge angle θ.
find g = 0.48 for this microstructure. This simple geometric model captures the main features of the FIB simulations with only a single parameter that depends on the details of the irradiation process. The present results demonstrate that, for films of a given geometry and microstructure, film deflection angles θ are only correlated with the volume removed from film interior, ΔV. Such a linear relationship is not easily verified in FIB experiments; ΔV is not readily accessible. On the other hand, the simulations show that ΔV (measured from atom trajectories) is a linear function of θ (Figure 5b) and θ is an approximately linear function of ion dose NGa (Figure 3), implying that ΔV is proportional to the ion dose NGa. Since both experiments (see Figure 2a in ref 21) and simulation demonstrate that deflection angle is proportional to ion dose, we also see that the experiments are consistent with the predicted variation of deflection angle with ΔV and hence with the proposed FIB deflection mechanism. Note that the proposed film deflection mechanism does not depend on details of the film microstructure. Of course, changing film
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b03976. Figure displaying the distribution of displaced atoms from SRIM calculations and method of estimation of net volume expelled from film interior (PDF) Animation displaying the evolution of system A (M1) during FIB simulations (AVI) Animation displaying the evolution of system B (M2) during FIB simulations (AVI) Animation displaying the evolution of system C (M3) during FIB simulations (AVI) Animation displaying the evolution of system D (M4) during FIB simulations (AVI) E
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Animation illustrating the Al atomic mass transport system A (M5) during FIB simulations (AVI) Animation illustrating the Al atomic mass transport system B (M6) during FIB simulations (AVI) Animation illustrating the Al atomic mass transport system C (M7) during FIB simulations (AVI) Animation illustrating the Al atomic mass transport system D (M8) during FIB simulations (AVI)
(21) Jun, K.; Joo, J.; Jacobson, J. M. J. Vac. Sci. Technol., B 2009, 27, 3043. (22) Cui, A.; Li, W.; Luo, Q.; Liu, Z.; Gu, C. Appl. Phys. Lett. 2012, 100, 143106. (23) Johannes, A.; Noack, S.; Wesch, W.; Glaser, M.; Lugstein, A.; Ronning, C. Nano Lett. 2015, 15, 3800−3807. (24) Kim, Y.-R.; Chen, P.; Aziz, M. J.; Branton, D.; Vlassak, J. J. J. Appl. Phys. 2006, 100, 104322. (25) Prewett, P. D.; Anthony, C. J.; Cheneler, D. Micro Nano Lett. 2008, 3, 25−28. (26) Chalapat, K.; Chekurov, N.; Jiang, H.; Li, J.; Parviz, B.; Paraoanu, G. S. Adv. Mater. 2013, 25, 91−5. (27) Dai, C.; Cho, J.-H. Nano Lett. 2016, 16, 3655−3660. (28) Gour, N.; Verma, S. Soft Matter 2009, 5, 1789. (29) Nam, H.-S.; Srolovitz, D. J. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 184114. (30) Nam, H.-S.; Srolovitz, D. J. Phys. Rev. Lett. 2007, 99, 025501. (31) Ziegler, J. F.; Biersack, J. P. Treatise on Heavy-Ion Science; Springer US: Boston, MA, 1985; pp 93−129. (32) Plimpton, S. J. Comput. Phys. 1995, 117, 1−19. (33) Brown, W. M.; Wang, P.; Plimpton, S. J.; Tharrington, A. N. Comput. Phys. Commun. 2011, 182, 898−911. (34) Das, K.; Freund, J. B.; Johnson, H. T. J. Appl. Phys. 2015, 117, 085304. (35) McDonell, W. J. Nucl. Mater. 1979, 85−86, 1117−1121. (36) Srolovitz, D.; Vitek, V.; Egami, T. Acta Metall. 1983, 31, 335− 352. (37) Baumer, R. E.; Demkowicz, M. J. Mater. Res. Lett. 2014, 2, 221− 226. (38) Ziegler, J. F.; Ziegler, M.; Biersack, J. Nucl. Instrum. Methods Phys. Res., Sect. B 2010, 268, 1818−1823.
of of of of
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. ORCID
David J. Srolovitz: 0000-0001-6038-020X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS C.W.P. thanks the Research Center for Applied Sciences, Academia Sinica, and Academia Sinica Career Development Award project no. 2317-1050100 for financial support and the National Center for High-Performance Computing for computational support. D.J.S.’s work was supported by the National Science Foundation, Division of Materials Research, under Grant No. DMR-1507013.
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