Self-Organized Origami Structures via Ion-Induced Plastic Strain

Movement and deformation due to stress relaxation occurs in a variety of natural or artificially-induced processes. In nature, some plants have evolved their organs as movable origami to increase their reproductive success. In ice plants, the opening of the seed capsule is caused by a water-actuated strain mechanism.1 After the rain, the cells are full of water, causing the expansion along the lid axis, and eventually the opening of the seed capsule. Similar to the ice plant seeds, various other objects move and deform through stress relaxation, ranging from curling of flowers,2 self-organization at nanometer scale,3, 4 to deformation of plasmid DNA in bacteria.5 New technologies could develop if such processes could be reproduced and controlled artificially, to create three-dimensional (3D) objects endowed with functionality inspired from the biological world. In material science, the origin of stresses (grain boundaries, impurities, lattice mismatch, thermal expansion, intersubstrate diffusion) and effects such as film curvature resulting from grain coalescence, heat absorption, and electromagnetic radiation have attracted a constant interest.6–11 Combining strain engineering with thin film lithography has allowed the assembly of simple 3D structures, such as pipelines, helices, and tubes,12–17 with potential applications ranging from biology to optics18–20 However, in order to create structures that would function as complex nanodevices, one needs a technology that enables us to control the assembly process at a much better precision than the scale of the designed structure.

In this paper, we show how to achieve the control of plastic relaxation at nanometer scale via ion processing. The concept is demonstrated by two experimental techniques, the first with low-energy ions in reactive ion etching (RIE), and the second with high-energy ions in a focused ion beam (FIB) microscope. The RIE technique is a novel concept that allows the folding of thin film structures at small radii of curvature by generating a plastic near-surface compressive stress on one side of the film, resulting in the bending in the upward (or downward) direction. Based on this concept, self-organized structures used for example to capture microparticles are demonstrated. With the FIB technique, the metal film is locally irradiated with a Ga⁺ beam to fold the structures. We fabricate complex nanoscale 3D structures with fold radius as small as 10 nm. Transmission electron microscopic (TEM) images and energy-dispersive X-ray spectroscopy (EDX) at different depths across a section of the irradiated films show that the upward bending of the structures is associated with the accumulation of Ga atoms near the bottom of the film. These experimental results are supported by numerical simulations of ion bombardment. Finally, at the end of the paper we present a simple theoretical model relating the induced compressive stress to the chemical potential imbalance produced by the ion treatment.

We start by presenting the first technique. The essential observation enabling the creation of origami is that the deformation of a metal film and the curvature radius obtained by RIE depend strongly on the boundary conditions imposed on the film. As shown in Figure 1a, the radius of curvature of a Ti 5 nm/Al 30 nm/Cr 20 nm strip increases with the width of the structure. This experimental result cannot be explained by elastic theory: a finite-element simulation (Supporting Information, Section I) shows that the radius of curvature would depend only weakly on the strip width. TEM/EDX analysis also shows that Ti is etched away during the RIE process. This allows us to formulate a new concept for nanostructure RIE-assisted self-assembly, in which two sacrificial layers are used, a main one (Si) and a secondary one (Ti). The etching of the main sacrificial layer is faster and creates free boundaries by the release of the film, while the etching of the secondary layer is slower and allows us to control precisely the final configuration. The mechanism of bending is as follows: the etching of the secondary layer results in an increase of the surface chemical potential, which drives interface and surface atoms into the nearby grain boundaries within the polycrystalline matrix of the metal. This results (see also the theoretical model at the end of the paper) in the accumulation of compressive stress, which relaxes and drives the strain (bending) of the final structure.

Figure 1. a) Scanning electron microscopic (SEM) image of self-rolling strips made from a Ti 5 nm/Al 30 nm/Cr 20 nm film. The strip widths are varied from 200, 250, … 500 nm in one set, and 600, 800, … 1400 μm in the other. (inset) SEM image of strips made from Cr 5 nm/Al 30 nm/Cr 20 nm. This shows that replacing the Ti adhesion (secondary) layer with Cr reduces the effect of the width-dependence of the radius of curvature. b) SEM image of a metallic flower (cage) made from a Ti 5 nm/Al 25 nm/Cr 20 nm film. c) Microparticles of lactose are trapped in self-organized structures made from the thin film metal. The scale bar represents 4 μm.

A range of self-assembled structures can be created by applying this concept. Here, we demonstrate the fabrication of micrometer-sized cages (Figure 1b) by using the RIE-induced plastic strain described above. Such self-assembled microcages are functionalized structures that can be used for trapping particles, as described below. Particle trapping may occur naturally on a flat surface due to adhesive forces; increasing the surface-volume fraction enhances the trapping rate significantly. But life forms such as sponges have developed a much more efficient mechanism of capturing food particles from the sea water, by combining adhesive surfaces with geometrical restrictions that regulate the water flow rate and velocity.21 The fluid is controlled in a way that particles can get in relatively easily, but can hardly escape once inside. A similar functionality exists in our self-assembled structures due to the combination between structural geometry and surface tension. We demonstrate the capturing of microparticles by self-organized cages made from Ti/Al/Cr thin film. The particles are synthesized by a gas-phase technique;22 they are composed mainly of lactose monohydrate and L-leucine. The size of each cage was slightly bigger than the size of the particles which we intend to capture, see Figure 1c. Particles were found trapped in some cages, after a drop of toluene containing microspheres was spin-coated on top of the substrate.

Observing the trapped particles with SEM at a high scanning current (nA) causes the legs of the cage to move due to differences in the thermal expansion coefficient and the electrical conductivity between particles and metal cages. We have monitored the dynamics in real-time. The SEM current firstly caused the expansion and the melting of the particle surface. After a few seconds, the legs of the cage began to squeeze and pull particles towards the bottom of the trap, as shown in the last two images in Figure 1c. Interestingly, empty traps are insensitive to static charge; observing an empty trap with an SEM high current does not cause any movement. We have also checked that empty trap structures are very robust against artificially-induced electric discharge in the air.

Next, we describe the fabrication of nanometer-scale origami by the FIB technique. The effect of ion irradiation in solid films has been long studied in various single and polycrystalline solids,23–29 but most of the studies were done with bulk materials or deposited films with fixed boundaries. Solid samples have been observed to expand along the axis perpendicular to the ion-beam direction.30 More recent studies demonstrate that swift ions cause grain rotation in nanocrystalline materials.31, 32 On silicon nitride membranes, it has been shown that ion-beam irradiation can produce deflections33 and folding with a 1 μm fold radius.34, 35 In our experiments, we find that sweeping Ga⁺ ions across a metallic nanocrystalline cantilever causes strong bending towards the beam. The results confirm a recent hypothesis36 that if the peak of compressive stress is in the bottom half of the membrane, it will cause the membrane to bend upward. Here, we show that these processes are reproducible and can be controlled with the extremely high level of precision required for the assembly of complex three-dimensional devices at nanometer-scale.

Applying FIB to lithographically engineered films allows the assembly of origami at very small scales (see Figure 2, and the video in the Supporting Information). In practice, the ion-beam processing can be done at various beam currents and dwell times, depending on size of the structures and the degree of bending required for a single exposure.

Figure 2. SEM images of cubic structures assembled by ion-beam induced plastic deformation. The nanobox is made from a Ti/Al/Cr multilayer metal film.

The technique is universal; we find that origami can be made by both multilayer (Figure 2, and Supporting Information, Figure S3) and single-layer films (see Supporting Information, Figure S4), as long as the stopping range of the ions is of the same order of magnitude as the thickness of the film. We have experimented on several Al cantilevers with thicknesses between 20 and 55 nm and found that Ga⁺ ions cause bending towards the beam direction. To understand the bending process, we study the irradiated Al films using TEM and EDX analysis. We find that the bending and plastic deformation occurs along the ion-track from the front to the back surfaces, see Figure 3. In all the samples, we see the expansion of volumes near the back surface, suggesting that there is atomic flow from the front to the back. Away from the bending, columnar grains are observed (Figure 3g). When the FIB is focused far away from a fixed end, the irradiation produces the bending of the whole structure, see Figure 3h. The TEM images demonstrate that the plastic deformation of the beam is related to the insertion of ions into the grain boundaries of the nanocrystalline metal. This finding is in agreement with results over the last decade or more, showing that plastic deformation in nanocrystalline materials is associated with atomic mobility at grain boundaries.37–40 In contrast, in the classic mechanism of plastic deformation in coarse-grained polycrystalline solids, the main role is played by the movement of dislocations (defects) inside individual grains, without any dynamics at the grain boundary. For example for copper, the shift from dislocation-mediated plasticity in the coarse-grained material to grain boundary sliding occurs at a grain size of about 10 to 15 nm.41

Figure 3. TEM analysis. a) SEM image of an Al sample for TEM analysis. b) Cartoon pictures describing the fabrication of a TEM sample. The folding in each step is directed by FIB. c) Optical microscopic image of some samples, placed on top of a TEM grid. d) TEM image of a sample after FIB line fluence of 1.56 × 10⁴ ions/nm. The inset shows the same sample at a lower magnification; the lowest part (dark color) is the fixed part (near the vertical pad), as shown in (a). e,f) Sample after the FIB line fluence of 9.36 × 10³ ions/nm. g) Columnar grain in the unradiated region. h) Sample after the FIB line fluence of 9.36 × 10³ ions/nm. The left and the right images are taken from different TEM angles. Note that the distance between the irradiated part and the fixed boundary is larger than in (e,f). i) Sample after the FIB line fluence of 9.36 × 10³ ions/nm. The inset shows a higher magnification image. j) EDX spectrum from the region irradiated with the FIB line fluence of 1.87 × 10⁴ ions/nm. The data is collected from the area specified by the circle in the inset image.

For keV Ga⁺ ions penetrating into metal matrices,42, 43 the dominant loss mechanism of the ionic kinetic energy is by atomic collisions, which sputters the atoms at the surface and displaces those from the more in-depth lattice. If only independent binary collisions occur, the displacement can be described by the time-dependent Boltzmann transport equation.44 Typically, the displacement energy is in the order of 10 eV, an order of magnitude higher than the binding energy.45 For our samples, the analysis of the trace of Ga⁺ by energy dispersive X-ray (EDX) spectroscopy allow us to compare the spectra from different regions in the sample. We find that the ions will stop predominantly near the back of the film, see Figure 3j. This means that most of the damage occurs before the ions come to stop, that is on the upper surface of the film. This damage consists of atoms being dislocated and scattered predominantly in the direction of motion of the ions, that is towards the back surface of the film. If the distance between successive displacement collisions is in the order of atomic distance, the collisions will cause a region of void (vacancies) and a shell of surrounding interstitial atoms.46 The formation of unstable high-pressure interstitial regions could produce atomic (viscous) flow towards the back surface of the film. The resolidification (relaxation) of the remaining atoms near the front pulls the surrounding metallic grains towards each others, and eventually closes the void. Besides atomic and ionic flux, phonons and recoils are also generated during the relaxation process. Numerical simulations (see the Supporting Information, Figure S5) confirm that these effects occur mainly near the front surface of the film, and as a result the ions are indeed expected to stop predominantly at the back surface of the film. Thus, the release of kinetic energy of the ions will change locally the chemical potential of the atoms, producing a chemical potential difference between the back and the front surface.

In the remaining part of the paper, we aim at providing a simple unified theoretical description (see Figure 4) for the flow of ions and atoms into the grain boundaries. By solving a kinetic equation, we find that the stress in the steady state is directly proportional to the difference in the chemical potential produced by ion processing. In the case of RIE, this chemical potential is produced by the etching of the secondary sacrificial layer, while in the case of FIB it is produced by atomic displacement. When an atom moves into a grain boundary, a compressive stress σ_c builds up.47 Defining N_gb as the number of adatoms that causes σ_c, we obtain for the total stress σ

• ((1))

Figure 4. Heuristic model of FIB processing. a) Schematic images showing the side view of the FIB processing across a metal strip. b) After ion irradiation, the columnar grain is broken into smaller grains and clusters. The atoms near the top surface are sputtered. The irradiated region within the thermal spike along the ion track becomes a viscous fluid. Energy from ions is transferred, and the system relaxes via plastic flow. The atoms are driven into the grain boundary at the bottom, due to the increase of the chemical potential at the upper part of the track. c) Adatom insertion creates compressive stress σ_c in the plane perpendicular to the ion-beam direction. The cooling of the viscous fluid causes contraction and generation of tensile stress σ_t.

Here, σ₀ corresponds to the compressive stress from an adatom/ion insertion into each of the atomic planes in the grain boundary, σ_t is the tensile stress, a is the atomic spacing, and h_g is the height of the grains in the direction perpendicular to the compressive stress, see Figure 4.

The flow of atoms or ions into the grain boundaries is driven by the difference in the chemical potential Δμ between the final and initial states. The rate of this process is Γ(Δμ) = −C_KΔμ, where C_K is a proportionality constant (see Supporting Information, Section IV). From this, we obtain a kinetic equation

• ((2))

where Δμ = δμ − δΩ comprises both the contribution from the ion flux and that from the mechanical stress, and Ω = a³ is the atomic volume.

To proceed, we assume that the resolidification of the top region occurs after the relaxation of compressive stress. Since tensile stress is developed during the cooling (recrystallization) of the thermal spike,48 this means that initially the process is driven mainly by the compressive component, i.e., σ ≈ σ_c. In this regime, we can obtain a kinetic equation by differentiating Equation (1) and using the expression for ∂N_gb/∂t as in Equation (2),

• ((3))

which shows that the system relaxes exponentially fast, with relaxation rate 1/τ = C_Kσ_oaΩ/h_g.

In the steady state, ∂σ_st/∂t = 0, we obtain the simple result

• ((4))

After the ion-beam processing reaches a steady state, the change in the chemical potential δμ is directly proportional to the FIB fluence, while the stress σ gives the degree of bending, which can be determined experimentally. This heuristic model implies that two identical origami beams will bend to the same degree towards the ion-beam, if they are equally irradiated at the same position with the same FIB fluence (see, for example, Figure S3, Supporting Information). Equation (4) therefore allows us to calibrate the FIB fluence needed to obtain the desired degree of bending in an origami structure.

In summary, we demonstrate the top-down fabrication of complex nanoscale three-dimensional structures from polycrystalline metallic films by controlling the stress induced by RIE and FIB. The relaxation of the stress causes the film to form a precisely-determined configuration. The stress is generated through the induced flow of atoms into the grain boundaries, a process that happens, in the case of RIE, at the surface due to the removal of a sacrificial layer, while for the FIB technique the stress is local and in-depth. The combined RIE/FIB fabrication concept presented here provides a technology platform for future applications of strain engineering at micro- and nanoscopic scales.

Experimental Section

Sample Fabrication: The origami films are made by electron beam lithography, starting with the process of transferring a designed pattern from a CAD file onto a photoresist layer by exposing parts of the resist to the electron beam. The exposed resist is then removed from the silicon substrate by dipping the whole substrate in a developer made from the diluted solution of methyl isobutyl ketone (MIBK) in isopropanol (IPA). After development, the unexposed part of the resist is left on the substrate. This layer is used as a mask in the metal deposition process. An electron-gun evaporator, with the pressure of about 10⁻⁶ mbar, is used to deposit metallic thin films.

Reactive Ion Etching: The etching takes place in a plasma of SF₆ 300 sccm and O₂ 5 sccm, at the pressure of 100 mTorr, and the power of 80 W. This results in the etching of silicon, as well as of Ti film. The etching of Ti layer causes the adatom insertion into the grain boundaries, resulting in the development of compressive stress.

Focused Ion-Beam Processing: The ion-beam manipulation is done in an SEM/FIB dual beam microscope (Helios Nanolab 600, the equipment combines a scanning electron microscope and a focused ion (Ga⁺) beam microscope). In this work, cubic structures, as shown in Figure 2, are processed by the acceleration voltage of 30 kV, FIB current of 1.5 pA, and 1 μs dwell time. Intended fold lines of length 700 nm are drawn by FIB with a line fluence of about 2.67 × 10⁴ ions/nm.

TEM Analysis: After electron beam lithography, 50-nm-thick Al films are deposited on top of the silicon substrate. The FIB processing is done after releasing the nanostrips from the silicon substrate by reactive ion-etching (RIE) (the bigger parts are still undetached at this step, to provide a fixed boundary for the ion-beam induced relaxation), see Figure 3a,b. The sample shown in Figure 3e is processed with a 30 kV acceleration voltage, and a 1.5 pA ion beam current. A 300-nm-long fold line across the Al strip is drawn by the FIB with an irradiation time of 300 ms. After the structure is completely folded, the other parts of the TEM sample are detached by RIE. A micromanipulator (MMO-202ND 3-axis hanging joystick oil hydraulic micromanipulator) is then used to pick the sample up from the original substrate, and to place it on the top of a TEM grid. Transmission electron microscopy (TEM) measurement was carried out with a JEOL 2200FS double aberration corrected FEG microscope, operated at 200kV.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements

K.C. conceived the experiments, fabricated the samples and developed the theoretical concepts. H.J. and K.C. conducted the TEM/EDX analysis. N.C. and K.C. performed the FIB processing. J.L. and K.C. designed the particle traps. K.C. and G.S.P. wrote the manuscript. B.P. and G.S.P. supervised the project. The authors thank Gennadiy P. Nikishkov for sharing the analysis and finite element simulation of strained metal film, Xuefeng Song for helping with the micromanipulator, and Ken Elder, Cristi Achim, Tapio Ala-Nissila, and Chun-Wei Pao for stimulated discussions. The authors would also like to acknowledge financial support from Thailand Commission on Higher Education, NGSMP of Finland, and the Academy of Finland (Project no. 135135 and 141559). This work made use of the Aalto University Nanomicroscopy Center (Aalto-NMC) premises and Micronova Nanofabrication Center.