Three-dimensional (3D) nanofabrication, aiming to produce 3D microstructures/nanostructures with versatile physical properties and desired functionalities, forms the basis of modern information technology. For example, the basic complementary metal-oxide semiconductor technologies employ the repetitive surface patterning with optical lithography and consequential removal of sacrificial layers for the 3D construction of integrated electronic circuits [1]. Similarly, two-dimensional (2D) electron-beam lithography and focused ion beam (FIB) milling have been widely employed in multilayer stacking/lithography for 3D nanomanufacturing [2–4]. Meanwhile, to achieve direct 3D nanofabrication, translational direct laser writing has been developed with polymer skeleton and subsequent material inversion [5]. More recently, unconventional kirigami and origami methods [6], which unify the art and science of cutting and folding flat 2D objects to create 3D geometries, have been developed as promising schemes for microfabrication/nanofabrication and have attracted much attention in frontier fields such as microelectromechanical/nanoelectromechanical systems (MEMSs/NEMSs) [7], biomedical devices [8,9], and mechanical and photonic materials [10–16]. Different from traditional 3D fabrication techniques, microscale/nanoscale kirigami/origami enables the direct shape transformation from 2D patterns to 3D architectures without the need of precise 3D translation in direct laser writing [5,17] or accurate alignment during indirect multilayer stacking [18]. As a result, the fabricated nanogeometries can be greatly enriched in a variety of material platforms, which have exhibited great potentials for the generation of exceptional mechanical, optical, electronic, and biological functionalities [6]. However, current kirigami/origami strategies are still under the preliminary development, in which the desirable extensibility for later integration has yet been explored.

To develop an extensible scheme for 3D complex nanofabrication and drive this technique toward the manipulation of visible light, here we introduce a new strategy for FIB-based multilayer nano-kirigami in a commercial silicon nitride (SiN) film window coated with gold thin film. By employing an FIB-based Boolean irradiation, multilayer and cascaded 3D pinwheels are realized, which demonstrate the extensible stacking of nano-kirigami structures in the out-of-plane direction and are consistently verified by a modified elastoplastic mechanical model. Importantly, the upper flat plates and deformable features of the 3D pinwheels provide great potentials in manipulation of both phase and intensity of visible light. The reported method and study could be helpful to build a novel platform for 3D nanofabrication and find potential applications in MEMSs/NEMSs, optical spectroscopy, nanophotonics, biophotonics, etc.

The general FIB-based nano-kirigami [19] normally includes three procedures, i.e., the preparation of nanofilms (as the “nanopaper”), the cutting of nanopatterns with high-dose FIB (as the “nanoscissors”), and the 3D deformation of the 2D nanopatterns with low-dose FIB (as the “nanohand”). In the last procedure, two irradiation schemes can be adopted to induce deformations, namely, local irradiation and global irradiation [19]. While the local irradiation induced discontinuous boundaries (as in later content) and the uniform global irradiation induced deformation in all structural areas, here a Boolean-type FIB irradiation scheme is proposed for cascaded and multilayer nano-kirigami, as shown in Fig. 1. This scheme involves the controlled spatial deformation of the 2D nanostructure into 3D nanoarchitectures by FIB irradiation with deliberately designed irradiation strategies, which include non-irradiated, irradiated, or overlapped areas, as shown in Fig. 1(c). It is named as Boolean irradiation in order to differentiate it from the uniform global irradiation. As illustrated in Fig. 1(b), the global low-dose irradiation covers the whole sample area, which induces deformations across the overall sample, including the undesirable deformation in the central part. In such a case, it is challenging for subsequent extensible building of multilayer nanostructures with freely designed morphologies due to entirely deformed areas that turn the fabrication out of focus. Moreover, the wholly deformed structures deflect the normally incident light in all directions, especially for the short visible wavelengths. In comparison, with the proposed Boolean-irradiation scheme in Fig. 1(c), the final ring-shaped Boolean irradiation is designed through subtraction operation of the two concentric circles. As a result, the arm areas of the pinwheel are selectively deformed, while the central part remains flat for later process and applications [right in Fig. 1(c)]. This is very advantageous for extensible manufacturing of nanostructures with increased complexity and flexibility. For example, as shown in Fig. 1(d), a four-layer nested pinwheel structure is designed by on-site cascaded milling and ring-shaped irradiation. It is anticipated that the outer parts of each layer can be dynamically twisted and rotated during the irradiation process, while the inner parts are passively rotated and translated without shape changes. Moreover, such multilayer complex structures can be realized via programed milling and irradiation processes, which are extremely challenging for traditional 3D nanofabrication methods.

To implement the irradiation schemes, here we use a more general SiN film window (20 nm in thickness, Norcada Inc.) coated with 80-nm-thick gold film as the “nanopaper,” instead of the lift-off gold films suspended on copper grids [19,20]. The commercial SiN films are extremely flat, smooth, and easy-to-handle compared with the home-processed Au film that required sophisticated skills and time-consuming preparations. Meanwhile, the size of the SiN film window can be as large as 5mm×5mm, which is very advantageous for large-scale nanofabrication compared with that of Au film suspended on copper grids (normally with the flat area on the level of 100μm×100μm). Moreover, by using Au/SiN bilayer film, the discontinuous boundary in Au monolayer film induced by FIB local irradiation can be overcome. As shown in Fig. 2(a), when the hinges of a pop-up plate structure are gradually thinned and folded, the hinge area gets rough and even broken due to the induced stress and the mobility of gold atoms during FIB irradiation, as in the inset of Fig. 2(a). This negative effect can be avoided in the Au/SiN bilayer film. As shown in the inset of Fig. 2(b), by controlling the dose of FIB irradiation, the gold atoms on the predesigned lines are completely removed from the film, and the bottom SiN layer remains as the smooth joint of the 3D nanostructure. Such clean boundary is very desirable to fabricate a series of isolated nanoparticles on curved SiN stripe, as illustrated in Fig. 2(c). It should be noted that compared with the fabrication on the Au monolayer, the FIB irradiation dosage required for the same fabrication was increased by ∼30% when using the Au/SiN bilayer film.

To test the schemes in Fig. 1, various patterns are designed as in the first column of Figs. 2(d)–2(h). With the high accuracy of the FIB system (FEI Helios 600i), the designed patterns can be well reproduced on the bilayer film [the column (ii) of Figs. 2(d)–2(h)] by high-dose FIB milling (>600pC·μm−1). It is important to note that the nano-kirigami method is a topography-guided 3D nanofabrication, that is, the final formation of 3D nanostructures is highly dependent on the topographic distribution of the stress in all subunits. Therefore, both structural designs and irradiation schemes are critical. In Fig. 2(d), for example, an axisymmetric flower-like structure with bended petals is fabricated, of which the central part cannot be deformed out of the plane by low-dose irradiation (<40pC·μm−1) due to the stresses destructively canceled at the center. In comparison, the nanostructure with rotational symmetry in Fig. 2(e) exhibits strong twisting and bending, indicating that the axial symmetry should be avoided to achieve dramatic twisting. Moreover, to increase the height of the deformed structures, a 3D pinwheel with three rotational arms is designed in Fig. 2(f), of which both the arms and central part are deformed under global FIB irradiation, agreeing well with the illustration in Fig. 1(b). In the case of Boolean irradiation, the same 2D pattern of Fig. 2(f) is irradiated by FIB under a ring-shaped area, as depicted in Fig. 2(g). It can be seen that besides the bending and twisting of the three arms, a smooth and flat plate in the center is preserved as in panel (iii) of Fig. 2(g), in a drastic contrast to that of Fig. 2(f). Moreover, the flat part of the pinwheel can be flexibly enlarged by specific designs, as the example shown in Fig. 2(h).

It should be mentioned that the structural stability during shape transformation needs careful considerations. It is found that when the structural size increases, the instability of the final deformation increases as well, such as the slightly tilted structure in panel (iii) of Fig. 2(h), as well as the reported spiral structures with only one leg connected to the master film [21]. Such a kind of instability is caused by the scanning direction and limited step of FIB systems. To address this limitation, the number of pinwheel supporters is increased. As shown in Fig. 3(a), the pinwheels with four supporting arms exhibit better stability in all scales.

With the aforementioned considerations, a scheme of cascaded multilayer nano-kirigami can be developed. As in Fig. 3(a), a multilayer four-arm pinwheel structure is realized from the inner layer to the outer layer (indicated by the horizontal arrow) by multiple high-dose milling and low-dose Boolean irradiation with FIB. During the fabrication, each annular exposed area is obtained by Boolean subtraction operation of two predesigned concentric circles. In such a case, the supporting arms of each layer bend and twist during the irradiation process, while the central parts are merely rotated and translated passively without local deformation, showing obviously the topographic characteristic of the nano-kirigami and overwhelming the global irradiation scheme regarding the structural complexity and flexibility. Moreover, the multilayer nano-kirigami structure can also be fabricated from the outer to the inner layer, as shown in Figs. 3(b) and 3(c). In this case, the supporting arms of the outer layers were bent and twisted during the low-dose irradiation process after the milling in each layer, while the inner unprocessed parts were translated vertically as the next layer for subsequent milling and Boolean irradiation (the ion beams need to be re-focused on each vertically shifted layer during the milling and annular irradiation). Such observations clearly prove the robustness of the Boolean-irradiation scheme and extensibility of such 3D nanofabrication (i.e., the number of layers can be increased on demand). Furthermore, these 3D exotic nanostructures have not been seen with the traditional nanofabrication techniques or the other kirigami methods, which could greatly enrich the variety of 3D nanogeometries in both designs and fabrications.

The accurate modeling of the complex nano-kirigami geometries is crucial for structural design and functionality prediction. To this end, a fundamental understanding of the nano-kirigami process is necessary. It is known that when energetic Ga ion beam bombards the thin film, some gallium atoms are implanted into the film, some gold atoms are sputtered away from the surface, some gold atoms within the film are dislocated, and some gold and gallium atoms re-deposit onto the surface [22–25]. These cascaded displacements caused by knock-on events introduce complicated stresses and strains across the film (defined as σin-plane) [19–22], which determine the structural formation through the following equations with zero net force (F) and net moment (M) across the film by [22] where h is the sample thickness. Therefore, the distribution of local stress is critical. Previous studies with global irradiation simplified the free-standing Au film with a bilayer mechanical model [19], in which tensile stress concentrates in the top amorphous layer and passive deformation occurs in the bottom layer. Specifically, the residual stress distribution in the model can be described by [19]

Here, z is the coordinate in the thickness direction; ht and hb are the thicknesses of the top plastic-deformation layer and the bottom elastoplastic-deformation layer, respectively. σt and σb are the residual stress in the top and bottom layers, respectively. σ0in-plane and k are the first- and second-order coefficients in the asymptotic expansion of stress in the bottom layer, with higher-order terms discarded due to the ultra-small thickness of the films. However, when the scheme of Boolean irradiation is adopted, the increased boundaries with such a model cause complications and even deviations in simulations. For example, the non-irradiated annular areas of multilayer pinwheels show severe local deformations when Eq. (2) is merely employed, as noted by the circles in Fig. 3(d), which deviate from the actual case in Figs. 3(a) and 3(c). This could be caused by an overlooked effect in which FIB irradiation on thin films can result in the softening effect of Young’s modulus [26]. To address these issues, we hereby develop a modified model by incorporating the bilayer model with modulus softening effects. In this modified model, the distribution of elastic modulus for all involved materials is determined by where EAu=70GPa and ESiN=270GPa are the Young’s modulus of the corresponding bulk materials, respectively. The parameter α (smaller than one) is used to define the extent of the modulus softening of the exposed Au layer upon the FIB irradiation. By adopting such a modified model in simulations with the finite element method, the four-layer nano-kirigami structure in Fig. 3(e) is directly calculated in one step and matches perfectly with the experimental results in Figs. 3(a) and 3(c), proving the robustness and accuracy of both experiments and calculations. Moreover, the versatile experimental nanostructures in the column (iii) of Fig. 2 are well reproduced by the numerical simulations in the column (iv) of Fig. 2. These observations clearly prove that the prescribed 2D patterns of various geometries can result in dramatically different 3D configurations under the topography-guided stress equilibrium.

The versatile geometries realized by nano-kirigami represent a new type of nanophotonic structures. For example, benefiting from the flatness of the central part during the Boolean-type FIB irradiation, as illustrated in Fig. 4(a), the pinwheels with deformable height can be employed to manipulate the phase and intensity of visible light. As schematically shown in Fig. 4(b), when the central plate rises with a height of h with respect to the bottom layer, an extra reflection phase shift (Δϕ) will be introduced under normal incidence [Fig. 4(c)]. For example, when the pinwheel is exerted by different prescribed stress, the height of its central plate increases correspondingly with a nearly linear relation, as plotted in the left of Fig. 4(d), resulting in a height of 222 nm under σt=1GPa (in Au film). Meanwhile, the reflection phase distribution at different states varies in a different manner, as the finite-difference time-domain simulation results for the red (633 nm), green (532 nm), and blue (473 nm) wavelengths shown in Fig. 4(c). It can be clearly seen that the generated phase shift varies from 0 to nearly −2π, as plotted in the right of Fig. 4(d). It should be mentioned that the slopes of the curves vary with different wavelengths since Δϕ=−2πneffh/λ, where neff is the effective refractive index of the medium and λ is the operating wavelength.

Since the heights of the pinwheels are potentially tunable under dynamic electrostatic or mechanical forces [27,28], the large-range phase engineering in Figs. 4(c) and 4(d) could provide a useful approach for the manipulation of visible light. To test the feasibility, an array of the deformed pinwheels with Δϕ=−π is arranged in a square lattice with periodicity of 2 μm. As shown in Fig. 4(e), a strong interference pattern is clearly formed at z=2μm under normal incidence. Such an interference pattern is highly dependent on the height of the deformed pinwheels and varies significantly with wavelength since Δϕ∼h/λ, as plotted in Fig. 4(f). Therefore, the deformable features of the nano-kirigami structures make it promising for the dynamic modulation of visible light through reconfiguring their heights, which could provide a novel methodology for efficient beam steering employed in optical displays and light/laser radar systems.

In summary, we have demonstrated an efficient method to fabricate exotic 3D nano-kirigami nanostructures. Based on a systematic consideration from the aspects of fabrication sequences, structural symmetry, and extensible integration, cascaded multilayer nano-kirigami structures have been realized under Boolean-type FIB irradiation, which are highly extendable in the out-of-plane direction and widely applicable in commercial Au/SiN bilayer nanofilms for large-scale manufacturing. The 3D complex structures have been well reproduced by developing a modified elastoplastic mechanical model that included the softening of material modulus, which provides a reliable guidance for the design and prediction of desirable functionalities. Moreover, the engineering of phase and intensity by nano-kirigami structures has been numerically demonstrated by employing the deformed pinwheels with deliberately designed height. Therefore, our work paves a new way for fabricating sophisticated and complex 3D nanostructures for advanced photonic applications in beam steering, optical reconfiguration, holographic displays, metasurface devices, MEMSs/NEMSs, optical sensors, optomechanical devices, etc.

Acknowledgment. The authors thank Laboratory of Microfabrication, Institute of Physics, CAS for assistance in FIB facilities and useful discussions.