Large-Area Nanolattice Film with Enhanced Modulus, Hardness, and Energy Dissipation

We present an engineered nanolattice material with enhanced mechanical properties that can be broadly applied as a thin film over large areas. The nanolattice films consist of ordered, three-dimensional architecture with thin-shell tubular elements, resulting in favorable modulus-density scaling (n ~ 1.1), enhanced energy dissipation, and extremely large material recoverability for strains up to 20% under normal compressive loading. At 95.6% porosity, the nanolattice film has demonstrated modulus of 1.19 GPa and specific energy dissipation of 325.5 kJ/kg, surpassing previously reported values at similar densities. The largest length scale in the reported nanolattice is the 500 nm unit-cell lattice constant, allowing the film to behave more like a continuum material and be visually unobservable. Fabricated using three-dimensional colloidal nanolithography and atomic layer deposition, the process can be scaled for large-area patterning. The proposed nanolattice film can find applications as a robust multifunctional insulating film that can be applied in integrated photonic elements, optoelectronic devices, and microcircuit chips.

. Fabrication process of ordered 3D nanolattice thin-film. a. A 3D photoresist template was fabricated using colloidal phase lithography. SEM image shows ordered 3D photoresist structure (D = 500 nm, λ = 325 nm). b. Photoresist template was conformally coated using atomic layer deposition technique. SEM image shows 40 nm Al2O3 conformally coated on photoresist template. c. Photoresist template removal to achieve hollow shellular 3D nanolattice film. SEM shows a free-standing 3D nanolattice with 40 nm shell thickness.

Supplementary Information B: Cross-sectional images of nanolattice samples
All the nanolattice samples tested for mechanical properties have a free-standing thin-shell structure. Figure S2 shows the cross-sectional micrographs of remaining nanolattice samples. All the samples have architectural arrangement consisting of primary hollow tubular columns surrounded by secondary thin-shell structures. The secondary shell structure helps to further enhance the robustness of the nanolattice.
ZnO nanolattices with shell thickness smaller than 30 nm were difficult to fabricate, as the structure collapses during the template removal process. Figure S3 shows the top view and crosssectional SEM image of 10 nm ZnO nanolattice after removing the resist template. The porous morphology is due to the polycrystalline nature of ALD ZnO.

Supplementary Information C: Nanoindentation of nanolattice material
The schematic in Figure S4a shows load P applied through a spherical diamond indenter on a uniform nanolattice film of thickness t = 1 µm on silicon substrates. The spherical diamond indenter has a radius of 10 μm and covers a few unit cells of nanolattice film during indentation.
The nanolattice film was tested for mechanical properties using the cyclic incremental loading approach. This approach involves selecting a maximum load to be applied on a nanolattice sample, which then will be divided over 10 loading-unloading cycles with exponential increment in load.
The maximum load and incremental load were kept constant for a particular sample while indenting at multiple locations. Details of maximum load and incremental loads for various nanolattice samples are listed in Table S1. During each unloading sub-cycle, the nanoindenter was unloaded to 5% of the load applied in that cycle. This ensured that the load was applied at the exact same location during all subsequent incremental cycles by maintaining continuous contact between indenter and sample surface. This also helped in avoiding possible errors that may arise during initial imperfect contact if the indenter was fully unloaded.  (µN)  1  2  3  4  5  6  7  8  9  10   Al2O3   40  50  90  157  349  635  963  1366 1837 2383 3000  30  50  70  137  267  437  654  920  1231 1592 2000  20  50  60  79  108  159  227  295  383  486  600  15  50  54  68  90  120  158  206  262  328  400  10  25  27  33  44  60  79  103  131  164   The nanolattices have few imperfections arising from particle assembly defects during the self-assembly step. To ensure the data collected during nanoindentation was from defect-free regions, post indent SEM images of all the samples were taken. Figure S5 shows the loaddisplacement curve for a 45 nm ZnO nanolattice when the indent was made on a defect. Due to the presence of the defect, the structure collapsed during loading. Due to structure collapse, a dramatic increase in displacement was recorded at lower loads. Inset shows SEM with indentation residue on a defect. Only the nanoindentation data collected from defect-free regions were considered for calculating mechanical properties of the nanolattice. All the samples studied in this work were tested at 30 different locations. Out of these tests, about 15-25% were rejected due to the indents made on grain boundaries or point defects.   Table S3.
Specific energy dissipation calculation: Energy dissipated by the nanolattice film was the plastic work done on the structure during compressive loading. To calculate the specific energy dissipation by nanolattice film, the plastic work done in all the loading cycles before 'pop-in' was added together to get the cumulative plastic work. This cumulative plastic work was then divided by the total volume (V ) displaced by the spherical nanoindenter during loading to calculate energy dissipation per unit volume (J/mm 3 ). To accurately analyze the energy absorbing properties of the nanolattice material, the total failure volume zone within the lattice during nanoindentation was evaluated by finite element modeling of the nanolattice. This volume is important in estimating the specific energy dissipation, since the inelastic energy of the nanolattice material from the force-displacement curve is attributed to irreversible damage within the lattice film elements.

Finite element modeling (FEM):
Three-dimensional (3D) finite element analysis (FEA) of the indentation of Al2O3 and ZnO nanostructures were carried out in Abaqus 6.14. The nanolattice structure was modeled as a plate supported by thin-shell hollow pillars with average radius of 125 nm in a square lattice with spacing of 500 nm. The 3D FEA model is illustrated in Figure S6. A quarter of the nanolattice structure was modeled in view of the 4-fold symmetry of the structure.
For both Al2O3 and ZnO nanostructures, isotropic linear elastic behaviors and 20-node quadratic brick with reduced integration elements (C30D20R) were used. The mechanical For Al2O3, a Young's modulus of 180 GPa and a Poisson's ratio of 0.24 were assigned [2] whereas for ZnO, a Young's modulus of 146 GPa and a Poisson's ratio of 0.30. [3] The shell thicknesses of both structures were varied to reflect the fabricated structures. The indenter tip was modeled as an analytical rigid structure with a diameter of 20 µm. In each simulation, distribution of the maximum principal strain was recorded. To calculate the energy dissipation, the volume in which the maximum principal strain is equal or above the critical strain value was used.
Representative results from the FEA simulations are shown for 10 and 40 nm thick Al2O3 structure are shown in Figure S7. Figure S7 (Movie A and B). To obtain the volume, the nanolattice model was subjected to the same indentation depth used in the experiments. Figure S7(b) and (d) depict the volume where the local strain exceeds the critical strain of 2 and 1.05% for the 10 and 40 nm samples, respectively. The total volume was multiple by a factor of 4 to calculate the total failure volume. Buckling was observed for Al2O3 structures with thickness below 30 nm. For these cases, in order to avoid convergence issues, artificial damping was added to the model. It was assured that the ratio between the artificial damping energy and the strain energy of the model was no more than 5%. A table summarizing the FEA simulation results for all samples are shown below in Table S2.  Figure S8 shows

Supplementary Information E: Failure mode analysis
To analyze the failure mode, the geometry of a primary tubular column in the nanolattice material was simplified as a hollow cylindrical column. During ALD, the outer radius of this column remains constant and the thickness of the layer increases towards the center. From SEM images, the averaged outer radius was estimated to be about 125 nm. The aspect ratio of tubular columns in nanolattice was about 4:1, which prevents the Euler buckling failure mode. So the nanolattice failed either by fracture of top planer layer or by shell buckling of tubular column. The equation for stress required to fracture a thin plate is: Where, is the fracture toughness of the ALD material. The fracture toughness of 1.89 MPa*m 0.5 and 1.4 MPa*m 0.5 were used for Al2O3 and ZnO, respectively. [4,5] The stress required for shell buckling of hollow cylindrical column is given by: where E is the Young's modulus of ALD material and v is Poisson's ratio. The moduli of 165 GPa and 129 GPa, and Poisson's ratios of 0.24 and 0.349 were used for Al2O3 and ZnO, respectively. [6,7] In Figure S9  work, the shell thickness ranged from 30 nm -95 nm, so all the samples fail by fracturing of the top planer layer around holes. Figure S10 shows the failure mode analysis for ZnO nanolattice. Figure S10. Failure mode analysis of ZnO nanolattice.

Supplementary Information F: Recoverability analysis of Al2O3 nanolattice
The post-indent top-view SEM images of Al2O3 nanolattices with shell thickness lower than the critical thickness do not have the indentation residue like the thick-shell nanolattice samples. The failure mode analysis indicates that thinner lattices fail by buckling of the tubular column during compressive loading. The top planer layer gets elastically stretched during loading and remains undamaged unlike thicker nanolattices. When these thinner nanolattices were unloaded, the buckled tubular columns elastically recovered to regain their shape. This shape recovery was also facilitated by the elastically deformed top-planer layer regaining its original shape. This recovery can be observed from the load-displacement curve of thinner Al2O3 nanolattices ( t  10 nm), which show a negative force after complete unloading of the indenter.
This negative force is the adhesion force resulting from the Van der Waal's attraction between spherical diamond indenter and the recovering nanolattice film. This non-zero adhesion force confirms that the nanolattice was in contact with the diamond indenter even when the tip has retracted, since the film the recovered to its original height. To verify this negative force is due to contact, the Van der Waal's forces between the tip and the nanolattice film can be calculated. The surface energy of Al2O3 and diamond are 2.6 J/m 2 and 5.24 J/m 2 , respectively. [8] The total work of adhesion at the interface is given by: The adhesion force acting between the nanolattice and the spherical diamond indenter is related to the contact radius a through the indenter radius R and indentation depth h , which is given by: The top layer of nanolattice in contact with the diamond indenter has hexagonal symmetry of holes, which reduces the actual contact area between the nanolattice and indenter. For thinner nanolattices, this area was about 0.43 times the total area. By assuming this contact area to be circular, the contact radius was calculated to be about 235 nm for 4 nm Al2O3 nanolattice. Under external loading conditions, the contact between the nanolattice and indenter remains Hertzian. [9] Therefore, the force of adhesion is given by: The presence of the Van der Waal's adhesion force demonstartes the tip and film maintain contact, indicating that the films have recovered to the original height.
The negative adhesion force was also observed for thicker nanolattices ( t  10 nm) during unloading. However, unlike the thinner nanolattices, the force goes to zero before the indenter is completely unloaded. This demonstrates that the tip loses contact with the film during unloading, indicating nanolattices with cr tt  do not show complete recovery due to brittle fracture. Figure   S8 shows the adhesion force for 40 nm Al2O3 nanolattice, which is representative of the indentation curve for thicker shells. The averaged values for adhesion force are 1.77 μN, 1.41 μN, 0.57 μN, and 1.92 μN for 15 nm, 20 nm, 30 nm, and 40 nm alumina nanolattices, respectively. Note these values are comparable to the thinner shell samples, which is expected given the tip and nanolattice materials are the same. The adhesion for the thicker nanolattice films may be smaller due to nonconformal contact of the more rigid film. Figure S11. Adhesion force for 40 nm Al2O3 nanolattice.