Controlling Vertical Asymmetry of Nanocrystals Through Anisotropic Etching‐Assisted Nanosphere Lithography

Nanosphere lithography, a low‐cost fabrication technique, depends on the self‐assembly of nanoscale features to create nanostructures in a hexagonally close‐packed structure. In this article, the fabrication of 3D nanostructures over a large surface‐area with anisotropy along the growth direction through the combination of chemical and physical plasma etching is reported. The anisotropy stems from etching the nanosphere mask and the substrate at different rates. Due to the dynamic masking effect, a systematic variation of etching time gives rise to intriguing nanostructures with sharp edges that have strong potential for plasmonic applications, with the possibility of manipulating electromagnetic radiation. The structures obtained include nanocylinders, truncated hexagon‐based pyramids, circular pads on a conical base, and nanocones from a single‐layer nanosphere mask. Simulations of the fabrication process offer further insight into the understanding of nanostructure formation. A good agreement between predicted results and experiments confirms the potential of our numerical design. In addition, the optical properties of the nanostructures are investigated by UV–vis and the experimental findings are consistent with simulations based on a finite‐difference time‐domain method. The nanostructures described in this study contribute to the emerging 3D plasmonics and 3D magnonics, with strong potential for a significant impact on biosensor applications.

Nanosphere lithography (NSL) [31][32][33][34][35][36] is a popular fabrication technique which depends on the self-assembly of nanoscale features to attain the periodic nanostructures.This technique has been studied extensively since the last decade due to certain advantages like simplicity of the process, cost, and time effectiveness, and easily industrializable.The bottleneck to this technique is that there is less scope for structural variation with conventional NSL.The structures are conventionally sixfold symmetric as the nanosphere mask self-assembles in a hexagonal close-pack fashion.The shapes are large triangular pillars in case of deposition and triangular holes or cylindrical pillars of different aspect ratios and gaps in case of etching.Recently, the NSL technique is taken to the next level, where innovative nanostructures have been developed.These nanostructures exhibit a variety of shapes and symmetries along their surfaces, and also possess asymmetrical characteristics along their thickness (3D structures).[41] All the processes are carried out within meticulously engineered nanofabrication conditions.For instance, Darvill et al. [41] described the formation of nanomushroom structures by means of etching process with a temperature gradient.Ganguly et al. [33] showed that the azimuthal and polar angle of the deposition shower can be varied with respect to the substrate for shadow mask deposition either in steps or even continuously at a constant (or varying) angular velocity to create structures having different 3D shapes and special symmetry.
In this article, we systematically study the role of anisotropic etching-assisted monolayer and bilayer NSL to construct a library of anisotropic 3D nanostructures and assess their unique plasmonic characteristics and potential novelty in the field.The technique involves a well-defined approach with varying etching times in a two-step etching process keeping the rest of the experimental conditions constant.The anisotropy along the thickness is achieved by a combination of physical and chemical etching as well as the difference between the etching rates of the mask and the substrate.Structures like nanocylinders, truncated hexagon-based pyramids, circular pad on conical base, and nanocones are obtained from a monolayer mask.Cylindrical to triangular prism-shaped nanoholes and pyramids with curved edges are obtained from a bilayer mask through a systematic variation of the etching condition.MATLAB simulation is used to understand the formation of structures by physical etching.Absorption spectra of the structures are experimentally characterized using UV-vis spectroscopy while the electric field distribution and absorption profile are analyzed using Lumerical simulation.The study has an important contribution to expanding the scope of NSL in emerging 3D plasmonics and 3D magnonics research.

Fabrication of Micro/Nanostructures
In the first step of sample preparation, 10 Â 10 mm silicon substrate was ultrasonicated in acetone and isopropyl alcohol for 5 min.The sample was cleaned by using a steady flow of distilled water on a wet bench.The substrate was dried on a hot plate at 50 °C.In the next step, the Si wafer was treated with O 2 plasma to remove organic impurities on the substrate and make the surface hydrophilic. [42,43]We found that this treatment had a significant impact on the mobility of micro/nanoparticles mask units helping them to spread over the surface of Si in a hexagonal close-packed (HCP) lattice structure.Without plasma cleaning, the nanosphere masking process faced several difficulties such as random agglomeration, multilayer formation, island formation, point defect (i.e., missing particle) dislocations, and the uneven gap between particles.Solution of polystyrene micro/ nanobeads of 2 μm and 500 nm diameter and methanol were mixed in a 1:4 volume ratio.The molar ratio of the solvent as well as the surface area of the substrate played a crucial role in the self-assembly process.The solvent provided mobility to the nanobeads allowing weak surface tension force to overcome frictional force to assist the self-assembly process until it got evaporated.The evaporation rate, in contrast, was a function of the surface area of the solution that determined the time window for the dynamics of the beads crucial for a self-assembled HCP configuration.The polystyrene nanobead solution was spin-coated onto the Si substrate at a maximum revolutions per minute (RPM) of 1500 for 100 s.The centrifugal force assisted in spreading the liquid evenly across the surface, removing any excess liquid, and tightly packing the beads so that they touched each other.As a result, nanosphere masks were obtained in an HCP geometry, covering a large area in both monolayer and bilayer configurations.The variations in substrate rotation [44,45] speed, dwell time, the volume of the drop-cast liquid, and the concentration of the nanobead solution determined the relative coverage ratio of monolayer and bilayer masks on the substrate.In addition to affecting the coverage area, these factors also influenced the formation of the HCP pattern, including the likelihood of defects and dislocations within the array.The next step underwent a two-step etching process.First, the nanospherical masks were treated with oxygen plasma in the reactive ion-etching chamber.The oxygen-plasma-etching time is represented with t1 in the following discussion.The oxygen plasma etched the polystyrene without affecting the silicon substrate resulting in the reduction of the bead's diameter.Hence, the diameter of the beads and their separation were determined by the value of t1.Furthermore, the silicon substrate was etched in the reactive ion etching chamber using a gas combination of SF 6 and CHF 3 .The Si-etching time is represented with t2.The etching parameters are shown in Table 1.
The part of the silicon masked by the polystyrene beads remained unetched while the exposed part of silicon got etched giving rise to a periodic nanostructured surface profile.Finally, a loosely bound polystyrene mask was removed from the substrate by ultrasonicating the sample in water for 5 min.Once the structure was prepared, a layer of Ti (3 nm)/Au (30 nm) was deposited onto the surface of the sample using an e-beam evaporator with a deposition rate of 0.3 Å s À1 for the spectroscopic analysis.Ti was used as an adhesion layer between Si and Au.

Spectroscopy Analysis
UV-vis absorption spectroscopy measurement was carried out to investigate the spectroscopic behavior of nanostructures.Light was irradiated over the structure in the normal incidence configuration to obtain an absorption spectrum with varying wavelength.For the spectroscopic measurement, UV/vis/nearinfrared spectrometer (PerkinElmer, model: Lambda 1050) was employed, and the reflection module (150 mm InGaAs integration sphere) was used to collect the data.The measurements were carried out in the reflection mode under ambient temperature.The sample was securely positioned within a sample holder designed to block external light.The wavelength of the incident monochromatic light beam was systematically varied from 400 to 800 nm with a step resolution of 2 nm.The instrument was initially calibrated using a standard sample provided by the instrument manufacturer to establish a baseline of 100% reflectance.Following calibration, the actual measurements were performed.

Simulation
For a better understanding of the 3D nanostructures and their applications, simulation studies were essential to explain the formation of structures, obtain the fabrication parameters, and analyze the plasmonic properties.MATLAB simulation was used to understand the mechanism of the structures obtained using the nonuniform etching-assisted NSL technique.In the simulation, the substrate was defined by an equation of a plane.Monolayer and bilayer micro/nanobead masks were represented by sets of spheres, each having specific coordinates and diameters.These spheres were organized in either a monolayer or bilayer pattern following an HCP fashion to mimic the experimental arrangement.The diameter of the spherical mask was regarded as a time-dependent parameter, continuously decreasing overtime at a rate corresponding to the etching rate of the polystyrene beads.Additionally, a dense array of parallel straight lines was introduced to symbolize the ion beams.The density of these lines influenced the resolution of the final output.In the study, these lines were oriented perpendicular to the substrate plane, indicating the direction of normally incident plasma.The detailed information of model equation was explained in Section S1, Supporting Information.At each time point, equations governing the positions of the nanospheres and ion beams were solved.A real solution signified that the ion beam made contact with the mask without touching the substrate.
Conversely, an imaginary solution indicated that the ion beams did not intersect the spheres and instead collided with the substrate.In the latter scenario, the solutions between the substrate plane and the ion beam lines provided precise coordinates where the etching dose was applied.This etching dose was integrated overtime and mapped across the entire substrate area, enabling the calculation of the depth of etching, ultimately resulting in the desired structure.The structure appeared vertically inverted when compared to the ion dose mapping as a higher quantity of ions correlated with increased etching, ultimately leading to the formation of the base of the structure.The plasmonic performance of the periodic nanostructures was studied with the 3D finite-difference time-domain (FDTD) method using Lumerical FDTD Solutions by integrating the loss function over the entire simulation volume and calculating the divergence of the Poynting vector.In the simulations, the mesh grid was set as 1 nm.Periodic boundary conditions were imposed in the x and y directions, while a perfectly matched layer was imposed in the z direction.Periodic boundary conditions simply copied the fields at one edge of the simulation domain and insert them at the other edge, providing that the light was injected at a normal incidence.The power monitors in our simulations returned the amount of power that was absorbed, transmitted, and reflected.Additionally, we calculated extinction, absorption, and scattering cross sections using a total-field scattered-field source as described in the later part of this article.

Oxygen Etching
Figure 2 shows results for reactive oxygen ion etched nanosphere mask sample with varying time t1 (=0-5 min).The scanning electron microscope (SEM) images of the nanosphere mask (2 μm initial diameter) after etching with varying time are shown in Figure 2a.As the etching time increases, the diameter of the beads reduces with an increasing gap between the spheres although, the lattice constant of the mask structure remains unchanged.Inset shows a magnified image of a single bead revealing the surface morphology of the mask element resulting from etching.It is observed that the porosity of the surface increases for larger t1 due to the deformation of polystyrene by energetic ions.A smooth spherical surface gradually turns into dendrite structures on a solid spherical core as t1 increases from 0 to 5 min.The transformation happens due to reactive interaction as well as the sputtering of material by oxygen plasma on a polystyrene surface.The observed surface roughness response to oxygen plasma exposure aligns with prior findings in the literature. [46,47]Furthermore, a quantitative analysis is conducted to evaluate the degree of degradation, which involves measuring the porosity of the nanosphere (see Figure 2c).This is accomplished through a distinctive method that involves analyzing the intensity profile of SEM images as discussed in the later part of this section.Figure 1b shows the variation of the diameter (d) of the solid spherical core (excluding the tentacular extension) with time.The value of d decreases with time; however, the variation is nonlinear.The etching rate is found higher for smaller values of d.To analyze the etching mechanism, the curve is fitted as d ¼ d 0 ð1 À R:t1Þ, where, R, is the etching rate which has two components chemical (R c ) and physical (R p ).For reactive chemical etching R c is constant considering constant power and gas flow rate giving rise to a linear variation of d.The nonlinear component comes from the physical part of the etching.Considering the physical ion beam having an equal special distribution of energy, the ionic energy received by a spherical mask is proportional to the area of the circular cross section (A) of the sphere passing through its center as shown in inset of Figure 2b.S being the exposed surface area, A/S ratio increases with decreasing diameter resulting in a higher etching rate at smaller d which can be approximated as R P ∝ t1.Hence, the curve in Figure 2b is nicely fitted by a quadratic polynomial as The etching rate constants are obtained from the fitting as R c = 0.11 m À1 and R ' p = 0.06 m À2 .The surface degradation of polystyrene with oxygen etching has been analyzed by studying the intensity profile of normal incidence SEM images of single bead shown in inset of Figure 2a.The changing intensity of a pixel of an image has been color mapped to the variation in height using MATLAB (Figure S2, Supporting Information).In the next step, the differential of the color map has been computed as the absolute difference of the intensity values of the neighboring pixel (Figure S3, Supporting Information).A large value in a differential color map indicates a region with a sharp change in height indicating roughness/porosity while a smaller value indicates that the variation of height is more gradual indicating a solid/ smoother surface.In Figure 2c, the average value of the differential per pixel for a single particle is plotted as a function of t1.The value increases with etching time indicating increased porosity.It is interesting to note that there is a remarkable increase in the porosity just after t1 = 3 min.The sudden surge in porosity indicates that the outer layer of polystyrene beads receives an adequate energy dose from the ion beam, resulting in a sudden change in its plasticity characteristics, ultimately leading to increased deformation.An inverse relation between diameter and porosity has been observed by comparing Figure 2b,c.

Silicon Etching
After the oxygen etching, the sample undergoes SF 6 and CHF 3 etching for the removal of silicon.The final structure depends on the starting diameter of the polystyrene beads.Figure 3 shows the effect of direct SF 6 and CHF 3 etching having no prior oxygen etching of the polystyrene beads (t1 = 0).Figure 3a-d shows the SEM results with increasing silicon-etching time t2.case, the arms of the triangles do not exhibit a concave shape; instead, they appear as straight lines which are attributed to the chemical assistance to the etching process.The simulated result shown in Figure 3f corresponds to δd = 50%.The experimental structure in Figure 3d looks similar to Figure 3f except for the fact that the top surface of the elements is hexagonal rather than circular.Another difference is that the elements are interconnected from their base to their nearest neighbors giving the shape of an interconnected truncated hexagonal pyramid.The reason behind this hexagonal formation is the proximity effect [39,40,[48][49][50] of the mask elements resulting in a unique flow dynamic of ions within a constricted region.The effect is also observed for the bilayer mask.When the gap between the masks is narrow, reactive oxygen has lesser access to the region resulting in a lower rate of chemical etching.The mask having HCP orientation, the nonuniform reaction occurs in six symmetry sides of a spherical mask resulting in a hexagonal interconnected structure (see Figure S4, Supporting Information).No proximity effect is not accounted for the simulation of Figure 3f.Hence, it appears as isolated truncated cones.The initial arrangement of the nanospheres is shown on the right side of the simulated structure.For the simulated result of Figure 3g, a small (10%) overlapping between the HCP spheres is considered to account for the proximity-induced nonuniform etching rate (see nanospheres arrangement on the right).The presence of this overlapping area necessitates an extended etching duration, effectively causing a lower rate of etching, which in turn gives rise to the structural attributes associated with the proximity effect.Essentially, this overlap introduces a delay in the etching process within that region, leading to the formation of interconnected bridge structures that extend from an element to its six nearest neighbors, as depicted in the experimental observation shown in Figure 3d.Thus, the simulation substantiates our understanding of the proximity scenario.
Figure 4 shows results for SF 6 and CHF 3 etching with prior oxygen etching t1 = 1 min.The left image in Figure 4a shows an oxygen-etched spherical mask with the diameter reduced by 300 nm acting as the initial state for SF 6 and CHF 3 etching.The middle one of the panel shows a normal view SEM image of silicon structures after SF 6 and CHF 3 etching followed by removal of the mask (inset shows magnified image).The bright spot at the center of the circular structure corresponds to the sharp tip.On the right, SEM image of the tip of a single nanocone is shown at a slanting angle of 52°.The apex of the cones is achieved with a radius of curvature varying between 5 and 25 nm. Figure 4b-g shows the tilted SEM image of the structures with SF 6 and CHF 3 etching for t2 = 1.5, 3, 4.5, 6, 7.5, and 9 min, respectively.The structures look like cylinders, truncated hexagonal pyramids, truncated cones with a wide circular plateau on the top, sharp cones, interference of six-sided waves, and random rough surfaces respectively.Figure 4h-j is the simulated result with δd = 1%, 50%, and 100%, respectively, which largely reproduces the experimental result of Figure 4b,c,e.The discrepancy between hexagonal and circular forms between Figure 4c,i is discussed in the previous section.The helipad structure in Figure 4d is an intermediate state between Figure 4i,j.The wide circular plateau appears on the top as deformed/residual polystyrene spread over the silicon surface (Figure 2a, image t1 = 5 min inset) protecting a larger circular area on the top.Figure 4f,g illustrates the cases where no protective mask is left.Hence, the Si structures gradually disappear with exposure to reactive ions.
It is interesting to observe that the structures in Figure 3 and 4 have certain similarities and dissimilarities.For instance, both the structures illustrated in Figure 3d and 4c are truncated hexagonal pyramids but parameters like aspect ratio, slanting-angle inter-element separation and the area of the truncated planes are different.The latter requires Si etching for a shorter time.In other words, a similar structure can be achieved with a smaller t2 when t1 is larger.For instance, the Si etching time of 3(d) is 4.5 min and 4(c) is 3.0 min.The conical structure (Figure 4e) appears for t1 = 1 min and t2 = 6 min which also occurs for t1 = 2 min and t2 = 3 min, however, with a different geometric dimension (Figure S5, Supporting Information).Henceforth, we can infer that in the two-step etching process t1/t2 ratio can be used as a functional tool to control the shape, aspect ratio vertical slope edge sharpness gap, and other geometric parameters.

Bilayer Mask
In this section, we discuss the structures obtained from the bilayer mask (see Figure S6, Supporting Information, for SEM images of the bilayer mask).The structures in Figure 5a-f are obtained using increased oxygen plasma etching followed by a constant time SF 6 and CHF 3 etching for t2 = 1.5 min.Figure 5a is the SEM image of the initial structure without oxygen etching (t1 = 0).The structure looks like periodic cylindrical holes.To understand the formation of the holes, the initial geometric configuration of the bilayer nanospheres is illustrated in Figure 5g.The green and yellow circles indicate the position of the bottom and top nanospheres in the HCP configuration.Triangular openings are periodically created by spherical masks at the bottom which are partially or completely covered by the upper layer of the mask as shown in the figure.The close spacing of holes within the densely packed bilayer nanosphere mask gives rise to the proximity effect, leading to the nonuniform flow dynamics of the reactive gas.This, in turn, results in changes in the curvature of the edges or the formation of nonuniform trenches in the final feature.The layers together leave a small asymmetric hexagonal exposure of %10% of the size of the nanosphere.The size of the hexagon being very small it appears as a circular hole on Si after etching.The hole becomes a triangular prism for t1 = 1.0 min.It is interesting to note that in this case symmetry is threefold as opposed to the sixfold symmetric structure in Figure 2b as alternate neighboring triangular elements are missing.The initial geometric configuration of this structure is shown in Figure 5h where alternate triangles are either completely closed or completely open.geometric configuration of the structure is shown in Figure 5i.The structures in Figure 5a-c and f are simulated in Figure 5j-m, which are in good agreement with each other.In the simulation only, uniform physical etching is considered.A disparity in the structural edge characteristics between the experimental and simulated data can be ascribed to the proximity effect around the narrowed region.Much like the architectures derived from 2 μm beads diameter as previously discussed, analogous structures are also obtained using beads with a diameter of 500 nm, as shown in Figure S7, Supporting Information.

Spectroscopic Study
In this section, we observe the spectroscopic properties of goldcoated nanocrystals.Figure 6a shows experimentally observed absorption spectra for nanocone structures with a periodicity of 2 μm and 500 nm.The thickness of the silicon substrate is 500 μm.Hence, the transmission coefficient is approximated to be zero.The value of absorption is obtained as A = 1-R.
As the wavelength varies from 400 to 800 nm, the absorption coefficient decreases for both the lattice constants.At lower wavelengths below 500 nm, the slope is relatively flat, followed by a steeper decline until 600 nm.Afterward, another period of flatter variation is observed until 800 nm.The absorption coefficient is higher for 500 nm periodicity over the entire range of visible wavelength.
The simulation results for absorption spectra of the same conical structure are summarized in Figure 6b.The curves have a largely similar trend as observed in Figure 6a.The value of A decreases with λ exhibiting a flat peak around 460 nm.The value  of A is higher for 500 nm periodicity same as observed in Figure 6a.However, the difference in values of A between the two lattice parameters is found more significant in the lower wavelength range, but it diminishes as λ increases.This feature is not observed in the experimental spectra in Figure 6a.The differences between the experiment and simulation may stem from the limitation of Si wafer thickness in the experiment, defects associated with NSL, and surface roughness of the deposited thin film.Figure 6c shows simulated absorption spectra for the truncated cone.The spectral variation exhibits substantial similarity.The structure with 500 nm periodicity again has a larger absorption than 2 μm.This holds true for the other structures as well.
While the optical spectra generally stay consistent despite changes in the lattice structure, the electric field distribution profile of the structures undergoes significant alterations depending on their shape.Furthermore, the lattice constant of the structures is vital in determining the presence and location of electromagnetic hotspots at a specific wavelength.In this section, the electric field, E, distribution is simulated with λ varying between 500 and 1400 nm, for different structures at two different 2 μm and 500 nm. Figure 7 shows cross-sectional view of the field distribution for λ in the xz plane corresponding to the highest electric field, E max .The value of λ is mentioned in each figure.The color corresponds to the intensity of the electric field.Figure 7a shows the electric field distribution of the conical structure with 2 μm periodicity.In this case, plasmonic waves are generated along the surface of the cone forming a damped standing wave pattern from the vertex toward the base at λ = 870 nm.Hence, a strong electric field concentrates around the vertex (E max = 14), although there exists a shadow (smaller E) region exactly at the top of the cone.The intensity profile is found symmetric along x and y.On the contrary, when the periodicity is reduced to 500 nm (Figure 7b), a highly concentrated hotspot is generated (E max = 35) at the tip of the cone (λ = 800 nm) while the damped standing wave along the surface disappears (see Figure S8, Supporting Information).Figure 7c,d illustrates the electric field distribution characteristics of a truncated hexagonal pyramid shape, with each figure representing a different lattice constant.In both cases, the edges of the top surface exhibit a strong electric field.Nonetheless, the maximum electric field values (E max ) are lower compared to conical structures (8.4 and 8.0, respectively).In Figure 7c, the maximum intensity occurs at lower λ (=677 nm) than in Figure 7d (λ = 785 nm). Figure 7c depicts additional lower maxima formed between the center and edge of the top surface, resulting in the creation of a ringlike electric field pattern on the surface.
Figure 7e,f shows the helipad structures with a periodicity of 2 μm and 500 nm, respectively.In this structure, a hot ringlike electric field is created around the top circular plate.In the first case, the intensity is concentrated at the bottom edge of the disc while in the latter case, it spans along the width of the ring with a slight inclination along the top.Both E max and λ are found larger for 500 nm structures as compared to 2 μm structures.From the observation, we infer that electric field distribution is highly sensitive to the shape and aspect ratio of the structural feature.Smaller structures with sharp edges are likely to produce larger and more concentrated electric fields resulting in a large density of the electric field.

Conclusions
In conclusion, this study presents a novel fabrication process for creating 3D asymmetric nanocrystals using anisotropic etchingassisted NSL.By combining chemical and physical ionic plasmaetching techniques, anisotropy along the height of the structures is obtained.The resulting nanostructures exhibit sharp-edged periodic arrangements of nanoelements with controlled geometric parameters.The fabricated structures included various shapes such as nanocylinders, truncated hexagon-based pyramids, circular pads on conical bases, and complete nanocones.The structures from bilayer masks varying from cylindrical to triangular prism-shaped nanoholes and pyramids with curved edges add a new dimension to this research.Our numerical simulations deliver good agreement between predicted results and experiments.They help to understand the details of the formation mechanism of these nanostructures.Furthermore, theoretical analysis for the absorbance and electric field distributions, based on a FDTD method, show consistent with the experimental findings.Thus, altogether, our simulation scheme has been proven as an efficient design tool to efficiently guide and optimize further developments.The enhanced plasmonic properties of the periodic nanostructures make them promising candidates for amplifying and sensing weakly scattered characteristic signals in various applications, including SERS and spintronic-based memory applications.Overall, this research expands the scope of NSL by introducing anisotropic 3D nanostructures and provides insights into their formation and optical properties.The findings contribute to the emerging fields of 3D plasmonics and 3D magnonics.This opens up new possibilities for surface engineering with functional magnetic, plasmonic, photonic, and catalytic properties in diverse applications such as sensors, memory devices, waveguides, filters, thermal dissipators, and chemical systems.
Figure 3b (t2 = 1.5 min) looks like triangular holes created by the triangular gap of polystyrene beads.With the increasing time t2, the triangular holes become bigger and deeper as shown in Figure 3c (t2 = 3.0 min), finally revealing hexagonal cylindrical/truncated conical structures connected to each other as shown in Figure 3d (t2 = 4.5 min).Figure 3e-g shows the corresponding simulated results.The structure depicted in Figure 3e arises from the etching of Si.During this process, it is considered that the diameter (d) of the nanospheres experiences a nominal decrease of 1%, denoted as a decrease in diameter δd = 1%.Experimentally observed structures in Figure 3b,c have good agreement with Figure 3e.Nevertheless, in the experimental

Figure 2 .
Figure 2. a) Scanning electron microscope (SEM) images of nanosphere mask with increased exposure to oxygen plasma.The white scale bars in the figures and insets correspond to 2 μm and 500 nm, respectively.The insets show the surface morphology of a single nanosphere in each of the cases.b) Variation of the nanosphere diameter with etching time.Inset: schematic illustration of physical-etching rate depending on the ratio between the circular cross section (A) of the sphere and (S) the exposed surface area.c) Variation of porosity with time.

Figure 1 .
Figure 1.Schematic illustration of the procedure for the basic etching-assisted NSL process.

Figure 3 .
Figure 3. Nanosphere mask without oxygen etching (t1 = 0): a) initial nanosphere mask; b-d) Structures with different Si-etching times, t2; e-g) Simulated structures corresponding to (b-d) with δd representing the reduction of nanosphere diameter (%).The upper section of Figure 2f, g showcases the initial arrangement of nanospheres employed in the simulated structure.The white lines at the bottom of (a-d) correspond to 2 μm.
Figure 5c,d are the top views and 45°slanted view of the structure with t1 = 2.0 min.Here, the triangles become larger, and the structure of the prism grew asymmetrically along the depth having the arms of the triangles being curved, convex for the outer triangle and concave for the inner triangle.This happens due to over-etching on the top and under-etching at the bottom of the triangular cavity due to a nonuniform density profile of reactive ions.With further etching (t1 = 3 min) vertically asymmetric curved-edged pyramids are obtained as shown in Figure 5e (top view) and Figure 5f (slanted 45°view).The structure has two types of peaks, one high and one low.The high peaks are the sharp tip of the pyramid, and the low peak is the joining of the edges of the three pyramids.The initial (a) (

Figure 4 .
Figure 4. a) Left: nanosphere mask after 1 min of oxygen etching (t1 = 1 m); middle: normal-view SEM image of periodic nanocone structure (inset: magnified view); right: 52°slanted image of a single nanocone.b-g) Nanostructures with increasing silicon-etching time t2.h-j) Simulated structures resembling (b,c) and (e), respectively.Here, δd is the percentage reduction of nanosphere diameter.The white scale bars at the bottom of the SEM images (except those mentioned) correspond to 2 μm.

Figure 5 .
Figure 5. a-f ) SEM images of bilayer mask lithography with increasing mask-etching time, t1, at constant Si-etching time, t2.g-i) Diagrams of the initial geometric configuration of the bilayer mask before silicon-etching exposure.j-m) Simulated structures of the lattices.The white scale bars at the bottom of the SEM images correspond to 2 μm.

Figure 6 .
Figure 6.Absorption spectra of a nanocone array with two different lattice constants.a) Experiments, b) numerical simulation, and c) numerical simulation of the absorption spectra of a truncated nanocone structure for comparison.

Figure 7 .
Figure 7. a-f ) Simulation of the electric field distribution for three different structures at two different lattice constants, namely, 2 μm (left panel) and 500 nm (right panel).The x and z coordinates are measured in μm while the color bar is measured in V m À1 .

Table 1 .
Gas flow rates and power used for the two-step etching process.ICP and SCCM correspond to inductively coupled plasma and standard cubic centimeters per minute respectively.