1. Introduction

The scale invariance of Maxwell’s equations dictates that a structured electromagnetic material designed for operation at a wavelength, λ₁, can be scaled by a factor γ, to operate at a different wavelength, λ₂, where γ = λ₂/λ₁, provided the materials respond accordingly, simply by scaling all the physical dimensions by γ [1]. Scale invariance has the very tangible benefit that new theories on structured electromagnetic concepts and devices, such as photonic crystals [1] and metamaterials [2], can be demonstrated at long wavelengths with centimeter-scale unit cells, where fabrication constraints are relaxed, with the promise that the new theory will also function at short wavelengths (optical, IR). Furthermore, the ability to control light matter interactions by structuring materials in all three spatial dimensions leads to several optical phenomena unique to three-dimensional structure such as chirality [3,4 ] and toroidal excitations [5], which are not present in 1-D and 2-D systems. Unfortunately, the practice of micro-fabrication is not scale invariant – fabrication of micrometer-scale structures is vastly more difficult than fabrication of centimeter-scale structures. Modern, advanced micrometer-scale fabrication approaches such as those used in the semiconductor fabrication industry are highly optimized to create 2-D structures. Fabrication of 3-D structures at the micrometer and sub-micrometer scale is even more challenging and currently represents an enormous barrier to application of next generation structured electromagnetic research designed for operating wavelengths in the IR and visible wavelength ranges.

Despite the challenges of 3-D fabrication, several micrometer-scale 3-D fabrication approaches have recently emerged. Some approaches such as direct laser writing [6,7 ], interferometric lithography [8–10 ], and particle self-assembly [11] are capable of creating striking 3D structures, however the achievable form factors are highly constrained by the fabrication approach and not necessarily compatible with commercial CMOS fabrication facilities, a trait which would provide significant leverage for scaling and high volume manufacturing. Other techniques such as layer-by-layer (L-b-L) fabrication [12–15 ] and nano-origami [16,17 ] use CMOS compatible materials, but again have limitations in the types of structures they can create. L-b-L fabrication is severely limited in making structures with complicated profiles in the vertical direction, requiring many layers to adequately capture fine structure in the vertical direction, while nano-origami cannot create dense arrays of unit cells because the vertical surfaces of the 3-D structure must be laid out in the 2-D plane of the wafer prior to the folding operation which converts the planar pattern into a 3-D structure.

Recently, we used a process similar to nano-stencil lithography [18–20 ] termed membrane projection lithography (MPL) [21–23 ] to create dense arrays of 3D unit cells in an organic polymer material system, decorated with metallic inclusions. The resulting structures exhibited electromagnetic scattering behavior that was unique to their fully 3-D unit cell structure, however the polymer is highly absorptive in the thermal infrared range, and is not typically used in CMOS fabrication. In this work, we present the translation of the MPL process to an entirely inorganic, CMOS-compatible material system, and the demonstration of a versatile suite of array geometries, unit cell shapes and metallic inclusions decorating the individual unit cells.

With the advent of photonic crystals, the nomenclature and analysis techniques of solid state physics have assumed a prominent role in the study of structured electromagnetic materials. Many of the properties of a photonic crystal, and indeed many structured electromagnetic materials, can be derived from the underlying lattice spatial group. In the most general solid state description, however, a crystal is defined as a lattice combined with a basis, where the unit cells are positioned on a spatial lattice, and the interior of the unit cell contains a basis, structure on a finer granularity. In this sense, MPL offers a viable route to structuring the interior of the unit cell with a functionalized basis, and potentially, further control over light/matter interaction. This advance paves the way for creation of not only micrometer scale structured electromagnetic materials, but a wide variety of 3-Dimensional micrometer scale applications using commercial semiconductor fabrication equipment and materials.

2. Fabrication

The MPL process is schematically depicted for a single unit cell in a cubic geometry in Fig. 1 . Briefly, starting from a silicon substrate (a.), micrometer-scale topography is etched into a silicon substrate (b.). The topography is backfilled with a sacrificial material (c.), and the surface is chemically mechanically planarized (CMP) flat (d.). A membrane material is then deposited (e.), and patterned with the desired shape of the inclusion (f.). The sacrificial material is evacuated from the underlying topography through the patterned membrane (g.) yielding a patterned membrane suspended over the 3-D topography. Directional semiconductor operations such as metal evaporation can be performed at an angle with respect to the substrate surface (h.) and repeated numerous times (i.), projecting a deposited replica of the membrane pattern on the surface of the underlying topography. Removal of the membrane yields a decorated micrometer-scale 3D silicon structure (j.). The MPL process is captured at four points during processing in the SEM images appearing at the bottom of Fig. 1. In (k.), high aspect ratio cavities with square cross section are etched into a silicon substrate. In (l.), the patterned AlN membrane sits over the backfilled cavity. The large keyholes in the oxide backfill are typical of high aspect ratio backfilling, and can be eliminated by adjusting the deposition conditions of the oxide backfill, but since the backfill material is sacrificial the keyholes do not represent an issue as long as they do not extend up to the AlN membrane. For lower aspect ratios cavities, a dense backfill is achieved. In this case the keyhole formed a “coaxial” dot in the center of the SRR. The presence of this dot has only a small impact on the scattering performance of the SRR. In both cases, the hydrofluoric etch is able to completely evacuate the cavity through the patterned membrane. In (m.), the AlN membrane is now suspended over the cavity after dissolution of the SiO₂ backfill material. Finally, in (n.) the unit cells are shown after two consecutive evaporations on neighboring walls. Occasionally, lift-off defects are apparent, where either the membrane pattern was insufficiently cleared, or where the inclusion lost adhesion to the silicon wall, but the process is robust, with extremely high yield over the entire cm² die.

 

Fig. 1 a.) Starting silicon wafer; b.) Etch cavity; c.) Backfill cavity with silicon dioxide; d.) Chemically mechanically polish wafer; e.) Deposit aluminum nitride membrane; f.) Pattern membrane; g.) Evacuate backfill oxide; h.)-i) Perform directional evaporations onto interior faces of cavity; j.) Perform liftoff to remove metal coated membrane; k.) SEM image of cubic silicon cavities; l.) SEM image of backfilled cavities with patterned membrane; m.) SEM image of evacuated cavities with patterned membrane suspended over cavity; n.) SEM image of unit cells decorated with 2 gold split ring resonators (basis) per unit cell (after liftoff).

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The MPL approach can be used to decorate the interior faces of a wide variety of “negative-space” unit cell geometries. In addition to the cubic-cavity geometry shown in Fig. 1, hexagonal, cylindrical and asymmetric cavities can all be patterned this way. Figure 2 contains low magnification (a,c,e) and higher magnification images (b,d,f) of cubic, cylindrical and hexagonal cavities arrayed in a 2-D rectangular and 2-D triangular lattices. It is also possible to decorate the exterior faces of “positive-space” structures, such as blocks, cylinders and conical structures. Figure 2(g), 2(h) contain SEM images of silicon pillars decorated with metallic crosses.

 

Fig. 2 SEM Images of:a.) a square lattice with cubic unit cell; b.) a square lattice with cubic unit cells, filled with a 3-rectangular patch basis; c.) a triangular lattice of cylindrical unit cells; d.) a triangular lattice of cylindrical unit cells with a single 0.25 micrometer plasmonic basis; e.) a triangular lattice of hexagonal unit cells; f.) a triangular lattice of hexagonal unit cells with a single tri-pole metallic basis; g.) a square lattice of silicon rectangular parallelepiped unit cells; h.) a square lattice of rectangular parallelepiped unit cells with a single metallic cross as the basis.

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MPL is conceptually simple however some of the details are crucial to successful patterning using this approach. Identification of a suitable material system is necessary. The backfill material must possess a dissolution mechanism which will affect neither the silicon nor the patterned membrane. The membrane material must have sufficient structural integrity and manageable internal stress to survive as a suspended membrane as well as possess a dissolution mechanism for removal after processing which will not damage either the underlying silicon topography or the deposited material. A silicon-silicon dioxide-aluminum nitride material system for the substrate/backfill/membrane materials satisfies these requirements. Silicon is routinely etched into 3-D topography with high aspect ratio in semiconductor and MEMs applications, and the process of backfilling and CMP with silicon dioxide (SiO₂) is similarly an established semiconductor process. Aluminum nitride (AlN) is both mechanically stable, relatively immune to dissolution in hydrofluoric acid (used to remove the SiO₂ backfill) and yet can be dissolved in a basic etch (pH ~10) SC1 (H₂O_:NH₄OH: H₂O₂, 5:1:1 at 70 °C), a standard clean used in the semiconductor industry.

In a purely rectangular geometry, evaporation at 45 degrees relative to the surface normal results in deposition of a structure on the side-wall with the same linear scale as the mask pattern. Deposition at angles other than 45 degrees results in z-axis displacement of the center of the pattern with respect to vertical wall and either compression (for angles shallower than 45 degrees) or elongation (for angles steeper than 45 degrees) of the vertical scale of the structure (Fig. 3(a) ). Regardless of the angle of deposition, the finite thickness of the membrane results in linewidth clipping, where the width of lines oriented orthogonal to the evaporation direction are reduced by t/tanθ where t is the thickness of the membrane (Fig. 3(b)). Finally, during deposition, accumulation of metal on the top of the membrane leads to a reduction of the clear aperture of the membrane pattern, and a dynamic change in the extent of the decoration during deposition. This effect is more prominent on the edge of the decoration formed by the top edge of the membrane pattern, and is apparent as the “smeared” appearance of the inclusion in the SEM image in Fig. 3(c). The ultimate resolution of this technique is a function of many variables including the desired pattern, membrane thickness, and required inclusion thickness. We have successfully created structures ~100 nm in linewidth using MPL.

 

Fig. 3 a.) Schematic showing the effect compression/elongation effect with deposition angle; b.) schematic showing the impact of membrane thickness on inclusion dimensions; c.) Schematic and SEM image showing the impact of accumulation during deposition on inclusion shape.

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The power of MPL arises from the fact that, in addition to control over the unit cell shape, the 3D unit cells can be arranged in any of the 2D Bravais lattices. Figure 3 shows a schematic depiction of a cubic unit cell arrayed in each of the 5 2D-Bravais lattices. With the lattice determined by the layout of the unit cells, the basis is modified by the membrane pattern shape and number and direction of evaporations. Note, while the examples shown in Fig. 2 all demonstrate evaporation on a planar surface, the direction of evaporation could be chosen so that the inclusion landed on a seam between two faces, or a corner, so that the resulting inclusion becomes fully three-dimensional. By performing the MPL process in deposited films of polysilicon, layer-by-layer fabrication of all 14 3-dimensional Bravais lattices is possible.

While enormously flexible, the MPL approach does possess some limitations on the types of unit cells and inclusions that can be constructed. First, the membrane pattern must be self-supporting, so that it can remain intact after cavity evacuation. The self-supporting requirement excludes patterns with closed loops. Second, while it is possible to form cavities by oblique angled etching, further processing following the MPL approach would be extremely challenging, so that unit cells with non-orthogonal sidewalls are excluded on the basis of practicality. Finally, the evaporation operation is a purely geometric operation, such that the angle of evaporation relative to the wafer normal varies from the center of the wafer to the edge of the wafer. For a 150 mm wafer located 50 cm from the evaporation source, this angular deviation represents a Δθ = 8.5 ° from center to edge. With the addition of a collimating baffle and substrate motion, this angular deviation can be removed for wafer level processing. In this work, however, all evaporations shown were performed on die-level samples with ~1° of angular variation across the sample.

3. Characterization

The ability to create complex 3-D structures allows access to 3-D coupling mechanisms between incident photons and the plasmonic inclusions which are inaccessible in planar, 2-D structures. Consider the vertically oriented split ring resonators (SRR) shown in Fig. 4 . The inset schematic on the left shows an SRR oriented such that the gap is parallel to the wafer surface. This SRR (E-SRR) can be excited by both the electric field and the magnetic field of a normally incident photon with propagation vector k. For the E-SRR, an E-field polarized across the gap capacitively excites conduction electrons in the metal to flow around the loop [24]. Alternatively, when a B-field penetrates the loop of the E-SRR, electrons are inductively excited and current flows around the SRR to reduce the total magnetic flux through the loop in accordance with Lenz’s law. Because the E and B fields are orthogonal, both the electric and magnetic excitations occur for the same incident polarization (termed Polarization A),while in the orthogonal polarization (Polarization B), the SRR is not excited by eitherelectromagnetic field component (the E-Field orthogonal to gap, while the B-field is parallel to the loop). By contrast, the magnetically driven SRR (B-SRR, right inset schematic) with the gap oriented in the vertical direction can only be excited magnetically by a TEM incident photon. Because the gap is oriented in the vertical direction, a normally incident E-field cannot capacitively couple to this structure for either polarization, however the incident B-field can still inductively excite the SRR when it possesses a component normal to the plane of the loop (Polarization B).

 

Fig. 4 a.) Schematic depiction of an MPL cubic unit cell arrayed in all five 2D-Bravais lattices; b.) SEM image of the MPL process performed in a deposited polysilicon film. The ability to use deposited films allows the use of standard layer-by-layer fabrication techniques and enables creation of all 14 3D Bravais lattices.

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The CMOS-compatible MPL fabrication process was used to fabricate a variety of tetragonal unit cells 2 μm x 2 μm X 3.5 μm (length x width x depth) with 300 nm thick walls (unit cell period 2.3 μm). The 26 x 32 mm full field reticle of the ArF stepper (248 nm) was divided into 6 individual 1 cm^2 sub-die, and stepped across the 150 mm wafer, resulting in 18 full field die per wafer. While the unit cells etched into the silicon were identical, the six sub-die each had unique plasmonic inclusion patterns in order to explore a variety of different plasmonic motifs. The E-SRR and B-SRR structures are fabricated from the same membrane pattern by orienting the angled deposition at the appropriate wall. In this case, the angle of deposition was ~30 degrees, resulting in a slight stretching of the vertical dimension of the deposited patterns.

The graph in Fig. 5 contains a plot of the reflectivity of the sample versus wavelength. The data was collected in a SOC-100 Hemispherical Directional Reflectometer, and analyzed by a Nicolet-7600 FTIR using a standard DTGS detector. The HDR has a measurement range of angles from ~10 degrees to ~70 degrees. The data shown was collected at 10 degrees relative to the surface normal. A gold mirror is used as a reference to establish “perfect” reflectivity of 100%. The data presented in this paper is plotted as raw, un-normalized data on this scale. The solid curves in the graph are plots of the inactive polarization for both the E-SRR and B-SRR, where the SRR is not excited by the incident field. A planar silicon substrate with index of refraction of ~3.4 has a nominal Fresnel reflectivity of ~54%, representing a natural upper bound in the expected reflectivity for a bare sample. While there are some differences in relative magnitudes of both of the inactive polarization curves, the overall trend of the curves as well as the location and relative strengths of the spectral features are similar. The curves with the symbols are the active polarization response for both the E-SRR and the B-SRR. It is apparent that in both structures, when the incident polarization excites the SRR, obvious, high contrast, symmetric resonant peaks appear in the reflected signal. There is a noticeable red-shift in the spectral position of the peaks for the E-SRR. Most of the shift in peak location can be attributed to the vertical stretching of the patterns – while the length of both “arms” of the E-SRR were increased by evaporation at 30 degrees, resulting in a longer resonant wavelength, only the “spine” of the B-SRR was stretched, resulting in a shorter resonance wavelength.

 

Fig. 5 Graph of the unnormalized measured reflectivity for two orientations of split ring resonator and two incident polarizations (angle of incidence = 10°).

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Now consider the case in Fig. 6 , where the basis of the unit cell contains both a vertically oriented B-SRR and a vertically oriented E- SRR on adjacent faces created by performing two successive depositions, one on each face, prior to liftoff. The individual SRRs still only respond to either Polarization A (E-SRR) or polarization B (B-SRR), but now, because the SRRs are arranged orthogonally in such close proximity, when current flows in the individual SRRs, the resulting magnetic field inductively couples to the neighboring SRR, altering the electromagnetic response. Comparison of the spectra in Fig. 5 to those in Fig. 4 reveals a new resonant peak in the B-polarization at around 12 micrometers, as well as the presence of a “shoulder” on the short wavelength side of the resonant peak in the A-polarization at around 5 micrometers.

 

Fig. 6 Graph of the unnormalized measured reflectivity for both incident polarizations for a square array of cubic unit cells with a 2-SRR basis. Circled regions indicate emergence of features due to coupling between the neighboring SRRs.

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4. Conclusions

We have demonstrated a robust, large area fabrication method capable of micrometer scale, 3D structures arrayed in a variety of in-plane lattice morphologies, unit cell geometries and inclusion motifs. The technique uses standard semiconductor processing equipment and CMOS compatible materials. This fabrication approach allows nearly complete freedom in choice of in-plane lattice, unit cell geometry and basis selection so that a structured electromagnetic material can be designed and optimized for particular applications. Since the layers are CMP flat, multi-layer materials can be created by employing the MPL process in a layer-by-layer fashion, building up bulk materials constructed of rationally designed constituent unit cells. In order to navigate this large design space in both fabrication and electromagnetic behavior, sustained modeling and theory work is required to build the requisite insight.