Hybrid Metal–Semiconductor Nanostructure for Ultrahigh Optical

Oct 8, 2015 - (g) Angle-integrated reflection spectra of perforated metal films with (dashed blue trace) and without (dotted red trace) protruding sil...
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Hybrid MetalSemiconductor Nanostructure for Ultrahigh Optical Absorption and Low Electrical Resistance at Optoelectronic Interfaces Vijay K. Narasimhan,† Thomas M. Hymel,† Ruby A. Lai,‡ and Yi Cui*,†,§ †

Department of Materials Science and Engineering, Stanford University, 476 Lomita Mall, Stanford, California 94305, United States, ‡Department of Physics, Stanford University, 382 Via Pueblo, Stanford, California 94305, United States, and §Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States

ABSTRACT Engineered optoelectronic surfaces must control both the flow of light and the flow of

electrons at an interface; however, nanostructures for photon and electron management have typically been studied and optimized separately. In this work, we unify these concepts in a new hybrid metalsemiconductor surface that offers both strong light absorption and high electrical conductivity. We use metal-assisted chemical etching to nanostructure the surface of a silicon wafer, creating an array of silicon nanopillars protruding through holes in a gold film. When coated with a silicon nitride antireflection layer, we observe broad-band absorption of up to 97% in this structure, which is remarkable considering that metal covers 60% of the top surface. We use optical simulations to show that Mie-like resonances in the nanopillars funnel light around the metal layer and into the substrate, rendering the metal nearly transparent to the incoming light. Our results show that, across a wide parameter space, hybrid metalsemiconductor surfaces with absorption above 90% and sheet resistance below 20 Ω/0 are realizable, suggesting a new paradigm wherein transparent electrodes and photon management textures are designed and fabricated together to create high-performance optoelectronic interfaces. KEYWORDS: photon management . light trapping . Mie resonators . transparent conductors . metal nanowire networks . metal-assisted chemical etching

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variety of nanostructured surfaces, including nanopillars,1 nanocones,2 nanowires,36 inverted pyramids,7 nanospheres,8 nanoshells,9 and nanodomes,10 have enabled strong, broad-band absorption in semiconductors for optoelectronic applications. Dielectric nanostructures are extremely effective at coupling and directing light across an interface between the outside world and optically active materials owing to a rich set of optical phenomena, including gradual refractive index matching, scattering, and coupling to guided modes.11,12 However, in many applications, a nanostructured optical interface must also serve as a conduit for electrical current between the semiconductor and an external circuit. In addition to providing photon management, the interface must offer high electrical conductivity. Typically, electrical conductivity at this interface has been provided by depositing NARASIMHAN ET AL.

a separate transparent electrode over the photon management structure, which reduces resistance while letting light pass through to underlying layers. Sputtered indium-doped tin oxide (ITO) is the most common transparent conductor currently used; however, sputtering ITO evenly over highly textured surfaces can be challenging, and the thick layers needed for applications that require very low resistance result in long sputtering times and thus lower device throughput.13 Metal nanowire networks are a promising alternative.1416 However, when high surface conductivity is desired, the concomitantly high metal surface coverage required can result in significant reflection loss and thus decreased absorption in the active layer.17 Thus, the surface coverage of metal networks is limited to about 10% for practical applications.18 Despite the need for both strong absorption and high conductivity at many VOL. XXX



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* Address correspondence to [email protected]. Received for review July 1, 2015 and accepted October 8, 2015. Published online 10.1021/acsnano.5b04034 C XXXX American Chemical Society

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ARTICLE Figure 1. Comparison of perforated gold films on silicon substrates with and without silicon nanopillars protruding through the holes. (a) Schematic, (b) false-color 25° tilted-view SEM (scale bar = 500 nm, with gold in yellow), and (c) digital photograph (scale bar = 1 mm) for a 16 nm thick gold grid sitting atop a planar silicon substrate. The surface, which is 65% covered by metal, is highly reflective. (d) Schematic, (e) false-color 25° tilted-view SEM micrograph (scale bar = 500 nm, with gold in yellow), and (f) digital photograph (scale bar = 1 mm) for an identical 16 nm thick gold film with silicon nanopillars protruding through the holes. The patterned area is dark red, indicating a significant decrease in reflection. (g) Angle-integrated reflection spectra of perforated metal films with (dashed blue trace) and without (dotted red trace) protruding silicon nanopillars. The perforated gold film on the planar substrate exhibits 50% integrated reflection averaged over the solar spectrum, while the film with protruding silicon nanopillars has only 19% reflection. The reflection can be further reduced to 10% by coating the metalsilicon nanopillar sample with a 50 nm silicon nitride antireflection layer (solid black trace).

optoelectronic interfaces and the commensurate size scale of semiconductor photon management structures and metal nanowire networks, these nanostructured materials have been studied and developed in relative isolation. In particular, the transparency of metal nanowire networks is optimized and measured considering the network in isolation, that is, suspended in free space or sometimes on a transparent substrate. At real interfaces with nanostructured semiconductors, NARASIMHAN ET AL.

the profile of the light, and therefore the performance of the network, could differ significantly. Here, we demonstrate that unifying a metal nanowire grid with extremely high surface coverage and a photon management texture in a single optoelectronic interface can simultaneously improve optical absorption and electrical conductivity, overcoming the conventional trade-offs encountered when designing these structures separately. VOL. XXX



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RESULTS We began by examining the optical properties of a high-surface-coverage metal film perforated with nanoscale holes sitting on top of a planar silicon substrate. Figure 1a,b shows a schematic and the scanning electron micrograph (SEM) of a 16 nm thick gold film patterned with an array of 295 nm  295 nm square holes with a center-to-center spacing of 500 nm. The patterned film on the planar silicon substrate appears shiny and reflective, only slightly darker than the unperforated gold areas surrounding it (Figure 1c). This appearance is expected considering the high surface coverage of the metal: 65% of the silicon surface is covered with gold. Next, we examined the properties of an identical gold film with silicon nanopillars protruding from the substrate through the holes. We fabricated this structure with metal-assisted chemical etching (MACE),22 using the patterned gold film to anisotropically etch the silicon. This process is described in more detail in the Methods section and shown schematically in Figure 2. The gold acts as a catalyst for the etching of silicon, and thus the gold film sinks into the substrate, creating an array of nanopillars that protrude through holes in the film. The silicon nanopillars are thus automatically aligned to the holes in the metal film in a single step.

Figure 1d,e shows a gold film identical to that shown in Figure 1a,b through which an array of silicon nanopillars protrudes from the substrate 330 nm above the metal film. The change in the optical properties of this surface is dramatic; the patterned area in the etched sample with protruding nanopillars is a deep red color (Figure 1f). We measured the combined specular and diffuse reflection (R) of the goldsilicon surfaces at different angles of incidence. The reflection spectra of the two samples confirms the dramatic change conferred by the nanopillar array (Figure 1g): the perforated film on the planar substrate reflects, on average, 50% of the incident light, whereas the etched sample with protruding silicon nanopillars reflects only 19% of the light. By adding a 50 nm thick silicon nitride antireflection coating, the reflection of the nanopillar sample decreases further, to 10%. Considering that the gold film still occupies 65% of the top surface of the silicon in these samples, the magnitude of the change in the reflectance is surprising. To explain the remarkable optical properties of the film, we next performed detailed simulations of a model of our structure using S4, a freely available frequency modal method software package.23 Figure 3a shows the simulated reflection spectra for a silicon substrate with a metal film with 300 nm wide holes on a 500 nm spacing with a 15 nm thick gold layer, with and without protruding silicon nanopillars. The surface with nanopillars protruding 330 nm above the metal demonstrates much less reflection, confirming our experimental observations. Moreover, Figure 3a also shows the simulated reflection spectra for a structure coated with a 50 nm thick silicon nitride layer, both with and without the embedded metal film. The difference is negligible (2%), suggesting, as hypothesized, that the presence of the metal does not have a significant impact on the optical properties of this architecture. We also simulated the electric field patterns in the structures. Field patterns at an incident wavelength of 550 nm are also shown in Figure 3. While the patterned metal film sitting on top of a planar silicon surface strongly reflects incoming light (Figure 3b), the

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Our design is based on nanopillars with small aspect ratios (∼1:1). These structures have been shown to act as broad-band light “funnels” by strongly coupling and confining light into Mie-like resonances that leak into the substrate through the small volume beneath each pillar.1921 By aligning nanopillars protruding from a substrate through the holes in a metal film, we expected that most of the electric field intensity would be concentrated in the nanopillars and thus not over areas of the substrate covered by the metal. Therefore, we hypothesized that even in metal films with high surface coverage and small holes, the introduction of dielectric nanopillars would substantially reduce the reflection losses from the metal, allowing light to be easily absorbed in the underlying substrate.

Figure 2. Metal-assisted chemical etching process. (a) Process flow illustrating the key steps for fabricating a gold film with protruding silicon nanopillars using metal-assisted chemical etching. A silicon substrate with a patterned gold film is immersed into a solution of hydrofluoric acid and hydrogen peroxide to create the nanopillar array. (b) Detailed schematic of the etching step. The silicon directly beneath the gold layer is oxidized and attacked, resulting in the metal layer sinking into the substrate. The silicon nanopillars are thus self-aligned with the holes in the metal film. NARASIMHAN ET AL.

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nanopillar structure confines light within a Mie-like resonance in the pillar that leaks into the substrate and circumvents the metal almost entirely, as predicted (Figure 3c). We performed further simulations to explore the optical properties of structures with different geometries and materials. One of the most interesting findings from these simulations was the dramatic effect of the nanopillar height on the optical properties of the structure. As shown in Figure 4, a pillar array that protrudes even 50100 nm above a metal film is NARASIMHAN ET AL.

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Figure 3. Detailed optical simulations showing leaky Mielike resonances in gold films with protruding silicon nanopillars. (a) Simulated normal incidence absorption as a function of wavelength for the perforated metal film sitting atop a planar silicon surface (dotted red trace), the metal film with protruding silicon nanopillars (dashed blue trace), the perforated film with protruding silicon nanopillars covered with a 50 nm silicon nitride anti-reflection coating (solid black trace), and a gold-free silicon nanopillar array with a 50 nm silicon nitride coating (dashed black trace). In these simulations, the metal film has 300 nm  300 nm holes on a 500 nm spacing, and the gold is 15 nm thick. The nanopillars also measure 300 nm  300 nm laterally and protrude 330 nm through the holes in the metal film. The surfaces with protruding nanopillars have a simulated reflection lower than that of the perforated films on planar substrates, and the effect of the metal layer on the reflectance spectrum is negligible. (b) Cross section (through the center of a hole) of the simulated electric field intensity with 550 nm incident light for the perforated metal film sitting atop a planar silicon surface (scale bar = 100 nm). Silicon and gold outlines are shown for clarity. Light is strongly reflected from the film. (c) Cross section (through the center of a pillar) of the simulated electric field intensity with 550 nm incident light for the perforated gold film with protruding silicon nanopillars with a silicon nitride coating (scale bar = 100 nm). Silicon, gold, and nitride outlines are shown for clarity. A Mie-like resonance confines light inside the pillar, and the light leaks from the pillar into the substrate, circumventing the metal film.

sufficient to greatly suppress reflection as compared to simply filling the holes in the metal with silicon. We observed this finding experimentally during the etching process. Video S1 in the Supporting Information shows that the surface covered by the patterned metal film undergoes a significant color change from shiny gold to red to dark purple as the etching reaction proceeds and the nanopillars begin to protrude through the metal surface. Other results from our simulations are shown in Figure S1. We found that integrated absorption above 90% is possible even with metal layers 50 nm thick, suggesting that highly absorptive optoelectronic surfaces with extremely high conductivity could be manufactured. Simulations of the width and spacing of the pillars showed that the minimum reflection values correspond to nanopillar arrays with a surface coverage of just less than 50%. Also, high absorption from metalsemiconductor hybrid interfaces is expected in a number of other optical material systems, including gallium arsenide and indium phosphide. While the specific spectral features in each absorption spectrum generally shift with increasing size in any dimension, our simulations show that high absorption in substrates covered by metal films with protruding dielectric nanopillars is possible across a variety of geometries and materials. With these insights in hand, we fabricated three additional samples, varying the width of the gold lines and the etching time to produce metalsilicon nanopillar hybrid surfaces with different geometries, as shown in Figure S2. Figure 5ac shows an electron micrograph, the 5° off-normal incidence absorption spectrum (the smallest angle measurable in the integrating sphere), and average absorption as a function of angle of incidence for our best sample (a digital photograph is provided in Figure S3). This structure has pillars that are 320 nm wide by 150 nm tall with a 500 nm center-to-center spacing. Remarkably, with a 50 nm thick silicon nitride anti-reflection layer, the structure has an average angle-integrated absorption of 97% over the standard reference solar spectrum.24 Further, absorption above 90% is preserved even to angles of incidence as high as 40°. From simulations of the electric field distribution in this structure, we deduce that only 4.2% of the incoming light is absorbed in the metal. Owing to the modal profile of the resonances in the nanopillars, almost all of the interface's absorption takes place in the silicon (see Figure S4). Despite the fact that 60% of the top surface of the silicon is covered with a metal film, the structure demonstrates strong, broad-band absorption across the visible spectrum and at a variety of angles of incidence. All four hybrid surfaces we fabricated had high conductivity while also demonstrating extremely high absorption. Each sample had a sheet resistance of less than 20 Ω/0 (compared to 10 kΩ/0 for the silicon

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Figure 4. Effect of the nanopillar height on simulated reflection. The simulated short-wavelength reflectance from a perforated metal film with silicon filling its holes (dotted red trace) is still very high, whereas reflection drops significantly if the silicon protrudes 50 nm (dashed blue trace) or 100 nm (solid black trace) above the metal surface. For these simulations, we assumed 200 nm square holes with a 450 nm center-to-center spacing in a 50 nm thick metal film. All structures were assumed to be covered with a 50 nm thick silicon nitride coating.

substrates with the native oxide removed). These values were possible owing to the high metal coverage of over 40%. Despite the high metal coverage, all the samples demonstrated more than 89% absorption averaged over the standard reference solar spectrum24 from 400 to 900 nm (compared to 61% for the bare silicon substrate). In fact, the performance of the optoelectronic interfaces we designed is equivalent to placing the highest performing transparent electrodes from the literature atop semiconductors coated with an ideal anti-reflection coating (see Figure S5). To demonstrate the potential of a metalsilicon hybrid nanostructure in an optoelectronic device, we compare the front surface reflectance between 400 and 900 nm of the interface in Figure 5 with the reported front surface reflectance of a PERC-type silicon solar cell with front metal contacts25 in Figure S6. The reference silicon solar cell shows a front surface reflectance of 6.5% averaged over the standard reference solar spectrum compared to 2.8% from the gold silicon hybrid structure. Remarkably, despite its lower reflectance, the metalsilicon hybrid interface has close to 12 times the metal coverage of the reference solar cell (60% versus 5.1%). Even including the calculated 4.2% absorption loss in the metal, the optical losses of the hybrid structure are comparable to those of the silicon solar cell (the absorption losses of the front metal contacts were not reported directly for the reference cell). The advantage of enabling higher metal coverage in a solar cell while maintaining similar optical performance is that the series resistance could be substantially reduced. For example, the lateral resistance in the emitter comprises one-sixth of the total series resistance in the reference PERC solar cell; by providing a high-coverage grid with nanoscale NARASIMHAN ET AL.

Figure 5. Optical characterization of the best performing hybrid metalsilicon nanopillar interface. (a) Tilted-view SEM micrograph (scale bar = 500 nm). In this structure, the nanopillars are 320 nm wide with a 500 nm center-to-center spacing and protrude 150 nm from the 16 nm thick gold film. (b) 5° Off-normal absorption spectrum for bare silicon (dotted red trace), the as-made goldsilicon nanopillar surface shown in (a) (dashed blue trace), and the gold silicon nanopillar surface covered with a 50 nm silicon nitride coating (solid black trace). (c) Absorption of the goldsilicon nanopillar hybrid surface with a 50 nm silicon nitride coating as a function of incident light angle, averaged over the standard hemispherical reference solar spectrum.24 Absorption as high as 97% is observed in this sample, and absorption above 90% is preserved even at high angles of up to 40° from the normal even though 60% of the top surface is covered with gold.

lines, this resistance (0.1 Ω cm2) could essentially be eliminated. With an appropriate metal contact stack, the nearly continuous metal coverage of the metal silicon hybrid interface could thus result in a higher fill factor while maintaining the same short circuit current. VOL. XXX



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DISCUSSION There are a variety of applications in which highcoverage metal films with nanoscale holes would be desirable to provide dense, highly conductive electrical pathways to a semiconductor. These include electrodes for photosensors, solar cells, light-emitting diodes (LEDs), and displays;26 conductive patches for transparent antennas;27 interconnects for fully transparent electronics;28 and even current collectors for transparent batteries.29 However, to date, there has been no way to cover a semiconductor surface with a high fraction of metal without incurring significant reflection loss at the interface. Only plasmonic resonances have been extensively studied for achieving extraordinary transmission through high-coverage metal films,3032 and these resonances are very sensitive to the shape and size of the holes.3335 Plasmonmediated extraordinary transmission is fairly narrowband and polarization-sensitive; even state of the art structures report only 5080% transmission36,37 for certain colors and greatly suppressed transmission in the rest of the spectrum. By contrast, we have shown through simulations and experiments that the strong enhancement of transmission above 90% through metal films created by resonances in semiconductor nanopillars is universal across a wide parameter space of geometries and optically important material systems. While fabrication complexity, ohmic contact, junction resistance, and impurities would all have to be carefully considered, our results provide strong evidence that metal films with protruding dielectric nanostructures could make a compelling candidate system for high-performance interfaces in a variety of optoelectronic applications. Moreover, the process we have designed to fabricate metalsemiconductor hybrid nanostructures is very versatile. The metal grid is automatically selfregistered to the nanopillar array, so no subsequent patterning or alignment is required after the formation

METHODS Fabrication of the Metal Film with Protruding Dielectric Nanopillars by Metal-Assisted Chemical Etching. To fabricate the structure, we started with silicon substrates (n-type, 110 Ω cm, 36 350 μm thick). We removed the native oxide by immersion in a 2% hydrofluoric acid solution. We then diluted ma-N 2405 negative-tone electron-beam lithography resist (Micro Resist Technology) 1:1 with mr-T 1090 thinner (Micro Resist Technology) and spin-coated it onto the silicon pieces at 4000 rpm for 40 s. After spin-coating, we baked the sample on a hot plate at 90 °C for 1 min and exposed an array of square areas with a dose of 240 μC/cm2 in a JEOL JBX-6400FS electronbeam lithography system with a 100 keV beam energy.

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of the photon management structure. All processing occurs at low temperatures, below 90 °C, and the dramatic optical change associated with etching could be useful for end point detection or for monitoring process uniformity. MACE can be used to etch many metalsemiconductor systems, including single-crystal and polycrystalline silicon38 and IIIV substrates39 using aluminum, silver, platinum, palladium, rhodium, and gold catalysts (or combinations thereof).40,41 Etching with thicker metal films, which would demonstrate lower resistivity, is also possible.42 Further, our simulations and experiments have demonstrated a wide design space for strong absorption and high conductivity in metalsemiconductor hybrid nanostructures, which suggests that the structure could tolerate polydispersity in the nanopillar geometry, making scalable random patterning of the metal layer, for example, by nanosphere lithography43 or metal dewetting,44 a viable option. It is also possible that by tuning the pattern of the metal grid and the photonic properties of the dielectric resonators, the architecture could harness photonic crystal effects and be useful not only for high absorption and coupling but also for extraordinary reflection, for example, as an intermediate reflector in a tandem solar cell45 or as a light-extracting structure for LEDs.46

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However, the contact-emitter resistance and the surface passivation of the nanostructure would need to be carefully considered to ensure improved efficiency.

CONCLUSION Our simulations and experiments have confirmed that metalsemiconductor nanopillar hybrid structures can exhibit high conductivity with robust, broad-band absorption across a very wide parameter space of materials and geometries. In our best sample, we observed 97% average absorption with a sheet resistance of only 16 Ω/0. More importantly, we have shown that in a hybrid optoelectronic interface, the optical absorption profile of the photon management structure can be used to greatly enhance transmission through a high-coverage metal nanowire network. These results suggest a new paradigm wherein transparent electrodes and photon management textures should be designed and fabricated together to create high-performance optoelectronic interfaces.

We developed the pattern by immersion in Microposit MF-319 (DOW Chemical) for 30 s, followed by a water rinse and drying with a nitrogen gun. We next prepared the sample for wet etching by cleaning it in an RF plasma system for 10 s (Plasma-Prep, 2% O2 and 98% Ar) to descum the resist and leave the surface of the silicon oxygen-terminated. We evaporated a nanoporous 16 nm thick gold film onto the sample at 0.5 Å/s in a Kurt J. Lesker LAB 18 electron-beam evaporator system. We then immersed the patterned, metalized silicon substrate into a solution of hydrofluoric acid (12.04 M) and hydrogen peroxide (0.82 M) for 610 s. Though there is some disagreement as to the exact mechanism of MACE, a proposal that

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H2 O2 þ 2Hþ f 2H2 O þ 2hþ

(1)

Si þ nhþ þ 6HF f H2 SiF6 þ nHþ þ 0:5(4  n)H2 v

(2)

In the first step, the hydrogen peroxide is decomposed to water at the metal surface and in the process transfers holes to the silicon via the metal. Next, the hole-rich silicon, now in an oxidized state, reacts with the hydrofluoric acid to form the soluble species H2SiF6 and hydrogen gas. Etching proceeds anisotropically directly beneath the metal, and the metal sinks into the nanostructure, resulting in a patterned metal film with a self-aligned protruding array of nanopillars in a single step. Metal-assisted chemical etching is possible with both thin47 and thick metal films.42 We rinsed the samples with deionized water after etching. We then removed the resist using heated N-methyl pyrrolidone and heated acetone, sometimes with sonication. For some samples, we used a PlasmaTherm Versaline high-density plasma-enhanced chemical vapor deposition system to perform a low-temperature (90 °C) deposition of silicon nitride. Optical Measurements. We used an integrating sphere setup (painted with Spectraflect paint) with a white light source and monochromator, as reported elsewhere,10 to measure the total (specular and diffuse) reflection spectra of the goldsilicon surfaces at different angles of incidence. The reflectance was measured over angles of incidence ranging from 5 to 45° such that specular reflection from the sample would not escape the integrating sphere through the sphere's aperture. Transmission through the samples was below the measurement threshold of the setup. The average reflectance or absorptance was calculated as a weighted average over the standard reference solar spectrum24 from 400 to 900 nm. Optical Simulations. We conducted electromagnetic simulations using S4, a free frequency modal method solver.23 We used standard refractive index values from two online sources, namely, http://refractiveindex.info/ for the metals and silicon nitride and http://www.filmetrics.com/refractive-index-database/ for the semiconductors (Si, GaAs, and InP). We used a plane wave source with equal parts s- and p-polarized light. We used 24 spatial frequency modes in most simulations to calculate reflection spectra and the fields in our structure with enough resolution. For finer resolution in some simulations, we increased the number of modes to 37 or 100. Data points were taken at wavelengths 10 nm apart from 400 to 900 nm. Fields were extracted on a 5 nm grid spacing. Electrical Measurements. Our structure included two large gold pads electrically connected to each side of the patterned metal film. We applied a conductive adhesive to each pad and used a two-point probe measurement to measure the resistance (R) of the sample. The sample size was measured in an optical microscope, and the sheet resistance (Rs) was calculated using the expression Rs = R  W/L, where W and L are the width of the pads and the distance between the pads, respectively. Conflict of Interest: The authors declare no competing financial interest. Supporting Information Available: The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.5b04034. Video of the MACE process (AVI) Additional optical simulations and all data collected from fabricated samples (PDF) Acknowledgment. This material is based upon work supported by the Department of Energy through the Bay Area Photovoltaic Consortium (BAPVC) under Award Number DE-EE0004946 and was also supported by the Stanford Global Climate and Energy Project (GCEP). The authors would like to acknowledge the support of the staff at the Stanford Nano Shared Facilities and the Stanford Nanofabrication Facility, especially R. Tiberio and C. Knollenberg. V.K.N. would like to thank the International Fulbright Science and Technology Fellowship

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Program for support, and he would also like to thank P.-C. Hsu and I. Karakasoglu for helpful discussions. V.K.N. conceived the structure. V.K.N., T.M.H., R.A.L., and Y.C. designed and reviewed results from the experiments. V.K.N. conducted the etching, AR coating, and characterization experiments, analyzed the results, and performed electromagnetic simulations. T.M.H. and R.A.L. provided some silicon wafers. V.K.N. and T.M.H. optimized the gold thickness and surface treatment for the MACE process and performed sheet resistance measurements. V.K.N. prepared the figures with layout and design assistance from R.A.L. and T.M.H. All authors helped prepare the text of the manuscript.

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explains most experimental observations is that the reaction proceeds by a two-step mechanism:22

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