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Transparent Metallic Fractal Electrodes for Semiconductor Devices Farzaneh Afshinmanesh, Alberto Curto, Kaveh Milaninia, Niek F. van Hulst, and Mark Brongersma Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl501738b • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014
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Nano Letters
Transparent Metallic Fractal Electrodes for Semiconductor Devices Farzaneh Afshinmanesh 1, Alberto G. Curto 1,2, Kaveh M. Milaninia 1, Niek F. van Hulst 2,3, Mark L. Brongersma 1,* 1
Geballe Laboratory for Advanced Materials, 476 Lomita Mall, Stanford, California 94305-4045 ICFO – Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain 3 Instituciό Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain 2
* To whom correspondence should be addressed. E-mail: [email protected]. Abstract – Nanostructured metallic films have the potential to replace metal oxide films as transparent electrodes in optoelectronic devices. An ideal transparent electrode should possess a high, broadband, and polarization-independent transmittance. Conventional metallic gratings and grids with wavelength-scale periodicities, however, do not have all of these qualities. Furthermore, the transmission properties of a nanostructured electrode need to be assessed in the actual dielectric environment provided by a device, where a high-index semiconductor layer can reflect a substantial fraction of the incident light. Here we propose nanostructured aluminum electrodes with space-filling fractal geometries as alternatives to gratings and grids and experimentally demonstrate their superior optoelectronic performance through integration with Si photodetectors. As shown by polarization and spectrally resolved photocurrent measurements, devices with fractal electrodes exhibit both a broadband transmission and a flat polarization response that outperforms both square grids and linear gratings. Finally, we show the benefits of adding a thin silicon nitride film to the nanostructured electrodes to further reduce reflection. Keywords – Nanostructured transparent electrodes, Space-filling fractals, Metallic gratings, Si optoelectronics Main Text - Transparent conducting oxides (TCOs) such as indium tin oxide (ITO) or zinc oxide (ZnO) play an important role in technologies such as solar cells, light emitting diodes, and electronic displays for which large area electronic and optical access are required. Despite their success, there is a growing interest in replacing these materials to reduce the cost of electrodes, to increase their mechanical flexibility, to avoid device degradation when combined with organic materials, and to enhance their optical transmission1-4. Importantly, any such candidate needs to simultaneously preserve excellent optical and electronic properties when integrated in optoelectronic devices. One promising electrode technology that has recently emerged employs metallic nanostructures arranged in periodic, aperiodic, or random arrays5-7. Such high-conductivity metal nanowire arrays can have advantageous electronic and optical properties over conventional (e.g., ITO) and alternative (e.g., carbon nanotube meshes and graphene) electrode materials5,8-9. Unlike conventional electrode materials, for which the achievement of a lower sheet resistance typically comes at the expense of a lower optical transmission, nanostructured metal electrodes provide a more desirable trade-off between these quantities5,9. As the electrical conductivity of noble metals
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tends to be about 2 orders of magnitude higher than for transparent oxides, various designs can provide a very low sheet resistivity (few / ). However, more work is needed to identify the best possible design in terms of the optical transmission, especially for the case where such electrodes are placed on high refractive index semiconductor materials. Such studies would be of great value to engineers developing the next generation of solar cells and optoelectronic devices. This is particularly relevant in light of the recent progress in nanofabrication techniques that enable large-area, low-cost application of complex nanostructured metallic electrodes, including nano-imprint 10-11, rolling mask 12, and nanosphere13 lithography techniques, solution processing or lamination of metallic nanowire meshes5,7, and electrospinning9. These methods offer excellent control over the nanostructure size, geometry and in some cases also the spatial arrangement. Moreover, in solar cell technologies, metallic contacts of silver (Ag) and aluminum (Al) are already commonplace, significantly lowering the barrier to the introduction of next-generation nanostructured metallic electrodes. In this work we analyze the optical transmittance of different nanostructured electrode designs, from simple gratings and grids to complex fractal-shaped electrodes. We first demonstrate that linear gratings exhibit a high, yet polarization-dependent transmission while square grids with similar geometrical parameters show a low, yet polarization-independent transmission. To obtain high polarization-independent transmission, more advanced electrode designs are necessary. Fractals have been studied14-18 and applied commercially19 in the microwave regime as broadband or multi-band electromagnetic antennas. In the optical and near infrared regime, fractal antennas have been proposed for broadband near-field concentration20-21 and enhanced transmission and resolution22. Here, we demonstrate nanostructured metallic films with fractal-shaped slits as transparent optical electrodes with high polarization-independent transmission. The proposed fractal slit patterns, known as space-filling curves, efficiently cover the entire surface of the electrode. We experimentally compare the optoelectronic performance of these fractal electrodes by placing them on top of a silicon (Si) substrate to form a planar back-to-back metalsemiconductor-metal Schottky detector. Through photocurrent measurements, we demonstrate that space-filling fractal networks can substantially outperform grids and slightly outperform gratings while providing a polarization-independent response. A space-filling fractal electrode is built up from a set of locally parallel vertical and horizontal metallic lines. For this reason, the essential physics of their behavior appears already in simpler linear gratings consisting of parallel wires. It is therefore of value to analyze this basic electrode configuration before we analyze the more complex fractal structures. First, we determine the spectral response of a linear grating and compare its optical performance in an air environment to the case when it is placed on a substrate made of silica glass (SiO2) or Si. We find that the substrate critically affects both the grating transmission and losses in the metal. We model the grating using a finite element method (COMSOL Multiphysics) with material properties from Ref. 23. We consider an Al grating with thickness h = 40 nm, periodicity P = 450 nm, and nanowire width w = 100 nm (Figure 1). We compare the polarization-averaged transmission and metal losses of this grating for illumination from the air side in three situations: freely standing in air, on a glass substrate and on a silicon substrate (blue, green and red lines in Figure 1a). For the cases of air and on a glass substrate, transmission is high. The situation is rather different when a Si substrate is present, as in many optoelectronic devices; a high reflectivity of around 45% is found due to the high refractive index of Si in this wavelength range (3.5 < nSi < 6). A similarly high reflectivity is also observed for a bare Si substrate (solid gray line). A lower transmission is observed for the case of a square grid (Figure 1b), and losses in the metal are higher compared to a grating with the same period. Finally, the metal losses in the gratings and grids tend to be lower for structures on a silicon substrate than on the other media.
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To better understand the transmission through optically thin gratings, we also analyze these results for a normally-incident light wave with the electric field perpendicular to the nanowires (TM polarization) and parallel to them (TE polarization) as shown in Figure 1c. The main process for the transfer of optical energy through the gratings is the excitation of fundamental TM or TE gap modes between two parallel metallic nanowires. The TM gap mode does not exhibit a cut-off, which implies a broadband transmission. The TE gap mode approaches cut-off for the longer wavelengths. However, a sharp cut-off for TE does not exist since the Al layer is very thin and the evanescent decay length of the TE gap mode is larger than the Al thickness, which facilitates evanescent coupling24. For both TM and TE excitations and all substrates, there are abrupt changes in transmission and enhancements in the metal absorption due to the excitation of surface plasmons and 1 diffraction orders (at 0 = P = 450 nm and red-shifted to 0 = P . nsubstrate = 650 nm for glass) along the grating-air and grating-substrate interfaces. For 0 < P and for both polarizations, both zero-order and the 1 diffraction orders exist in transmission and reflection. For P < 0 < P . nsubstrate , the 1 diffraction orders are present in transmission into the substrate but not in reflection in air. For 0 > P . nsubstrate, the 1 diffraction orders cannot be excited and optical energy is transferred only through fundamental TM and TE gap modes. In the case of a grid, due to the presence of square apertures, transmission is more similar to a TE grating response at the longer wavelengths and more similar to a TM grating response at the shorter wavelengths. The averaged transmission of a grid over different substrates is lower than a grating with similar geometric parameters due to modal cut-off and also higher metal coverage. Many of the spectral features explained above for linear gratings are also present for grids. The metal loss peaks are more pronounced for the grid because surface waves can couple to localized nanowire resonances in one direction and propagate along nanowires in the orthogonal direction. A more detailed analysis of transmission through gratings and grids is provided in the Supplementary Information (Supplementary Figures S1-S3). As the periodicity of a grating or a grid increases for a constant wire width, the transmission into the silicon substrate averaged over wavelength and polarization increases (Figure 1d). Despite the polarization-dependent transmission of a grating, the averaged transmission of an optically thin grating is always higher than that of a grid with similar geometric parameters. Moreover, if we compare gratings and grids with similar metal filling ratios at a fixed wire width (i.e., comparing different periods), both geometries provide a similar averaged transmission but a different sheet resistance; a grid has a larger periodicity than a grating with a similar filling ratio and it will possess a higher sheet resistance, proportional to the period (RSH = (/h)(p/w), where is the metal resistivity). More advanced electrode designs are necessary to obtain high, polarization-independent transmission. In this Letter, we demonstrate experimentally that nanostructured metallic films with space-filling fractal-shaped slits can serve as alternative transparent electrode geometries that satisfy the requirements above. Examples of such fractal patterns that can effectively cover a surface with a dense pattern of metal lines and slits are Hilbert and Peano curves25-27 (Figure 3c,d). These continuous, two-dimensional curves can be thought of as the path of a continuously moving point that never crosses itself and efficiently covers the surface of the electrode. They naturally have as many horizontal as vertical line segments, implying a polarization-independent response. Additionally, by avoiding the square apertures present in grids, they do not suffer the decrease in transmission due to modal cut-off at long wavelengths observed in square grids. We experimentally compare the performance of our proposed fractal-shaped electrodes with gratings and grids integrated on a Si photodetector through a set of polarization and spectrally
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resolved photocurrent measurements. The measurement platform consists of a patterned Al electrode integrated on a Si substrate, forming a planar back-to-back metal-semiconductor-metal Schottky detector (Figure 2). Light impinges on the electrode from the air side. The patterned electrode transmits light into the silicon substrate, which generates electron-hole pairs. These charges are separated and extracted via the lateral electrodes to produce a photocurrent. The generated photocurrent is a direct measure of the electrode’s ability to transmit light. This photocurrent platform allowed us in the past to obtain very good agreement between simulated and experimental photocurrent spectra 28-30 and we now leverage it to characterize the proposed electrodes. To obtain the wavelength- and polarization-resolved photocurrent responses of the different nanostructured electrodes, we use a supercontinuum white light source spectrally filtered by an acousto-optic tunable filter. The beam then passes through a linear polarizer and a half-wave plate to control the incident polarization. Light is gently focused on the device into a ~1.5 m-diameter spot with a microscope objective (50x, 0.42 NA). The device is mounted on a piezo-stage and is electrically reverse biased at 1V using a set of wire bonds. For sensitive detection of the photocurrent, the laser beam is modulated with a chopper and the modulated photocurrent is amplified and detected with a lock-in amplifier. At each polarization and wavelength, a photocurrent image of a device is obtained by raster scanning the laser beam over it. The device responsivity (in units of A/W) at each polarization and wavelength is defined as the maximum spatial photocurrent normalized to the input laser power, found by raster scanning the laser beam. We have checked the linearity of the detector response versus the illumination power at several wavelengths across the spectral range of interest (See Figure 4S). Based on this observation, photocurrent measurements afford a simple quantitative comparison of the transmission properties of different electrode geometries at any wavelength of interest. In analyzing the spectral dependence of the photocurrent, it worth noting that the internal quantum efficiency (IQE) of the detectors can be wavelength dependent as different wavelengths of light generate different spatial distributions of the photogenerated carriers. As such the collection efficiencies for the carriers generated at different wavelengths can be different. The wavelength-dependence in the carrier collection will in general depend on the surface/bulk recombination processes that can suppress the collection efficiencies primarily at shorter/longer wavelengths. These can be processes are critically dependent on the processing and device configuration and the spectral properties of the photocurrent are not necessarily identical to the spectral transmission properties. For our devices, we found that the spectral dependence of the IQE at the applied reverse bias of 1V is quite flat across the considered wavelength range from 450 nm – 750 nm (Figure 5S). This indicates that photocurrent spectra can be used to get a good 1st order impression of the spectral transmission properties of our electrodes. To fabricate the nanostructured electrodes, we start with an n-type silicon wafer that is initially immersed in 2% hydrofluoric acid for a few seconds to remove the native oxide. Then, 3 nm of Cr and 40 nm of Al is deposited on the silicon wafer by electron beam evaporation. The wafer is covered with a positive resist (PMMA 950K) and the nanowire networks and contact pads are defined by electron beam lithography (JEOL JBX 6300, 100 keV). They are subsequently etched by Ar-ion sputtering. The PMMA mask is then removed by soaking the wafer in heated 1165 remover for 24 hours followed by ultrasonication and then O2 plasma cleaning. Scanning electron microscopy (SEM) images of the e-beam fabricated linear grating, grid, Hilbert and Peano fractals are shown in Figures 3a-d. The area of each electrode geometry is ~ 12 m 12 m. The Al nanowire width is 100 nm in all cases, and the grating and grid periodicities and the minimum spacing between two parallel nanowires for fractals (p in Figure 2) is 450 nm. As it will be shown
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later, we choose these wire width and spacing values to obtain spatially uniform photocurrents, and to avoid diffraction effects in reflection on the air side, respectively. All our devices offer broadband responsivities from 450 to 750 nm, as indicated by the responsivity maps of each device as a function of polarization angle and wavelength in Figure 3eh. Similar to the grid, the Hilbert and Peano fractals show polarization-independent responses, yet with much higher average responsivities. The polarization and spectrally averaged responsivity of these devices are also shown in Figure 3e-h. The averaged responsivities of a Hilbert and a Peano fractal are 40% and 34% higher than a grid and 7% and 2% higher than a grating, respectively. To gain direct quantitative information of the performance of one electrode over another, one can divide the photocurrent spectra from two relevant electrodes. An example is shown in Supplementary Figure 6S, where the polarization and wavelength dependent response of various electrodes is compared to that of a continuous 40 nm thick Al film electrode. Normalizing the measured photocurrents of the Hilbert fractal to that of an unpatterned Al electrode, we obtain on average more than 21x enhancement in photocurrent by patterning the electrode with fractal nanowires (Supplementary Figure 6S). The physics of light transmission through fractal networks is similar to the case of gratings. A strong transmission is associated with the excitation of fundamental TM or TE propagating gap modes between two parallel metallic wires. A simple way to visualize this is by decomposing a fractal structure into regions where metallic wires are parallel in horizontal and vertical directions. A decomposed Hilbert fractal based on this principle is shown in Figures 4a,b. We can view each case as a group of finite size gratings with different numbers and lengths of nanowires. Horizontal gratings primarily transmit vertically-polarized light whereas vertical ones primarily let horizontally-polarized light to pass through. Optical microscopy images obtained in reflection for different polarizations of illumination (Figures 4c,d, where w = 200 nm and p parameter = 450 nm) display complex patterns with dark and bright areas; the dark areas in the reflection image match well the regions in the decomposed fractal structure where we expect high transmission due to the excitation of a TM propagating gap mode. By making the metallic wires of this fractal narrower (w = 150 nm, hence corresponding to a larger gap), the contrast between dark and bright regions decreases in the reflection images (Figures 4e,f) due to better coupling to the TE gap mode. Dark regions featuring a lower reflectivity also correspond to regions of higher transmission and higher photocurrent. In the spatial photocurrent maps of this fractal at 0 = 600 nm (Figure 5a-c), the regions of high photocurrent for two orthogonal polarizations follow the regions of low optical reflection in Figures 4e,f. For this fractal, the difference in photocurrent between the dark and bright red regions at 0° and 90° polarization angels is about 5%. The spatial photocurrent at 45° is uniform and is the average of the photocurrents at 0° and 90°. A uniform spatial transmission and photocurrent is in general desirable. This can be achieved by using narrower wires, as demonstrated by the relatively uniform reflection images of this fractal for w = 100 nm (Figure 4g,h, structure also used in Figure 3c). In general, light transmission through each grating-like section of a fractal is lower than a similar grating because the nanowires are shorter resulting in light scattering at the nanowire edges. In addition, the number of parallel nanowires is smaller, which reduces the transmission efficiency. However, unlike the grid, there is no modal cut-off present for the fractal nanowire networks. To obtain the optimum geometrical parameters of a fractal for an application of interest, the geometry parameters of the grating (P, w and h) can be optimized first. Then the optimized parameters can be readily used for fractals to obtain a high polarization-independent transmission, which has a similar spectral trend as the polarization-averaged transmission of a grating.
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Finally, the transmission into silicon of our nanostructured electrodes can be further improved by reducing reflection. Silicon has a high reflectivity of about 40% in the visible and a properly designed free-standing metal grating is highly transmissive (Figure 1a). However, by placing a transparent grating on a silicon substrate, more light is reflected than by a bare silicon surface (gray and red curves in Figure 6). To reduce this reflection and enhance transmission into silicon, we propose to combine our electrodes with a thin film of silicon nitride (Si3N4) acting as an antireflection coating (inset of Figure 6). By adding a 60 nm thick layer of silicon nitride to a grating, our simulations show that reflection drops well below the value for Si (see purple curve in Figure 6). This thickness corresponds to the thickness of a conventional anti-reflection coating on Si cells. Since the physics of light transmission through fractals is very similar to gratings, by integrating a metallic fractal with a silicon nitride layer, we expect to obtain an anti-reflective, transparent, broadband, and polarization-independent electrode. In summary, we have introduced nanostructured metallic films with fractal-shaped slits as new transparent electrode geometries that have high broadband and polarization-independent transmission. Through integration with silicon photodetectors and photocurrent measurements, we have shown the superior performance of the fractal geometries as compared to gratings and grids with similar geometrical parameters. The proposed electrodes can be integrated in cameras and displays, where the typical size of a pixel is similar to the demonstrated electrodes. In solar applications, these fractal networks could play a dual functionality both as a transparent electrode and as an efficient light-trapping layer for thin film cells. Adding a mesh of mesoscale metal wires can further improve the sheet resistance of the proposed electrodes for large area applications 31. Finally, we have shown that grating design principles can be used to systematically design more complex electrodes such as fractals for many optoelectronic applications.
Competing Financial Interests: The authors declare no competing financial interest. Acknowledgement We greatly acknowledge support from Bay Area Photovoltaics Consortium funded by the U.S. Department of Energy.
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References: (1) Hecht, D. S.; Hu, L; Irvin, G. Emerging transparent electrodes based on thin films of carbon nanotubes, graphene, and metallic nanostructures. Adv. Mater. 2011, 23, 1482513. (2) Kang, M. G.; Guo, L. J. Nanoimprinted semitransparent metal electrodes and their application in organic light-emitting diodes. Adv. Mater. 2007, 19, 1391–1396. (3) Wu, Z. C.; Chen, Z. H.; Du, X.; Logan, J. M.; Sippel, J.; Nikolou, M.; Kamaras, K.; Reynolds, J. R.; Tanner, D. B.; Hebard, A. F.; Rinzler, A. G. Transparent, Conductive Carbon Nanotube Films. Science 2004, 305, 1273–1276. (4) Ellmer, K. Past achievements and future challenges in the development of optically transparent electrodes. Nat. Photon. 2012, 6, 809 – 817. (5) Lee, J. Y.; Connor, S. T.; Cui, Y.; Peumans, P. Solution-processed metal nanowire mesh transparent electrodes. Nano Lett. 2008, 8, 689–692. (6) Hu, L.; Kim, H. S.; Lee, J. Y.; Peumans, P.; Cui, Y. Scalable Coating and Properties of Transparent, Flexible, Silver Nanowire Electrodes. ACS Nano 2010, 4, 2955 – 2963. (7) Gaynor, W.; Burkhard, G.F.; McGehee, M.D; Peumans, P. Smooth nanowire/polymer composite transparent electrodes. Adv. Mater. 2011, 23, 2905 – 2910. (8) van de Groep, J.; Spinelli, P.; Polman, A. Transparent Conducting Silver Nanowire Networks. Nano Lett. 2012, 12, 3138-3144. (9) Wu, H.; Kong, D.; Ruan, Z.; Hsu, P.; Wang, S.; Yu, Z.; Carney, T. J.; Hu, L.; Fan, S.; Cui, Y. A transparent electrode based on a metal nanotrough network. Nature Nanotechnol. 2013, 8, 421 – 425. (10) Kang, M. G.; Kim, M. S.; Kim, J.; Guo, L. J. Organic solar cells using nanoimprinted transparent metal electrode. Adv. Mater. 2008, 20, 4408 – 4413. (11) Kang, M. G.; Park, H. J.; Ahn, S. H.; Xu, T.; Guo, L. J. Toward low-cost, highefficiency, and scalable organic solar cells with transparent metal electrode and improved domain morphology. IEEE J. Sel. Top. Quantum Electron. 2010, 16, 1807 – 1820. (12) Kobrin, B; Barnard, E. S.; Brongersma, M. L.; Kwak, M. K.; Guo, L. J. Rolling mask nanolithography—the pathway to large area and low cost nanofabrication. Proc. SPIE 2012, 8249, 82490O. (13) Cheng, K.; Cui, Z.; Li, Q.; Wang, S.; Du, Z. Large-scale fabrication of a continuous gold network for use as a transparent conductive electrode in photo-electronic devices. Nanotechnol. 2012, 23, 425303. (14) Zhu, J.; Hoorfar, A.; Engheta, N. Peano antennas. IEEE Antennas Wireless Propag. Lett. 2004, 3, 71 – 74. (15) McVay, J.; Hoorfar, A.; Engheta, N. Space-filling curve RFID tags. IEEE Radio and Wireless Symposium 2006, 199 – 200. (16) Werner, D.H.; Ganguly, S. An overview of fractal antenna engineering research. IEEE Antennas and Propag. Mag., 2003, 45, 1, 38 – 57. (17) McVay, J.; Hoorfar, A.; Engheta, N. Peano high-impedance surfaces. Radio Sci. 2005, 40, RS6S03. (18) Puente, C.; Romeu, J.; Pous, R.; Garcia, X.; Benitez, F. Fractal multiband antenna based on the Sierpinski gasket. Electron. Lett., 1996, 32, 1, 1 – 2. (19) www.fractenna.com; www.fractus.com (20) Volpe, G.; Volpe, G.; Quidant, R. Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet. Opt. Express, 2011, 19, 3612 – 3618. (21) Sederberg, S.; Elezzabi, A. Sierpinski fractal plasmonic antenna: a fractal abstraction of the plasmonic bowtie antenna. Opt. Express, 2011, 19, 10456 – 10461.
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(22) Matteo, J.; Hesselink, L. Fractal extensions of near-field aperture shapes for enhanced transmission and resolution. Opt. Express. 2005, 13, 636 – 647. (23) Rakic, A. D.; Djurišic, A. B.; Elazar, J. M.; Majewski, M. L.; Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Opt 1998 , 37, 5271–83. (24) Catrysse, P. B.; Fan, S. Nanopatterned Metallic Films for Use As Transparent Conductive Electrodes in Optoelectronic Devices. Nano Lett. 2010, 10, 2944 – 2949. (25) Hilbert, D. Über die stetige Abbildung einer Linie auf ein Flächenstück. Mathematische Annalen, 1891, 38, 459 – 460. (26) Peano, G. Sur une courbe, qui remplit toute une aire plane. Mathematische Annalen, 1890, 36, 157 – 160. (27) Sagan, H. Space-Filling Curves. Springer-Verlag 1994, ISBN 0387942653. (28) Afshinmanesh, F; White, J. S.; Cai, W.; Brongersma, M. L. Measurement of the polarization state of light using an integrated plasmonic polarimeter. Nanophotonics. 2012, 1(2), 125 – 129. (29) Barnard, E. S.; Pala, R. A.; Brongersma, M. L. Photocurrent mapping of near-field optical antenna resonances. Nature Nanotechnol, 2011, 6, 588 – 593. (30) Pala, R. A.; White, J. S.; Barnard, E. S.; Liu, J.; Brongersma, M. L. Design of Plasmonic Thin-Film Solar Cells with Broadband Absorption Enhancements. Adv. Mater, 2009, 21, 3504 – 3509. (31) Hsu, P.; Wang, S; Wu, H.; Narasimhan, V.; Kong, D.; Lee, H. R.; Cui, Y. Performance enhancement of metal nanowire transparent conducting electrodes by mesoscale metal wires. Nat. Commun., 2013, 4, 10.1038/ncomms3522.
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Figures
Figure 1. Nanostructured metals as transparent electrodes on low and high refractive index substrates. (a, b) Simulated polarization-averaged transmission and loss in the metal wires of an Al grating and an Al square grid placed on different substrates. The different colors of the curves show different substrates with blue, green, and red corresponding to a freestanding grating, a grating on glass and a grating on Si, respectively. The periodicity (P) of the grating and grid is 450 nm, the nanowire width (w) is 100 nm, and the Al thickness (h) is 40 nm. For reference, transmission into silicon (solid gray line) and into glass (dash-dotted gray line) without any metallic structures on the top shows the original transmission of the substrates. A transmission of 1 corresponds to perfect (i.e. 100%) transmission. (c) Simulated TM and TE transmission of a grating on glass and silicon. (d) Simulated wavelength-and-polarization-averaged transmission into silicon as a function of periodicity for Al gratings and grids (w = 100 nm), averaged over the 450-1000 nm spectral range. The solid gray line shows the averaged transmission into bare silicon, without any nanostructures.
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Figure 2. A planar Al-Si-Al Schottky photodetector with an electrode patterned with a Hilbert fractal. The light transmitted through the fractal electrode generates electron-hole pairs that are extracted as photocurrent. The blown-up image shows the main geometrical parameters defining the fractal pattern, where w is the width of the nanowire and p is the spacing between two adjacent parallel nanowires.
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Figure 3. Performance of different electrode geometries. Scanning electron microscopy images of Al electrodes patterned with (a) a linear grating, (b) a grid, (c) a Hilbert fractal, and (d) a Peano fractal. The width of the Al nanowires is 100 nm in all images. The periodicity of the grating and the grid and p parameter defined in Figure 2 for fractals is 450 nm. (e)-(h) Measured responsivity for each electrode as a function of the illumination polarization and wavelength. 0° and 90° linear polarization angles correspond to incident electric field being normal (TM) and parallel (TE) to the grating nanowires, respectively. Wavelength-and-polarization-averaged responsivities of grating, grid, Hilbert fractal, and Peano fractal electrodes are 0.144 A/W, 0.110 A/W, 0.154 A/W, and 0.147 A/W, respectively. Note that to allow direct comparison between simulated transmission and measured responsivity, the simulated transmission of an electrode must be multiplied by λ0e/hc to be equivalent to the measured responsivity, where e is the electron charge, h is Planck’s constant and c is the speed of light in vacuum.
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Figure 4. Spatial decomposition of a fractal electrode into perpendicular directions. (a,b) Hilbert fractal (inset) decomposed into its constituent vertical and horizontal lines. The red arrows show directions of favorable electric fields in each case. (c-h) Optical reflection microscopy images of Hilbert fractals with different wire width for illumination under two orthogonal linear polarizations. Top row corresponds to horizontal polarization and bottom row to vertical polarization. The spacing parameter p (defined in Figure 2) is 450 nm in all of them and the nanowire width (w) decreases from left to right: w = 200 nm in (c,d) 150 nm in (e,f) and 100 nm in (g,h). Decreasing wire width results in more uniform spatial reflection and transmission. For wire width w = 100 (used in Figure 3c), transmission is relatively uniform resulting in a spatially homogenous photocurrent.
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Figure 5. Spatial distribution of photocurrent for a Hilbert fractal electrode with wide nanowires. Photocurrent images are recorded under incident linear polarization angles of 0, 45, and 90° at = 600 nm for fractals with spacing p = 450 nm and nanowire width w = 150 nm. For this nanowire width, the difference between dark and light red regions is around 5%. Each photocurrent map is normalized to its own maximum. Corresponding optical reflection images are shown in Fig. 4e,f.
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Figure 6. A silicon nitride film reduces reflection losses into a silicon substrate. Simulations of optical reflection under normal incidence for an unpatterned silicon substrate (solid gray curve), a silicon substrate covered with an aluminum grating with P = 450 nm and w = 100 nm (red), and a silicon substrate covered with both an aluminum grating and a silicon nitride layer as an anti-reflection coating (purple) with geometry parameters shown in the inset.
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Transparent Metallic Fractal Electrodes for Semiconductor Devices Farzaneh Afshinmanesh, Alberto Curto, Kaveh Milaninia, Niek F. van Hulst, and Mark Brongersma Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl501738b • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014
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Transparent Metallic Fractal Electrodes for Semiconductor Devices Farzaneh Afshinmanesh 1, Alberto G. Curto 1,2, Kaveh M. Milaninia 1, Niek F. van Hulst 2,3, Mark L. Brongersma 1,* 1
Geballe Laboratory for Advanced Materials, 476 Lomita Mall, Stanford, California 94305-4045 ICFO – Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain 3 Instituciό Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain 2
* To whom correspondence should be addressed. E-mail: [email protected]. Abstract – Nanostructured metallic films have the potential to replace metal oxide films as transparent electrodes in optoelectronic devices. An ideal transparent electrode should possess a high, broadband, and polarization-independent transmittance. Conventional metallic gratings and grids with wavelength-scale periodicities, however, do not have all of these qualities. Furthermore, the transmission properties of a nanostructured electrode need to be assessed in the actual dielectric environment provided by a device, where a high-index semiconductor layer can reflect a substantial fraction of the incident light. Here we propose nanostructured aluminum electrodes with space-filling fractal geometries as alternatives to gratings and grids and experimentally demonstrate their superior optoelectronic performance through integration with Si photodetectors. As shown by polarization and spectrally resolved photocurrent measurements, devices with fractal electrodes exhibit both a broadband transmission and a flat polarization response that outperforms both square grids and linear gratings. Finally, we show the benefits of adding a thin silicon nitride film to the nanostructured electrodes to further reduce reflection. Keywords – Nanostructured transparent electrodes, Space-filling fractals, Metallic gratings, Si optoelectronics Main Text - Transparent conducting oxides (TCOs) such as indium tin oxide (ITO) or zinc oxide (ZnO) play an important role in technologies such as solar cells, light emitting diodes, and electronic displays for which large area electronic and optical access are required. Despite their success, there is a growing interest in replacing these materials to reduce the cost of electrodes, to increase their mechanical flexibility, to avoid device degradation when combined with organic materials, and to enhance their optical transmission1-4. Importantly, any such candidate needs to simultaneously preserve excellent optical and electronic properties when integrated in optoelectronic devices. One promising electrode technology that has recently emerged employs metallic nanostructures arranged in periodic, aperiodic, or random arrays5-7. Such high-conductivity metal nanowire arrays can have advantageous electronic and optical properties over conventional (e.g., ITO) and alternative (e.g., carbon nanotube meshes and graphene) electrode materials5,8-9. Unlike conventional electrode materials, for which the achievement of a lower sheet resistance typically comes at the expense of a lower optical transmission, nanostructured metal electrodes provide a more desirable trade-off between these quantities5,9. As the electrical conductivity of noble metals
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tends to be about 2 orders of magnitude higher than for transparent oxides, various designs can provide a very low sheet resistivity (few / ). However, more work is needed to identify the best possible design in terms of the optical transmission, especially for the case where such electrodes are placed on high refractive index semiconductor materials. Such studies would be of great value to engineers developing the next generation of solar cells and optoelectronic devices. This is particularly relevant in light of the recent progress in nanofabrication techniques that enable large-area, low-cost application of complex nanostructured metallic electrodes, including nano-imprint 10-11, rolling mask 12, and nanosphere13 lithography techniques, solution processing or lamination of metallic nanowire meshes5,7, and electrospinning9. These methods offer excellent control over the nanostructure size, geometry and in some cases also the spatial arrangement. Moreover, in solar cell technologies, metallic contacts of silver (Ag) and aluminum (Al) are already commonplace, significantly lowering the barrier to the introduction of next-generation nanostructured metallic electrodes. In this work we analyze the optical transmittance of different nanostructured electrode designs, from simple gratings and grids to complex fractal-shaped electrodes. We first demonstrate that linear gratings exhibit a high, yet polarization-dependent transmission while square grids with similar geometrical parameters show a low, yet polarization-independent transmission. To obtain high polarization-independent transmission, more advanced electrode designs are necessary. Fractals have been studied14-18 and applied commercially19 in the microwave regime as broadband or multi-band electromagnetic antennas. In the optical and near infrared regime, fractal antennas have been proposed for broadband near-field concentration20-21 and enhanced transmission and resolution22. Here, we demonstrate nanostructured metallic films with fractal-shaped slits as transparent optical electrodes with high polarization-independent transmission. The proposed fractal slit patterns, known as space-filling curves, efficiently cover the entire surface of the electrode. We experimentally compare the optoelectronic performance of these fractal electrodes by placing them on top of a silicon (Si) substrate to form a planar back-to-back metalsemiconductor-metal Schottky detector. Through photocurrent measurements, we demonstrate that space-filling fractal networks can substantially outperform grids and slightly outperform gratings while providing a polarization-independent response. A space-filling fractal electrode is built up from a set of locally parallel vertical and horizontal metallic lines. For this reason, the essential physics of their behavior appears already in simpler linear gratings consisting of parallel wires. It is therefore of value to analyze this basic electrode configuration before we analyze the more complex fractal structures. First, we determine the spectral response of a linear grating and compare its optical performance in an air environment to the case when it is placed on a substrate made of silica glass (SiO2) or Si. We find that the substrate critically affects both the grating transmission and losses in the metal. We model the grating using a finite element method (COMSOL Multiphysics) with material properties from Ref. 23. We consider an Al grating with thickness h = 40 nm, periodicity P = 450 nm, and nanowire width w = 100 nm (Figure 1). We compare the polarization-averaged transmission and metal losses of this grating for illumination from the air side in three situations: freely standing in air, on a glass substrate and on a silicon substrate (blue, green and red lines in Figure 1a). For the cases of air and on a glass substrate, transmission is high. The situation is rather different when a Si substrate is present, as in many optoelectronic devices; a high reflectivity of around 45% is found due to the high refractive index of Si in this wavelength range (3.5 < nSi < 6). A similarly high reflectivity is also observed for a bare Si substrate (solid gray line). A lower transmission is observed for the case of a square grid (Figure 1b), and losses in the metal are higher compared to a grating with the same period. Finally, the metal losses in the gratings and grids tend to be lower for structures on a silicon substrate than on the other media.
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To better understand the transmission through optically thin gratings, we also analyze these results for a normally-incident light wave with the electric field perpendicular to the nanowires (TM polarization) and parallel to them (TE polarization) as shown in Figure 1c. The main process for the transfer of optical energy through the gratings is the excitation of fundamental TM or TE gap modes between two parallel metallic nanowires. The TM gap mode does not exhibit a cut-off, which implies a broadband transmission. The TE gap mode approaches cut-off for the longer wavelengths. However, a sharp cut-off for TE does not exist since the Al layer is very thin and the evanescent decay length of the TE gap mode is larger than the Al thickness, which facilitates evanescent coupling24. For both TM and TE excitations and all substrates, there are abrupt changes in transmission and enhancements in the metal absorption due to the excitation of surface plasmons and 1 diffraction orders (at 0 = P = 450 nm and red-shifted to 0 = P . nsubstrate = 650 nm for glass) along the grating-air and grating-substrate interfaces. For 0 < P and for both polarizations, both zero-order and the 1 diffraction orders exist in transmission and reflection. For P < 0 < P . nsubstrate , the 1 diffraction orders are present in transmission into the substrate but not in reflection in air. For 0 > P . nsubstrate, the 1 diffraction orders cannot be excited and optical energy is transferred only through fundamental TM and TE gap modes. In the case of a grid, due to the presence of square apertures, transmission is more similar to a TE grating response at the longer wavelengths and more similar to a TM grating response at the shorter wavelengths. The averaged transmission of a grid over different substrates is lower than a grating with similar geometric parameters due to modal cut-off and also higher metal coverage. Many of the spectral features explained above for linear gratings are also present for grids. The metal loss peaks are more pronounced for the grid because surface waves can couple to localized nanowire resonances in one direction and propagate along nanowires in the orthogonal direction. A more detailed analysis of transmission through gratings and grids is provided in the Supplementary Information (Supplementary Figures S1-S3). As the periodicity of a grating or a grid increases for a constant wire width, the transmission into the silicon substrate averaged over wavelength and polarization increases (Figure 1d). Despite the polarization-dependent transmission of a grating, the averaged transmission of an optically thin grating is always higher than that of a grid with similar geometric parameters. Moreover, if we compare gratings and grids with similar metal filling ratios at a fixed wire width (i.e., comparing different periods), both geometries provide a similar averaged transmission but a different sheet resistance; a grid has a larger periodicity than a grating with a similar filling ratio and it will possess a higher sheet resistance, proportional to the period (RSH = (/h)(p/w), where is the metal resistivity). More advanced electrode designs are necessary to obtain high, polarization-independent transmission. In this Letter, we demonstrate experimentally that nanostructured metallic films with space-filling fractal-shaped slits can serve as alternative transparent electrode geometries that satisfy the requirements above. Examples of such fractal patterns that can effectively cover a surface with a dense pattern of metal lines and slits are Hilbert and Peano curves25-27 (Figure 3c,d). These continuous, two-dimensional curves can be thought of as the path of a continuously moving point that never crosses itself and efficiently covers the surface of the electrode. They naturally have as many horizontal as vertical line segments, implying a polarization-independent response. Additionally, by avoiding the square apertures present in grids, they do not suffer the decrease in transmission due to modal cut-off at long wavelengths observed in square grids. We experimentally compare the performance of our proposed fractal-shaped electrodes with gratings and grids integrated on a Si photodetector through a set of polarization and spectrally
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resolved photocurrent measurements. The measurement platform consists of a patterned Al electrode integrated on a Si substrate, forming a planar back-to-back metal-semiconductor-metal Schottky detector (Figure 2). Light impinges on the electrode from the air side. The patterned electrode transmits light into the silicon substrate, which generates electron-hole pairs. These charges are separated and extracted via the lateral electrodes to produce a photocurrent. The generated photocurrent is a direct measure of the electrode’s ability to transmit light. This photocurrent platform allowed us in the past to obtain very good agreement between simulated and experimental photocurrent spectra 28-30 and we now leverage it to characterize the proposed electrodes. To obtain the wavelength- and polarization-resolved photocurrent responses of the different nanostructured electrodes, we use a supercontinuum white light source spectrally filtered by an acousto-optic tunable filter. The beam then passes through a linear polarizer and a half-wave plate to control the incident polarization. Light is gently focused on the device into a ~1.5 m-diameter spot with a microscope objective (50x, 0.42 NA). The device is mounted on a piezo-stage and is electrically reverse biased at 1V using a set of wire bonds. For sensitive detection of the photocurrent, the laser beam is modulated with a chopper and the modulated photocurrent is amplified and detected with a lock-in amplifier. At each polarization and wavelength, a photocurrent image of a device is obtained by raster scanning the laser beam over it. The device responsivity (in units of A/W) at each polarization and wavelength is defined as the maximum spatial photocurrent normalized to the input laser power, found by raster scanning the laser beam. We have checked the linearity of the detector response versus the illumination power at several wavelengths across the spectral range of interest (See Figure 4S). Based on this observation, photocurrent measurements afford a simple quantitative comparison of the transmission properties of different electrode geometries at any wavelength of interest. In analyzing the spectral dependence of the photocurrent, it worth noting that the internal quantum efficiency (IQE) of the detectors can be wavelength dependent as different wavelengths of light generate different spatial distributions of the photogenerated carriers. As such the collection efficiencies for the carriers generated at different wavelengths can be different. The wavelength-dependence in the carrier collection will in general depend on the surface/bulk recombination processes that can suppress the collection efficiencies primarily at shorter/longer wavelengths. These can be processes are critically dependent on the processing and device configuration and the spectral properties of the photocurrent are not necessarily identical to the spectral transmission properties. For our devices, we found that the spectral dependence of the IQE at the applied reverse bias of 1V is quite flat across the considered wavelength range from 450 nm – 750 nm (Figure 5S). This indicates that photocurrent spectra can be used to get a good 1st order impression of the spectral transmission properties of our electrodes. To fabricate the nanostructured electrodes, we start with an n-type silicon wafer that is initially immersed in 2% hydrofluoric acid for a few seconds to remove the native oxide. Then, 3 nm of Cr and 40 nm of Al is deposited on the silicon wafer by electron beam evaporation. The wafer is covered with a positive resist (PMMA 950K) and the nanowire networks and contact pads are defined by electron beam lithography (JEOL JBX 6300, 100 keV). They are subsequently etched by Ar-ion sputtering. The PMMA mask is then removed by soaking the wafer in heated 1165 remover for 24 hours followed by ultrasonication and then O2 plasma cleaning. Scanning electron microscopy (SEM) images of the e-beam fabricated linear grating, grid, Hilbert and Peano fractals are shown in Figures 3a-d. The area of each electrode geometry is ~ 12 m 12 m. The Al nanowire width is 100 nm in all cases, and the grating and grid periodicities and the minimum spacing between two parallel nanowires for fractals (p in Figure 2) is 450 nm. As it will be shown
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later, we choose these wire width and spacing values to obtain spatially uniform photocurrents, and to avoid diffraction effects in reflection on the air side, respectively. All our devices offer broadband responsivities from 450 to 750 nm, as indicated by the responsivity maps of each device as a function of polarization angle and wavelength in Figure 3eh. Similar to the grid, the Hilbert and Peano fractals show polarization-independent responses, yet with much higher average responsivities. The polarization and spectrally averaged responsivity of these devices are also shown in Figure 3e-h. The averaged responsivities of a Hilbert and a Peano fractal are 40% and 34% higher than a grid and 7% and 2% higher than a grating, respectively. To gain direct quantitative information of the performance of one electrode over another, one can divide the photocurrent spectra from two relevant electrodes. An example is shown in Supplementary Figure 6S, where the polarization and wavelength dependent response of various electrodes is compared to that of a continuous 40 nm thick Al film electrode. Normalizing the measured photocurrents of the Hilbert fractal to that of an unpatterned Al electrode, we obtain on average more than 21x enhancement in photocurrent by patterning the electrode with fractal nanowires (Supplementary Figure 6S). The physics of light transmission through fractal networks is similar to the case of gratings. A strong transmission is associated with the excitation of fundamental TM or TE propagating gap modes between two parallel metallic wires. A simple way to visualize this is by decomposing a fractal structure into regions where metallic wires are parallel in horizontal and vertical directions. A decomposed Hilbert fractal based on this principle is shown in Figures 4a,b. We can view each case as a group of finite size gratings with different numbers and lengths of nanowires. Horizontal gratings primarily transmit vertically-polarized light whereas vertical ones primarily let horizontally-polarized light to pass through. Optical microscopy images obtained in reflection for different polarizations of illumination (Figures 4c,d, where w = 200 nm and p parameter = 450 nm) display complex patterns with dark and bright areas; the dark areas in the reflection image match well the regions in the decomposed fractal structure where we expect high transmission due to the excitation of a TM propagating gap mode. By making the metallic wires of this fractal narrower (w = 150 nm, hence corresponding to a larger gap), the contrast between dark and bright regions decreases in the reflection images (Figures 4e,f) due to better coupling to the TE gap mode. Dark regions featuring a lower reflectivity also correspond to regions of higher transmission and higher photocurrent. In the spatial photocurrent maps of this fractal at 0 = 600 nm (Figure 5a-c), the regions of high photocurrent for two orthogonal polarizations follow the regions of low optical reflection in Figures 4e,f. For this fractal, the difference in photocurrent between the dark and bright red regions at 0° and 90° polarization angels is about 5%. The spatial photocurrent at 45° is uniform and is the average of the photocurrents at 0° and 90°. A uniform spatial transmission and photocurrent is in general desirable. This can be achieved by using narrower wires, as demonstrated by the relatively uniform reflection images of this fractal for w = 100 nm (Figure 4g,h, structure also used in Figure 3c). In general, light transmission through each grating-like section of a fractal is lower than a similar grating because the nanowires are shorter resulting in light scattering at the nanowire edges. In addition, the number of parallel nanowires is smaller, which reduces the transmission efficiency. However, unlike the grid, there is no modal cut-off present for the fractal nanowire networks. To obtain the optimum geometrical parameters of a fractal for an application of interest, the geometry parameters of the grating (P, w and h) can be optimized first. Then the optimized parameters can be readily used for fractals to obtain a high polarization-independent transmission, which has a similar spectral trend as the polarization-averaged transmission of a grating.
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Finally, the transmission into silicon of our nanostructured electrodes can be further improved by reducing reflection. Silicon has a high reflectivity of about 40% in the visible and a properly designed free-standing metal grating is highly transmissive (Figure 1a). However, by placing a transparent grating on a silicon substrate, more light is reflected than by a bare silicon surface (gray and red curves in Figure 6). To reduce this reflection and enhance transmission into silicon, we propose to combine our electrodes with a thin film of silicon nitride (Si3N4) acting as an antireflection coating (inset of Figure 6). By adding a 60 nm thick layer of silicon nitride to a grating, our simulations show that reflection drops well below the value for Si (see purple curve in Figure 6). This thickness corresponds to the thickness of a conventional anti-reflection coating on Si cells. Since the physics of light transmission through fractals is very similar to gratings, by integrating a metallic fractal with a silicon nitride layer, we expect to obtain an anti-reflective, transparent, broadband, and polarization-independent electrode. In summary, we have introduced nanostructured metallic films with fractal-shaped slits as new transparent electrode geometries that have high broadband and polarization-independent transmission. Through integration with silicon photodetectors and photocurrent measurements, we have shown the superior performance of the fractal geometries as compared to gratings and grids with similar geometrical parameters. The proposed electrodes can be integrated in cameras and displays, where the typical size of a pixel is similar to the demonstrated electrodes. In solar applications, these fractal networks could play a dual functionality both as a transparent electrode and as an efficient light-trapping layer for thin film cells. Adding a mesh of mesoscale metal wires can further improve the sheet resistance of the proposed electrodes for large area applications 31. Finally, we have shown that grating design principles can be used to systematically design more complex electrodes such as fractals for many optoelectronic applications.
Competing Financial Interests: The authors declare no competing financial interest. Acknowledgement We greatly acknowledge support from Bay Area Photovoltaics Consortium funded by the U.S. Department of Energy.
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Figures
Figure 1. Nanostructured metals as transparent electrodes on low and high refractive index substrates. (a, b) Simulated polarization-averaged transmission and loss in the metal wires of an Al grating and an Al square grid placed on different substrates. The different colors of the curves show different substrates with blue, green, and red corresponding to a freestanding grating, a grating on glass and a grating on Si, respectively. The periodicity (P) of the grating and grid is 450 nm, the nanowire width (w) is 100 nm, and the Al thickness (h) is 40 nm. For reference, transmission into silicon (solid gray line) and into glass (dash-dotted gray line) without any metallic structures on the top shows the original transmission of the substrates. A transmission of 1 corresponds to perfect (i.e. 100%) transmission. (c) Simulated TM and TE transmission of a grating on glass and silicon. (d) Simulated wavelength-and-polarization-averaged transmission into silicon as a function of periodicity for Al gratings and grids (w = 100 nm), averaged over the 450-1000 nm spectral range. The solid gray line shows the averaged transmission into bare silicon, without any nanostructures.
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Figure 2. A planar Al-Si-Al Schottky photodetector with an electrode patterned with a Hilbert fractal. The light transmitted through the fractal electrode generates electron-hole pairs that are extracted as photocurrent. The blown-up image shows the main geometrical parameters defining the fractal pattern, where w is the width of the nanowire and p is the spacing between two adjacent parallel nanowires.
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Figure 3. Performance of different electrode geometries. Scanning electron microscopy images of Al electrodes patterned with (a) a linear grating, (b) a grid, (c) a Hilbert fractal, and (d) a Peano fractal. The width of the Al nanowires is 100 nm in all images. The periodicity of the grating and the grid and p parameter defined in Figure 2 for fractals is 450 nm. (e)-(h) Measured responsivity for each electrode as a function of the illumination polarization and wavelength. 0° and 90° linear polarization angles correspond to incident electric field being normal (TM) and parallel (TE) to the grating nanowires, respectively. Wavelength-and-polarization-averaged responsivities of grating, grid, Hilbert fractal, and Peano fractal electrodes are 0.144 A/W, 0.110 A/W, 0.154 A/W, and 0.147 A/W, respectively. Note that to allow direct comparison between simulated transmission and measured responsivity, the simulated transmission of an electrode must be multiplied by λ0e/hc to be equivalent to the measured responsivity, where e is the electron charge, h is Planck’s constant and c is the speed of light in vacuum.
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Figure 4. Spatial decomposition of a fractal electrode into perpendicular directions. (a,b) Hilbert fractal (inset) decomposed into its constituent vertical and horizontal lines. The red arrows show directions of favorable electric fields in each case. (c-h) Optical reflection microscopy images of Hilbert fractals with different wire width for illumination under two orthogonal linear polarizations. Top row corresponds to horizontal polarization and bottom row to vertical polarization. The spacing parameter p (defined in Figure 2) is 450 nm in all of them and the nanowire width (w) decreases from left to right: w = 200 nm in (c,d) 150 nm in (e,f) and 100 nm in (g,h). Decreasing wire width results in more uniform spatial reflection and transmission. For wire width w = 100 (used in Figure 3c), transmission is relatively uniform resulting in a spatially homogenous photocurrent.
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Figure 5. Spatial distribution of photocurrent for a Hilbert fractal electrode with wide nanowires. Photocurrent images are recorded under incident linear polarization angles of 0, 45, and 90° at = 600 nm for fractals with spacing p = 450 nm and nanowire width w = 150 nm. For this nanowire width, the difference between dark and light red regions is around 5%. Each photocurrent map is normalized to its own maximum. Corresponding optical reflection images are shown in Fig. 4e,f.
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Figure 6. A silicon nitride film reduces reflection losses into a silicon substrate. Simulations of optical reflection under normal incidence for an unpatterned silicon substrate (solid gray curve), a silicon substrate covered with an aluminum grating with P = 450 nm and w = 100 nm (red), and a silicon substrate covered with both an aluminum grating and a silicon nitride layer as an anti-reflection coating (purple) with geometry parameters shown in the inset.
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Laser power (W)
Responsivity (A/W)
Al
Cr Si
Transparent electrode
Current (A) -V ACS Paragon Plus Environment
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Polarization
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Wavelength (nm)
