Article pubs.acs.org/journal/apchd5
Tunable Visibly Transparent Optics Derived from Porous Silicon Christian R. Ocier,†,‡ Neil A. Krueger,†,‡ Weijun Zhou,§ and Paul V. Braun*,† †
Department of Materials Science and Engineering, Frederick Seitz Materials Research Laboratory, and Beckman Institute, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States § The Dow Chemical Company, 2301 N. Brazosport Boulevard, B-1470, Freeport, Texas 77541, United States S Supporting Information *
ABSTRACT: Visibly transparent porous silicon dioxide (PSiO2) and PSiO2/titanium dioxide (TiO2) optical elements were fabricated by thermal oxidation, or a combination of thermal oxidation and atomic layer deposition infilling, of an electrochemically etched porous silicon (PSi) structure containing an electrochemically defined porosity profile. The thermally oxidized PSiO2 structures are transparent at visible wavelengths and can be designed to have refractive indices ranging from 1.1 to 1.4. The refractive index can be increased above 2.0 through TiO2 infilling of the pores. Applying this oxidation and TiO2 infilling methodology enabled tuning of a distributed Bragg reflector (DBR) formed from PSi across the visible spectrum. At the maximum filling, the DBR exhibited a transmission of 2% at 620 nm. Simulations match well with measured spectra. In addition to forming DBR filters, phase-shaping gradient refractive index (GRIN) elements were formed. As a demonstration, a 4 mm diameter radial GRIN PSiO2 element with a parabolic, lens-like phase profile with a calculated focal length of 1.48 m was formed. The calculated focal length was reduced to 0.80 m upon the addition of TiO2. All the structures showed broad transparency in the visible and were stable to the materials conversion process. KEYWORDS: gradient refractive index, distributed Bragg reflector, spectral filter, phase-shaping optics orous silicon (PSi) first attracted attention due to its potential for visible light emission.1,2 While the emission did not reach the level required for PSi to compete with other solid-state emitters, it has remained of interest because of its optical versatility.3 Of greatest relevance to this report, the porosity and thus the refractive index of PSi can be explicitly defined by the current density applied during its electrochemical etching.4 A time-varying current density can be used to define the refractive index along the PSi etch pathway, an approach that has enabled fabrication of elements such as distributed Bragg reflectors (DBRs),5,6 rugate filters,7,8 vertical microcavities,9−11 and three-dimensional gradient refractive index (GRIN) microoptics.12 The fact that the optical response of PSi is highly sensitive to foreign media penetrating its porous microstructure,13−15 in combination with the well-defined optical signatures of PSi-based 1D photonic elements, has been shown to provide a powerful platform for chemical and biological sensing.15−20 The large experimentally accessible refractive index range of PSi21 (1.4 to 2.5 at a wavelength of 800 nm) provides a unique design space for forming structures that control photon propagation. Below about 1 μm, even though PSi absorbs significantly less than an equivalent thickness of Si, it remains absorptive (particularly starting in the visible spectrum). Applying PSi for absorption-intolerant applications with visible light, such as imaging and photovoltaic devices, requires an approach to eliminate the absorbing Si. The simplest means to accomplish this is to oxidize PSi into porous silicon dioxide
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© XXXX American Chemical Society
(PSiO2).22,23 While oxidation reduces absorption in the visible to near zero, it also reduces the range of the possible refractive index contrast, as the refractive index of SiO2 is significantly less than Si. PSi or PSiO2 can also be used as a host or template, where materials are introduced into the pore volume and the Si or SiO2 is optionally removed. To date, both PSi and PSiO2 have been demonstrated to serve as sacrificial templates,24,25 but only for polymers,24 which offer no significant advantage over PSiO2 in terms of refractive index contrast or transparency window, and carbon,25 which lacks transparency in the visible spectrum. Mesoporous PSi has also been used as a host for metals,26−28 but the resulting structures are opaque. Transparent, high refractive index materials such as ZnO,29 TiO2,30 or SnO231 have been deposited into PSi templates via sol−gel chemistry29,30 and atomic layer deposition (ALD),31 but neither approach fills the PSi void volume densely enough for a template inversion process due to calcination (sol−gel) or pinch-off (ALD).32 Here, rather than attempting to use the approach of infilling the PSi followed by etching of the PSi to form a high refractive index structure, we take PSi with electrochemically programmed refractive index profiles and combine thermal oxidation with ALD to generate high refractive index contrast, visibly transparent optical elements. Reflectance and transReceived: December 15, 2016 Published: February 28, 2017 A
DOI: 10.1021/acsphotonics.6b01001 ACS Photonics XXXX, XXX, XXX−XXX
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mittance spectroscopy demonstrates that thermal oxidation converts PSi to optically transparent PSiO2 with retention of the embedded index profile. Subsequent infiltration of the PSiO2 with TiO2 by ALD can be used in a controlled fashion to increase the refractive index, the degree of which is controlled by the number of ALD TiO2 infilling cycles. This conversion methodology is applied to a PSi DBR, and we show that the optical evolution can be readily predicted from the properties of similarly fabricated optically homogeneous PSiO2 and PSiO2/ TiO2 thin films. In a separate demonstration, a radial GRIN PSi structure is converted into a PSiO2 optic possessing a lens-like parabolic phase profile with an effective focal length that is greatly reduced by its transformation into a high refractive index contrast PSiO2/TiO2 composite element.
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RESULTS AND DISCUSSION The process for converting PSi into a PSiO2/TiO2 optical element is depicted in Figure 1. First, a PSi film with the desired
Figure 2. Optical spectra and optical constant dispersion relations for optically monolithic as-fabricated PSi, oxidized (PSiO2), and PSiO2/ TiO2 films. The top row shows the optical spectra in transmission and reflection, and the bottom row gives the refractive index and extinction coefficients.
row), shown by the high transmittance of PSiO2 at visible wavelengths (Figure 2, middle top row). Infiltration with TiO2 increases the refractive index of the film (Figure 2, right bottom row) while maintaining the visible transparency (Figure 2, right top row). The observed increase in the refractive index of PSiO2/TiO2 is consistent with the introduced TiO2 reducing the void volume of PSiO2 (Figure 3a) in accordance with a Bruggeman effective medium approximation (EMA) (Table S1, Supporting Information), as can be shown for a series of optically homogeneous films subjected to different levels of TiO2 filling. The films prepared with higher current densities (265 and 405 mA cm−2) possess more void volume that can be filled with TiO2 through at least 45 ALD cycles, while the film prepared at the lowest current density (125 mA cm−2), and thus lowest void volume, accommodates only ∼15 TiO2 ALD cycles. Since there is a complicated relationship between the degree of TiO2 infilling, SiO2 volume fraction, and void volume fraction, the refractive indices for a series of optically homogeneous PSiO2/ TiO2 films (Figure 3b) etched at different current densities do not exhibit a simple current density-dependent refractive index trend (e.g., the lowest current density yielding the highest refractive index). Rather, the highest refractive index resulted from an intermediate etch current, thus intermediate void volume fraction, as this film contained significant volume fractions of both SiO2 and TiO2. Since ALD infiltration causes the structure to pinch off shortly after 45 cycles, the films etched at a higher current density contained a significant void (air) volume fraction, and the films etched at a lower current density consisted mostly of SiO2. Understanding the relationship between etch current and ALD infilling is important in the design of PSiO2/TiO2 optical elements, as there is not a simple one-to-one mapping of PSi porosity to the final GRIN profile after conversion into a PSiO2/TiO2 element. While we have done this for only one ALD infilling procedure, experimental determination for a full range of etch and infilling conditions is experimentally straightforward (albeit time-consuming). PSi-based DBRs and microcavities have been proposed as the basis of sensors18−20,35 and spectral filters.36−38 While these 1D PSi elements function well at visible wavelengths for reflection-
Figure 1. Schematic illustrating the process for transforming PSi into an optically transparent PSiO2/TiO2 composite. After electrochemical formation, the PSi is electrochemically detached and mechanically transferred onto quartz with solvent. The PSi is then thermally oxidized and filled with TiO2 via ALD to complete the transformation process.
porosity gradient is electrochemically etched into a Si wafer. At the end of the PSi etch, the edges of the PSi element are mechanically scribed and an electropolishing pulse is used to detach the PSi from the Si wafer (except at the edges). The element is then transferred onto a transparent, thermally stable quartz substrate using a gentle stream of ethanol. After careful rinsing with hexanes to limit capillary forces upon drying,33 followed by drying in air at room temperature, the PSi is left in intimate contact with the quartz substrate. The PSi on quartz is then subjected to a two-part thermal oxidation under dry oxygen, first at 500 °C to stabilize the microstructure34 and then at 925 °C to fully convert PSi into PSiO2. Finally, the PSiO2 film on quartz can be infiltrated with TiO2 by ALD, forming a PSiO2/TiO2 composite optical element with the degree of TiO2 filling being used to modulate the optical response. The refractive index and the extinction coefficient of the structure after each processing step are extracted from reflectance and transmittance spectra collected from optically homogeneous films (i.e., PSi formed using a constant current density) (Figure 2 and Figure S1, Supporting Information). Asfabricated, PSi is highly dispersive and possesses a nonzero extinction coefficient (Figure 2, left bottom row), manifested by a transmittance that drops off steeply toward shorter wavelengths (Figure 2, left top row). Oxidation to PSiO2 eliminates extinction across the visible spectrum (Figure 2, middle bottom B
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Figure 3. (a) Bruggeman EMA-determined void volume in the PSiO2 scaffold as a function of TiO2 infiltration ALD cycles. Traces correspond to samples formed starting with optically monolithic PSi fabricated at the indicated current density. (b) Refractive index dispersion relations for the same PSiO2−TiO2 structures filled with TiO2 after 45 ALD cycles.
Figure 4. (a) Measured transmission spectra of a PSiO2/TiO2 DBR at increasing levels of TiO2 infilling. 0 (purple), 10 (blue), 20 (green), to 35 (red) ALD cycles. (b) Calculated spectra simulated using the expected effective refractive index for the high- and low-index layers. (c) Schematic of a PSiO2−TiO2 DBR on quartz. (d) SEM micrograph showing a few layers of the PSiO2/TiO2 DBR.
based applications that tolerate optical losses, they are not appropriate for absorption-sensitive applications. In this work, we show that PSi can serve as the starting point for optically transparent elements that can retain the index profile etched into the film after its conversion to PSiO2. To demonstrate this material’s applicability for spectral filters, a 30-period PSi DBR is first fabricated with alternating current density pulses of 265 and 405 mA cm−2, generating a stopband located at 530 nm with a poor out-of-band transmittance due to the PSi absorption (Figure S3, Supporting Information). After oxidation of PSi to PSiO2, the stopband shifts to ∼440 nm (Figure 4a, purple trace), which is only ∼10 nm blue-shifted from the predicted position (Figure 5a) as determined by transfer-matrix calculations39 using the EMA data from Figure 3a and the measured layer thicknesses of the DBR (Figure S4, Supporting Information) as input parameters. The PSiO2 DBR exhibits markedly improved transmittance outside of the stopband compared to the as-fabricated PSi structure, but the depth of the stopband is diminished due to the reduced refractive index contrast (Figure 4b) (some of the decrease may also be due to the reduced sensitivity of the detector below ∼460 nm). After infiltration with 10 TiO2 ALD
Figure 5. (a) Calculated and measured DBR stopband peak positions and (b) stopband peak shifts, as a function of TiO2 infilling cycles.
cycles, the stopband red-shifts to ∼492 nm (Figure 4a, blue trace) and the depth of the stopband increases. The measured spectral position of the stopband is again slightly blue-shifted from the transfer-matrix calculation, but the calculated shift of the stopband position (Figure 5b) is in excellent agreement with measurements. The agreement between simulations and experiment is maintained as infilling via additional TiO2 ALD cycles red-shifts the stopband of the PSiO2/TiO2 composite C
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DBR across the visible spectrum, all while maintaining high out-of-band transmittance. Given the tunability of the refractive index and the broadband transparency of PSiO2/TiO2 from the UV (limited by the TiO2 absorption edge) into the IR (where SiO2 and TiO2 both begin to absorb), these structures lend well to transmission-based optical devices and spectral filters,40−42 as well as for other absorption-sensitive applications. The conformal nature of the ALD process does limit the filling capacity of an optical stack to its lowest void volume (due to pinch off), potentially limiting the refractive index contrast. In our designs, a refractive index contrast up to ∼0.3 refractive index unit, defined here as Δn = nmax − nmin, was demonstrated. While this is lower than what is possible in porous silicon,12 it exceeds the maximum difference available to most visibly transparent GRIN materials, such as those made of polymers.43 As demonstrated here, this contrast is sufficient for creating, for example, optical filters. In future work, building off our prior work,12 we plan to apply this conversion methodology to form three-dimensional GRIN optics, where the interplay between index profile, index contrast, and form factor can be exploited to enable photonic functionalities that are inaccessible with planar configurations. The refractive index of PSi can also be modulated in 2D and 3D, creating PSi 2D and 3D GRIN structures, which can be transformed into visibly transparent GRIN optical elements. For purely planar etch configurations, generating complex index gradients requires a spatially varying current density for 2D GRIN and a combination of spatially and time-varying current density for 3D GRIN elements. Building off previous work,44−47 we constructed a planar, 2D PSi GRIN structure with the spatially varying current density from a “pin” electrode positioned in close proximity (∼2 mm) to the Si surface. This results in a radially varying current density that can be observed as concentric fringes in the PSi (Figure 6a). After oxidation to PSiO2, the GRIN profile (Figure 6b, blue trace) and radial thickness profile (Figure 6c) are determined by spatially resolved reflectance spectroscopy and scanning electron microscopy, respectively. These measurements are then used to extract the phase profile by taking the product of the spatially varying refractive index and the film’s physical thickness, yielding the parabolic phase profile shown in Figure 6d. While the PSiO2 GRIN profile alone would form a diverging lens (i.e., greatest porosity, and thus lowest refractive index, in the center), because the GRIN element is thickest in the center, the measured radial phase profile, Δϕ(r) (Figure 6d, blue trace), exhibits a converging lens-like parabolic shape with a calculated focal length, f, of 1.48 m extracted from fitting the curve to48 −π 2 Δϕ(r ) = r λf (1)
Figure 6. (a) Optical image of a PSi element etched with a lateral refractive index gradient. (b) Refractive index derived from spatially resolved reflectance spectroscopy across the PSiO2 and PSiO2/TiO2 samples. The upward facing parabolic index profile of PSiO2 (blue trace) is inverted after the introduction of TiO2 (red trace). (c) Sample thickness measured at discrete points by scanning electron microscopy. (d) Phase difference profile with a parabolic curvature extracted from the optical constants and physical geometry of the sample and the calculated resulting focal length.
Now the signs of the GRIN and physical thickness profiles are the same, decreasing the radius of curvature of the phase profile (Figure 6d, red trace) and reducing the calculated focal length of the PSiO2/TiO2 radial GRIN element to 0.80 m. While the large focal length of the PSiO2/TiO2 radial GRIN lens relative to its 4 mm diameter in this configuration limits possible applications, the fundamental approach used to form the GRIN lens could likely be applied to other PSi GRIN geometries such as those formed by photoelectrochemical etching,49 direct imprinting via metal-assisted chemical etching,50 and shape-defined etching.12 Our material conversion process, coupled with these PSi fabrication techniques, offers an opportunity to broaden the spectral compatibility of PSi structures for transformation and GRIN optics at both the macro- and microscale.
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CONCLUSION We have shown that the combination of thermal oxidation and TiO2 infiltration by ALD offers an opportunity to fabricate high refractive index contrast, visibly transparent GRIN optical elements starting from absorptive PSi structures. Optical characterization of homogeneous thin films confirms that thermally oxidized PSiO2 exhibits transparency and can be engineered to have a refractive index ranging from 1.1 to 1.4 and that, following TiO2 ALD infilling, the maximum available refractive index could be increased up to 2. By applying the conversion methodology to a well-understood PSi DBR structure, we predict and demonstrate control of the optical response, specifically the position of the stopband. At maximum infilling, the stopband has a transmission of 2% (620 nm). We demonstrate conversion of a 2D PSi radial GRIN structure into
where λ is the wavelength of light (630 nm here) and r is the radial position. The fact that the PSiO2 radial GRIN element is expected to function as a converging lens indicates that the optical response is dominated by the physical thickness profile. While the initial GRIN profile is diverging in nature (opposite in sign to the thickness profile), the GRIN profile can be reversed by TiO2 infilling, making it convergent as well. After 60 TiO2 ALD cycles, the PSiO2/TiO2 element’s GRIN profile (Figure 6b, red trace) is inverted relative to the starting PSiO2 structure because lower refractive index regions in the PSiO2 feature greater void volume and accommodate more high refractive index TiO2 (as previously demonstrated in Figure 3). D
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precursors for TiO2 deposition, which was carried out at a chamber temperature of 140 °C. This recipe, developed with the assistance of Cambridge Nanotech, used (for both precursors) a stopvalve opening time of 0.3 s, a precursor pulse time of 180 s, and a precursor dwell time of 180 s. Optical Characterization. Reflectance and transmittance spectra were collected using a Si PDA spectrometer (Control Development, Inc.) hooked up to an Axio Observer D1 inverted microscope (Carl Zeiss, Inc.) with a white-light halogen lamp serving as the source. The microscope features a motorized sample stage that can take defined steps, which enabled spatially resolved measurements used to characterize the radial GRIN structure and transformed element.
a visibly transparent element possessing a lens-like phase profile and a GRIN profile that is enhanced by the TiO2 infilling, showing the potential for postfabrication adjustments to the calculated focal length. Given these results, we speculate that the conversion methodology can be coupled with strategies for defining PSi element topography, such as lithographically defined 3D GRIN structures12 and photomediated electrochemical etching,49 to yield transparent, phase-shaping optical elements.
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METHODS PSi Etching and Electropolishing. All PSi structures were formed from single-side-polished, highly doped (ρ ≈ 0.001− 0.005 Ω cm) p-type Si (Prolog Semicor Ltd.). Etching was carried out in a polypropylene cell with an exposed etch area of ∼1.20 cm2. Contact to the back of the Si wafer was established with a stainless steel electrode. Current was delivered to the cell by an SP-200 research grade potentiostat/galvanostat (BioLogic Science Instruments) and pulsed with a duty cycle of 33% at a frequency of 1.33 Hz (unless specified otherwise). After etching, all structures were thoroughly rinsed with ethanol. The electrolyte was composed of a 1:1 volume ratio of 48% hydrofluoric acid (aq) (Sigma-Aldrich) and 100% ethanol (Decon Laboratories). A 5 mm diameter Pt−Ir inoculating loop (Thomas Scientific) served as the counter electrode (except for radial GRIN structures, discussed below) and was located at the center of the cell ∼25 mm from the etch surface to provide a uniform current density across the sample. The radial GRIN PSi structure was formed using the process described above with the exception that the Pt−Ir pin placed ∼2−3 mm from the etch surface served as the counter electrode. An average current density of 150 mA cm−2 was applied with the aforementioned duty cycle and pulse frequency. Electropolishing was carried out with an electrolyte composed of a 1:3 volume ratio of 48% hydrofluoric acid (aq) and 100% ethanol. The 5 mm Pt−Ir ring served as the counter electrode, and a current density of 300 mA cm−2 was applied with a duty cycle of 20% at a frequency of 0.40 Hz. Before the electrochemically induced detachment, a stainless steel syringe needle was used to mechanically score and release the edges of the PSi layer to allow the film to remain flat for printing. After the electropolishing process, all PSi structures were carefully rinsed with ethanol in such a fashion that the free-standing PSi structure glided from the Si wafer and onto a 25 mm × 25 mm × 1 mm quartz slide. Once on the quartz substrate, all PSi structures were then gently rinsed with hexanes and allowed to dry in air. Thermal Oxidation. Dried PSi structures on quartz were loaded into an alumina boat, centered within an alumina furnace tube, and loaded into a CM 1600 Series furnace connected to a dual argon (Ar) and oxygen (O2) inlet. Under Ar flow, the temperature of the furnace was increased from room temperature to 500 °C at 200 °C/h. Next, the Ar flow was replaced with O2 gas and held for 1 h at 500 °C. After purging O2 from the furnace, the temperature was increased to 925 °C at a rate of 125 °C/h under flowing Ar. Again, O2 gas replaced Ar and the furnace was held at 925 °C for 1 h in order to fully oxidize the PSi into PSiO2. After oxidation, the furnace was purged with Ar and then cooled to room temperature at a rate of 125 °C/h with flowing Ar. TiO2 ALD Deposition. The ALD system (Cambridge Nanotech) used water and tetrakis(dimethylamido)titanium as
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.6b01001. Additional optical characterization calculations and data (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Paul V. Braun: 0000-0003-4079-8160 Author Contributions ‡
C. R. Ocier and N. A. Krueger contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy “Light-Material Interactions in Energy Conversion” Energy Frontier Research Center under grant DE-SC0001293 and the Dow Chemical Company. This research was carried out in part in the Materials Research Laboratory Center for Microanalysis of Materials and the Micro and Nanotechnology Laboratory at the University of Illinois.
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REFERENCES
(1) Canham, L. T. Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers. Appl. Phys. Lett. 1990, 57, 1046−1048. (2) Lehmann, V.; Gösele, U. Porous silicon formation: A quantum wire effect. Appl. Phys. Lett. 1991, 58, 856−858. (3) Gal, M.; Reece, P. J.; Zheng, W.; Lerondel, G. Porous silicon: a versatile optical material. Proc. SPIE 2003, 5277, 9−16. (4) Smith, R. L.; Collins, S. D. Porous silicon formation mechanisms. J. Appl. Phys. 1992, 71, R1−R22. (5) Frohnhoff, S.; Berger, M. G. Porous silicon superlattices. Adv. Mater. 1994, 6, 963−965. (6) Vincent, G. Optical properties of porous silicon superlattices. Appl. Phys. Lett. 1994, 64, 2367−2369. (7) Lorenzo, E.; Oton, C. J.; Capuj, N. E.; Ghulinyan, M.; NavarroUrrios, D.; Gaburro, Z.; Pavesi, L. Porous silicon-based rugate filters. Appl. Opt. 2005, 44, 5415−5421. (8) Ilyas, S.; Böcking, T.; Kilian, K.; Reece, P. J.; Gooding, J.; Gaus, K.; Gal, M. Porous silicon based narrow line-width rugate filters. Opt. Mater. 2007, 29, 619−622.
E
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Porous Silicon by Atomic Layer Epitaxy. J. Electrochem. Soc. 1996, 143, 683−687. (32) Xu, Y.; Zhu, X.; Dan, Y.; Moon, J. H.; Chen, V. W.; Johnson, A. T.; Perry, J. W.; Yang, S. Electrodeposition of Three-Dimensional Titania Photonic Crystals from Holographically Patterned Microporous Polymer Templates. Chem. Mater. 2008, 20, 1816−1823. (33) Belmont, O.; Bellet, D.; Bréchet, Y. Study of the cracking of highly porous p+ type silicon during drying. J. Appl. Phys. 1996, 79, 7586−7591. (34) Pap, A. E.; Kordás, K.; Tóth, G.; Levoska, J.; Uusimäki, A.; Vähäkangas, J.; Leppävuori, S.; George, T. F. Thermal oxidation of porous silicon: Study on structure. Appl. Phys. Lett. 2005, 86, 041501. (35) Snow, P. A.; Squire, E. K.; Russell, P. S. J.; Canham, L. T. Vapor sensing using the optical properties of porous silicon Bragg mirrors. J. Appl. Phys. 1999, 86, 1781−1784. (36) Weiss, S. M.; Haurylau, M.; Fauchet, P. M. Tunable Porous Silicon Mirrors for Optoelectronic Applications. MRS Online Proc. Libr. 2002, 737 (F3), 50. (37) Bisi, O.; Ossicini, S.; Pavesi, L. Porous silicon: a quantum sponge structure for silicon based optoelectronics. Surf. Sci. Rep. 2000, 38, 1−126. (38) Weiss, S. M.; Fauchet, P. M. Electrically tunable porous silicon active mirrors. phys. status solidi (a) 2003, 197, 556−560. (39) Peumans, P.; Yakimov, A.; Forrest, S. R. Small molecular weight organic thin-film photodetectors and solar cells. J. Appl. Phys. 2003, 93, 3693−3723. (40) Brudieu, B.; Bris, A. L.; Teisseire, J.; Guillemot, F.; Dantelle, G.; Misra, S.; Cabarrocas, P. R. i.; Sorin, F.; Gacoin, T. Sol−Gel Route Toward Efficient and Robust Distributed Bragg Reflectors for Light Management Applications. Adv. Opt. Mater. 2014, 2, 1105−1112. (41) Eisler, C. N.; Abrams, Z. e. R.; Sheldon, M. T.; Zhang, X.; Atwater, H. A. Multijunction solar cell efficiencies: effect of spectral window, optical environment and radiative coupling. Energy Environ. Sci. 2014, 7, 3600−3605. (42) Xu, L.; Yao, Y.; Bronstein, N. D.; Li, L.; Alivisatos, A. P.; Nuzzo, R. G. Enhanced Photon Collection in Luminescent Solar Concentrators with Distributed Bragg Reflectors. ACS Photonics 2016, 3, 278− 285. (43) Beadie, G.; Shirk, J. S.; Rosenberg, A.; Lane, P. A.; Fleet, E.; Kamdar, A. R.; Jin, Y.; Ponting, M.; Kazmierczak, T.; Yang, Y.; Hiltner, A.; Baer, E. Optical properties of a bio-inspired gradient refractive index polymer lens. Opt. Express 2008, 16, 11540−11547. (44) Li, Y. Y.; Kim, P.; Sailor, M. J. Painting a rainbow on silicon − a simple method to generate a porous silicon band filter gradient. Phys. Status Solidi A 2005, 202, 1616−1618. (45) Collins, B. E.; Dancil, K. P. S.; Abbi, G.; Sailor, M. J. Determining Protein Size Using an Electrochemically Machined Pore Gradient in Silicon. Adv. Funct. Mater. 2002, 12, 187−191. (46) Ilyas, S.; Gal, M. Gradient refractive index planar microlens in Si using porous silicon. Appl. Phys. Lett. 2006, 89, 211123. (47) Ning, H.; Krueger, N. A.; Sheng, X.; Keum, H.; Zhang, C.; Choquette, K. D.; Li, X.; Kim, S.; Rogers, J. A.; Braun, P. V. TransferPrinting of Tunable Porous Silicon Microcavities with Embedded Emitters. ACS Photonics 2014, 1, 1144−1150. (48) Goodman, J. W. Introduction to Fourier Optics; Roberts & Company, 2005. (49) Barth, D. S.; Gladden, C.; Salandrino, A.; O’Brien, K.; Ye, Z.; Mrejen, M.; Wang, Y.; Zhang, X. Macroscale Transformation Optics Enabled by Photoelectrochemical Etching. Adv. Mater. 2015, 27, 6131−6136. (50) Azeredo, B. P.; Lin, Y.-W.; Avagyan, A.; Sivaguru, M.; Hsu, K.; Ferreira, P. Direct Imprinting of Porous Silicon via Metal-Assisted Chemical Etching. Adv. Funct. Mater. 2016, 26, 2929−2939.
(9) Pellegrini, V.; Tredicucci, A.; Mazzoleni, C.; Pavesi, L. Enhanced optical properties in porous silicon microcavities. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 52, R14328−R14331. (10) Ghulinyan, M.; Oton, C. J.; Bonetti, G.; Gaburro, Z.; Pavesi, L. Free-standing porous silicon single and multiple optical cavities. J. Appl. Phys. 2003, 93, 9724−9729. (11) Reece, P. J.; Lérondel, G.; Zheng, W. H.; Gal, M. Optical microcavities with subnanometer linewidths based on porous silicon. Appl. Phys. Lett. 2002, 81, 4895−4897. (12) Krueger, N. A.; Holsteen, A. L.; Kang, S.-K.; Ocier, C. R.; Zhou, W.; Mensing, G.; Rogers, J. A.; Brongersma, M. L.; Braun, P. V. Porous Silicon Gradient Refractive Index Micro-Optics. Nano Lett. 2016, 16, 7402. (13) Bjorklund, R. B.; Zangooie, S.; Arwin, H. Adsorption of Surfactants in Porous Silicon Films. Langmuir 1997, 13, 1440−1445. (14) Anderson, M. A.; Tinsley-Bown, A.; Allcock, P.; Perkins, E. A.; Snow, P.; Hollings, M.; Smith, R. G.; Reeves, C.; Squirrell, D. J.; Nicklin, S.; Cox, T. I. Sensitivity of the optical properties of porous silicon layers to the refractive index of liquid in the pores. physica status solidi (a) 2003, 197, 528−533. (15) Lin, V. S.-Y.; Motesharei, K.; Dancil, K.-P. S.; Sailor, M. J.; Ghadiri, M. R. A Porous Silicon-Based Optical Interferometric Biosensor. Science 1997, 278, 840−843. (16) Chan, S.; Fauchet, P. M.; Li, Y.; Rothberg, L. J.; Miller, B. L. Porous Silicon Microcavities for Biosensing Applications. phys. status solidi (a) 2000, 182, 541−546. (17) Stewart, M. P.; Buriak, J. M. Chemical and Biological Applications of Porous Silicon Technology. Adv. Mater. 2000, 12, 859−869. (18) Rong, G.; Saarinen, J. J.; Sipe, J. E.; Weiss, S. M. High Sensitivity Sensor Based on Porous Silicon Waveguide. MRS Online Proc. Libr. 2006, 934, 0934. (19) Rong, G.; Najmaie, A.; Sipe, J. E.; Weiss, S. M. Nanoscale porous silicon waveguide for label-free DNA sensing. Biosens. Bioelectron. 2008, 23, 1572−1576. (20) Mulloni, V.; Pavesi, L. Porous silicon microcavities as optical chemical sensors. Appl. Phys. Lett. 2000, 76, 2523−2525. (21) Ilyas, S.; Gal, M. Optical devices from porous silicon having continuously varying refractive index. J. Mater. Sci.: Mater. Electron. 2007, 18, S61−S64. (22) Salonen, J.; Lehto, V.-P.; Laine, E. Thermal oxidation of freestanding porous silicon films. Appl. Phys. Lett. 1997, 70, 637−639. (23) Berger, M. G.; Arens-Fischer, R.; Thönissen, M.; Krüger, M.; Billat, S.; Lüth, H.; Hilbrich, S.; Theiß, W.; Grosse, P. Dielectric filters made of PS: advanced performance by oxidation and new layer structures. Thin Solid Films 1997, 297, 237−240. (24) Li, Y. Y.; Cunin, F.; Link, J. R.; Gao, T.; Betts, R. E.; Reiver, S. H.; Chin, V.; Bhatia, S. N.; Sailor, M. J. Polymer Replicas of Photonic Porous Silicon for Sensing and Drug Delivery Applications. Science 2003, 299, 2045−2047. (25) Kelly, T. L.; Gao, T.; Sailor, M. J. Carbon and Carbon/Silicon Composites Templated in Rugate Filters for the Adsorption and Detection of Organic Vapors. Adv. Mater. 2011, 23, 1776−1781. (26) Granitzer, P.; Rumpf, K. Porous SiliconA Versatile Host Material. Materials 2010, 3, 943. (27) Oskam, G.; Long, J. G.; Natarajan, A.; Searson, P. C. Electrochemical deposition of metals onto silicon. J. Phys. D: Appl. Phys. 1998, 31, 1927. (28) Fukami, K.; Tanaka, Y.; Chourou, M. L.; Sakka, T.; Ogata, Y. H. Filling of mesoporous silicon with copper by electrodeposition from an aqueous solution. Electrochim. Acta 2009, 54, 2197−2202. (29) Singh, R. G.; Fouran, S.; Agarwal, V.; Mehra, R. M. Photoluminescence studies of ZnO/porous silicon nanocomposites. J. Phys. D: Appl. Phys. 2007, 40, 3090. (30) Li, J.; Sailor, M. J. Synthesis and characterization of a stable, label-free optical biosensor from TiO2-coated porous silicon. Biosens. Bioelectron. 2014, 55, 372−378. (31) Dücsö, C.; Khanh, N. Q.; Horváth, Z.; Bársony, I.; Utriainen, M.; Lehto, S.; Nieminen, M.; Niinistö, L. Deposition of Tin Oxide into F
DOI: 10.1021/acsphotonics.6b01001 ACS Photonics XXXX, XXX, XXX−XXX
