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Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S3 — May. 5, 2014
  • pp: A930–A940
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Near-unity broadband absorption designs for semiconducting nanowire arrays via localized radial mode excitation

Katherine T. Fountaine, Christian G. Kendall, and Harry A. Atwater  »View Author Affiliations


Optics Express, Vol. 22, Issue S3, pp. A930-A940 (2014)
http://dx.doi.org/10.1364/OE.22.00A930


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Abstract

We report design methods for achieving near-unity broadband light absorption in sparse nanowire arrays, illustrated by results for visible absorption in GaAs nanowires on Si substrates. Sparse (<5% fill fraction) nanowire arrays achieve near unity absorption at wire resonant wavelengths due to coupling into ‘leaky’ radial waveguide modes of individual wires and wire-wire scattering processes. From a detailed conceptual development of radial mode resonant absorption, we demonstrate two specific geometric design approaches to achieve near unity broadband light absorption in sparse nanowire arrays: (i) introducing multiple wire radii within a small unit cell array to increase the number of resonant wavelengths, yielding a 15% absorption enhancement relative to a uniform nanowire array and (ii) tapering of nanowires to introduce a continuum of diameters and thus resonant wavelengths excited within a single wire, yielding an 18% absorption enhancement over a uniform nanowire array.

© 2014 Optical Society of America

1. Introduction & Motivation

2. Results and discussion

2.1 Uniform nanowire arrays

The absorbed photocurrent of 25.0 mA/cm2 in the uniform nanowire array is impressive given the material volume, but needs to increase further to be competitive with the current world record thin film GaAs short circuit current of 29.7 mA/cm2 or approach the 4n2 Lambertian limit of 32.6 mA/cm2 for 150 nm planar equivalence [44

44. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 42),” Prog. Photovolt. Res. Appl. 21(1), 827–837 (2013). [CrossRef]

]. As shown in Fig. 1, the absorption in a uniform nanowire array is highly spectrally-dependent. While near-unity absorption is achieved at resonant wavelengths, off-resonance absorption is significantly lower. In order to approach thin film GaAs optical performance, the absorption must be near-unity across the spectrum. Towards this end, directed optical design can be used (i) to numerically increase the number of resonances within a nanowire array or (ii) to extend the wavelength span of a resonance. Using a detailed understanding of the leaky mode resonances in nanowires provided by the eigenvalue equation [Eq. (1)], both of these methods are pursued via modest modifications of nanowire array geometry.

2.2 Multi-radii nanowire arrays

Conceptually, the simplest extension of the electromagnetic principles observed in the uniform nanowire arrays to achieve broadband absorption is to introduce multiple nanowire radii in a single small unit cell array. Because the leaky mode resonances depend only on nanowire radius and not on array period, the inclusion of multiple nanowire radii in one array leads to an increase in the number of leaky mode resonances available without altering or eliminating the already existing resonances. Multiple scattering between neighboring wires enables incident light of a given wavelength to be re-directed towards the nanowire with the appropriate spectral resonance, as illustrated in Fig. 2(a).
Fig. 2 (a) Schematic of the mechanism of scattering and coupling into resonant leaky radial optical waveguide modes in the nanowire array with multiple radii; (b) Aerial view of one unit cell of the array with multiple nanowire radii and schematic of radial modes in nanowires of various radii, labeled with their TM11 resonant wavelengths; (c) Absorption vs. wavelength for each individual wire in the optimized multi-radii wire array depicted in (a) with arrows indicating corresponding curve/peak and wire radius
Notably, this mechanism will become less efficient as the distance between identical radius nanowires approaches and exceeds the nanowire scattering cross section.

To illustrate this concept, we consider an array containing 4 different nanowire radii (45, 55, 65, and 75 nm), arranged in a repeating 2x2 unit cell to create an infinite array [Fig. 2(a) and Fig. 2(b)]. Each of these nanowires supports leaky modes at different resonant wavelengths, depending on its radius. To demonstrate this, the light absorption in the multi-radii array was simulated and the absorption in each wire was separately recorded. Figure 2(c) shows a plot of the fraction of incident power absorbed in each nanowire as a function of wavelength. The four dominant peaks correspond to the TM11 modes of the nanowires, which red shift with increasing radius, as predicted by the eigenvalue equation [Eq. (1)]. The predicted resonant wavelength for the TM11 modes of the 45, 55, 65, and 75 nm radii nanowires are 515, 590, 675, and 760 nm, respectively, as indicated in Fig. 2(b) and Fig. 2(c). In this case, the peaks in the absorption curve are slightly red-shifted with respect to the predicted resonant wavelengths. We expect that this is due to spectral overlap of the neighboring TM11 resonances. Additionally, the absorption curves for the largest radii nanowire (r = 75 nm) exhibits a second absorption peak in the blue region, which corresponds to the TM12 resonance, predicted to occur at 440 nm. Field profiles of nanowire cross sections within this array confirm coupling into the TM11 and TM12 modes, as discussed above. Therefore, we conclude that a multi-radii nanowire array increases the number of spectral resonances and results in broader absorption than for a uniform nanowire array.

2.3 Nanocone arrays

The second approach taken to achieve near-unity array absorption across the spectrum is to extend the wavelength span of a single mode excited in an array of cylindrical wires by modifying the geometry to consist of an array of nanocones. To extend its resonance wavelength range, a nanowire can be tapered to form a truncated nanocone, which has a continuum of radii and, thus, a spectrum of resonant wavelengths for a single mode.

To illustrate that a nanocone array exhibits resonant absorption via the same leaky radial waveguide modes as for the nanowires, a three-dimensional map of the absorbed power was recorded as a function of wavelength for a nanocone with a tip radius of 40 nm and base radius of 100 nm. A schematic of the array is shown in Fig. 3(a).
Fig. 3 (a) Array of optimized GaAs truncated nanocones with tip radii of 40 nm, base radii of 100 nm and heights of 3 µm, labeling x, y, and z dimensions and indicating the vertical cross section shown in (c); (b) Absorption in a single truncated nanocone integrated over x and y, its radial cross section, (red indicating strong absorption and blue indicating little to no absorption) as a function of both wavelength and position along the z axis (labeled in a); (c) xz (vertical) cross sections of absorption for a single nanocone illuminated at wavelengths of 400, 500, 600, 700 and 800 nm
Figure 3(b) displays a plot of power absorbed in the nanocone as a function of wavelength and position along its vertical axis. Because the nanocone is tapered, the vertical coordinate, z, is equivalent to a varying radius coordinate, where z = 3 µm corresponds to a radius of 40 nm and z = 0 µm corresponds to a radius of 100nm. The largely red diagonal peak stretching from z = 0 µm and λ ~900 nm up to z = 3 µm and λ ~500 nm, the most prominent feature of Fig. 3(b), is the absorption into the resonant TM11 mode. To confirm coupling into the TM11 mode of the nanocone, radial cross sections of the absorbed power at the resonant wavelength-radius pairs indicated by the prominent diagonal peak in Fig. 3(b) were observed and found to match that of TM11 modes. Additionally, these wavelength-radius pairs match the eigenvalues predicted by Eq. (1). In addition to the strong TM11 peak observed in Fig. 3(b), a second, fainter diagonal peak is visible stretching from z = 0 µm and λ ~500 nm up to z ~1.5 µm and λ ~450 nm. The TM12 mode is responsible for this resonant absorption. The peak slowly fades away for larger z as the nanocone radius decreases and ultimately disappears around r = 70 nm (or z = 1.5 µm) where the mode is no longer accessible due to the dispersion curve of GaAs. The diagonal character of both the TM11 and TM12 peaks demonstrates that these modes have a spectrum of resonant wavelengths in a nanocone, as intended.

Another interesting feature of Fig. 3(b) is the sinusoidal variation of the absorbed power along the z axis. This modulation in absorption is due to longitudinal resonances, and the overall absorbed power intensity profile of Fig. 3(b) is explained by a linear combination of longitudinal resonances and radial resonances. This phenomenon is more clearly discernible from xz cross sections of the power absorbed in a nanocone, displayed in Fig. 3(c) for wavelengths of 400, 500, 600, 700, and 800 nm. All five of these cross sections illustrate the longitudinal modes present in the nanocone which give rise to the characteristic vertical oscillations in absorption intensity. Focusing on the four longer wavelength cross sections, the radial TM11 resonance shifts downward to larger radius with increasing wavelength and has multiple lobes in the vertical direction due to its convolution with the longitudinal resonances. No strong radial mode is visible for the 400 nm wavelength cross section because GaAs absorbs strongly in this region and light does not penetrate deep enough into the nanocone to establish a radial mode. Additionally, in the 500 nm wavelength cross section, the character of the TM12 mode is visible at the bottom of the nanocone, as an additional radial absorption peak becomes visible at the rim of the nanocone. From this detailed analysis of nanocone absorption, we conclude that arrays of truncated nanocones exhibit spectrally-extended resonances and provide another method to achieving a more broadband optical absorption response in nanowire arrays.

2.4 Optimization

As previously mentioned, the optimizations were performed under the constraint of constant fill fraction (5%) and constant nanostructure height (3 µm), corresponding to a 150 nm planar equivalent thin film. For comparison, the planar equivalent thin film absorbs 10.5 mA/cm2 and the uniform array of 65 nm radius nanowires [Fig. 4(a)] absorbs 25.0 mA/cm2. The absorption curves for these cases are displayed in Fig. 1 and Fig. 4(c) as the black and red lines, respectively. Note that partial spectral averaging has been used for the planar layer to smooth out the Fabry-Perot resonances (see Methods for details). All nanostructures are positioned on top of an infinite Si substrate and embedded in a 30 nm layer of SiOx to emulate SAG-MOCVD as-grown structures [27

27. S. Hu, C. Chi, K. T. Fountaine, M. Yao, H. A. Atwater, P. D. Dapkus, N. S. Lewis, and C. Zhou, “Optical, electrical, and solar energy-conversion properties of gallium arsenide nanowire-array photoanodes,” Energy Environ. Sci. 6(6), 1879–1890 (2013). [CrossRef]

].

To find the optimum dimensions for the array of truncated nanocones, the tip radii of the nanocones were varied between 30 and 60 nm and the base radii were varied between 70 and 100 nm, in 10 nm increments, holding height and fill fraction constant at 3 µm and 5%. Optimum absorption occurred for an array of truncated nanocones with tip radii of 40 nm and base radii of 100 nm, achieving an absorbed photocurrent of 29.5 mA/cm2 and an 18% improvement over the uniform array absorption [Fig. 4(c), green line]. At these dimensions, the extended resonance spectrums of the two TM modes overlap by more than 50 nm, enabling the observed near-unity broadband absorption. The truncated nanocone absorption equals or exceeds that of the uniform array except in the region of the TM11 resonance of the uniform array (650-750 nm). The higher absorption in the uniform array in this spectral region is due to a difference in vertical distance over which the mode is resonant: the entire length of the uniform wire compared to only a small fraction of the nanocone length.

3. Conclusion

Using a theoretical understanding of the leaky mode resonant absorption in sparse nanowire arrays, modest geometric modifications were used to achieve near-unity broadband absorption. Arrays with multiple wire radii and tapering were simulated for GaAs nanowires and shown to achieve a 15 and 18% improvement, respectively, over a uniform array by increasing the resonant portion of the AM1.5 spectrum. For selective area growth using metalorganic chemical vapor deposition, the arrays of truncated nanocones are experimentally achievable by altering the growth conditions [45

45. P. Mohan, J. Motohisa, and T. Fukui, “Controlled growth of highly uniform, axial/radial direction-defined, individually addressable InP nanowire arrays,” Nanotech. 16(12), 2903–2907 (2005). [CrossRef]

] and the wire arrays with multiple wire radii are experimentally achievable by definition of the patterned substrate. The nanocone structure is also achievable via a crystal facet-selective wet etch, such as KOH for tapered silicon nanowires [43

43. J. Y. Jung, Z. Guo, S. W. Jee, H. D. Um, K. T. Park, and J. H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18(S3Suppl 3), A286–A292 (2010). [CrossRef] [PubMed]

]. We note that while a nanocone array is predicted to achieve marginally higher absorption than a multi-radii array, the effect of modifying the wire growth conditions and introduction of new exposed crystal facets may alter the electronic properties of the array. However, given the relatively small difference in their absorption performance (< 1 mA/cm2), both nanocone arrays and multi-radii wire arrays may be promising routes to improve the optoelectronic performance of semiconductor nanowire arrays as solar cells.

4. Methods

Optimizations of the multi-radii arrays and truncated nanocone arrays were performed using broadband (350-900 nm), infinite plane wave sources to conserve computational power. To ensure accurate results, the three best performing structures of each design were illuminated with single wavelength, infinite plane wave sources at 10 nm intervals, with a long pulse time of 50 fs to simulate steady-state illuminated behavior. Partial spectral averaging over 10 THz was used to extract an average response over the 10 nm intervals; consequently, Fabry-Perot resonances are not observed in the final absorption curves.

Absorption in the structures was calculated using two transmission monitors, one directly above the nanostructure and one directly below. The absorbed current, in mA/cm2, was calculated from the absorption as a function of wavelength by weighting the simulated absorption curve by the AM1.5G spectrum and integrating over wavelength. Plots of normalized power absorbed were calculated by recording the electric field intensity spatially and multiplying by the imaginary part of the permittivity of GaAs.

Acknowledgments

This material is based upon work performed by the Joint Center for Artificial Photosynthesis, a DOE Energy Innovation Hub, supported through the Office of Science of the U.S. Department of Energy under Award No. DE-SC0004993. K.T.F. is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1144469. C.G.K. was supported by a Caltech Summer Undergraduate Research Fellowship.

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44.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 42),” Prog. Photovolt. Res. Appl. 21(1), 827–837 (2013). [CrossRef]

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OCIS Codes
(160.6000) Materials : Semiconductor materials
(220.2740) Optical design and fabrication : Geometric optical design
(350.6050) Other areas of optics : Solar energy
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Light Trapping for Photovoltaics

History
Original Manuscript: February 10, 2014
Revised Manuscript: April 6, 2014
Manuscript Accepted: April 6, 2014
Published: April 18, 2014

Citation
Katherine T. Fountaine, Christian G. Kendall, and Harry A. Atwater, "Near-unity broadband absorption designs for semiconducting nanowire arrays via localized radial mode excitation," Opt. Express 22, A930-A940 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S3-A930


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References

  1. L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett.7(11), 3249–3252 (2007). [CrossRef] [PubMed]
  2. O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. M. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett.8(9), 2638–2642 (2008). [CrossRef] [PubMed]
  3. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat Commun3(692), 692 (2012). [CrossRef] [PubMed]
  4. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express17(22), 19371–19381 (2009). [CrossRef] [PubMed]
  5. J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G. Lo, and D. L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett.95(243113), 1–3 (2009).
  6. L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, and Y. Wang, “Theoretical analysis and modeling of light trappig in high efficiency GaAs nanowire array solar cells,” Appl. Phys. Lett.99(143116), 1–3 (2011).
  7. Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y. L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, and A. Javey, “Ordered arrays of dual-diameter nanopillars for maximized optical absorption,” Nano Lett.10(10), 3823–3827 (2010). [CrossRef] [PubMed]
  8. L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater.8(8), 643–647 (2009). [CrossRef] [PubMed]
  9. S. K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K. D. Song, H. G. Park, and C. M. Lieber, “Tuning Light Absorption in core/shell silicon nanowire photovoltaic devices through morphological design,” Nano Lett.12(9), 4971–4976 (2012). [CrossRef] [PubMed]
  10. K. Seo, M. Wober, P. Steinvurzel, E. Schonbrun, Y. Dan, T. Ellenbogen, and K. B. Crozier, “Multicolored Vertical Silicon Nanowires,” Nano Lett.11(4), 1851–1856 (2011). [CrossRef] [PubMed]
  11. B. Kayes, H. A. Atwater, and N. S. Lewis, “Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells,” J. Appl. Phys.97(114302), 1–11 (2005).
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