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Abstract
The optical absorptance from arrays of GaAs nanowires (NWs) was examined by the finite element method. Absorptance in cylindrical NWs, frustum nanocones (with base wider than the top) and inverted frustum nanocones (with top wider than the base) was compared. The introduction of higher order HE1n modes, the red-shift of the HE1n modes along the NW length due to NW tapering, and the red-shift of the modes due to increase of the overall NW diameter all contribute to a broadening of the absorption spectrum in conical NWs as compared to NWs with a constant diameter. The optical reflectance versus NW top diameter shows a minimum due to a balance between reflectance from the top of the NWs and reflectance from the substrate between NWs. The optimum geometry for photovoltaic energy conversion was determined from the total photocurrent. An optimum photocurrent of 26.5 mAcm-2 was obtained, corresponding to a conical NW morphology with base diameter of 200 nm, top diameter of 110 nm, and length of 2000 nm. An optimized inverse tapered conical morphology gave comparable performance.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Semiconductor nanowires (NWs) are being investigated for applications in photonic and optoelectronic devices [1–4]. In particular, the optical absorption in cylindrical III-V NW arrays has been investigated predominantly for GaAs [5–9] and InP material [10–13] mainly for photovoltaic applications. Control of the shape, size, and positioning of NWs are critical factors that determine device performance. Simulations indicate that the optimal absorption of the solar spectrum in cylindrical GaAs and InP NWs for normal light incidence (AM1.5G simulated solar spectrum) occurs when the NW diameter is ∼180 nm, the pitch (separation between NWs) is ∼360 nm, and the NW length is ∼2 μm [5–13]. With the optimum NW geometry, the absorptance exceeds 90% over the visible spectrum, which is much higher than that of thin films with thickness equal to the NW length (and excluding an anti-reflection coating). The improvement in optical absorptance of NW arrays as compared to thin films is due to the presence of leaky mode resonances (LMRs) within the NWs [14,15]. The HE1n set of modes can efficiently couple to vertically standing NWs, resulting in an optical antenna effect [16–18]. These modes produce resonant absorption peaks which shift to longer wavelengths with increasing NW diameter to satisfy the electromagnetic boundary conditions [14,15]. This phenomenon can be used to create wavelength selectivity for multispectral photodetectors [19,20] or broadband absorption for solar photovoltaic cells [21].
Generally, NWs with cylindrical cross-section have been studied with a few notable exceptions such as elliptical, square, hexagonal and triangular cross-sections where relatively minor differences in absorption were noted [22–25]. Also, the symmetry of the array lattice (typically square or hexagonal) has little effect on optical absorption for large inter-NW separations where there is negligible coupling of optical modes between adjacent NWs. A uniform array of cylindrical NWs of constant diameter may not be the optimum geometry to maximize optical absorptance. For example, to further improve absorption efficiency, arrays containing NWs with multiple diameters have been investigated [26–30]. More complicated morphologies, such as periodic diameter modulation in NWs, has also been investigated [31,32]. Another fruitful approach to improving optical absorptance involves tuning the NW morphology. Rather than a discrete set of NW diameters, it is possible to vary the diameter of NWs continuously in a tapered morphology. Nanocones, frustum nanocones, or related shapes [33–41] can improve optical absorption as compared to NWs with a constant diameter due to less reflection from the smaller top diameter and less transmission due to the larger base diameter. The gradual increase in diameter of the nanocones acts as a gradual refractive index profile that improves anti-reflection. Finally, the expanding diameter of the nanocone broadens the HE1n resonance absorption peaks, improving the broadband absorption. Alternatively, inverted frustum nanocone arrays (sometimes called light funnels) [42–45] or related structures [46,47] have recently been proposed, inspired by the working principle of the human retina [42,48]. The inverted nanocones can provide enhanced optical absorption compared to NWs due to the support of multiple optical modes.
NWs can be grown by either top-down etching or bottom-up growth methods [49]. Wet and dry etching methods are commonly used for the top-down fabrication of NWs. For example, NWs have been selectively etched with doping-dependent etchants [32]. Reactive ion etching (RIE) has also been used to fabricate cylindrical [50], conical [27,40] and inverted conical NWs [42]. However, the performance of NW devices produced by etching may be limited by the resulting surface roughness and high density of surface states. Alternatively, NWs may be produced by bottom-up growth with smooth sidewall facets and passivated by shell growth [51]. Impurity dopants can also be incorporated during growth of the NWs, in either an axial or core-shell geometry, to produce electrically active NW diodes. Bottom-up grown NWs are typically produced by epitaxy using the vapor-liquid-solid (VLS) method where seed particles, typically metallic droplets, are used to collect and nucleate the growth species into a NW array [49]. GaAs NWs can be grown by the self-assisted growth method where growth is seeded by a Ga droplet. The diameter of the NWs can be controlled by the size of the Ga droplet. Various NW morphologies, such as tapered, straight (cylindrical), or inverse tapered NWs, are possible by controlling the Ga droplet continuously during growth. For example, we recently showed that an inverted nanocone morphology could be achieved in GaAs NWs during molecular beam epitaxy (MBE) by controlling the Ga droplet size via growth conditions [52]. The inverted conical morphology is particularly advantageous because the small base diameter can be less than the critical diameter for misfit dislocations due to the lattice-mismatch between NWs and their substrate (e.g., GaAs NWs on Si), while the top diameter can be tuned for optimum absorptance of incident light. Here, we examine the optical absorptance in GaAs NWs for conical, straight and inverted conical morphologies (frustum nanocones), and optimize the geometry for absorption of the simulated solar spectrum.
2. Methods
The optical absorptance spectrum from 300 nm to 900 nm was simulated by the finite element method (FEM) using the RF module in COMSOL Multiphysics 5.3A software. FEM is a popular choice of solver, which is well suited for NW designs of arbitrary shape [53]. The electric field of the NWs was simulated using left-hand circularly polarized light with incident power weighted by the AM1.5D simulated solar spectrum [54].
The geometric unit cell was periodic in the x and y directions (z is along the length of the NW), simulating a square array of NWs. A port boundary is placed in the space above the NW to simulate the incoming wave. The reflected and transmitted power are found by integrating the power flowing through xy planes. Reflection is measured in the plane directly above the port boundary (which is transparent to the reflected wave), and transmitted power is obtained at several planes spaced evenly along the length of the NW. Perfectly matched layers (PMLs) were placed at the top and bottom of the NW geometry to absorb the reflected and transmitted light. The simulated geometry is shown in Fig. 1(d). The model geometry consisted of a GaAs NW sitting on a 500 nm slab of Si and surrounded by vacuum. As illustrated in Fig. 1, three NW morphologies were examined by varying the top and base NW diameter: a frustum cone (referred to as conical NWs), a straight (cylindrical) NW, and an inverted frustum cone (referred to as inverted conical NWs). The materials were defined by their wavelength-dependent refractive indices [55]. The NW pitch was fixed at 320 nm since this value was previously shown to produce optimum solar absorption for cylindrical NWs [5–13]. The top diameters were varied between 50 nm and 290 nm for one of three fixed base diameters: 50 nm, 100 nm and 200 nm. The 50 nm and 100 nm base diameters are particularly relevant because they are below the theoretical critical diameter for misfit dislocations in GaAs NWs on Si [56]. The NWs had a length of 1000 nm or 2000 nm.
Fig. 1. (a-c) Definition of NW morphologies. (d) Schematic of source, reflection and transmission planes.
3. Results and discussion
Figure 2 shows the simulated absorptance spectra for NWs with a base diameter of 100 nm and a length of 2000nm. The NW top diameter is given above each plot. The spectra have been subdivided into contributions from incremental segments of 500 nm length (segments A, B, C and D, from the top to the bottom of the NW, respectively). The total absorptance from the full 2000nm length of the NW is shown as the black curves in Fig. 2. The top diameter of 50, 70 and 90 nm give a conical NW morphology, while all other top diameters (>100 nm) give an inverted conical NW morphology. Figure 2 also shows the simulated absorptance spectrum for a 2000nm thick GaAs thin film for comparison with the NWs.
Fig. 2. Absorptance spectra for NWs with a base diameter of 100 nm and a length of 2000nm. The NW top diameter is given above each plot. Insets in the 50 nm and 290 nm panels illustrate the NW profile. The spectra have been subdivided into the contributions to absorptance from incremental segments of 500 nm length where A is the top 500 nm and D is the bottom 500 nm. The absorptance spectrum of a thin film is also shown in the bottom right panel.
Starting with a top diameter of 50 nm (top left panel of Fig. 2), the main absorption peak in each segment (A, B, C, D) is attributed to the HE11 resonance mode as confirmed by field patterns (for example, see Supplement 1, Fig. S1). For NWs with top diameter exceeding about 70 nm, the greatest contribution to the optical absorption occurs from the top 500 nm of the NW (segment A, green curves of Fig. 2). The HE11 absorption peak of segment A (green curves) continuously red-shifts as the NW top diameter increases from 70 nm to 290 nm. Below a top diameter of 110 nm, where the NW morphology is conical, the HE11 mode also red-shifts as the diameter increases from the top of the NW (segment A) to the bottom of the NW (segment B). This red-shift with increasing NW diameter is expected for the HE1n modes due to the dispersion relation that arises from the electromagnetic boundary conditions [14,15,19,20].
As the NW top diameter increases, higher order modes are introduced (for example, the peak at 445 nm for a top diameter of 170 nm is an HE12 mode; see Supplement 1, Fig. S2). The higher order modes also red-shift with NW top diameter and tapering, and begin to dominate the absorption spectrum above a top diameter of 170 nm. Mode coupling is expected as the NW top diameter approaches the pitch between NWs.
The introduction of higher order HE1n modes, the red-shift of the HE1n modes along the NW length due to NW tapering, and the red-shift of the modes due to increase of the overall NW diameter, all contribute to a broadening of the absorption spectrum in conical NWs as compared to NWs with a constant diameter. Similar trends are presented in the Supplemental document (Supplement 1, Figs. S3-S7) for different NW base diameters (50, 200 nm) and a different NW length (1000 nm). This broadening of the absorption spectrum is advantageous for solar photovoltaic energy conversion. It is noteworthy that the maximum in the total absorptance spectrum of the NWs exceeded that from the thin film in all cases due to the optical modes in the NWs.
In addition to the mode peaks, periodic ripples of small amplitude are observed in the total absorptance spectra of Fig. 2, particularly at large top diameters. These oscillations are due to multiple reflections from the top (GaAs/air interface) and base (GaAs/Si interface) of the NW forming a Fabry-Perot cavity. The period of the ripples increases with decreasing NW length, consistent with F-P modes (compare Fig. 2 (2000nm length) with Supplement 1, Fig. S5 (1000 nm length)).
Figure 3 shows the total reflectance and transmittance from the NWs (averaged over all wavelengths from 300-900 nm). The reflectance is given by:
where ${P_{ref}}$ is the reflected power, ${P_{in}}$ is the incident power at each simulated wavelength, and N is the number of wavelength increments in the summation (wavelength increment was 10 nm). Here, Pin is constant, not weighted by the solar spectrum. A similar calculation was performed for the transmittance where the transmitted power is measured in the plane at the base of the NW. A horizontal line representing the reflectance and transmittance from a thin film without any anti-reflection coating is also shown in Fig. 3.Fig. 3. (a) The total reflectance and (b) total transmittance versus top diameter for each of the NW morphologies, as well as a thin film. The legend indicates the NW base diameter. Dashed lines represent NWs with length of 1000 nm and solid lines indicate those with length of 2000nm.
As the NW top diameter increases, the reflectance approaches that of the GaAs thin film due to increasing reflectance from the top of the NWs. Conversely, as the NW top diameter decreases, there is an increasing contribution to reflectance from the exposed Si/air interface between the NWs. Consequently, NWs with small base diameters of 50 nm or 100 nm have a minimum reflectance near 170 nm, which can be understood as a balance between reflectance from the NW top and the substrate. As the base of the NW becomes thinner, the substrate surface can contribute more strongly to the reflection. This contribution from the substrate is evident in Fig. 3(a) by the greater reflectance for a 50 nm base diameter as compared to a 100 nm base diameter when the top diameter is below 170 nm. For the conical NWs with 200 nm base diameter, relatively little substrate is available for light reflection since the base of the NW nearly fills the unit cell. In this instance, a reflectance minimum is not observed, and the reflectance increases monotonically with the NW top diameter. Lengthening the NW contributes to a decrease in the reflectance since a taller NW has a smaller angle of escape for back-reflected light, increasing the likelihood of scattered light interactions with the sidewalls of the NW.
Figure 3(b) shows that transmission through the NW can be reduced by increasing the top diameter. For small top diameter, the lack of volume leads to large transmission. The ratio between the top and the bottom diameter of the NW also plays a role. A larger ratio means that a wider range of diameters is accessible along the length of the NW, which improves absorption at different wavelengths across the spectrum, according to the diameter dependence of the HE1n optical resonances. For comparison, Fig. 3 also shows the transmission and reflection for 1000 nm and 2000nm thin films without anti-reflection coatings.
The overall performance of NW arrays for solar energy conversion is determined by the absorptance, transmittance and reflectance. To quantify the expected photovoltaic performance of the various NW morphologies, the photocurrent density ($J$ in units of mA/cm2) generated by the AM1.5D simulated solar spectrum was calculated according to the following volume integral [9]:
where e is the fundamental charge, ${\varepsilon _0}$ is the permittivity of free space, P is the pitch of the square array, E is the electric field in the NW solved by COMSOL, and n and k are the real and complex components of the refractive index, respectively. As mentioned in the Methods section, the incident electric field is weighted by the AM1.5D simulated solar spectrum, so that |E|2 in Eq. (1) accordingly contains the spectral dependence of the solar spectrum. The integrand has units of m-3s-1 and represents the rate of photon absorption. The internal quantum efficiency is assumed to be unity; i.e., each photon produces one electron-hole pair that contributes to the photocurrent. The total photocurrent is the sum of the photocurrent over all wavelengths.The total photocurrent for each NW morphology is shown in Fig. 4 for two different lengths of 1000 nm (dashed lines) and 2000nm (solid lines). For comparison with the NWs, the horizontal lines indicate the photocurrent from a GaAs thin film without any anti-reflection coating. The photocurrent improves slightly by increasing the NW length from 1000 to 2000nm by reducing transmittance loss through the NW array, and likewise for the thin film. The optimum photocurrent (26.5 mAcm-2) corresponds to a conical NW morphology with base diameter of 200 nm, top diameter of 110 nm, and length of 2000nm. For the inverted conical morphology with a base diameter of 50 or 100 nm, the optimum photocurrent was 25.0 and 25.6 mAcm-2, respectively, with an optimum top diameter of 210 nm. Figure S9 of Supplement 1 shows the related electric field profiles. Previously reported optimized cylindrical NWs of 170 nm diameter also had photocurrents of 25.6 mAcm-2 [52], making the inverted cones on par with the cylindrical structures, while the cones demonstrated a slight improvement. However, the smaller base diameter of the inverted conical morphology would be advantageous to reduce misfit dislocations with a lattice-mismatched substrate such as silicon.
Fig. 4. Photocurrent versus top diameter generated in each of the NW morphologies. The legend indicates the NW base diameter. Dashed lines represent NWs with length of 1000 nm and solid lines indicate those with length of 2000nm.
In comparison, the photocurrent for the thin film GaAs (without any anti-reflection coatings) was much lower than that from the NWs due to substantial reflectance loss. The maximum possible photocurrent from GaAs under the AM1.5D spectrum, ignoring any reflectance or transmittance loss, is 29 mAcm-2. Thus, the optimum NW morphology achieves a photocurrent that approaches the best possible performance.
Kordrostrami et al. [36] showed that photocurrent improved by 13% for conical Si NWs but decreased by 5% for inverted conical NWs as compared to cylindrical NWs [36]. Ko et al. [31] compared cylindrical Si NWs to four different inverted conical geometries. They reported a short circuit current of 27.5 mAcm-2 for the best inverted cone. Shalev et. al [42] showed absorption enhancements of 65% and 36.6% for inverted Si cones and cylinders, respectively, as compared to a thin film (and a 1.8% improvement of inverted cones over cylinders). Wang and Leu [38] showed that Si conical NWs can absorb 74% of light in the solar spectrum compared to only 61% in cylindrical NWs. With respect to GaAs NWs, Fountaine et al. [57] demonstrated that GaAs conical NWs improve absorption over cylindrical NWs showing an increase in photocurrent from 25.0 mAcm-2 to 29.5 mAcm-2.
The dependence of pitch has not been explored in this work, although pitch can play an important role in light scattering and absorption [58]. If the pitch is too small, neighboring NWs compete for absorption, and reflection from the top of the NW array increases. On the other hand, if the pitch is too large, the NW absorption decreases since the NW density is too sparse. The optimum ratio between the top diameter and the pitch is a topic for future studies. However, we do not expect substantial further improvement with pitch, since the optimum NW geometry discussed above already provides nearly the maximum theoretical current density.
4. Conclusions
Optical absorptance in conical and inverted conical NW arrays support multiple HE1n modes that red-shift along the length of the NW as the diameter changes due to tapering. Conical NWs have superior anti-reflection properties compared to the inverted conical NWs by reducing reflectance loss from the substrate and NW top. Nevertheless, when both optical absorptance and reflectance are considered, the inverted conical NWs achieved only slightly less photocurrent than the conical NWs.
Funding
Natural Sciences and Engineering Research Council of Canada (NSERC CREATE TOP-SET (497981-2017), RGPIN-2018-04015).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. Y. Zhang, J. Wu, M. Aagesen, and H. Liu, “III–V nanowires and nanowire optoelectronic devices,” J. Phys. D: Appl. Phys. 48(46), 463001 (2015). [CrossRef]
2. N. I. Goktas, P. Wilson, A. Ghukasyan, D. Wagner, S. McNamee, and R. R. LaPierre, “Nanowires for energy: A review,” Appl. Phys. Rev. 5(4), 041305 (2018). [CrossRef]
3. R. R. LaPierre, M. Robson, K. M. Azizur-Rahman, and P. Kuyanov, “A review of III-V nanowire infrared photodetectors and sensors,” J. Phys. D: Appl. Phys. 50(12), 123001 (2017). [CrossRef]
4. R. R. LaPierre, A. C. E. Chia, S. J. Gibson, C. M. Haapamaki, J. Boulanger, R. Yee, P. Kuyanov, J. Zhang, N. Tajik, N. Jewell, and K. M. A. Rahman, “III-V nanowire photovoltaics: Review of design for high efficiency,” Phys. Status Solidi RRL 7(10), 815–830 (2013). [CrossRef]
5. H. Guo, L. Wen, X. Li, Z. Zhao, and Y. Wang, “Analysis of optical absorption in GaAs nanowire arrays,” Nanoscale Res. Lett. 6(1), 617 (2011). [CrossRef]
6. L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, and Y. Wang, “Theoretical analysis and modeling of light trapping in high efficiency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011). [CrossRef]
7. Y. Hu, R. R. LaPierre, M. Li, K. Chen, and J.-J. He, “Optical characteristics of GaAs nanowire solar cells,” J. Appl. Phys. 112(10), 104311 (2012). [CrossRef]
8. K. W. Robertson, R. R. LaPierre, and J. J. Krich, “Accurate wave optics modeling of nanowire solar cells using rigorous coupled wave analysis,” Opt. Express 27(4), A133–A147 (2019). [CrossRef]
9. A. H. Trojnar, C. E. Valdivia, R. R. LaPierre, K. Hinzer, and J. J. Krich, “Optimizations of GaAs nanowire solar cells,” IEEE J. Photovolt. 6(6), 1494–1501 (2016). [CrossRef]
10. N. Anttu, A. Abrand, D. Asoli, M. Heurlin, I. Åberg, L. Samuelson, and M. Borgström, “Absorption of light in InP nanowire arrays,” Nano Res. 7(6), 816–823 (2014). [CrossRef]
11. P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, and A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt: Res. Appl. 20(8), 945–953 (2012). [CrossRef]
12. J. Kupec, R. L. Stoop, and B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Opt. Express 18(26), 27589–27605 (2010). [CrossRef]
13. N. Anttu and H. Q. Xu, “Coupling of light into nanowire arrays and subsequent absorption,” J. Nanosci. Nanotechnol. 10(11), 7183–7187 (2010). [CrossRef]
14. K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics (Springer, 2008).
15. A.W. Snyder and J.D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
16. B. Wang and P. W. Leu, “Tunable and selective resonant absorption in vertical nanowires,” Opt. Lett. 37(18), 3756–3758 (2012). [CrossRef]
17. K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to Bloch photonic crystal modes,” J. Appl. Phys. 116(15), 153106 (2014). [CrossRef]
18. V. Dagytė and N. Anttu, “Modal analysis of resonant and non-resonant optical response in semiconductor nanowire arrays,” Nanotechnology 30(2), 025710 (2019). [CrossRef]
19. S. Mokkapati, D. Saxena, H. H. Tan, and C. Jagadish, “Optical design of nanowire absorbers for wavelength selective photodetectors,” Sci. Rep. 5(1), 15339 (2015). [CrossRef]
20. K. M. Azizur-Rahman and R. R. LaPierre, “Wavelength-selective absorptance in GaAs, InP and InAs nanowire arrays,” Nanotechnology 26(29), 295202 (2015). [CrossRef]
21. S. Mokkapati and C. Jagadish, “Review on photonic properties of nanowires for photovoltaics,” Opt. Express 24(15), 17345–17358 (2016). [CrossRef]
22. R. Ren, Y.-X. Guo, and R.-H. Zhua, “Enhanced absorption in elliptical silicon nanowire arrays for solar energy harvesting,” Opt. Eng. 53(2), 027102 (2014). [CrossRef]
23. L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10(2), 439–445 (2010). [CrossRef]
24. Y. Yu and L. Cao, “Leaky mode engineering: A general design principle for dielectric optical antenna solar absorbers,” Opt. Commun. 314, 79–85 (2014). [CrossRef]
25. Y. Zeng, Q. Ye, and W. Shen, “Design principles for single standing nanowire solar cells: going beyond the planar efficiency limits,” Sci. Rep. 4(1), 4915 (2015). [CrossRef]
26. B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, R. C. McPhedran, and C. Martijn de Sterke, “Nanowire array photovoltaics: Radial disorder versus design for optimal efficiency,” Appl. Phys. Lett. 101(17), 173902 (2012). [CrossRef]
27. K. T. Fountaine, W.-H. Cheng, C. R. Bukowsky, and H. A. Atwater, “Near-unity unselective absorption in sparse InP nanowire arrays,” ACS Photonics 3(10), 1826–1832 (2016). [CrossRef]
28. X. Yan, L. Gong, L. Ai, W. Wei, X. Zhang, and X. Ren, “Enhanced photovoltaic performance of nanowire array solar cells with multiple diameters,” Opt. Express 26(26), A974–A983 (2018). [CrossRef]
29. G. J. Lee, K. Park, M. S. Kim, S. Chang, T. J. Seok, H.-G. Park, G. Ju, K. Kim, and Y. M. Song, “Selective and sensitive photon sieve based on III–V semiconductor nanowire forest fabricated by lithography-free process,” Adv. Opt. Mater. 8(17), 2000198 (2020). [CrossRef]
30. F. Adibzadeh and S. Olyaee, “Optical absorption enhancement in vertical InP nanowire random structures for photovoltaic applications,” Opt. Quantum Electron. 52, 6 (2020). [CrossRef]
31. M. Ko, S.-H. Baek, B. Song, J.-W. Kang, S.-A. Kim, and C.-H. Cho, “Periodically diameter-modulated semiconductor nanowires for enhanced optical absorption,” Adv. Mater. 28(13), 2504–2510 (2016). [CrossRef]
32. S. Kim and J. F. Cahoon, “Geometric nanophotonics: Light management in single nanowires through morphology,” Acc. Chem. Res. 52(12), 3511–3520 (2019). [CrossRef]
33. Y. Zhan, X. Li, S. Wu, K. Li, Z. Yang, and A. Shang, “Enhanced photoabsorption in front-tapered single-nanowire solar cells,” Opt. Lett. 39(19), 5756–5759 (2014). [CrossRef]
34. B. Wang, E. Stevens, and P.W. Leu, “Strong broadband absorption in GaAs nanocone and nanowire arrays for solar cells,” Opt. Express 22, A386–A395 (2014). [CrossRef]
35. Y. Li, P. Gao, Q. Chen, J. Yang, J. Li, and D. He, “Nanostructured semiconductor solar absorbers with near 100% absorption and related light management picture,” J. Phys. D: Appl. Phys. 49(21), 215104 (2016). [CrossRef]
36. Z. Kordrostami and A. Yadollahi, “High absorption enhancement of invert funnel and conical nanowire solar cells with forward scattering,” Opt. Commun. 459, 125059 (2020). [CrossRef]
37. S. Jeong, M. D. McGehee, and Y. Cui, “All-back-contact ultra-thin silicon nanocone solar cells with 13.7% power conversion efficiency,” Nat. Commun. 4(1), 2950 (2013). [CrossRef]
38. B. Wang and P. W. Leu, “Enhanced absorption in silicon nanocone arrays for photovoltaics,” Nanotechnology 23(19), 194003 (2012). [CrossRef]
39. S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, and J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011). [CrossRef]
40. S. J. Gibson, B. van Kasteren, B. Tekcan, Y. Cui, D. van Dam, J. E. Haverkort, E. P. Bakkers, and M. E. Reiner, “Tapered InP nanowire arrays for efficient broadband high-speed single-photon detection,” Nat. Nanotechnol. 14(5), 473–479 (2019). [CrossRef]
41. G. Y. Abdel-Latif, M. F. O. Hameed, M. Hussein, M. A. Razzak, and S. S. A. Obayya, “Electrical characteristics of funnel-shaped silicon nanowire solar cells,” J. Photonics Energy 7(4), 047501 (2017). [CrossRef]
42. G. Shalev, S. W. Schmitt, H. Embrechts, G. Bronstrup, and S. Christiansen, “Enhanced photovoltaics inspired by the fovea centralis,” Sci. Rep. 5(1), 8570 (2015). [CrossRef]
43. A. Prajapati, Y. Nissan, T. Gabay, and G. Shalev, “Light trapping with silicon light funnel arrays,” Materials 11(3), 445 (2018). [CrossRef]
44. A. Prajapatia, Y. Nissana, T. Gabaya, and G. Shalev, “Broadband absorption of the solar radiation with surface arrays of subwavelength light funnels,” Nano Energy 54, 447–452 (2018). [CrossRef]
45. M. D. Ko, T. Rim, K. Kim, M. Meyyappan, and C. K. Baek, “High efficiency silicon solar cell based on asymmetric nanowire,” Sci. Rep. 5(1), 11646 (2015). [CrossRef]
46. L. Li, K.-Q. Peng, B. Hu, X. Wang, Y. Hu, X.-L. Wu, and S.-T. Lee, “Broadband optical absorption enhancement in silicon nanofunnel arrays for photovoltaic applications,” Appl. Phys. Lett. 100(22), 223902 (2012). [CrossRef]
47. G. Marko, A. Prajapati, and G. Shalev, “Subwavelength nonimaging light concentrators for the harvesting of the solar radiation,” Nano Energy 61, 275–283 (2019). [CrossRef]
48. A. M. Labin, S. K. Safuri, E. N. Ribak, and I. Perlman, “Muller cells separate between wavelengths to improve day vision with minimal effect upon night vision,” Nat. Commun. 5(1), 4319 (2014). [CrossRef]
49. P. C. McIntyre and A. Fontcuberta i Morral, “Semiconductor nanowires: to grow or not to grow?” Materials Today Nano 9, 100058 (2020). [CrossRef]
50. N. Dhindsa, A. Chia, J. Boulanger, I. Khodadad, R. LaPierre, and S. S. Saini, “Highly ordered vertical GaAs nanowire arrays with dry etching and their optical properties,” Nanotechnology 25(30), 305303 (2014). [CrossRef]
51. A. C. E. Chia, M. Tirado, Y. Li, S. Zhao, Z. Mi, D. Comedi, and R. R. LaPierre, “Electrical transport and optical model of GaAs-AlInP core-shell nanowires,” J. Appl. Phys. 111(9), 094319 (2012). [CrossRef]
52. D. P. Wilson, A. S. Sokolovskii, V. G. Dubrovskii, and R. R. LaPierre, “Photovoltaic light funnels grown by GaAs nanowire droplet dynamics,” IEEE J. Photovolt. 9(5), 1225–1231 (2019). [CrossRef]
53. N. Anttu, H. Mäntynen, T. Sadi, A. Matikainen, J. Turunen, and H. Lipsanen, “Comparison of absorption simulation in semiconductor nanowire and nanocone arrays with the Fourier modal method, the finite element method, and the finite-difference time-domain method,” Nano Express 1(3), 030034 (2020). [CrossRef]
54. https://www.nrel.gov/grid/solar-resource/spectra-am1.5.html
55. E.D. Palik, Handbook of Optical Constants of Solids, (Academic Press Inc., Washington, 1985).
56. G. E. Cirlin, V. G. Dubrovskii, I. P. Soshnikov, N. V. Sibirev, Y. B. Samsonenko, A. D. Bouravleuv, J. C. Harmand, and F. Glas, “Critical diameters and temperature domains for MBE growth of III-V nanowires on lattice mismatched substrates,” Phys. Status Solidi RRL 3(4), 112–114 (2009). [CrossRef]
57. K. T. Fountaine, C. G. Kendall, and H. A. Atwater, “Near-unity broadband absorption designs for semiconducting nanowire arrays via localized radial mode excitation,” Opt. Express 22(S3), A930–A940 (2014). [CrossRef]
58. N. Anttu, “Absorption of light in a single vertical nanowire and a nanowire array,” Nanotechnology 30(10), 104004 (2019). [CrossRef]
