Laterally assembled nanowires for ultrathin broadband solar absorbers

We studied optical resonances in laterally oriented Si nanowire arrays by conducting finite-difference time-domain simulations. Localized Fabry-Perot and whispering-gallery modes are supported within the cross section of each nanowire in the array and result in broadband light absorption. Comparison of a nanowire array with a single nanowire shows that the current density (JSC) is preserved for a range of nanowire morphologies. The JSC of a nanowire array depends on the spacing of its constituent nanowires, which indicates that both diffraction and optical antenna effects contribute to light absorption. Furthermore, a vertically stacked nanowire array exhibits significantly enhanced light absorption because of the emergence of coupled cavity-waveguide modes and the mitigation of a screening effect. With the assumption of unity internal quantum efficiency, the JSC of an 800-nm-thick cross-stacked nanowire array is 14.0 mA/cm, which yields a ~60% enhancement compared with an equivalent bulk film absorber. These numerical results underpin a rational design strategy for ultrathin solar absorbers based on assembled nanowire cavities. ©2014 Optical Society of America OCIS codes: (140.4780) Optical resonators; (350.6050) Solar energy; (050.0050) Diffraction

NW photovoltaics present unconventional light absorption characteristics because of their subwavelength cavity features.For example, the optical antenna effect explains how incident light can interact with a NW beyond the NW's physical cross section [26,27].Morphologydependent optical resonances in a NW cavity also lead to efficient light absorption over a broad range of wavelengths [8,27].Together, these features emphasize the need for further design and synthesis of NW cavities, which could improve absorption efficiencies and shortcircuit current densities (J SC 's) and surpass conventional limits.Photovoltaic studies regarding laterally oriented NWs have focused only on single-NW devices [5][6][7][8], whereas vertically oriented NW photovoltaics have been studied with respect to both single [13] and assembled [10][11][12] structures.To develop a next-generation platform for ultrathin solar cells, laterally oriented single NWs must be demonstrated in large-area arrays [25,28].In this study, we investigated the light absorption properties of laterally assembled NW arrays using threedimensional (3D) finite-difference time-domain (FDTD) simulations [29].First, an array comprising close-packed NWs was compared with a single NW on the basis of simulated absorption spectra and mode profiles for a number of different NW cross-sectional morphologies (various sizes and shapes).Second, examination of NW arrays with different pitches was performed to determine the optimal NW spacing, i.e., the spacing that yields the highest J SC .Finally, the absorption properties of multi-layered NW arrays were studied and compared with those of film structures with an equivalent thickness, providing insights into the feasibility of nanomaterial building blocks such as 3D ultrathin light absorbers.

Close-packed NW array with various cross-sectional morphologies
Figure 1(A) is a schematic of a hexagonal Si NW comprising a p-type core, an intrinsic shell, and an n-type shell.Such core/shell p/i/n Si NWs have been successfully demonstrated as single photovoltaic devices with a high solar-to-electric conversion efficiency [6][7][8].To describe the hexagonal cross section of a NW in our calculations, spatial resolutions of 5 / 3, 5, and 5 nm were imposed in the x-, y-and z-directions, respectively.A single NW and a NW array were placed on a transparent quartz substrate.The NW structures were homogeneously composed of crystalline Si [30].The absorption spectrum was calculated while the wavelength of a normal plane wave was scanned from 280 to 1000 nm with a step size of 5 nm.Details regarding the FDTD calculations can be found in other literature [7,8].
Transverse-electric (TE) and transverse-magnetic (TM) polarized absorption spectra were calculated for a single NW and a close-packed NW array (pitch = 230 nm) with equivalent NW height of 200 nm [Fig.1(B)].A 200-nm-thick Si film was also simulated as a reference [solid blue, Fig. 1(B)].Notably, for TE polarized light, the absorption efficiency of the NW array was higher than that of the single NW, whereas for TM polarized light, the single NW outperformed the NW array.This is consistent with previous studies [25,31].In addition, the peak positions of the three structures were nearly identical, except for the emergence of twodimensional (2D) whispering-gallery modes in the single NW and the NW array (peaks and mode profiles are denoted by * in Figs.1(B) and 1(C), respectively).To better understand the optical resonances of a NW array cavity, absorption mode profiles of the NW array were compared with those of the single NW [Fig.1(C)].We observed that each NW in the lateral NW array had the same set of cavity modes as a single isolated NW.A NW array supports no additional coupled mode because of the low quality factor of a single NW cavity.Therefore, if the light absorption in a single NW is appropriately tuned by tailoring the NW's morphology or composition [8,[14][15][16][17][18], a NW array composed of these single NWs will possess the same  The absorption spectra of a single NW and a close-packed NW array were investigated with respect to their cross-sectional morphologies.Subtly changing the morphology of a NW cavity enables the tuning of its light absorption at specific wavelengths [8], providing a key motivation for the continued development of NW photovoltaics.First, the cross-sectional shape of the NWs was changed from a hexagon to a circle [4][5][6] and then to a square [8] while keeping their height fixed at 200 nm [Fig.2(A)].Note that for the square cross-sectional shape, a 30-nm-thick SiO 2 conformal coating was introduced as a dielectric spacer to distinguish the rectangular NW array from a planar film structure [6,7].The calculation result shows that the absorption spectra of the single NW and the NW array are nearly identical for the same NW morphology.Second, the height of the hexagonal NWs was changed to 100 nm and 350 nm [Fig.2(B)].The larger NW exhibits an absorption spectrum that is preserved when the NW is assembled into a closed-packed NW array.In contrast, the smaller NW exhibits significantly less light absorption if it is assembled in a close-packed NW array.Although the optical antenna effect increases as nanostructures decrease in size, the diffraction effect due to the periodically assembled structures decreases [25,26,[32][33][34].Notably, the absorption efficiency of a NW array does not exceed unity, whereas a single NW can exhibit over-unity absorption efficiency at specific resonant wavelengths party due to the optical antenna effect [7,8,25].Therefore, we conclude that the conservation of absorption efficiency and J SC from a single NW to a NW array is valid across a range of NW morphologies, as long as the NW does not exhibit a strong optical antenna effect.

Current density of NW arrays with various pitch sizes
For periodically spaced nanostructures, the diffraction effect is primarily dictated by the pitch size of the array [32][33][34].To examine this further, we calculated the polarization-resolved absorption spectra of NW arrays as a function of pitch size, a [Fig.3(A)].For these calculations, periodic boundary conditions were applied along both directions of the NW assembly and the NW axis.For a NW array with an incomplete filling factor, the absorption efficiency was defined as the ratio of the absorption cross section to the total Si projected area (without considering void space) [27].The calculation result shows that although the number of absorption peaks across the spectrum is preserved even as the pitch size is varied, peak positions exhibit slight redshift with increasing pitch size.This redshift is attributed to the penetration of leaky NW cavity modes into the air-filled void space between NWs [27].More importantly, whereas for TE polarized light the absorption efficiency is marginally affected by different pitch sizes, for TM polarized light, the absorption efficiency is significantly enhanced as the pitch size increases up to 400 nm.The enhancement of TM illumination at a = 400 nm is still observed even with total (Si + air spacing) projected area.The enhancement results because the pitch of the array is similar to the wavelength range (400 − 500 nm) that is enhanced.To investigate this polarization dependence, we examined snapshots of the timeelapsed electric field intensity at λ = 450 nm (TE) and λ = 445 nm (TM) for a NW array with a = 400 nm [Fig.3(B)].The snapshots show that each NW element absorbs TM polarized light to a greater extent than TE polarized light, indicating that the optical antenna effect for each NW unit cell is enhanced for the TM polarization as pitch size increases [26,27].Finally, the J SC values of the NW arrays were calculated for a broad range of pitch size, with the assumption of unity internal quantum efficiency [Fig.3(C)] [7].A NW array comprising hexagonal NWs with a ~450 nm was found to yield the maximum J SC (8.7 mA/cm 2 ), which agrees with a previous theoretical work [32].The enhancement factor in J SC at the optimal a (filling factor ~50%) is approximately 35% compared with that for a close-packed array (a = 230 nm), which is an encouraging result in light of a recently developed NW assembly technique achieving an achievable array density of ~2 NWs per μm [28].The J SC of a NW array is determined by the interplay between the diffraction effect and the optical antenna effect, both of which are sensitive functions of pitch size.

Resonance features of multi-layered NW arrays
We previously studied optical resonances of various NW arrays in which NW elements are assembled along the horizontal direction.As a new design for solar absorbers that outperforms conventional bulk structures, we propose multi-layered NW arrays in which each layer is parallel (vertically aligned) or orthogonal (cross-stacked) to the neighboring layers, as shown in Fig. 4(A).Such vertically-stacked NW arrays can be implemented by the multiple applications of a NW assembly technique such as a lubricant contact printing method [28].We calculated the polarization-resolved spectra of double-layered NW arrays with either parallel or orthogonal orientation [Fig.4(B)].Note that for a cross-stacked NW array, the polarization direction of incident light was defined with respect to the uppermost NW plane.Comparison of the absorption spectra between the two array structures shows that the crossstacked NW array exhibits much greater light absorption than the vertically aligned NW array for both TE and TM polarizations.Notably, compared with horizontally and vertically aligned NW arrays, the cross-stacked NW array excites additional absorption peaks at long wavelengths (600 -800 nm).To elucidate the additional absorption peaks, we obtained absorption mode profiles from the cross-stacked NW array [Fig.4(C)].The boundary of the mode profiles corresponds to the unit cell of the cross-stacked NW array.The absorption mode profiles assigned to the new peaks (indicated by "1" and "2" in Figs.4(B) and 4(C)) indicate that the top NWs sustain normal cavity modes, whereas the bottom NWs sustain waveguide modes via a grating coupler resulting from the periodically spaced top NWs.For the waveguide modes, intensity maxima and minima appear alternately along the axis of a NW [35].On the other hand, the absorption profiles assigned to the normal peaks (indicated by "a" and "b" in Figs.4(B) and 4(C)) show that both the top and bottom NWs sustain an identical cavity mode.Note that the top and bottom images were acquired from the x-z and yz cross sections, respectively.Next, we compared the J SC as a function of total Si thickness for multi-stacked NW arrays with that for film structures [Fig.4(D)].The calculation result shows that the J SC of the crossstacked NW arrays was significantly higher than that of the 800-nm-thick film structures.For instance, a four-layered cross-stacked NW array yields a J SC of ~14.0 mA/cm 2 , indicating ~60% enhancement compared with an 800-nm-thick film structure.Notably, a similar J SC (~13.5 mA/cm 2 ) was calculated in a double-layered cross-stacked NW array with a bottom silver mirror that can be readily deposited on a transparent quartz substrate using a conventional evaporation technique [7].To explain such a large enhancement in J SC for multilayered NW arrays, we calculated the internal absorption distribution of the four-layered NW arrays and the 800-nm-thick film structures [Fig.4(E)].For the film structure, incident light was attenuated rapidly as it was swept from the top surface of the structure to the bottom surface.In contrast, the multi-stacked NW arrays exhibited relatively uniform light absorption across NWs, which enables each NW to sustain its localized absorption modes.Therefore, we postulate that a screening effect is mitigated in multi-stacked NW array, which accounts for its large absorption.
Finally, we calculated the absorption spectra of the four-layered cross-stacked NW array and the 800-nm-thick film structure [Fig.5(A)].The calculation result shows that the crossstacked NW array exhibits more absorption peaks than the film structure.Moreover, the amplitude of the absorption peaks is enhanced by a multiple diffraction effect originating from 3D periodic structures [36].As discussed in Figs.4(B) and 4(C), each absorption peak is identified as either a normal cavity mode (indicated by "a," "b," "c") or a new cavitywaveguide mode (indicated by "1," "2," "3") [Fig.5(B)].A 3D complex nanostructure based on nanowire building blocks can provide a new platform for an efficient solar absorber, surpassing conventional limits.

Conclusion
We studied the light absorption features of single-and multi-layered Si NW array cavities by performing FDTD simulations.Calculation results indicated that the absorption modes within each NW cavity are preserved when single NWs are combined to form NW arrays.This observation highlights an important design principle: the unique optical properties of single NWs are transferred to NW arrays, and NW arrays can thus be optimized at the single-NW level.The absorption of a NW array was significantly affected by the pitch size of the array, and it was maximized with a ~450 nm.Polarization-resolved studies revealed that the optical antenna effect along with the diffraction effect resulting from the surface modulation of NWs determines the total absorption in NW arrays.Light absorption and resultant J SC were further enhanced for multi-layered NW arrays because of new coupled modes and the mitigation of the screening effect.Designing solar absorbers based on assembled nanowire arrays is a unique strategy for realizing more efficient solar cells.

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208338 -$15.00USD Received 17 Mar 2014; revised 16 Apr 2014; accepted 16 Apr 2014; published 29 Apr 2014 (C) 2014 OSA absorption features as that of a single NW.This demonstrates the importance of optical design at the single-NW level.

Fig. 1 .
Fig. 1. (A) Schematic of a core-shell p/i/n Si NW (top) and a close-packed NW array (bottom) placed on quartz substrates.(B) TE (top) and TM polarized (bottom) absorption spectra of a film, a single NW, and a close-packed NW array each with a height of 200 nm.The peak denoted by * corresponds to the whispering-gallery mode in (C).The insets in each panel show a schematic describing the polarization direction.(C) TM absorption mode profiles of the single NW (top) at λ = 450, 470, 515, and 680 nm (left to right) and the NW array (bottom) at λ = 445, 480, 515, and 695 nm (left to right).

Fig. 2 .
Fig. 2. (A) Absorption spectra of a single NW and a NW array with circular (top) and square (bottom) cross-sectional shape.For the square NWs, a 30-nm-thick SiO 2 conformal coating was introduced.The height of each NW is 200 nm.(B) Absorption spectra of a single NW and a NW array with a height of 100 nm (top) and 300 nm (bottom).The cross section of both NW structures was hexagonal.

Fig. 3 .
Fig. 3. (A) TE (left) and TM polarized (right) absorption spectra of the NW arrays with various pitch sizes.The inset in the left panel shows a schematic of a NW array with a certain pitch size, a. (B) Snapshots of time-elapsed electric field intensity at λ = 440 nm with TE polarization (left) and λ = 445 nm with TM polarization (right) from a NW array with a = 400 nm.(C) Calculated current densities of NW arrays as a function of pitch size for TE, TM, and unpolarized (TE + TM) light.

Fig. 4 .
Fig. 4. (A) Schematics of vertically aligned (top) and cross-stacked (bottom) NW arrays.(B) TE and TM polarized absorption spectra of double-stacked NW arrays: a cross-stacked NW array and a vertically aligned NW array.Each NW element has a height of 200 nm.All simulations are for a close-packed array.(C) TM absorption mode profiles of the peaks, indicated by "a," "b," "1," and "2" in (B), corresponding to wavelengths of 580, 655, 690, and 715 nm, respectively.(D) Calculated current densities of vertically stacked NW arrays, crossstacked NW arrays, and film structures as a function of the number of stacks, i.e., film thickness.(E) Calculated internal absorption per unit NW or unit volume for four-layered vertically aligned and cross-stacked NW arrays and an 800-nm-thick film structure.The inset shows a schematic of a four-layered NW array and a film structure.