Comparative study of absorption in tilted silicon nanowire arrays for photovoltaics
© Kayes and Leu; licensee Springer. 2014
Received: 28 July 2014
Accepted: 22 September 2014
Published: 18 November 2014
Silicon nanowire arrays have been shown to demonstrate light trapping properties and promising potential for next-generation photovoltaics. In this paper, we show that the absorption enhancement in vertical nanowire arrays on a perfectly electric conductor can be further improved through tilting. Vertical nanowire arrays have a 66.2% improvement in ultimate efficiency over an ideal double-pass thin film of the equivalent amount of material. Tilted nanowire arrays, with the same amount of material, exhibit improved performance over vertical nanowire arrays across a broad range of tilt angles (from 38° to 72°). The optimum tilt of 53° has an improvement of 8.6% over that of vertical nanowire arrays and 80.4% over that of the ideal double-pass thin film. Tilted nanowire arrays exhibit improved absorption over the solar spectrum compared with vertical nanowires since the tilt allows for the excitation of additional modes besides the HE 1m modes that are excited at normal incidence. We also observed that tilted nanowire arrays have improved performance over vertical nanowire arrays for a large range of incidence angles (under about 60°).
Much solar cell research has focused on silicon (Si) nanowires, which have been demonstrated to be a promising active layer material for next-generation solar cells [1–10]. Nanowires may orthogonalize light absorption and carrier collection processes to facilitate high optical absorption and efficient collection of photogenerated carriers . Furthermore, nanowires have demonstrated light trapping properties, where their absorption is enhanced over that of planar Si [1–3, 9]. These structures may also be deposited on low-cost or flexible substrates using chemical vapor deposition or contact transfer methods . Various structures that break the symmetry of nanowire arrays such as nanocones [13–15] or aperiodic vertical arrays  have been demonstrated to have increased absorption over vertical nanowire arrays.
Tilting vertical nanowire arrays, which may be fabricated by a wet chemical etching with dry metal deposition method , may be an additional and simple way to improve their performance. In this paper, we investigate the optical performance of tilted nanowire arrays on a metal contact and compare their performance to that of vertical nanowire arrays. We systematically study the performance with regard to tilt angle and report how the nanowire tilt may be used to improve solar absorption and thus ultimate efficiency. While these two geometries have been compared previously in experiments , these comparisons have not been performed for structures with the same Si volume. We also demonstrate that this enhancement occurs over a broad range of incidence angles.
The optical constants for Si were taken from experimental measurement results in Palik’s Handbook of Optical Constants of Solids. A non-uniform mesh with a minimum size of 15 nm was used for the simulation. Perfectly matched layer boundary conditions were used for the upper boundary of the simulation cell , PEC boundary conditions were used for the lower boundary of the simulation cell, and appropriate boundary conditions were used for the side boundaries to model the periodic nature of the arrays.
Results and discussion
where α (E) is the energy-dependent absorption coefficient of Si. The ultimate efficiency of an ideal double-pass thin film with L = 684 nm is 17.9%.
By tilting the nanowires, higher average ultimate efficiencies may be achieved at nanowire array tilts between 38° and 72°. The ultimate efficiency is 32.2% and a maximum at β= 53°, which is indicated with a vertical dotted line. nm at this tilt angle. Figure 3b plots the absorption as a function of the wavelength and nanowire tilt angle β. The absorption shown is the average of the two polarizations. The optimum tilt of β = 53° is again marked with a dashed line in the contour plot. Normal incident light can only couple to HE 1m in vertical nanowires due to symmetry requirements . Distinct resonance peaks can be seen in the absorption spectrum of the vertical nanowire array. For tilts less than 38°, the ultimate efficiency decreases when compared to the vertical nanowire arrays. The minimum ultimate efficiency is 24.0% at β = 18°. Figure 3c plots the absorption spectra of the vertical nanowire array (β = 0°) and this tilted nanowire array. The absorption spectra of the β = 18° tilted nanowire array closely resembles that of the vertical nanowire array, but the magnitude of the various absorption resonances is lower. For small tilt angles, the ultimate efficiency decreases because the excitation efficiencies of the HE 1m modes decrease.
Absorption (%) in different spectral regions
Ideal double pass
Vertical nanowire array
Tilted nanowire array
The total solar absorption ( A sol ), short-circuit current density ( J sc ), and the ultimate efficiency ( η )
Ideal double pass
Vertical nanowire array
Tilted nanowire array
The performance of the vertical nanowire arrays is symmetric with respect to positive and negative incidence angles. While freestanding vertical nanowire arrays have better performance under TM-polarized incident light than TE [2, 8], our results indicate that vertical nanowire arrays on a perfect back reflector have the opposite trend where the ultimate efficiency is higher for TE polarization than TM polarization. The increased absorption under TM-polarized incident light in freestanding vertical nanowires is due to reduced transmission , whereas our system has no transmission due to the perfect back reflector.
In our simulations of tilted nanowires, the performance is symmetric with respect to positive and negative incidence angles for TE waves with electric field along the x-axis and TM waves with magnetic field along the y-axis. However, this symmetry is broken for TE incidence with electric field along the y-axis and TM incidence with magnetic field along the x-axis. The results shown for the tilted nanowire arrays are the average of the two orthogonal polarizations. The performance of the tilted nanowires is slightly better under positive incidence angles versus negative incidence angles, where the Poynting vector is closer to along the axis of the nanowire. In addition, the performance of the tilted nanowires is consistently higher than that of the vertical nanowire arrays for incidence angles under about 60°. For high angles of incidence, the performance of the vertical and tilted nanowires converge for both TE incidence and TM incidence.
We have performed a comparative study of the optical performances of tilted Si nanowire arrays on a perfectly electric conductor for photovoltaic applications using the finite difference time domain method. Our results show that the absorption enhancement in vertical nanowire arrays over Si thin films can be further improved through tilted nanowires. Optimized vertical nanowire arrays with a height of 1,000 nm have a 66.2% ultimate efficiency improvement over an ideal double-pass thin film of the equivalent amount of material. Tilted nanowire arrays, with the same amount of material, exhibit improved performance compared to vertical nanowires arrays over a broad range of tilt angles (from 38° to 72°). The optimum tilt of 53° has an improvement of 8.6% over that of the vertical nanowire arrays and 80.4% of the ideal double-pass thin film. Tilted nanowire arrays exhibit improved absorption over the infrared, visible, and ultraviolet regimes compared with vertical nanowires since the tilt allows for the excitation of additional modes besides the HE 1m modes that are excited at normal incidence. We also observed that tilted nanowire arrays have improved performance over vertical nanowire arrays over a large range of incidence angles (under about 60°).
This work was supported by a Mascaro Center for Sustainable Innovation Seed Grant. Computing resources were provided by the Center for Simulation and Modeling at the University of Pittsburgh.
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