Suitably engineered plasmonic nanoparticles have the potential to enhance the optical absorption of thin solar cells 1–5, which may not be able to support traditional light-trapping schemes, such as texturing 6, due to their thickness or their material composition. Sub wavelength metal nanoparticles can support optically driven localised surface plasmons (see for example Reference 7). These are collective oscillations of the conduction electrons confined inside the metal. At the certain wavelengths, determined by the particle geometry, material and the local environment, these oscillations become resonant and the particles strongly interact with light.
Silver nanoparticles, in both random and periodic 8, 9 arrays, can be engineered to have large scattering cross-sections at the localised surface plasmon resonance wavelength 10. If the particles are situated close to the surface of a solar cell a significant fraction of this scattered light is coupled into the cell over a large angular range, trapping the light inside the active region and increasing the photocurrent.
Suppression of the photocurrent from nanoparticle sensitised solar cells at wavelengths below the surface plasmon resonance has also been reported 11, which has been attributed to destructive interference between scattered and incident fields in the semiconductor substrate. This can lead to an overall decrease in short circuit current for cells with a good blue response 12. However, it has been demonstrated recently that this suppression can be avoided by locating nanoparticle arrays on the rear of solar cells 13.
In general, to achieve efficient light-trapping in a Si solar cell using plasmonic structures, a large scattering cross-section is needed for wavelengths at which transmission losses become significant. Additionally, parasitic absorption in the particle should be minimised, and a large fraction of the light scattered by the particle should be scattered into the solar cell. The scattering cross-section, Qscat, the absorption cross-section, Qabs, and the coupling efficiency, Fsubs, (defined as the fraction of the scattered light that is scattered into the Si), are sensitive to particle geometry 14, the optical response of the local environment 10, 15–17 and the distance from the semiconductor interface (determined by the thickness of the dielectric spacer layer between the particle and the semiconductor) 18. These parameters should be considered separately for particles located on the front or the rear of the solar cell due to asymmetry in the scattering behaviour of the particles 19. Design considerations have recently been established 18 for light-trapping with metallic nanoparticle arrays which showed that hemispherical Ag particles of diameter 100–200 nm within 20 nm of the Si interface achieve large dipolar resonances near the band edge of Si, which couple well to the substrate.
We present experimental results for light-trapping in 22 µm thick, c-Si solar cells using self-assembled Ag nanoparticle arrays. The experimental geometry is chosen to maximise the light-trapping efficiency of the nanoparticles, based on previously reported design considerations 13, 18, 19. Nanoparticles are located on the rear surface of the cells to decouple light-trapping and anti-reflection effects and to avoid suppression in the blue/green spectral region due to interference effects. In this configuration the particles can be optimised for light-trapping in the thin c-Si cells by engineering large Qscat and high Fsubs in the light-trapping spectral region, defined from a wavelength of 750 nm, where transmission losses exceed 10% for our solar cells, to the band edge of Si at 1180 nm. The localised surface plasmon resonances of the particles can be significantly red-shifted by over-coating with TiO2, which has a relatively high refractive index while keeping the nanoparticle diameters within a range to achieve high Fsubs and low Qabs. Additionally, the particles are kept close to the Si (within 20 nm) by using thin spacer layers, which include passivation layers, resulting in high Fsubs. This geometry allows the use of a traditional dielectric anti-reflection coating on the front surface of the solar cells. Inclusion of a detached rear reflector further improves the light-trapping provided by the nanoparticle array as light that is not initially coupled into the cell is given multiple scattering opportunities.
Self-assembly of nanoparticle arrays is a relatively cheap and easy fabrication method that is suitable for large area devices like solar cells. Self-assembled nanoparticles are fabricated by thermal evaporation of thin Ag layers, followed by low temperature annealing.
Photocurrent measurements were performed on 22 µm thick, bifacial c-Si solar cells, fabricated on p-type, 0·1 Ω-cm wafers with 50 Ω-cm phosphorous doped emitters. Figure 1(a) shows a schematic of the cell geometry. The cells were fabricated with a double dielectric layer structure of 10 nm of thermally grown SiO2 and 8 nm of Si3N4, deposited by low pressure chemical vapour deposition, on both front and rear surfaces of the cells. The oxide layer provides surface passivation for the cells and the nitride layer is a result of the cell fabrication process. All cell processing was completed pre-nanoparticle deposition.Random Ag nanoparticles were fabricated on one half of the rear surface of the finished solar cells. Eighteen nanometre layers of Ag were deposited by thermal evaporation followed by a 50 min anneal at 230°C, in an atmosphere of N2. This resulted in half of the rear surface of the cells being covered in nanoparticles, as illustrated in Figure 1(a). The cells were then coated on both front and rear surfaces with TiO2 by atmospheric pressure chemical vapour deposition at 200°C. All cells received a coating of 89 nm on the rear, and 82 nm on the front. The TiO2 thickness was determined using a single wavelength ellipsometer and the refractive index at a wavelength of 673 nm was measured to be 2·1. The 82 nm TiO2 coating on the front of the cells reduces reflection to below 10% for wavelengths of 700–1200 nm, and to less than 1% around 850 nm.
Results and Discussion
Scanning electron micrographs of the random nanoparticle arrays were taken at five points on the cells before over-coating with TiO2. Although nanoparticle size can be changed by varying the mass thickness of Ag deposited 20 the self-assembly method results in randomly positioned nanoparticles with a large distribution in diameter. Figure 1(b) shows one of the micrographs. The cross sectional area of each particle in the five micrographs was measured, and the diameter of the particles was taken to be equivalent to that of a circle of the same area. Figure 1(c) shows the particle size distribution calculated from all five micrographs and, inset, the percentage of the total number of particles which had the equivalent diameter. Over 89% of the particles had equivalent diameters between 50–204 nm, and the average equivalent diameter was 131 nm. The particles had a surface coverage of 36% and a ‘flattened’ hemispherical shape with a height of ∼ 50 nm, estimated from the surface coverage of the particles and the volume of Ag deposited. This geometry has been shown to couple well to the substrate 18.The spectral response of the solar cells was determined by measuring the photocurrent at each wavelength (bandwidth 5 nm). The external quantum efficiency (EQE) was then calculated from the known illumination intensity as the fraction of incident photons that are converted to electrical current. For each measurement, a ∼ 4 mm2 area on the front of the cell was illuminated. Measurements were taken separately on the half of the cell with nanoparticles on the rear and on the half of the cell without nanoparticles, for reference. Measurements were also taken with and without a detached Ag mirror behind the cells, with a reflectivity of 95% for wavelengths 750–1200 nm.Figure 2(a) shows experimental EQE measurements for a 22 µm thick, c-Si solar cell with a TiO2 ARC (ARC, dash-dot line), with a TiO2 ARC and a mirror (ARC + Mirror, solid line), with rear-located nanoparticles and a TiO2 ARC (NP + ARC, crosses) and with rear-located nanoparticles, a TiO2 ARC and a mirror (NP + ARC + Mirror, circles). Data for the same cell before TiO2 and nanoparticle deposition is included for reference (Ref, dashed line). At a wavelength of 750 nm transmission losses become significant for a 22 µm thick, c-Si cell and the data for cells with nanoparticles and/or mirrors exhibit EQE enhancements, compared to the ARC only case, due to the reduction in transmission at the rear of the cell. The cell with only a mirror present performs as well as the cells with nanoparticles on the rear up to a wavelength of 870 nm. This is due to the fact that specular reflection from the mirror increases the path length of light in Si to approximately 44 µm which absorbs 90% of the incident light up to a wavelength of 870 nm. Beyond this wavelength the nanoparticle arrays (crosses and circles) perform better than the cells with only a mirror present (bare line). By scattering light at high angles the nanoparticles can trap a significant portion of the light inside the Si by total internal reflection, leading to an increase in the path length of light in the cell, compared to cells with a mirror present. When a mirror is included behind the nanoparticles (circles), light that is not initially scattered by the particles into the Si substrate is reflected back to provide multiple scattering opportunities, increasing the EQE further.
Figure 2(b) shows the experimental EQE enhancements relative to the EQE of the cell with an ARC. In the limit of weakly absorbed light, near the band edge of Si at a wavelength of 1150 nm, the experimental EQE enhancement is 1.6 for a cell with a detached Ag mirror (bare line), 4.3 for a cell with the Ag nanoparticle array (crosses), and 5.6 when a detached mirror is included with the nanoparticle array (circles).To investigate the scattering characteristics of the random Ag nanoparticle arrays, the FDTD solutions package from Lumerical 21 was used for numerical simulations. These optical simulations allow us to calculate the normalised scattering and absorption cross-sections of the nanoparticle, (Qscat, Qabs), and the fraction of the scattered light that is scattered into the Si, (Fsubs). The simulations do not allow us to directly calculate the amount light trapped in the cell, as only light propagating in the Si at an angle greater than the critical angle (∼16° in Si) will be trapped. However, the two parameters Qscat and Fsubs provide a measure of the effectiveness of the light-trapping provided by the nanoparticle 5, and single-particle calculations have been shown to agree well with experimental results for random arrays 13.A single Ag hemisphere was modelled to approximate the shape of the nanoparticles, separated from a semi-infinite Si substrate by 10 nm of SiO2 and 8 nm of Si3N4 and coated with a conformal layer of 89 nm of TiO2. Perfectly matched layer boundary conditions were employed at all simulation boundaries. Radiation from the normally incident source was propagated from the Si substrate to the air, corresponding to the experimental case of nanoparticles on the rear of the Si solar cells. The source is 300 nm from the Si interface to minimise the amount of light absorbed in the substrate before reaching the nanoparticles. This allows the scattering cross section to be calculated for all wavelengths of interest. The dielectric functions were modelled using a Drude model for Ag based on data from Johnson and Christy 22 and a Drude-Lorentz model for Si, based on data from Green 23. The optical constants for the SiO2 layer were taken from Palik, and the refractive index of TiO2 was taken as 2.1, as measured experimentally. The total scattered power was determined by integrating the Poynting vector of the scattered field (equal to the total field minus the incident field) over a surface enclosing the particle. The normalised scattering cross-section was then calculated by dividing the total scattered power by the incident source power and normalising to the cross-sectional area of the particle. The absorption cross-section was calculated in a similar manner, using the Poynting vector of the total field (equal to the incident field plus the scattered field).Figure 3 shows calculated Qscat, Qabs and Fsubs for four Ag nanoparticle diameters, chosen as the mid points of the diameter ranges with over 15% of the total particle number from the experimental size distribution, shown in the inset of Figure 1(c). The weighted averages of Qscat, Qabs and Fsubs are also shown, calculated for the size distribution shown in Figure 1(c) (thick black lines). The 90 nm diameter particles have a peak Qscat at 781 nm corresponding to the dipolar surface plasmon resonance which red-shifts to 887 nm for d = 116 nm, to 990 nm for d = 142 nm and to 1121 nm for d = 170 nm. For the larger particle sizes (d = 142 and 170 nm) additional peaks in Qscat are observed at wavelengths around 600 nm, which are attributed to higher order surface plasmon excitations. In the light-trapping region, (750–1200 nm) the averaged Qabs is less than 0.5, while the average Qscat is larger than 3, with a broad peak of 4.5 at a wavelength of 935 nm. The coupling efficiency for all particles converges to 0.9 at long wavelengths, in agreement which previously reported results for hemispherical particles on thin spacer layers 18. Local minima in the Fsubs spectra are observed at around 600 nm for particles with d = 142 and 170 nm, corresponding to the higher order excitations which are known to coupled poorly to the substrate 18. The average Fsubs is 0·88 at 750 nm, converging to over 0.9 at longer wavelengths.
Given the experimental surface coverage of the particles of 36% we can conclude that, with an average scattering cross-section of over 3 and a coupling efficiency of over 90% in the light-trapping spectral region, a significant fraction of the incident light reaching the back surface of the cell is scattered by the nanoparticle array and coupled into the Si. However, the average Qscat will be decreased by the presence of non-optimal nanoparticle sizes. Furthermore we would expect that the large irregular particles seen in Figure 1 (b) would support higher order plasmon modes that are known to couple poorly with the substrate. In this analysis we have also ignored inter-particle interactions, which may reduce the scattering cross-section of the random arrays from that of the single particle case calculated here. Higher scattering cross-sections and coupling efficiencies, and hence larger experimental enhancements, may be achieved with a more regularly shaped particles with controlled inter-particle spacing and smaller size distribution. Additionally, recent work has shown that reducing the spacer layer thickness to less than 10 nm can significantly increase the strength of the scattering cross section for rear-located nanoparticles 19.To further quantify the light-trapping provided by the nanoparticle arrays we calculated the increase in the short circuit current density from the solar cell due to the light-trapping provided by the nanoparticles. The short circuit current density at each wavelength (Jsc(λ)) for a cell illuminated with the AM1·5 g spectrum is calculated from the experimentally measured EQE, shown in Figure 2, multiplied by the number of photons at each wavelength and the charge of an electron. Integrating Jsc(λ) over the measured spectrum (500–1200 nm) gives the total Jsc. The enhancement in photocurrent is calculated by dividing the Jsc for the nanoparticle sensitised cells by the Jsc of cell with only an ARC. For the reference case with only a detached mirror present the calculated enhancement is 9.0%. For a cell with a random Ag nanoparticle array on the rear (crosses) Jsc is enhanced by 10.0%, and with a detached Ag mirror and the particles (circles) the Jsc enhancement is increased to 13.0%.
Previous reported measurements for nanoparticle enhanced, 300 µm thick, wafer-based c-Si solar cells have utilised front-located nanoparticle arrays 24. These particles provide anti-reflection as well as light-trapping, and the quoted enhancements of 19% are calculated in comparison to planar Si cells with no ARC, over the whole wavelength spectrum from 300–1200 nm. In our experiment with rear-located nanoparticle arrays we are able to optimise the nanoparticle scattering for light-trapping and incorporate a dielectric ARC, which can be optimised independently. If we compare the anti-reflection and light-trapping provided by our experimental cell structures to a planar cell with no ARC the photocurrent is enhanced by 43.9%, increasing to 47.9% when the detached mirror is incorporated behind the cells. This result clearly illustrates the benefits of optimising the light-trapping and anti-reflection independently.
In summary, we demonstrate plasmonic light-trapping in thin c-Si solar cells. By independently optimising self-assembled, rear-located nanoparticle arrays for light-trapping and including a mirror and a dielectric ARC, we achieve a 47.9% enhancement in photocurrent, 13.0% due to light-trapping. Better control of the particle size, inter-particle spacing and the dielectric spacer layer thickness could result in larger scattering cross-sections in the light-trapping spectral region and therefore larger photocurrent enhancements.
The authors acknowledge the Australian Research Council for the financial support of this work.