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Light-trapping is essential to improve the performance of thin-film solar cells. In this paper, we perform a parametric optimization of 1-D square and sinusoidal grating structures that act as nanophotonic scatterers to increase light absorption in ultra-thin (10nm) solar cells. Our optimization reveals that the short-circuit current density in a device of active-layer thickness 10nm can be improved by a factor of ~5 in the presence of the scattering structure. More complex geometries allow for increased degrees of design freedom and potentially high enhancement of light absorption.
©2012 Optical Society of America
1. Introduction
Solar energy has the potential to become a significant source of energy in the near future [1]. However, the high cost associated with the active device materials has stymied their wide adoption. The material cost can be contained via the use of thin layers of active materials. In addition, thin-film photovoltaic cells have higher open-circuit voltages due to the lower recombination rates [2, 3]. Furthermore, such cells could be manufactured using considerably cheaper processes [2]. The main drawback of such cells is their poor absorption of sunlight. Light trapping schemes were proposed to increase the light absorption in these thin active layers [2, 4, 5]. Randomly textured surfaces are applied on the top surface. Light scattering from these textures increases the path length within the active material resulting in higher absorption. Such textures are typically applied for devices with thick active layers [6–8]. Sub-micrometer grating structures on the back surface of the active layer were used to increase light absorption in moderately thick device layers as well [9].
It is useful to consider light trapping for ultra-thin active layers. Thinner layers can potentially allow for inexpensive organic materials as well as to drive down costs even further for established materials like silicon. Furthermore in 3rd generation solar cells, which aim to achieve higher efficiencies via multiple bandgaps, strain in multiple materials layers constraints the active-device layers to thicknesses below 100nm [10]. In such device layers, it is advantageous to employ nanophotonics principles to trap light. Various designs that utilize subwavelength geometries such as surface nanopatterns [11, 12], backside gratings [13, 14], plasmonic nanostructures [15], embedded nanoparticles [16] and nanowires [17–19], have also been proposed. Such nanophotonic structures aims to encourage the excitation of guided mode resonances within thin active layers, which in turn, leads to increased absorption [20]. The principle is based on the increased number of available modes in the near-field of the active region. By applying wave optics, it is possible to go beyond the geometrical-optics limits at the expense of either broadband enhancement or restricted angular input [10, 21]. Theoretical approaches have also been developed to analyze such nanophotonic designs [22–24]. Many of these previous studies have focused on active layers that are over 100nm in thickness. Since the effect of light trapping due to nanostructures tend to be limited to a much smaller thickness, it is useful to study ultra-thin (~10nm) device layers. In this paper, we employ numerical analysis to optimize 1-D periodic geometries for enhanced light trapping in silicon solar cells with 10-nm thick active layers.
Specifically, we apply finite-difference-time domain (FDTD) [25, 26] to study the effect of a periodic structure atop a thin active layer. The inset in Fig. 1(a) shows one period of the simulated geometry where a square grating is the light trapping structure. The bottom-most layer is assumed to be a perfect reflector (which can also serve as the back electrical contact). The next layer is the active layer, whose nominal thickness is denoted as ta. In this paper, we assume crystalline silicon as the active-layer material. A cladding layer of thickness tc is placed directly on top of the active layer. Finally, a scattering layer of thickness ts is placed on top of the cladding layer. The scattering and cladding layers together form the light-trapping nanostructure. Here, we assume that the scattering and cladding layers are both made of SiO2. Material indices of refraction were obtained from standard Tables [27]. Bloch-periodic boundary conditions were applied to the left and right, while a perfectly-matched layer (PML) was assumed at the top. Sunlight defined by the AM1.5 spectrum [28] was assumed to be normally incident from the top. The effect of oblique incidence will be reported in a future paper.
Fig. 1 (a) Square-grating geometry for light and current enhancement. Inset shows the simulated geometry. The enhancement factors are computed as a function of the active-layer thickness. Note that the nanophotonic enhancement is highest when the active layer is thinnest. (b) Spectral-enhancement factor (J)λ shows strong enhancement for an incident wavelength of 500nm, which is close to the peak of the AM1.5 spectrum. This simulation was performed with an active-layer thickness of 10nm. The other parameters were Λ = 400nm, duty-cycle = 0.6, tc = 30nm, and ts = 90nm. The dashed black line at the bottom represents 1.
In order to quantify the impact of the nanophotonic structure, we begin by defining as the spectrally-cumulative time-averaged intensity distribution and S as the total power per unit grating period within the active layer.
where Λ is the grating period. The intensity refers to the total light intensity averaged over the two orthogonal polarizations of the incident light field. The light-enhancement factor, F is defined as the ratio of S in the presence of the nanophotonic structure (cladding and scattering layers) to its value when the structure is absent. Normalization with respect to the grating period is necessary to evaluate the effect of varying this period with respect to a reference period.In addition to light enhancement, we can also evaluate the effect of light trapping on the device performance by directly computing the short-circuit current density, jsc.
where Φ is the local photon flux in the active layer, IQE is the internal quantum efficiency of silicon and c is the velocity of light in silicon. The enhancement in short-circuit current density, J is defined as the ratio of jsc in the presence of the nanophotonic structure to jsc in the absence of the structure.It must be noted that the light scattered by the nanophotonic stack must couple in the near-field into multiple guided modes within the active layer in order to achieve light-absorption enhancement over a wide spectral range. It is difficult to design such a near-field scattering structure using inverse techniques [29]. However, one can employ parametric search methods to arrive at quasi-optimal solutions as we show in this paper. Furthermore, search techniques allow for direct implementation of fabrication constraints resulting in designs that are practical. It is also important not to under-estimate the difficulty of fabricating sub-micron-sized geometries over large areas as required in the case of light trapping for solar cells. One promising approach for such fabrication is based upon roll-to-roll nanoimprint lithography [30].
2. Optimization of the square-grating structure
The active-layer thickness is perhaps the most important parameter in the device since it affects the recombination rate of the light-generated carriers. In addition, the nanophotonic effect is predominant in a thin layer adjacent to the cladding layer. Hence, we calculated both F and J as functions of the active-layer thickness, ta, keeping all the other parameters fixed at ts = 90nm, tc = 30nm, and Λ = 400nm. We also assumed a grating duty cycle of 0.6. The results are shown in Fig. 1(a). As expected, the highest enhancement occurs for the thinnest active layer. The nanophotonic scattering effect is a near-field effect. Hence, the biggest impact will occur in the near field of the cladding structure. Note that as the active-layer thickness becomes larger than about 100nm, the effect of the grating is minimal. In the rest of the simulations, we assume an active-layer thickness of 10nm. The spectral-enhancement factors are defined as
The subscript “ref” indicates the reference cell in the absence of the nanophotonic-trapping stack (scattering and cladding layers). The solid blue line in Fig. 1(b) shows Jλ. The grating scatters strongly for an incident wavelength of 500nm, causing significantly higher light trapping within the active layer. Since the AM1.5 spectrum shows a maximum around 500nm, this grating design provides good light trapping for the entire spectrum as indicated later.
In addition, we also simulated and computed Jλ considering a reference cell with an anti-reflection coating (ARC) comprised of an unpatterned 85nm-thick fused silica layer atop the active layer. This thickness corresponds to λ/4n where λ = 500nm (the approximate peak of AM1.5) and n = 1.47. The results are plotted as a dotted red line in Fig. 1(b). At λ~500nm both TE and TM polarizations excite strong guided resonances in the silica nanostructure. These resonance fields can couple into the active layer directly under it, leading to strong light trapping effects [20, 22]. At other wavelengths, weaker resonances are excited leading to lower light trapping. At wavelengths above 1000nm, no resonances are excited but the structure acts as a sub-optimal anti-reflection coating. The highest value for Jλ is 2.3, lower than that compared with the bare reference device (solid blue line). In our following simulations, we utilized the bare device as our reference cell in order to more accurately illustrate the overall performance of the light trapping structure, which includes any anti-reflection effects as well. The incident AM1.5 spectrum is also plotted in Fig. 1(b) for reference.
Figure 2 shows the parametric analysis of the grating design on the two enhancement factors. The default parameter values were Λ = 400nm, duty-cycle = 0.5, tc = 30nm, and ts = 80nm. In Fig. 2(a), Λ was changed while all the other parameters were kept constant. It was noted that both the enhancement factors peaked sharply at Λ = 400nm. The duty-cycle was defined as the ratio of the width of the scattering layer to the period of the grating. In Fig. 2(b), the duty cycle was varied while all other parameters were fixed at their default values. The enhancement factors peaked at a duty-cycle of 0.6. Similarly, the cladding-layer thickness of 30nm also showed the best enhancement. Finally, the device showed maximum enhancement at a scattering-layer thickness of 90nm.From this simple single-parameter search, we conclude that the grating with the optimized parameters offer good enhancement, with J approaching 5.
Fig. 2 Parametric optimization of the square-grating geometry for light and current enhancement. The enhancement factors are plotted as a function of (a) the grating period, Λ, (b) the grating duty-cycle, (c) the cladding thickness, tc and (d) the scattering-layer thickness, ts. The default parameters were Λ = 400nm, duty-cycle = 0.5, tc = 30nm, and ts = 80nm.
3. Optimization of the sinusoidal-grating structure
The sinusoidal grating offers a smoother degree of control on the incident light. In addition, the sinusoidal grating may be fabricated using grayscale lithography. Hence, we explored the potential of this geometry on the enhancement factors. The simulation geometry is illustrated in Fig. 3(a) . The parametric optimization results are shown in Figs. 3(b)-3(d). Highest enhancement occurs when the period is 400nm and the cladding-layer thickness is 30nm (both similar to the square-grating). This peak is again attributed to the strong resonance at λ ~500nm within the scattering structure. However, the sinusoidal-grating allows for higher enhancement when the scattering-layer thickness is about 120nm. The sinusoidal grating provides a smoother scattering structure, so it would be expected to scatter normally incident light into fewer guided modes in the active layer. However, the broadband behaviour of the sinusoidal grating is similar or even slightly better than that of the square grating. This hints at the possibility of utilizing more complicated geometries for further enhancements.
Fig. 3 Parametric optimization of the sinusoidal-grating geometry for light and current enhancement. (a) Schematic of the proposed geometry. The enhancement factors are plotted as a function of (b) the grating period, Λ, (c) the cladding thickness, tc and (d) the scattering-layer thickness, ts. The default parameters were Λ = 400nm, tc = 30nm, and ts = 90nm.
4. Alternative geometries and materials
Besides the square-grating and sinusoidal-grating discussed above, we also explored the possibility of using more complex 1D geometries. Figure 4 shows the spectrally-cumulative intensity distribution in the active layer, for the case of a triangular-grating, an undercut-trapezoidal grating and a trapezoidal grating. Although, we have not performed parametric optimization on these geometries, by simply utilizing parameters that are analogous to those in the square grating, we can achieve enhancements around 5. Further optimization on these and related geometries including multi-dimensional parameter searches should provide even better enhancement factors. Note that the geometries considered here are accessible via modern nanofabrication technologies.
Fig. 4 Investigation of alternative geometries. The schematic of the geometry is shown on the top. The bottom figure shows a plot of the normalized spectrally-cumulative intensity distribution within the active layer. (a) Triangular-grating. (b) Undercut-trapezoidal grating. (c) Trapezoidal grating. The parameter values were Λ = 400nm, tc = 30nm, ts = 90nm, W = 240nm, θ1 = 77.5° and θ2 = 66°. The inset images show the normalized spectrally-cumulative intensity within the active layer.
Although we used crystalline silicon as the active layer, it is clear that the parametric search could be applied to other materials. A simple optimization was conducted for CdTe-based solar cell, which is a promising candidate for thin-film photovoltaics because of its high light absorption [31]. The optimal design with grating period of 400nm, cladding layer thickness of 20nm and scattering layer thickness of 120nm provides an enhancement factor of F = 5.2. The dielectric material of nanophotonic light trapping structure can also be replaced by a conductor such as ZnO. The structure now serves as the top electrical contact as well. In this case, an enhancement factor of F = 7.6 was achieved with amorphous silicon as the active material and incident AM1.5 spectrum. The optimized parameters of this sinusoidal grating were Λ = 400nm, tc = 20nm and ts = 120nm. Furthermore, a thin dielectric layer between the active layer and the metal reflector may be introduced to avoid parasitic loss at silicon-metal interface, if the perfect metal is replaced by a pratically real metal [13].
5. Conclusions
In this paper, we described the parametric optimization of 1-D square-grating and sinusoidal-grating structures for the enhancement of light absorption and short-circuit-current density in thin silicon solar cells. We note that the enhancement factors can be considerably improved by factors of 5 or more by the judicious choice of the geometric parameters. We have also exploited alternative 1D geometries and potential materials for photonic structures and active absorbers. The performance of such light trapping nanostructures under oblique incidence is another area of future study. The choice of geometric parameters is dependent on the material choices as indicated by our simulations of CdTe and amorphous-silicon solar cells. It is clear that numerical optimization of nanophotonic geometries is advantageous to improve the performance of thin-film solar cells.
Acknowledgments
We thank Lorenzo Bossi for assistance with MEEP, and Ganghun Kim for useful discussion and assistance with the simulations. We also thank Stewart Brock and Mark Ogden for help with the computational facilities. Fruitful discussions with Mike Scarpulla are also gratefully acknowledged. Funding from the Utah Technology Commercialization Grant and USTAR are gratefully acknowledged.
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