1. Introduction

Conventional photovoltaic cell design assumes a trade-off between the active layer thickness and device efficiency. From a ray-optics perspective, the thinner a layer is the less light it absorbs [1]. Recent developments in nanophotonics, however, have facilitated a modern treatment of solar cell light trapping where predicted absorption efficiencies exceed conventional ray-optics limits [2]. In this vein, researchers have proposed and demonstrated a variety of approaches to improve the absorption efficiency of ultra-thin solar cells with active layer thicknesses less than one micron. A particularly promising approach involves the use of optically resonant metallic (i.e. plasmonic) and dielectric nanostructures [3–8].

The most easily adopted nanophotonic light trapping technology would enable effective photon management while having a minimal impact on the design of current solar cells and their processing techniques. In this work, we focus on patterning the transparent electrode that is used in virtually any thin-film solar cell. Transparent electrodes based on transparent conductive oxides (TCOs), like indium doped tin oxide (ITO) or doped zinc oxide (ZnO) are commonly used to extract photocurrent from a solar cell while transmitting as much sunlight as possible. Research on these unique materials has been spurred by their successful use in solar cells and a variety of other applications, including pixelated displays, photodetectors, and touch-screens. High performance electrodes combine excellent optical transparency with a low sheet resistance. Smooth TCO layers merely serve as an anti-reflection coating and do not redirect nor trap light. For this reason, other transparent electrode materials including strongly scattering metallic nanowire meshes [9] and dielectric nanoparticles [10] are now pursued. However, the least invasive change to a solar cell design that affords some light trapping is roughening of the TCO layers [11, 12]. And while solar cells with nanostructured TCO layers have been demonstrated [13, 14], such studies do not present a systematic methodology that facilitates rational design of roughened or patterned TCO light trapping layers. Here we propose such a methodology and discuss some of the possible advantages over plasmonic light trapping strategies.

2. The proposed model system

Here we propose a scheme to improve thin-film solar cell absorption through a simple patterning step of an existing transparent electrode into an array of optically-resonant, dielectric nanobeams (Fig. 1). This architecture facilitates nanophotonic light trapping in an existing layer of the solar cell without the need to introduce new materials. By using continuous beams, the electrode function can be preserved while adding optical utility to this important layer in the cell. We first illustrate our scheme with an ultra-thin silicon solar cell platform with a ZnO transparent electrode. This model system is designed to bring out all of the essential light trapping physics and it is not intended to produce the best possible solar cell. We used a finite difference frequency domain (FDFD) algorithm, with tabulated silicon optical constants [15] and a Sellmeier model for ZnO [16], to compute the fields in the ZnO beams and Si layer. From these fields we can calculate the light absorption in the semiconductor layer and explore the mechanisms by which it can be enhanced across the solar spectrum. The choice of structure dimensions will be discussed below. After discussing this model system, the design and optimization of a TCO light-trapping layer for a realistic amorphous silicon (a-Si) solar cell will be discussed.

 

Fig. 1 Schematic of our model structure consisting of a periodic array of transparent conductive oxide (ZnO) beams placed on top of a thin crystalline Si layer. The structure is supported by a silica substrate. We characterize the square beams by their width, w, and we define the array by a grating pitch or a reciprocal lattice vector, G.

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3. Basic optical properties of dielectric resonators

Before analyzing the optical properties of the entire structure shown in Fig. 1, it is of value to briefly discuss the nature of the optical resonances supported by the nano-sized beams of ZnO. At a later stage, the interaction of the resonances with the Si layer is introduced. The Lorenz-Mie solution to Maxwell’s equations [17] reveals that dielectric structures that feature a high refractive index and a size that is comparable or smaller than the wavelength of incident light support strong optical resonances, known as Mie or leaky-mode resonances. The excitation of such resonances can lead to large local field enhancements in and near the structure in addition to strong optical scattering. Physically, these resonances result from constructive interference of light trapped inside of a nanostructure, akin to whispering-gallery or leaky-mode resonances in the larger micro-disk and -square resonators [18, 19]. The resonance conditions are dictated by the optical constants of the material as well as the polarization state, energy, and angle of incidence for the light [20]. This property of confined dielectrics has previously been exploited to realize very strong and tunable light scattering and absorption resonances [20, 21], produce films with vibrant structural colors [22], building blocks for solar cells [23], ultra-fast nanowire photodetectors [24], and to tailor the thermal emission of silicon carbide particles [25]. ZnO nanobeams with square cross-sections support dielectric resonances in the visible and near-infrared regimes. Although ZnO nanobeams with a variety of cross-sectional shapes support optical resonances [23], we have chosen a square cross-section to reduce our optimizable parameter space. These resonances vary with nanowire size and incident photon energy and they manifest themselves as peaks in the spectral scattering efficiency, Q_sca (Fig. 2). The scattering efficiency for nanobeams with a square cross-section is defined as the scattering cross-section normalized by the geometrical width of the beam. As such, objects exhibiting values of Q_sca exceeding 1 are strongly scattering entities that are well-suited for light trapping applications. Resonances exist for both transverse electric (TE) and transverse magnetic (TM) linear polarizations of light, where we define TE (TM) illumination as having its magnetic (electric) field along the long axis of the nanobeam. Figure 2 plots the scattering efficiency, Q_sca, for an isolated ZnO square nanobeam in air under TM illumination to illustrate how the scattering spectra are dictated by the nanobeam size (a qualitatively similar plot can be produced for TE illumination). As the size of the nanobeams is increased, its resonances redshift in energy and higher order resonances will appear across the solar spectrum. In order to exploit the resonant properties of ZnO nanobeams to concentrate or trap sunlight, we must align the particle resonances with the standard air-mass (AM) 1.5 solar irradiance curve shown in the background (grey) for Fig. 2. Following this line of thinking, it is expected that square ZnO nanobeams with a 275 nm width would be well-suited to trap sunlight in the proposed model cell (red curve, Fig. 2). Indeed, a more detailed analysis later in this letter shows that excellent absorption enhancements can be obtained with this beam size.

 

Fig. 2 Spectral dependence of the scattering efficiency, Q_sca, for square cross-section ZnO nanobeams in air. The dimensions, w, of the beams are indicated on the right-hand side and the spectra for different sizes are vertically offset in increments of 3 for clarity. The spectral dependence of the AM 1.5 solar irradiance is shown in the background (grey) for reference.

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4. Optimizing the light trapping in a thin Si layer with an array of ZnO nanobeams

Armed with knowledge of the optical resonances supported by individual ZnO nanobeams, we are ready to discuss the possibility to trap sunlight with an array of such beams. To this end, we will analyze how the absorption spectrum is impacted by the placement of a ZnO nanobeam array on top of a 50 nm thin Si film. Figure 3(a) illustrates both the AM 1.5 solar spectrum (orange curve), Φ(λ), and the spectral response of the bare silicon/silica stack (black curve), SR(λ). The peak in the spectral response at 450 nm corresponds to a Fabry-Perot resonance in the system while the decrease in the SR with increasing wavelength is representative of silicon’s spectral material absorption. Separating out the SR of the bare silicon/silica stack allows us to quantify the effect of any light trapping structure as an enhancement factor to the SR, Π(λ).

 

Fig. 3 A ZnO nanobeam array significantly enhances the absorption in a silicon layer at almost all wavelengths. (a) The AM 1.5 solar irradiance (orange) provides the spectral power density of sunlight and the spectral response of the silicon/silica stack (black) diminishes with longer wavelength, excepting a Fabry-Perot peak near 450 nm. (b) The absorption enhancement provided by the nanobeam array under both TE (blue) and TM (red) illumination exceeds that of a planar antireflection coating (green). (c) The product of the solar irradiance, the spectral response, and the absorption enhancement, integrated over wavelength, yields the short-circuit current density value. We find that the short-circuit current density generated in the silicon layer by the ZnO nanobeam array enhances that of the bare structure by 87% for unpolarized light, in comparison to the 46% enhancement gained using a planar antireflection coating. The unpolarized light enhancement was calculated by averaging the TE and TM enhancements, 78% and 95% respectively.

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To assess Π(λ), we numerically compute the absorption in the Si slab with the presence of a ZnO nanobeam array and normalize to the case without. For example, no light trapping structure at all would yield Π = 1. In these simulations, we assume a normally incident plane wave and calculate the absorption from ω · Im(ε_Si) ∮_V |E|²dV′, where Im(ε_Si) is the imaginary part of the dielectric constant of Si, E is the local electric field and the integration volume is the volume of the silicon layer.

Via an optimization procedure that is detailed below, we found that an array of 275 nm wide square ZnO nanowires with a 334 nm pitch optimally scatters unpolarized AM 1.5 sunlight to enhance absorption in the Si film. The magnitude of Π(λ) for this array is show in Fig. 3(b) for both TE- (blue) and TM- (red) polarized illumination. We have also provided the enhancement factor of an optimal planar 50 nm ZnO antireflection coating (green) as a comparison. The array enhances the silicon absorption at almost all wavelengths (Π > 1) and also outperforms the optimized planar ZnO antireflection coating. Several sharp peaks and broader features can be observed in the enhancement spectrum for the array structure whose origin will be discussed in the next section. In contrast to an analogous plasmonic particle array, the absorption enhancement here is comparable for either illumination polarization [3]. By integrating the product of the spectral response, the enhancement factor, and the AM 1.5 solar irradiance over the wavelength we can compute the short-circuit current density (assuming a unity internal quantum efficiency). We find that the ZnO nanowire array improves the short-circuit current density of the bare silicon/silica stack by 87% or nearly twice that of an optimum planar ZnO antireflection coating (Fig. 3(c)) for unpolarized sunlight. The unpolarized enhancement is found by averaging the TE and TM enhancements, 78% and 95% respectively.

5. Physical origin of the spectral features in the photocurrent enhancement

In order to allow rapid optimization of the light trapping performance of our arrays, we must first identify and understand the optical phenomena that give rise to the absorption enhancements. To do so we compute ”maps” of the absorption enhancement, Π, for a range of photon energies and array pitches for both TE and TM incidence (Figs. 4(a) and 4(b)). Rather than plotting Π against the array pitch in these maps, we choose to define a reciprocal lattice vector, G = 2π/P, to parametrize the array, where P is the array pitch. This is done in anticipation of the fact that coupling to the waveguided modes of the layered system play a key role in the optical absorption enhancements. As optical dispersion relations are commonly plotted in terms of E vs. the propagation constant, β, absorption plots in terms of E vs. G allow a very direct comparison. By comparing these plots, we will be able to assign certain absorption enhancement features to the coupling to specific optical modes supported by the solar cell. Note that the color-bar in these maps provides the absorption enhancement on a log₁₀ scale and that the absorption enhancement values exceed the upper bound of the color-bar, we have reduced the plotted range to enable visualization of both small and large enhancement features.

 

Fig. 4 Absorption enhancement maps and field intensity plots reveal the physics behind the absorption enhancements. (a,b) Absorption enhancement maps for TE (a) and TM (b) polarized illumination contain two classes of features: broad, G-invariant regions and narrow, G-dependent bands. The former can be assigned to Mie-like scattering resonances associated with individual ZnO nanobeams while the latter derive from coupling of light into diffracted and wave-guided modes by the array of nanobeams. (c) Magnetic field distribution for a Mie-like resonance, taken from the location marked C in (a). (d) Electric field distribution for a diffracted mode, taken from the location marked D in (b). (e) Electric field distribution for a wave-guided mode, taken from the location marked E in (b).

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The absorption enhancement maps contain a barrage of features that we subdivide into two categories: periodicity (or pitch) invariant features and pitch-dependent features. Both types of features exist in the TE and the TM absorption enhancement maps. The origin of these features can be deduced by analyzing their dispersive behavior (i.e. dependence on photon energy) shown in Figs. 4(a) and 4(b) in addition to the associated field distributions depicted in Figs. 4(c)–4(e). We will argue that the pitch or G-invariant features can be attributed to localized, single ZnO nanobeam resonances. The dispersive features result from the coupling of incident light to guided and diffracted modes in the structure. Interplay between the single nanobeam scattering resonances and the coupling to guided and diffracted modes facilitate the absorption enhancement. We will now discuss in more detail each of the two aforementioned categories.

The G-invariant features can be linked to the occurrence of Mie resonances supported by the individual ZnO nanobeams and perturbed by the presence of the silicon thin-film (Fig. 4(c)). Their excitation energies are close to, but shifted from, the resonances of individual nanobeams in air (red curve, Fig. 2). The absence of any dependence in the excitation energy on G indicates that the absorption enhancements are not affected by or linked to collective effects from many beams. Upon excitation of these resonances, a high concentration of the electromagnetic field can be seen inside and in the immediate vicinity of the ZnO nanobeams (Fig. 4(c)). The absorption enhancement due to single ZnO nanowire scattering weakens for smaller G (larger pitch) due to the increase in nanobeam spacing. For the beam dimensions we are considering, many resonances are observed across the solar spectrum with a bandwidth that closely matches the free spectral range. As such, broadband absorption enhancements are seen across the solar spectrum for both polarizations. This provides significant benefits over metallic nanobeams that support plasmonic resonances that can only be excited under TM polarization where the electric field is normal to the length of the beam [3, 5].

While the light scattering from single ZnO nanobeam resonances certainly contributes to the overall absorption enhancement, the coupling of incident light to guided and diffracted modes inside the structure generates the regions of highest magnitude in the absorption enhancement maps. The nanobeam array serves as a diffraction grating that supports diffracted modes that can be excited when incident light is redirected into the plane of the grating. Such modes feature significant field concentration in the plane of the grating (Fig. 4(d)). Similarly, the grating can couple incident light to optical modes supported by the high-refractive index semiconductor layer (Fig. 4(e)). In our sample geometry with an array placed on top of the Si film, the guided and diffracted modes of the beam-array and Si film interact, but the field plots still provide information on the nature of the basic modes that play a role in enhancing the light absorption. Coupling to guided and diffracted modes allows the light to take a path along the direction of the silicon/ZnO interfaces and increase the interaction length with the absorbing semiconductor material. For light to effectively couple to one of these modes, the incident photons must acquire an in-plane momentum with a magnitude given by the optical dispersion relation [26]. This condition is met when the reciprocal lattice vector of the array matches the propagation constant of the mode: G = β [27]. For this reason, the dispersive absorption features in the absorption enhancement maps follow the dispersion relations of the basic modes supported by the structure. In this way, it is possible to assign each absorption feature to the coupling of solar photons to a specific mode.

The ability to assign enhancement features in the absorption maps to the excitation of localized, diffracted, and waveguide modes of the cell opens the door to rational and intuitive design of the light trapping layer. With this knowledge, one can systematically vary the geometrical parameters of the cell and optimize the contributions from all of the relevant absorption enhancement features. For example, after identifying the features related to the excitation of local modes of ZnO beams, one can leverage knowledge of Mie scattering to guide the optimization of the beam dimension and geometry. This approach suggested that 275 nm square ZnO beams are close to optimum for trapping sunlight in a thin Si layer. The optimum pitch then can visually be estimated from the absorption enhancement maps (Figs. 4(a) and 4(b)) by identifying a pitch for which strong absorption enhancements occur near the peak of the solar spectrum. Using exact calculations of the short circuit current the structure dimensions of the nanobeams or the grating pitch can directly be deduced. While we restrict our analysis to normally incident light, these design principles remain valid for a range of incidence angles with the proviso that both the local ZnO optical resonances and the coupling conditions for guided and diffracted modes shift spectrally.

6. Application to a realistic thin-film solar cell design

In order to verify whether the proposed patterning of TCO films is capable of enhancing the light absorption in a realistic cell, we have investigated the enhancements in the short circuit current that can be obtained for a common single-junction amorphous silicon (a-Si) solar cell design. Our a-Si solar cell configuration consists of, from the bottom up, an optically thick aluminum reflector, a thin ZnO spacer layer (70 nm), an a-Si film (300 nm) and a ZnO nanobeam array (Fig. 5(a)). The thin ZnO spacer layer both passivates the a-Si interface and improves the optical performance of the structure. We have computed absorption enhancement maps for this configuration under both TE- and TM- illumination (Fig. 5(b)). We find that all of the previously described non-dispersive and dispersive features again appear in these maps. This indicates that single nanobeam Mie-like scattering resonances and light coupling into diffracted and guided modes can be exploited to enhance absorption in this cell. The simulated absorption enhancement values produced by an optimized ZnO nanobeam array on the a-Si stack are more modest than those calculated for the thin Si film. This is simply due to the fact that a 300 nm a-Si film captures significantly more sunlight than a 50 nm Si film. While the nanobeam array offers nearly across the board absorption enhancement compared to the bare Al/ZnO/a-Si stack, a more rigorous comparison would be between the nanobeam array and an optimized planar anti-reflection coating. We chose a top ZnO film thickness of 240 nm to optimally enhance light absorption in the a-Si layer by driving a Fabry-Perot resonance of the stack, while allowing for a sufficiently low sheet resistance to eliminate a voltage drop across the transparent contact. We find that an array of ZnO nanobeams performs better than the optimized planar ZnO film (Fig. 5(c)). The nanobeam array (blue) improves upon the planar film (green) in terms of reaching the maximum absorbing capacity of a 300 nm thick a-Si film (orange), where we define the maximum absorbing capacity as full absorption of the above-band gap portion of the AM 1.5 spectrum. The simulated short-circuit current density for an optimized nanobeam array is 21.1 mA/cm² versus 19.9 mA/cm² for the same a-Si cell with an optimized TCO-based anti-reflection coating (Fig. 5(d)). These numbers can be placed in context by realizing that the maximum achievable short-circuit current is 26.0 mA/cm², again based on perfect absorption of the above-bandgap photons.

 

Fig. 5 An optimized ZnO nanobeam array improves the optical performance of a realistic amorphous silicon solar cell. (a) An amorphous silicon solar cell stack consisting of an Al reflector, a ZnO spacer layer, a 300 nm a-Si layer and an array of ZnO nanobeams. The square ZnO nanobeams have a width of 240 nm and the array pitch is 408 nm. (b) TE and TM absorption maps for this structure consist of the same features as before, implying Mie-like resonances and the coupling of light into diffracted and wave-guided modes constitute the absorption enhancement physics. (c) The ZnO nanobeam array (blue) improves upon the performance of an optimized planar ZnO film (green) in terms of allowing the a-Si film to reach its absorbing capacity, defined as full absorption of the above-band gap portion of the AM 1.5 spectrum (orange). (d) The ZnO nanobeams improve the short-circuit current density of an optimal solar cell with a planar ZnO layer from 19.9 mA/cm² to 21.1 mA/cm². The maximum achievable short-circuit current density is 26.0 mA/cm², assuming complete absorption of the above-band gap AM 1.5 spectrum.

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The sheet resistance for a periodic TCO nanobeam array is given by $R_s=\rho \frac{P}{w^2}$, where ρ is the TCO resistivity, w is the square nanobeam width, and P is the array pitch. Based on a doped ZnO resistivity of 8.4 × 10⁻⁴ Ω-cm [28], we find an R_s of 59.5 Ω/□, competitive with other emerging transparent contacts [9]. For further decreased sheet resistance of the TCO layer and for passivation of the semiconductor surface, a thin continuous TCO layer (< 10 nm) beneath the resonators has minimal detrimental impact on the structure’s light trapping ability.

7. Conclusion

Modern solar cell design critically relies on the development of new architectures for light trapping and improving transparent electrode technology. Here we provide a dual solution by offering a rational design methodology that turns a smooth TCO layer into an effective nanophotonic light-trapping eletrode. Exploiting the ability of single TCO resonators to concentrate and scatter light along with an array’s capability to direct light into diffracted and waveguided modes allows dramatic absorption enhancements in a model silicon thin-film system. We have also shown that a TCO nanobeam array can significantly enhance the optical absorption in a realistic amorphous silicon cell, where the capacity to improve is greatly diminished. Our architecture provides two key advantages over an analogous plasmonic structure: polarization insensitivity and no need for additional materials. The principles described in this letter can also be used in reverse for light de-trapping from solid state emitters and this work opens the door to rational design of highly functional TCO layers for a variety of applications.