The scattering cross-section of a plasmonic nanoparticle is proportional to the intensity of the electric field that drives the plasmon resonance. In this work we determine the driving field pattern throughout a complete thin-film silicon solar cell. Our simulations reveal that by tuning of the thicknesses of silicon and transparent conductive oxide layers the driving field intensity experienced by an embedded plasmonic nanoparticle can be enhanced up to a factor of 14. This new insight opens the route towards more efficient plasmonic light trapping in thin-film solar cells.
© 2014 Optical Society of America
The photocurrent of a thin-film solar cell can be enhanced by scattering and trapping the weakly absorbed part of the spectrum . Conventionally, thin-film solar cells use textured interfaces to scatter light [2,3]. The scattering cross-section of plasmonic silver nanoparticles with a diameter on the order of 100 nm far exceeds their geometrical cross-section. Therefore a film of these particles provides a promising alternative means of light scattering. Stuart and Hall did pioneering work on the use of silver nanoparticles for enhancing the photocurrent of photo-detectors [4,5]. Subsequent research was focused on the use of these silver nanoparticles as light scattering elements for enhancing light trapping in solar cells [6,7]. It has been established that it is not beneficial to embed the nanoparticles in front or inside the absorber layer as this gives rise to reflection or recombination losses, respectively. Embedding the silver nanoparticles behind the absorber layer avoids these issues and is therefore most effective [8–10]. Recently, state-of-the-art performance has been demonstrated in thin-film silicon solar cells deposited onto a so-called plasmonic back reflector [11,12]. As indicated in Fig. 1, in such a back reflector the silver nanoparticles are embedded in a transparent conductive oxide (TCO) layer, above a planar silver mirror layer.
Stuart and Hall observed strong oscillations in the diffuse reflectance of silver nanoparticles on multi-layer structures . These oscillations were later identified as interference phenomena . Interference also strongly affects the scattering cross-section of silver nanoparticles embedded in a plasmonic back reflector. As illustrated in Fig. 1, the interference between incident light and the light reflected by the mirror creates a standing wave pattern consisting of nodes and anti-nodes. The plasmon resonance in a nanoparticle is driven by the total resultant electric field, to which we will refer as ‘driving field’. At an anti-node this driving field could be twice stronger than the field of the incident light. As the intensity is proportional to the field strength squared , the scattering cross-section of a nanoparticle positioned at an anti-node would be enhanced by a factor of four.
The separation between node and anti-node is one quarter of the wavelength. Therefore a nanoparticle at a given distance from the mirror can be at a node for one wavelength but at an anti-node for another wavelength. This means that the driving field enhancement needs to be tuned to the desired wavelength range by varying this distance [16–18]. Sesuraj et al. optimized the distance between nanoparticles and mirror using simulations and experiments [19,20]. However, the solar cell above the back reflector can affect the interference pattern, resulting in a different optimum nanoparticle position. Thus far the effect of the solar cell on the interference pattern has not been investigated. In this paper this effect is studied in detail using optical simulations. First our optical model is validated using reflection measurements on plasmonic back reflectors. The analysis is then extended to complete solar cells.
2. Plasmonic back reflector
The plasmonic back reflector consists of silver nanoparticles above a planar silver mirror, separated by a transparent spacer layer of aluminium doped zinc oxide (ZnO:Al). The strength of the driving field throughout this back reflector is calculated as a function of wavelength. Here we consider only the specular component giving rise to interference. This allows us to use a relatively simple and fast thin-film optics model . Our model calculates the coherent propagation of an incident electromagnetic wave. It takes into account the phase change upon reflection at each interface and the interference between all multiple internal reflections. Input for this model are the wavelength dependent complex refractive indices of each layer and the corresponding layer thicknesses. The optical constants of ZnO:Al were measured in house and those of silver were taken from literature . Note that only the multilayer structure in absence of silver nanoparticles is simulated and the effects of the particles on the driving field are not taken into account. Also the effect of the scattered light on the polarizability of the nanoparticles is not included . The validity of our simplifying assumptions will be demonstrated by comparing simulation and measurement results.
Figure 2 shows the intensity of the driving field in and above the Ag/ZnO:Al back reflector with ZnO:Al thicknesses of 60, 120, 180 and 240 nm. Note that on the left side of each figure the layer structure is indicated schematically, the wavelength is on the horizontal axis. The colour indicates the intensity of the driving field normalized to the intensity of the incident wave, where the intensity is defined as the square of the electric field amplitude E. The clearly visible standing wave pattern is caused by interference between incident and reflected light. Silver nanoparticles positioned at, for example, the air/ZnO:Al interface experience a weak driving field at some wavelengths and a strong driving field at other wavelengths. It is this field that drives their plasmon resonance.
The intensity of the driving field at one position, i.e. the ZnO:Al/air interface, is shown in Fig. 3. For a ZnO:Al thickness of 60 nm the driving field has a minimum at a wavelength around 400 nm. With increasing spacer layer thickness this minimum shifts to longer wavelengths and higher order minima appear at shorter wavelengths (indicated by the vertical arrows). A-Si:H solar cells require light scattering in the wavelength range 600 to 800 nm. These results seem to suggest that this can best be achieved by placing the plasmonic nanoparticles at a distance of 60 nm from the mirror, as this provides the strongest driving field in the relevant wavelength range (as indicated by the horizontal arrow). Whether this is still true when a solar cell is deposited onto the back reflector will be investigated in section 3.
To validate our approach the four different plasmonic back reflectors were also fabricated. The mirror was formed by evaporating a 200 nm planar silver film onto a flat glass substrate. On this mirror the ZnO:Al layer with an approximate thickness of 60, 120, 180 or 240 nm was deposited by RF-sputtering. Finally the silver nanoparticles were formed on this layer by depositing 12 nm of silver and annealing at 400°C, resulting in a metal-island film . The total reflectance Rtot and diffuse reflectance Rdif (excluding the specular reflection component) of the plasmonic back reflectors were measured using an integrating sphere. Since the back reflectors are not transparent, the absorbance can be calculated as A = 1 – Rtot.
Figure 4 shows the measured diffuse reflectance (dashed line) and absorbance (solid line) of the four back reflectors. Note that these give an indication of the nanoparticles’ scattering and absorption cross-section, respectively. We expect these cross-sections to be the product of both the particles intrinsic cross-sections and of the thickness dependent driving field shown in Fig. 3. Figure 4 shows that the measured diffuse reflectance and absorbance of the four plasmonic back reflectors with different spacer layer thicknesses are very different indeed. For the back reflector with 60 nm spacer layer both absorbance and diffuse reflectance show a dip around 400 nm. With increasing spacer layer thickness this dip shifts to longer wavelengths. We have shown previously that the plasmon resonance of comparable silver nanoparticles extends over a broad wavelength range without any dips in their intrinsic absorption or scatter cross-section . The measured dips are therefore expected to correspond to a dip in driving field intensity. This is confirmed by the excellent agreement of the positions of the simulated and measured dips shown in Figs. 3 and 4, respectively. In addition, the higher order minima predicted by the simulations are also observed experimentally. This indicates that the driving field plays a dominant role in both the absorption and scattering cross-section of the plasmonic nanoparticles embedded in the back reflector. It also shows that our optical model is a valid tool for studying these driving field effects.
3. Plasmonic thin-film solar cell
Next we extend the simulations to a complete thin-film silicon solar cell deposited onto the four plasmonic back reflectors considered above. Our purpose is to investigate the effect of the solar cell on the driving field at the location of the silver nanoparticles. Theoretically the best optical coupling of the scattered light into the a-Si:H layers can be achieved when the nanoparticles are directly at the a-Si:H/ZnO:Al interface [7,24]. However, we have experimentally demonstrated that the best solar cell performance is achieved when the particles are separated from this interface by a 30 nm ZnO:Al encapsulation layer . For this reason this spacer layer is included in our device simulations. The n-i-p hydrogenated amorphous silicon (a-Si:H) solar cell on top consists of 20 nm of n-type a-Si:H, 300 nm of intrinsic a-Si:H and 15 nm of p-type amorphous silicon carbide (a-SiC:H). The transparent front contact is 75 nm of indium tin oxide (ITO).
The optical constants of all these layers were measured in-house and used as input for the simulation of the driving field. The results are shown in Fig. 5. Again the layer structure is indicated schematically on the left side of each figure. Light with a wavelength less than 600 nm is completely absorbed in a-Si:H before it reaches the back reflector. Light with a longer wavelength is largely reflected by the back reflector and interference between incident and reflected waves creates a standing wave pattern. Also at specific combinations of position and wavelength an extremely high intensity can be observed. This results from constructive interference of multiple internal reflections, especially in ZnO:Al. As shown in Fig. 5(d), the light intensity reaches as much as nine times the intensity of the incident light in the center of the thickest ZnO:Al layer at λ = 1000 nm.
In the four solar cells the silver nanoparticles are embedded in the ZnO:Al layer at a distance of 60, 120, 180 or 240 nm from the mirror. Figure 6 (darker line) shows the calculated driving field intensity at this position. Although the distance to the mirror is the same as for the back reflector without solar cell (indicted by the lighter line), the driving field is very different. It can therefore be concluded that in order to maximize the driving field at the nanoparticle position, not only the nanoparticle-mirror distance but the entire solar cell has to be considered.
Figures 5 and 6 show that the driving field intensity is very sensitive to variations in the ZnO:Al thickness. The thicknesses of the other layers affect the driving field as well. To investigate the maximum obtainable driving field, the thickness of ITO, a-Si:H and ZnO:Al were varied. A simplex search algorithm was used to find the combination of layer thicknesses that results in the maximum driving field enhancement at any position in the ZnO:Al layer. The silver nanoparticles are assumed to be placed at the position of maximum driving field. Because a-Si:H solar cells require light scattering in the wavelength range 600 to 800 nm, the aim is to maximize the driving field specifically in this wavelength range. Figure 7(a) shows the result of the optimization and the corresponding layer thicknesses. At λ = 740 nm the driving field intensity experienced by a nanoparticle can be enhanced by as much as a factor of 14. This is much more than what is possible when considering just the back reflector without the solar cell on top. Note that this layer thickness combination is not unique. A similar enhancement can be obtained when the optical thickness of the a-Si:H layer is increased by an integer number of half wavelengths.
The peak shown in Fig. 7(a) is rather narrow while for a-Si:H solar cells strong light scattering throughout the entire wavelength range of 600 to 800 nm would be most beneficial. Our algorithm is flexible and can also be used to maximize the average driving field intensity in the wavelength range 600 to 800 nm. The result shown in Fig. 7(b) corresponds to the highest obtainable average driving field intensity in the wavelength range 600 to 800 nm. This demonstrates that over this broader wavelength range the scattering cross-section can still be enhanced by more than a factor of three.
We demonstrated that the standing wave pattern in a plasmonic back reflector changes dramatically when a solar cell is deposited on top. Therefore, when designing a plasmonic solar cell, the interference effects of all layers need to be taken into account. Calculations were performed using a fast thin-film optics model. By optimally tuning the TCO and absorber layer thicknesses, the driving field intensity experienced by embedded plasmonic nanoparticles can be enhanced up to a factor 14. This new insight opens the route towards more efficient plasmonic light trapping in thin-film solar cells.
This work has been funded by the Dutch STW Vidi grant-10782 of A.H.M. Smets.
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