We suggest a new type of efficient light-trapping structures for thin-film solar cells based on arrays of planar nanoantennas operating far from their plasmon resonances. The operation principle of our structures relies on the excitation of collective modes of the nanoantenna arrays whose electric field is localized between the adjacent metal elements. We calculate a substantial enhancement of the short-circuit photocurrent for photovoltaic layers as thin as 100–150 nm. We compare our light-trapping structures with conventional anti-reflecting coatings and demonstrate that our design approach is more efficient. We show that it may provide a general background for different types of broadband light-trapping structures compatible with large-area fabrication technologies for thin-film solar cells.
© 2013 osa
Recent extensive studies of thin-film solar cells (TFSC) aim for the production of large-area panels harvesting solar energy. Prospective TFSCs imply their implementation on flexible substrates compatible with the roll-to-roll processing . Such solar cells are characterized by a very small amount of purified semiconductor per unit area  which reduces the cost being useful also for ecology due to small amount of toxic waste [2, 3].
To fabricate efficient solar cells with a very small thickness, a conventional anti-reflecting coating (ARC) should be replaced by a light-trapping structure, since ARC cannot prevent the transmission of light through a very thin photovoltaic (PV) layer. This transmission results in energy loss and in substrate heating, which leads to an additional reduction of the solar cell efficiency [2, 3]. A light-trapping structure (LTS) is a structure capable to reduce both the reflection from a solar cell and transmission through its PV layer. We believe that the future progress in the physics and applications of TFSCs depends on the development of novel types of light-trapping structures .
Many suggestions for LTS are based on photonic crystals [5–8], optically dense arrays of semiconductor protrusions [9–11]), and plasmonic manostructures . LTS based on photonic crystals are attractive for crystalline solar cells but they are hardly compatible with the roll-to-roll technologies. Optically dense arrays of relatively high pyramidal or conical protrusions from the PV layer are compatible with amorphous materials, however these structures can hardly be referred as LTS. The array of prolate protrusions with mutually touching bases are optically dense. Therefore they are equivalent to an effectively continuous medium with a vertical gradient of refractive index . This gradient offers the suppression of reflection and not the light trapping. In other words, such structures operate as anti-reflecting coatings. The transmission through the PV layer is prevented in them only because the total optical thickness of the effective PV medium (both flat part and protrusions) does not meet the criteria of TFSC – it is sufficient for the total decay of the incident wave across it.
Some LTS are performed as regular plasmonic gratings located in the bulk of the structure (usually in between the photovoltaic layer and the substrate) [4, 12, 13]. Their functionality is similar to that of the semiconductor facets (textured coatings), conventionally used in wafer solar cells . These gratings can convert the incident plane wave into waveguide modes propagating along the optically thin PV layer. The operation of facets in the PV layer obeys certain basic restrictions [14, 15] known as the Yablonovich limit which practically prohibits their use for TFSC. This limit, however, is disabled in the case of plasmonic gratings by involving surface plasmon polaritons .
Many ideas of the efficient light trapping for TFSC are based on the use of plasmonic absorbers [4, 17–19] which are amorphous planar arrays of silver or gold nanoparticles with plasmon resonances within the operation band of solar cells. In these random arrays only averaged parameters (sizes of the particles and their surface density) can be optimized. Such structures are fabricated using rather cheap self-assembly technologies. However, to our opinion the high level of parasitic losses in these LTS makes them hardly promising. Amorphous plasmonic arrays operate as effective lossy layers and their common drawbacks are high losses in metal nanoparticles and scattering losses. Though they successfully prevent the transmission through an optically thin PV layer, no one of them (to our knowledge) stands the comparison with a conventional ARC.
The efficient conversion of the incident plane wave into evanescent wave packages (hot spots) whose electric field is concentrated mainly inside the semiconductor can be achieved in regular grids of rather thick (50 nm or more) silver or gold nanoparticles (e.g., Refs. [19–22]). We call such regular nanoparticles nanoantennas (NA) because they meet the definition of the antenna (recall that antenna is an object which efficiently transforms near electric and/or magnetic fields into electromagnetic radiation and vice versa). If the array of NA is properly designed the energy of solar light received by NA is then transformed into a set of hot spots located mainly beyond NA (so that to avoid the parasitic dissipation). If these hot spots are at least partially located inside the PV layer the incident energy is converted into electricity. This is the useful PV absorption that reduces both reflection from te structure and transmission through the PV layer. Note, that beside plasmonic NA dielectric optical cavities can also operate as NA . Such cavities if weakly coupled to the substrate are not excited by incident plane waves, however their coupling to the semiconductor substrate (PV layer) is strong .
Arrays of NA used as LTS for TFSC do not scatter the incident wave since they are regular and their unit cell is sufficiently small (usually it is smaller than the wavelength within the major part of the operational band, so that the grating lobes do not arise). Properly designed NA can offer a rather significant enhancement of the PV absorption in TFSC without a noticeable dissipation of the solar energy in their metal elements [19–23]. However, known NA, even those called broadband ones still possess a common drawback: their optical response is strongly resonant. This results in a rather narrow total band in which the enhancement of the PV absorption is achieved. This concerns also NA which demonstrate multifrequency operation –several plasmon resonances in the operational band [19–21]. There are some works describing specific NA with relative bandwidth larger than 30%, however in these cases they possess rather high dissipative losses making them similar to plasmonic absorbers (as in ).
In this paper, we suggest and study a novel type of light-trapping structures based on arrays of low-loss metal NA whose operational band does not coincide with plasmon resonances. Since the response of our NA is weakly resonant, a broadband operation without noticeable dissipation in the metal becomes possible.
2. Physics of the enhanced light trapping
A schematic view of our LTS is shown in Fig. 1. This design employs the advantages of collective oscillations excited in the visible or infrared spectral range by an incident plane wave in a lattice of Ag nanobar-based NA. We demonstrate that such weakly-resonant LTS can enhance substantially the PV absorption in very thin (100–150 nm) underlying semiconductor layers that may increase significantly the overall spectral efficiency of realistic TFSC. Our LTS are in-plane optically isotropic being also independent on the light polarization. We discuss possible implementations of our concept in the solar cell technology and analyze in detail two specific examples of TFSC: inter-band TFSC based on CuIn(1−x)GaxSe2 (CIGS) and silicon TFSC.
The oscillations excited by the incident light in our structure are analogous to the collective oscillations discussed in  for arrays of parallel metal bars operating in the far-infrared (THz) range and termed domino modes. Such modes exist in a broad range of wavelengths and are excited by the electric field whose vector is orthogonal to the bar axis. However, the cross-polarization (that equals zero after averaging over the unit cell) is also excited. The main feature of domino modes is the advantageous distribution of the local electric field which is concentrated in the spacings between the bars. The internal electric field in metal is very small – the field penetrates beneath the metal surface to the distance which is much smaller than the skin-depth. In principle, this is, possible since the skin-depth is defined for a plane wave and for an infinite flat metal surface. Consequently, these oscillations demonstrate low dissipation. Notice, that in  only the lower domino mode has been studied representing the so-called spoof plasmon. We have found that at higher frequencies than those considered in  there are several high-order dispersion branches including those of the leaky waves. The excitation of domino modes in the visible range and in the leaky regime has been first considered in . In this work domino modes were excited in the array of parallel Ag nanobars by an incoming beam with the grazing incidence on the array plane. However, our later simulations reveal that these modes are also excited for any angle of incidence as well as in the presence of a substrate or without any substrate. The domino modes can be excited even by a normally incident plane wave. The presence of several leaky branches offers these modes excited at several eigenfrequencies. These modes are characterized by the domination of higher multipole moments (of the order 2–6) of any bar over its dipole moment.
There are two conditions of their excitation: the transversal sizes of the bars must be of the same order and not very small compared to the distances between them and the minimal size of the bar should be sufficiently larger than the skin-depth in the flat metal. The optical losses in metal should be small enough. Plasmonic properties of the metal are not important for the excitation of these modes and they can be probably also observed for an array of perfectly conducting bars. The presence of the substrate results in the red shift of their frequency range. Also, in the presence of the strongly refractive substrate optimal ratio between the thickness and the width of nanobars changes compared to that discussed in . To achieve the broadest range of eigenfrequencies the thickness of the bar should be nearly twice as smaller as the width. In other words, nanobars located on top of a semiconductor should be modified into nanostrips. The domino modes can be excited for optically long strips (as well for rather short ones). However, for light-trapping purposes their length is restricted: the unit cell of the grating should not significantly exceed the operational wavelength in order to avoid high scattering losses in grating lobes.
When domino modes are excited by an incident plane wave in an array of Ag nanobars located in free space as in , the absorption of these modes is very weak. The excitation of these modes implies that the electromagnetic energy is stored between the strips without taking part in the energy transport i.e. these modes have no impact to both reflectance and transmittance. The situation changes dramatically if the strips are located in an absorbing host or on an absorbing surface. Then the electromagnetic energy of the evanescent fields concentrated in between the bars (strips) will be absorbed in the ambient, and both reflection and transmission of the incident wave will be suppressed. This property of domino modes determined our general design approach. Since substantial nanostrips turned out to be efficient in conversion of incident wave fields into near fields accompanied by an absorption these nanostrips (in the regime of domino modes) can be adequately referred as NA. We have studied several possible geometries of the unit cell and finally revealed that the best functionality is achieved for the geometry presented in Fig. 1. Since the solar light is not polarized an array of parallel nanostrips has been replaced by two mutually orthogonal arrays. This modification ensures the isotropy of the polarization response in the horizontal plane. We have studied domino-modes arrays of nanostips with non-tapered cross sections located on top of the silicon substrate. Then the domino modes are excited in the visible range within the band of relative width 25–30%. The enlargement of this band up to 50% has been achieved by tapering of nanostrips when they become trapezoidal. The operational band of our NA (through broader than those of previously known NA) is still narrower than the operational band of a practical solar cell. This means that an additional requirement to our design solution arises: beyond the band of domino modes within the operational band our NA should not worsen the operation of the solar cell. Such worsening could correspond to the strong reflection from the metal elements if the surface density of the metal is too high. In other words, the array of NA should be geometrically rather sparse. This sparsity is inherent to our structure depicted in Fig. 1 whose top view is similar to a square mesh of split wires. The distance between tapered nanostrips is sufficiently small for the excitation of domino modes and sufficiently large to avoid the critical reflection beyond the band of these modes. This explains the advantage of the suggested general design solution.
The excitation of domino modes helped to almost completely damp the transmission of light through the PV layer. The reflection in the band of these modes is suppressed rather weakly. Therefore a sub-micron dielectric superstrate of a polymer (e.g. polyethylene) has been introduced in the suggested design to additionally damp the reflection. The superstrate also plays the role of chemical passivator for the material of NA (silver).
Another useful design solution is the location of an additional dielectric layer between the PV layer and the carrying substrate. The carrier is assumed to be performed of a non-purified amorphous silicon. Due to the optical contrast with two semiconductors the additional dielectric layer helps to create the reflecting Fabry-Perot cavity between its lower boundary and the upper surface of the structure. In absence of the optical absorption in the PV layer such a cavity would correspond to the almost total reflection (and damped transmission). However, if the maximum of the standing wave corresponds to the center of the photo-absorbing layer this absorption increases and reflection losses are also suppressed. We think, that this design strategy is also rather original. In ARC one uses the Fabry-Perot resonance of the transmittance matching the surface impedance of the ARC to that of free space. However, in our case, when the photo-absorbing layer is as thin as 100–150 nm the ARC regime is not helpful. Even in the presence of the optical absorption the most of the incident solar flux is transmitted through a so thin PV layer and is lost in the substrate. Therefore, on the first stage of our simulations we neglect the optical losses in the structure and engineer the Fabry-Perot resonance of reflection, when the maximum of the standing wave resulting from the incident and reflected ones would be located inside the PV layer. Then we introduce optical losses in our simulations and see (as expected) that the transmittance keeps very small, whereas the reflectance strongly decreases.
This light-trapping effect has been achieved due to the enhancement of the PV absorption at the maximum of the standing wave where the local electric field is doubled. This mechanism of the light-trapping is weakly influenced by NA and is not very broadband. Its bandwidth strongly depends on the permittivity of the intermediate dielectric layer we introduce in order to create the resonant reflection in our lossless simulations. For it the rather high refraction of this layer (close to 2) is required. It corresponds to such materials as SiO, AlInP, Si3N4, TiO2 and some others. For SiO we have achieved the relative bandwidth of the Fabry-Perot cavity 15%. This band can be located near the band of domino modes. Then the total band of enhanced PV absorption can have the width 60%. Notice, that the complex permittivity of Al-doped ZnO (AZO) is also close to 4 in the most part of the visible range and in the near IR range (and the imaginary part is sufficiently small). AZO is used in transparent electrodes of TFSC (see e.g. in [3, 23]), and the intermediate dielectric layer (in our simulations – SiO) can be replaced by AZO, keeping nearly same results. In this case the bottom contact mesh is not needed.
To show that our design approach can be applied to different PV media and different operational bands we have considered two TFSC: one based on CIGS and one based on Si. Both design solutions are illustrated by Fig. 2. The unit cells of the LTS shown in Fig. 2 refer to the region located in the gaps between the wires of the upper electrode collecting the photocurrent. Here we do not consider the regions shaded by the contact mesh assuming that they are much smaller than the area open to the sunlight.
3. Design and numerical modeling
We calculate numerically the power absorbed by a unit cell of the TFSC structure with LTS illuminated by a normally incident wave within the operation band Δω = [ω1, ω2] of the photovoltaic layer. Our numerical simulations were carried out using both Ansoft HFSS and CST Studio software packages. The meshing has been refined so that the result would not depend on the computational grid, and the convergence was carefully controlled. First, we made the HFSS simulations for an amorphous TFSC based on CuInSe2 (left panel on Fig. 2). The PV layer of total thickness 110 nm (55 nm of p-doped and 55 nm of n-doped material) was located between a polymer coating of thickness d that we varied within the range 100...1000 nm and a layer of SiO whose thickness was also varied as well as all the sizes of NA. The layer of SiO is located on the optically thick substrate of amorphous Si which was simulated using the perfectly matched layer distanced far enough from the bottom interface.
A very small thickness of the PV layer was selected mainly to show the light-trapping capacity of our LTS. However, the value 110 nm can correspond to a practical design of a TFSC [26,27], since for CIGS it is smaller than the diffusion length of minor carriers and larger than the depletion region of the p-n junction. Under these conditions the increase of the PV absorption results in the proportional increase of the short-circuit photocurrent [19, 28]. For the given type of CIGS the PV band of CIGS and that of noticeable optical losses in this material effectively overlap forming the operational range λ = 660...1200 nm. Such solar cells are called interband ones . The doping level of CIGS was assumed to be the same as in work , and the optical constants of the doped CIGS were taken from . The optical constants of the polymer superstrate were taken from  (for the wavelength region 660...780 nm), and  (for the region 780...1200 nm). The optical constants of SiO were taken from , those of the substrate – from . We have calculated following parameters: spectral density A(ω) of the PV absorption, spectral density Am(ω) of the parasitic absorption (in metal elements), reflectance R(ω) from the structure and transmittance T(ω) to the substrate.
For two source options of the HFSS package – wave port and incident plane wave – we obtained a practical coincidence for all calculated parameters. Next, we repeated the same simulations using the CST Microwave Studio. The excellent agreement of results obtained by these two different methods (one is based on the finite elements method, the other – on the FDTD method) convinced us that our modeling is reliable. Most part of simulations was done using the CST package without duplication by the HFSS one.
The optimal thickness of the polymer layer is d = 270 nm and for SiO it is equal 295 nm. Other geometric parameters of the optimized structure can be found from Fig. 2 where all dimensions are given in scale. All edges and corners of metal elements were smoothed so that to avoid parasitic local field enhancement which could result in the harmful dissipation. After the proper smoothing the results weakly depend on the curvature of the metal surface.
The main purpose of our simulations was to calculate the spectrum of power A(ω), absorbed in the PV layer per unit cell. This value is integral of the local power density taken over the volume V of the PV layer per unit cell:
We are interested in the relative value – the gain granted by our LTS. Following to (3) the gain in the short-circuit photocurrent due to our LTS is given by the comparison of the power absorption <A> in presence and in absence of LTS. We have calculated this values for three cases: our LTS, an optimized blooming layer, and open surface of the TFSC without any covering. After calculating <A> for two cases – when the TFSC is enhanced by our LTS and by a conventional ARC, we obtain the gain due to the replacement of the ARC by our LTS:35]. The optimal parameters of the blooming layer (refraction index n and thickness d) correspond to the maximum of G0, and the optimal parameters of the LTS correspond to the maximum of G. The optimal blooming was achieved for the film of polystyrene (n = 1.57 − 1.58 in the range 660...1200 nm) with thickness d = 440 nm.
Now, let us discuss the simulation results. The analysis of the local field distributions over the unit cell has shown that the domino modes are excited within the wavelength range 600...900 nm. In the range 900...1000 nm the Fabry-Perot cavity is formed with standing wave having the maximum inside the PV layer. In Figs. 3(a,b), we show the local field distribution at λ = 810 nm in the central vertical cross section of the unit cell and in the horizontal plane P1. This plane corresponds to the boundary between NA and a thin insulating layer of amorphous silica electrically isolating NA from the semiconductor (see also in Fig. 1). We have checked that the thickness of the insulating layer within the range 2–20 nm has no impact to any of simulated values (A, Am, R, T). In Fig. 3(a) we observe a rather strong reflected field. At this wavelength the power reflectance is R ≈ 0.2. An optimal blooming layer without NA at this wavelength allows R ≈ 0.1. However, inspecting the field distribution in Fig. 3(a), we observe the practical absence of the transmitted field. The decrease of the transmittance due to our LTS at this wavelength turns out to be 20-fold. As a result, the LTS turns out to be more advantageous than the ARC.
In Fig. 4(a), we show the spectral photo-absorption A(ω) for three cases: with our LTS, with a blooming layer, and without any structure on the top of the photovoltaic layer. The impact of the reflectance is illustrated by Fig. 4(b). It is seen that domino-modes correspond to the suppressed reflection (for the open surface the averaged value of R is R ≈ 0.4) though this nearly 5-fold suppression is not as strong as that offered by the ARC. The most significant reflectance corresponds to longer waves, where, fortunately, the solar radiation drops. Moreover, in the range 1000...1200 nm the value ε″ responsible for the absorption decreases quite significantly. The photocurrent is mainly formed within the domain 660...1000 nm. Using formulas (4) and (5) we obtained G = 1.29 and G0 = 1.32. The gain granted by the LTS compared to the open surface is equal 70% which is, to our knowledge, the best known result for a custom-design semiconductor TFSC with PV layer of thickness 100–150 nm. We believe that the obtained enhancement is sufficient to justify the fabrication costs of our LTS. Below, we discuss the possibility to fabricate our LTS in a way which seems to be rather inexpensive under the condition of the mass production and compatibility with the roll-to-roll processing.
Our second numerical example corresponds to the silicon solar cell whose operation band is practically coincide with the range of the visible light. For this latter case, the dimensions shown in Fig. 2 have been numerically optimized for the PV layer of thickness 150 nm (75 nm of p-doped and 75 nm of n-doped Si). The density of carriers in the layer was assumed to be 3 · 1018 cm−3 for the p-doped part and 1019 cm−3 for the n-doped part. Optical constants were taken from . The dielectric superstrate of our LTS is here amorphous silica (the same material turned out to be optimal for the ARC in the reference structure). The in-scale drawing of the structure is shown in the right panel of Fig. 2(b). The optimal size of the unit cell (840 nm) turned out to be larger than the wavelength in the whole operational band: the condition of domino modes contradicts in this case to the condition of the absence of scattering. However, the scattering losses related to grating lobes turned out to be much smaller than the reflection losses. Therefore the excitation of domino modes is more important than the exact absence of grating lobes. The optimal thickness of the silica superstrate is equal d = 325 nm, however the result weakly depends on d within the range d = 320...390 nm (the maximal difference is 3%).
The operation of our LTS is illustrated by Fig. 5. The domino modes are excited in the region λ = 500...780 nm. In Fig. 6, we show the frequency dependence of the photovoltaic absorption A(ω) for three cases as above: LTS, ARC (blooming layer), and non-coated solar cell. Again, in the range of domino-modes the reflectance is suppressed. At 450...500 nm the reflection is reduced due to the Fabry-Perot resonance. Resonant optical losses of Si are responsible for the weak reflectance below λ =450 nm.
The gain in the PV absorption granted by our LTS in accordance with Eq. (3) is equal G = 1.17. Compared to the non-coated TFSC, our LTS gives the gain 64% (G0 = 1.40). This result is slightly worse than that obtained above for the TFSC based on CIGS due to non-negligible fields inside the metal elements, as one can see in the right panel of Fig. 5.
4. Fabrication issues
Finally, we discuss briefly possible technologies for the fabrication of suggested arrays of NA with a dielectric superstrate in a way compatible with the roll-to-roll processing  for large-area TFSC panels. First, such arrays of NA can be fabricated on a polymer film using the replication technology , the latter implies a quartz template whose surface repeats the profile of the nanoantenna arrays. Using the method described in , one can obtain a vast amount of plastic replicas with metal nanoantennas reproduced with practically the same resolution as that of the template. Besides polyethylene, these plastic substrates can be made of polyamide, polymethylmetaacrylate, polytetrafluorethylene, polystyrene, etc. Pieces of the film of the size 0.5–1 mm with printed nanoantenna arrays can be prepared separately from solar cells so that the cost of every piece is expected to be reasonably low. Then these pieces can be placed on the top of a solar cell in the gaps between the wires of the mesh electrodes. If this is done in a vacuum camera and under mechanical pressure, a strong bonding between polymer and silica covering the surface of the solar cell can be achieved. In accord to our estimates, this bonding would be sufficient for adhesion, and the NA will be fixed on solar cells as well as plastic superstrate. Finally, the thickness of the superstrate can be reduced chemically to the optimal value. This procedure is feasible if the gaps between the wires of the contact mesh are as large as 0.5–1 mm which are typical values for mesh electrodes of TFSC structures.
Alternatively, our structures can be fabricated by using conducting polymers  or any other flexible transparent electrodes. Then the NA can be fabricated on the top of a solar cell protected by a silica insulator being covered by a flexible conducting coating. This coating will play twofold role: that of an upper electrode and also a superstrate for light-trapping structures. To prevent an ohmic contact with the superstrate, the nanoantenna arrays can be passivated by a very thin layer of Al2O3 obtained by atomic layer deposition. In both these cases our design approach seems to be compatible with the concept of the roll-to-roll processing.
We have suggested a novel approach for a design of the light-trapping solar-cell nanopatterned structures which allows a significant enhancement of the photovoltaic absorption in the layers as thin as 110 (CIGS) and 150 (Si) nm. We have studied two specific examples and demonstrated their material-independent properties, so our approach can be applied to a variety of solar cells operating in the visible and infrared frequency range. More importantly, the light-trapping functionality of our structures is broadband, as not based on spectrally narrow resonances. Light trapping in the structures originates from the excitation of collective modes of a lattice of silver nanoantennas realized in the form of tapered nanostrips. The NA can be excited for different geometric parameters within a vast frequency spectrum so that the internal field localized in metal is much smaller than the field in the gaps between the metal elements, so that strong losses in the metal elements are avoided. We have demonstrated that our nanoantenna arrays operate noticeably better than the anti-reflecting coatings. Additionally, we have discussed the design issues with respect to possible fabrication of these nanoantenna arrays.
This work has been supported by the Ministry of Education and Science of Russian Federation, the Dynasty Foundation and the Australian Research Council. The authors thank K.R. Catchpole and H. Savin for useful discussions and suggestions.
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