1. Introduction

Solar cell technology can provide virtually limitless clean energy by converting solar irradiation into electricity. In order to enable widespread implementation of solar cells, module cost efficiency indicators such as the cost per peak power output (€/Wp) need to be improved. Low-crystallinity semiconductors such as amorphous silicon and organics are inexpensive relative to crystalline silicon, but their poor charge transport properties demand that they are used in thin films (the order of a few μm or less) so that collection paths for charge carriers are short. This leads to incomplete light absorption; much of the incident light is reflected out of the system again. Thus, thin-film solar cell manufacturers must endeavor to reach a compromise between good charge transport properties (thinner films) and high absorption (thicker films) [1]. It is possible to overcome this compromise by using thin films (with good charge transport) combined with light-trapping, where incident light is trapped in the semiconductor film and ultimately absorbed. In this way we simultaneously obtain low-cost, highly absorbing solar cells with good charge transport properties [2]. Light-trapping structures can take many forms as outlined in recent publications [2,3]. Of particular interest is plasmonic light-trapping, where metallic (typically Ag or Au) nanostructures enable excitation of localized surface plasmons (LSPs, non-propagating excitations of conduction electrons within a metallic nanostructure) and or surface plasmon polaritons (SPPs, surface bound electromagnetic waves that propagate along metal-dielectric interfaces) which traps light at the respective metal-semiconductor interface. For a number of typical semiconductor-metal configurations, this light is preferentially absorbed in the semiconductor [4], leading to an overall enhancement in the absorption over the flat (no metallic nanostructure) case. Providing the implementation of the light-trapping structure does not modify the solar cell’s internal quantum efficiency (a measure of charge transport properties), the absorption enhancement corresponds to an enhancement in the power conversion efficiency.

A wide variety of plasmonic solar cells (PSCs) has been investigated experimentally and theoretically towards achieving performance superior to that of a flat layer solar cell (Fig. 1(a) ). It is possible to group PSCs into three main classes: nanoparticles dispersed in the semiconductor layer (Fig. 1(b)), the nanostructured metallic electrode (Fig. 1(c)) and in-scattering nanoparticles (Fig. 1(d)) [2,4]. Each PSC is fundamentally different in terms of absorption enhancement mechanisms.

 

Fig. 1 (a) Standard (flat) solar cell architecture. The direction of incident light is indicated. (b–d) Three classes of plasmonic solar cells designed to achieve enhanced semiconductor light absorption.

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Nanoparticles (NPs) dispersed in the semiconductor layer (Fig. 1(b)) can, in addition to enhancing the absorption, also improve the series resistance [5]. Absorption enhancement is typically observed in the near-field of the NP and it has recently been argued that this enhancement arises primarily due to the excitation of scattered modes at the NP (rapidly absorbed in highly absorbing materials), as opposed to excitation of LSP modes [6,7]. However, Zhu et al. found that light trapping in this geometry relies heavily on plasmonic excitation, by showing a strong fall-off in enhancement for nanometer-thin NP dielectric shells [8]. Excitation of SPPs on the flat back-electrode is also possible in this PSC via scattering at the NPs. The relative importance of NP scattering and absorption is highly size- and shape-dependent [6,9]. Dispersed NP organic PSCs using nanowires [10], truncated octahedral NPs [7] and NP clusters [11] have recently been reported with significant efficiency enhancements of up to 23% [7].

Nanostructured electrodes (Fig. 1(c)) can be easily incorporated into standard solar cell design in place of the planar metallic electrode. Design of nanostructured electrodes can draw greatly from research in metallic nanostructures such as gratings [12], void [13,14] and hole arrays [15,16]. It is possible to excite both LSPs on the protrusions/voids and SPPs on the intervening planar surface. The role of the nanostructured electrode is two-fold: one, to enhance absorption in the active layer and two, to collect charge carriers. A number of reports demonstrate enhanced efficiencies of up to 20% [17] and attribute the enhancements to scattering as well as the excitation of plasmonic modes [17–20].

The in-scattering NPs geometry (Fig. 1(d)) can achieve light-trapping by scattering incident light at wide angles into the active layer. This increases the light path length in the cell and can lead to total internal reflection. It is also possible for this scattered light to excite SPPs on the back interface and photonic modes in the active layer. An efficiency enhancement of 8% has been reported for amorphous silicon solar cells with Ag NPs separated from the active layer by a 20 nm intervening indium tin oxide layer [21]. Near-field absorption enhancement due to the NPs is also possible if their separation from the semiconductor is sufficiently small. A number of groups have recently reported efficiency enhancements by embedding metallic nanoparticles in a layer of a hole-conducting polymer, PEDOT:PSS, adjacent to an organic semiconductor film [22–24]. For the purposes of this paper, we consider this geometry as a hybrid of the dispersed NP and in-scattering NPs PSC geometries and instead refer the interested reader to a recent report [25].

We note that dielectric particles can also be used to excite SPPs on metal surfaces [26] and to provide scattering. However, metallic nanoparticles (mainly Au and Ag) have primarily been considered for this application, largely because of their ability to exhibit strong resonant scattering (e.g. the resonance scattering cross-section of a 20 nm Ag NP embedded in Si is 30 times larger than its geometric cross section) [9].

Previous optimization studies have focused on individual PSC geometries in detail [8,25,27]. We aim to directly compare three fundamentally different PSCs in order to identify the most promising geometry, understand the nature of the absorption enhancement and estimate the likely maximum absorption enhancement that can be expected. To the best of our knowledge this is the first instance of such a report.

2. Method

The Finite Element Method (FEM) is invoked using commercially available software (COMSOL) to model light absorption in the flat SC and the three PSC geometries. The suitability of the FEM for reproducing experimental results in light trapping solar cells has been established previously [28]. We numerically solve the time-harmonic wave equations in the electric field E and the magnetic field H:

 

Fig. 2 (a) Relevant geometry parameters for the simulations, shown here for the dispersed nanoparticle plasmonic solar cell. They can be similarly applied to the other two geometries. (b) Boundary conditions. (c–e) Absorption enhancement exhibited by plasmonic solar cells relative to a planar solar cell. The values are calculated by integrating semiconductor absorption spectra within the wavelength range 350-1000 nm with AM1.5G illumination intensity. (c) Dispersed nanoparticles. (d) Nanostructured electrode. (e) In-scattering nanoparticles.

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The outcome of each simulation is the electromagnetic field profile defined for all wavelengths in the range 350–1000 nm. From this profile, the absorption A(λ) in the active layer, the (planar) electrode and the NPs can be calculated by integrating the energy dissipation density within the appropriate 2D volume according to:

A blend of two common organic semiconductors: PCPDTBT/PC70BM (poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b‘]-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)]/ [6,6]-phenyl-C71-butyric acid methyl ester, is chosen as the active material. Silver is used for both the nanoparticle and electrode material. The active layer thickness is fixed at 60 nm. The NP shape is chosen to be rectangular, as much of the literature in plasmonics is based on the use of rectangular gratings [12,29–31] and the same shape is used for all three PSC geometries to facilitate a direct comparison. The corners of the NP are rounded (2 nm radius) to eliminate inaccuracies that arise when performing FEM simulation on geometries with sharp corners [32]. The height of the nanostructure is fixed at 30 nm, which is comparable to the dimensions of nanoparticles commonly reported in PSCs and relevant plasmonic structures [9,12,23,31]. The period of the array and the width of the NPs are varied independently, allowing an optimization of light absorption in the active layer (Fig. 2(a)). We model a simplified solar cell: a glass substrate (n = 1.4), a semiconductor/active layer and a metallic electrode and nanostructure. In order to ensure clear conclusions about the mechanisms facilitating light-trapping can be drawn, we do not consider additional layers, such as charge transport layers, in the simulation geometry. A perfect antireflection coating at the air-glass interface is assumed—we illuminate at normal incidence from within the glass (Fig. 2(b)) at a distance of 250 nm from the active layer. The three PSC geometries can be realized by modifying the flat geometry (Fig. 1(a)) by placing the NP at the appropriate location in the layer stack: centered in the active layer (Fig. 1(b)), on the back electrode (Fig. 1(c)) or embedded in the substrate above the active layer (Fig. 1(d)). The spacing between the active layer and the NP in the in-scattering geometry is fixed at 30 nm, chosen to be consistent with experimental reports of this geometry [21,33]. Values of complex refractive indices are obtained from the literature [34,35].

3. Results and discussion

3.1 Optimization study

The absorption in the active layer for the dispersed NP geometry under TM polarized illumination is shown in Fig. 2(c) for NP widths ranging from 10–120 nm and periods ranging up to 600 nm. Absorption enhancements (relative to a flat solar cell (Fig. 1(a)) exceeding 1 are observed for a large range of NP widths and periods. It is important to note that the volume of active material in this configuration is decreased due to the presence of the NP. Despite this, the total amount of light absorbed in the active layer is increased—the absorption enhancement due to the presence of the NP outweighs the reduction in absorption due to the omitted semiconductor material. A maximum absorption enhancement of 45% (enhancement factor of 1.45) is observed for a NP width of 40 nm and a period of 190 nm. At low periods the content of active material rapidly decreases (the active layer is crowded with silver) and the active absorption drops correspondingly. At large periods, where the density of features becomes small, the absorption enhancements tend towards 1, as expected. The peak of the curve is located at a value of feature width and period for which the culmination of light-trapping effects integrated across the investigated spectrum is maximized. Under TE illumination the absorption is less than that of a flat layer for all values of NP width and period (Fig. 3(a) ). No plasmonic excitation is possible with this polarization, and scattering from the particle does not compensate for the reduction in semiconductor volume.

 

Fig. 3 Absorption enhancement exhibited by plasmonic solar cells relative to a planar solar cell for TE-polarized light (a,c,e). Polarization-averaged absorption enhancement (b,d,f).

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A maximum enhancement in absorption in the OSC of 33% is observed for the nanostructured electrode PSC with a NP width of 80 nm and a period of 190 nm (Fig. 2(d)) under TM illumination. Like the dispersed NP case, this is despite the 2D volume of semiconductor being reduced. The absorption under TE illumination is reduced for most combinations of NP width and periods, although a small absorption enhancement (1%) is observed for NP width 10 nm and period 600 nm. The higher performance of the nanostructured electrode PSC compared to the dispersed NP PSC for TE polarized light is likely due to the shadow effect present in the dispersed NP PSC.

The absorption enhancement provided by the in-scattering NP geometry with TM illumination is less than one for all simulated values of period and NP width (Fig. 2(e))—the active layer absorption of all simulated configurations are lower than that of the flat layer. The reasons for this will be discussed in the following section. However, an absorption enhancement of up to 4% is observed for TE polarization; absorption of TE-polarized light exceeds that of TM-polarized light for this PSC geometry. We identify more efficient scattering into the semiconductor layer in the absence of localized plasmonic excitation at the nanoparticles as an important contributing mechanism for this. Excitation of low-order TE waveguide modes within the semiconductor layer [29] is not observed upon a rigorous inspection of the spectra – which is to be expected given the small difference in refractive index between the organic material (n~2) and glass (n = 1.4), leading to poor mode confinement within the semiconductor material.

By combining the absorption enhancements for TM- and TE- polarized light according to Eq. (4), we obtain the polarization-averaged absorption enhancement of these devices (Figs. 3(b), 3(d), 3(f)). These results apply for three-dimensional structures with an axis of symmetry as described in section 2 (c.f. line gratings). The optimized value for each PSC is shown in Table 1 .

Table 1. Optimized Plasmonic Solar Cell Geometries

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3.2 Dependence on semiconductor layer thickness

The previous optimization was carried out for a fixed value of the active layer thickness of 60 nm. The absorption enhancement of a PSC over a planar cell is highly dependent on this value. Taking the optimized dispersed NP geometry (NP width = 60 nm, period = 330 nm), we vary the thickness of the active layer, maintaining the center of the 30 nm high NP at a distance of 30 nm above the electrode. In doing so we effectively increase the amount of semiconductor material that the light must pass through before it can interact with the NPs. The absorption values (integrated across the 350–1000 nm wavelength range under 1 sun) of a flat and a PSC geometry are shown in Fig. 4 for active layer thicknesses up to 600 nm. The flat curve demonstrates a typical oscillatory dependence on active layer thickness, which arises from Fabry-Pérot resonances [36]. This oscillatory behavior is also observed for the PSC. We note that the peaks of the PSC pattern are slightly shifted from those of the flat geometry. This confirms that the NPs affect the coherent interference of the light in the active layer [37].

 

Fig. 4 Dependence of the active layer thickness on A_av for the dispersed nanoparticle and flat solar cells.

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For an active layer thickness of 60 nm, we observe an absorption enhancement of 19% as shown in Table 1. Even higher enhancements are possible—a maximum of 22% is observed for an active layer thickness of 100 nm. As the active layer thickness further increases, the PSC curve converges with that of the flat geometry. This is consistent with a filter effect: the majority of light is absorbed before it reaches the NPs. Non-negligible enhancement is observed for active layer thicknesses as large as 600 nm.

Finally we note that the active layer absorption for a 60 nm PSC exceeds that of all flat SCs with active layers thinner than 160 nm (indicated by the dashed line in Fig. 4). In other words, light trapping enables the absorption of a 60 nm thick semiconductor film in a PSC to be equivalent to that of a 160 nm flat film. By considering the area of the unit cell in each case, and accounting for the reduction in active material due to the presence of the NP, it follows that light-trapping enables an active material volume reduction of 65%.

3.3 Spectral characteristics of light-trapping

In order to focus on the role of plasmonic excitation on light trapping, we restrict our attention to TM illumination for the remainder of this paper. The absorption and reflection spectra of the flat and (TM-) optimized PSC structures are directly compared in Fig. 5 , and corresponding spatial absorption profiles for selected wavelengths are shown in Fig. 6 . Similar results are observed for the polarization-averaged optimized PSCs. The spectra have not been scaled by the solar spectrum. As the in-scattering geometry indicates a reduction of absorption in the active layer for all simulated values of period and NP width, there is no optimum configuration with non-zero NP width. In order to nevertheless compare the spectra with that of the other geometries to gain an insight into the loss mechanisms, we choose period = 40 nm and NP width = 190 nm (the same as those of the dispersed NP geometry).

 

Fig. 5 Redistribution of incident light (TM polarized) for the dispersed NP (circles, NP width = 40 nm, period = 190 nm), nanostructured electrode (squares, NP width = 80 nm, period = 190 nm) and in-scattering NP (triangles, NP width = 40 nm, period = 190 nm) plasmonic solar cells and the flat solar cell (black line). (a) Absorption in organic semiconductor. (b) Reflectance. (c) Absorption in the nanoparticle. (d) Absorption in the electrode. Note for the nanostructured electrode, the absorption in the planar electrode and the (attached) nanoparticle are calculated separately.

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Fig. 6 Spatial absorption profiles under TM polarization for selected wavelengths. (a,d): Dispersed nanoparticle solar cell (nanoparticle width = 40 nm, period = 190 nm) at wavelengths 470 nm (a) and 700 nm (d). (b,e) Nanostructured electrode (nanoparticle width = 80 nm, period = 190 nm) at wavelengths 470 nm (b) and 700 nm (e). (c) Flat solar cell at wavelength 470 nm. (f) In-scattering nanoparticle solar cell (nanoparticle width = 40 nm, period = 190 nm) at wavelength 360 nm. The color scale indicates the power dissipation density relative to the maximum in (a).

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The dispersed NP geometry semiconductor absorption exceeds the absorption in the flat geometry at all simulated wavelengths (Fig. 5(a)). Two main peaks are seen at 570 and 750 nm. A LSP resonance is observed as a sharp increase in the NP absorption at low wavelengths (the peak lies below 350 nm) (Fig. 5(c)). We see high active absorption at the same spectral position (Fig. 5(a))—implying that light-trapping at this wavelength could be due to resonant near-field enhancement due to LSP excitation. No other LSP resonances are identified via peaks in the NP absorption spectrum. However, a spectrally broad enhancement in the semiconductor absorption is seen which cannot be solely accounted for by near-field enhancement due to (resonant) LSP excitation; scattering must play a large role. In section 3.3 we directly show that scattering alone can account for large absorption enhancements of the order observed here. We note that the small peak in the NP absorption at 600-650 nm (Fig. 5(c)) does not indicate a LSP resonance; it coincides with a dip in the absorption spectrum of the semiconductor (Fig. 5(a)), also observed in the electrode absorption (Fig. 5(d)). The absorption at 470 nm (Fig. 6(a)) is significantly more localized than in a flat SC (Fig. 6(c)), predominately occurring about the two front corners of the NP. This absorption pattern is similar with that observed for scattering into a highly absorbing material (see section 3.4). The absorption at 700 nm is preferentially localized at the back corners, which leads to intense absorption between the NP and the back electrode (Fig. 6(d)). This suggests that this structure could also be optimized to excite nanocavity modes [30]. The peak at 550 nm features localization (not shown) at both the front and back corners.

Like the dispersed NP geometry the active layer absorption for the nanostructured electrode geometry is significantly larger than that for the flat geometry (Fig. 5(a)) across the entire wavelength range addressed in this study. Strong absorption occurs between the NP and the top of the active layer at 470 nm (Fig. 6(b)). This is not however, due to a Fabry-Pérot resonance for this reduced active layer thickness (30 nm, between the NP and the edge of the active layer). Simulations where the thickness of the active layer for planar SCs is varied (Fig. 4), reveal no resonance for a layer thickness of 30 nm at the wavelength 470 nm (Fig. 6(b)). Therefore the NP itself must be fundamental to this absorption enhancement. As the absorption is quite delocalized and plasmonic absorption enhancement only extends into organic materials from a few to 10 nm [8,38], we attribute this delocalized absorption to back-scattering provided by the NP and not to near-field enhancement due to LSP excitation. The bulk of the absorption at 700 nm is similarly delocalized although localized absorption is also observed along the sides of the NP (Fig. 6(e)).

The origin of the poor performance of the in-scattering layer in this study is largely due to enhanced reflection. The back-scattering that occurs due to the NPs has the effect of dramatically increasing the reflectance for a wide wavelength range (Fig. 5(b)), leading to a reduction in absorption in the active layer (Fig. 5(a)). Given the large spacing between the NP and the active material, near-field enhancement is also unavailable. We see therefore, that the wide angle in-scattering provided by the NPs does not outweigh the detrimental effect of back-scattering. The absorption in the NPs due to LSP resonances (Fig. 5(c)) at 360 (Fig. 6(f)) and 400 nm also represents a loss, although only over a narrow wavelength range. It is expected that further simulation studies of this PSC would indeed find an enhancement if other geometries and material combinations are considered [4,9].

3.4 Ideal vs. non-ideal conductors

The importance of scattering in the absorption enhancement is explored further by comparing silver NPs with perfectly conducting NPs for the dispersed NP PSC. Plasmonic excitation is not possible for the perfectly conducting NPs; the only available enhancement mechanism is scattering. The semiconductor absorption spectra for period = 190 nm and NP width = 40 nm (as optimized for silver in section 3.1 for TM-polarized light) are shown in Fig. 7(a) . A large absorption enhancement of 20% is seen for perfectly conducting NPs, which demonstrates that plasmonic excitation is not necessary for significant light trapping with this geometry. The localization of the absorption at the corners (Fig. 7(b)) closely resembles that observed in the case of silver NPs (Figs. 6(a) and 6(b)). The localization of the light arises because the scattered modes are absorbed before propagating more than a few nanometers into the high absorbing material. This demonstrates that near-field enhancement due to LSP excitation is not necessary for light-trapping using metallic nanostructures: significant enhancements are possible via scattering alone. This corroborates the findings of previous reports [6,7]. We note that even higher enhancement values are possible via scattering alone; 35% is observed for a perfectly conducting NP of width 60 nm and period 230 nm.

 

Fig. 7 (a) TM semiconductor absorption for a flat solar cell (black line) and dispersed nanoparticle plasmonic solar cells with silver (circles) and perfectly conducting nanoparticles (squares), period = 190 nm, nanoparticle width = 40 nm. (b) Spatial absorption profiles with a perfectly conducting nanoparticle at 700 nm. The color scale indicates the power dissipation density relative to the maximum in 6(a).

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3.5 Practical considerations for plasmonic solar cell fabrication

The above investigation finds excellent light-trapping properties for both dispersed nanoparticle and structured electrode organic solar cell architectures. Methods for fabricating ordered structured electrodes in solar cells have been well documented [19,39]. Conversely, the ordered deposition of metal nanoparticles such that they rest in the middle of a solution-processed organic layer has not yet, to the best of our knowledge, been experimentally demonstrated (although very conceivable for organic solar cells featuring materials that can be evaporated, such as CuPc). However, high order is not critical for strong light trapping in this configuration, as observed experimentally with nanoparticles randomly dispersed within the active layer [7,10,11]. We find (Fig. 3(b)) the nanoparticles in the optimized configuration have a spacing of 330 nm, which far exceeds the distance over which LSP-LSP interaction takes place in an organic semiconductor (the plasmonic near field of a small nanoparticle extends to a distance of the order of 10 nm from the nanoparticle [38]). Therefore, light-trapping due to LSP excitation at sufficiently widely spaced nanoparticles can be considered independent of the degree of order, and only on the density of the nanoparticles. A similar argument applies for scattering. Although excitation of diffraction modes is order sensitive, random arrays of metallic nanoparticles are known to (incoherently) scatter strongly due to the large scattering coefficient of individual particles [9,33]. Therefore, the important parameter is the density of nanoparticles [8], implicitly defined here by the period of the nanoparticle array.

We also note that the presence of additional layers between the substrate and the organic layer such as the transparent electrode (typically indium tin oxide or aluminum-doped zinc oxide) and charge transport layers (PEDOT:PSS in non-inverted solar cells or TiO₂ or ZnO in inverted solar cells) affects the distribution of absorption within the semiconductor and as a result, the parameters of the optimal metallic nanostructure will vary between material system. Absorption in indium tin oxide electrodes represents an energy loss mechanism for both plasmonic and flat solar cells.

For the nanostructured electrode geometry, intervening layers between the semiconductor and the electrode could have a large effect, depending on the material and material thickness. In non-inverted solar cells, thin layers (< 1 nm) of LiF are often used. This would not be expected to strongly inhibit near-field effects (which extends out into the organic semiconductor up to around 10 nm from the metal surface) or light-trapping due to scattering at the electrode. A thick (5-10 nm) layer of Ca, which absorbs significantly and does not support plasmonic excitation, often used to modify the work function of the back-electrode, would significantly inhibit the absorption enhancement in the semiconductor. Conversely, a 5–10 nm layer of WO₃, which is optically transparent and often employed in inverted organic solar cells, may inhibit near-field enhancement but not light-trapping via scattering.

4. Conclusion

Plasmonic solar cells have been compared and optimized using finite element simulations to ascertain promising structures for high performance solar cells. The largest absorption enhancement observed for a 60 nm film of standard organic semiconductor is 19%, obtained by uniformly dispersing silver nanoparticles of width 60 nm with a periodicity of 330 nm. The absorption in a 60 nm film with this light trapping configuration is equivalent to that of a 160 nm flat film, representing a huge reduction in semiconductor consumption. Light-trapping is beneficial for all active layer thicknesses up to 600 nm. We find evidence of near-field plasmonic enhancement, but show that it is not necessary; strong absorption enhancement in the semiconductor is possible via scattering alone. This technique can be applied to a wide range of low-cost semiconductors to find the critical device thickness below which light-trapping is required. If satisfactory charge transport is possible for thin films of this thickness, then light-trapping is unnecessary. If not, thinner films (with better charge transport properties) with light-trapping are preferable.