A directionally selective multilayer filter is applied to a hydrogenated amorphous silicon solar cell to improve the light trapping. The filter prevents non-absorbed long-wavelength photons from leaving the cell under oblique angles leading to an enhancement of the total optical path length for weakly absorbed light within the device by a factor of κr = 3.5. Parasitic absorption in the contact layers limits the effective path length improvement for the photovoltaic quantum efficiency to a factor of κEQE = 1.5. The total short-circuit current density increases by ΔJ sc = 0.2 mAcm−2 due to the directional selectivity of the Bragg-like filter.
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The enhancement of the optical path length w opt of the incoming solar light within the photovoltaic absorber material of solar cells is a key issue for improving the performance of these devices and at the same time reducing material consumption [1,2]. The span of photon energies relevant for light trapping in solar cells is limited to a range more or less close to the band gap energy of the absorber material, where its absorption coefficient is relatively low such that this light cannot be absorbed within a single or double path through the absorber. To improve the absorptance and, in consequence, the quantum efficiency of the solar cell scattering at textured surfaces is routinely used in both thin-film and crystalline silicon solar cell technologies. The theoretical maximum path length of weakly absorbed light was calculated by Yablonovitch  to be4,5]5,6] but may also result from combining statistical, directionally insensitive light trapping with an angular selective filter [7–9]. Such directionally selective configurations also result in an enhancement of the theoretical Shockley Queisser limit  of the solar cell efficiency via the reduction of radiative losses in analogy to the efficiency enhancement obtained by concentration of the incident light .
As shown previously [8,9], directionally selective filters combined with a Lambertian scatterer may significantly enhance the light trapping of crystalline silicon solar cells. Due to the restricted acceptance angle these gains are only realized if the solar cells are tracked to the incident angle of the sunlight. First experimental studies  already demonstrated that a Bragg filter attached to an amorphous Si solar cell improves the external quantum efficiency within a certain spectral range. However, an increase of the integral short-circuit current density was not observed until now.
The present paper reports the experimental realization of a directionally selective filter consisting of a multilayer stack deposited onto the glass superstrate of a hydrogenated amorphous Si (a-Si:H) solar cell. We compare the reflection and the external quantum efficiency before and after filter deposition to quantify the improvement of light trapping. We demonstrate that the optical path length within the device is enhanced by up to a factor of κr = 3.5 where a factor of κEQE = 1.5 contributes to the improvement of the short-circuit current density of the solar cell by up to ΔJ sc = 0.2 mAcm−2.
Figure 1 depicts a schematic cross section of the experimental a-Si:H solar cell. A Bragg-like filter consisting of 73 alternating layers of SiO2 and Ta2O5 with a total thickness of 5.5 µm was deposited by a plasma ion assisted deposition process by mso Jena Mikroschichtoptik GmbH. Due to the Bragg-effect the transmission and reflection of the filter are spectrally and directionally selective. The design of the filter allows perpendicularly incident radiation with wavelengths λ smaller then the threshold wavelength λth to traverse the filter with almost no absorption loss. Radiation that passed the filter and the glass superstrate is scattered by the etched front transparent conductive oxide layer (TCO) into the photovoltaic absorber material. The absorber consists of a p-type (p), an intrinsic (i), and an n-type (n) layer. A second TCO layer and silver (Ag) act as reflector and electrical back contact. Traversing the different layers of the solar cell, the radiation is partly absorbed. The non-absorbed fraction of the light reflected at the rear side impinges onto the filter`s rear side under angles varying -in most cases- from the perpendicular incident angle. According to the Bragg characteristic, the filter is transparent for perpendicularly incident and opaque for obliquely incident angles. Thus, most non-absorbed photons are reflected back into the solar cell. The light paths for photons of high wavelengths therefore increase. The threshold wavelength λth of a Bragg filter shifts to lower wavelengths with increasing incidence angle θ according to 
Here, d is the thickness of one layer of the filter and n the refractive index of its material. The quantities λ0 and λ1 denote the threshold wavelengths at sin θ = 0 and sin θ = 1, respectively. Though not representing the full physics of our non-periodic multilayer Bragg-like stack, Eq. (3) is sufficiently accurate to explain our experimental results as will be shown below.
The external quantum efficiency is used to quantify the light trapping effect. In order to have a good comparison we measured the external quantum efficiency of each investigated solar cell before and after depositing the filter. We tested the filter on two different superstrates for the a-Si:H solar cells (textured SnO2:F on AsahiU glass and etched  ZnO:Al on Corning glass). The absorber layer thickness was varied between approx. 175 nm and 410 nm.
Figure 2 (a) shows the total reflectance of an a-Si:H solar cell measured for perpendicularly incident light using an integrating sphere. The thickness of the absorber layer is 322 nm, the superstrate used here is Corning glass with etched ZnO:Al . The reflectance of the solar cell without filter (black line, reflectance r 0(λ)) rises for higher wavelengths where the light path becomes smaller than the absorption length of photons in the solar cell material. After the deposition of the filter the reflectance r fi(λ) is substantially decreased in the wavelength range 650 nm < λ < 770 nm due to the directional selectivity of the filter suppressing re-emission of non-absorbed light. For λ ≥ λ0 = 767 nm, the reflectance r fi steeply rises to unity when the Bragg condition [Eq. (3)] is met for normal incidence. In the wavelength range 350 nm < λ < 650 nm, we observe a slight reduction of reflectance due to the antireflective properties of the filter. The filter induces a high reflectance for λ < 350 nm, i.e. in a spectral range that is not important for a-Si:H solar cells. Figure 2(b) shows the difference Δr(λ) = r fi(λ)-r 0(λ) highlighting a reduction of the reflectance by 40% at λ = 764 nm.
The external quantum efficiency (EQE) of a solar cell is defined as the number of elementary charges measured at the contacts divided by the number of photons impinging on the device. Figure 2(c) depicts the external quantum efficiency EQE of the same sample. The difference ΔEQE(λ) = EQE fi(λ)-EQE 0(λ) between the external quantum efficiency EQE fi(λ) with filter and EQE 0(λ) without filter is shown in Fig. 2(d). The difference ΔEQE(λ) essentially reflects the features already observed in Fig. 2(b). The wavelength interval where the quantum efficiency decreased significantly corresponds to the range where the filter is opaque, i.e. λ < 350 nm. The antireflective effect of the filter results in an increase of EQE fi with respect to EQE 0 in the wavelength range 420 nm < λ < 550 nm. An enhancement of EQE fi is also observed in the range 650 nm < λ < 770 nm due to the directional selectivity of the filter. Integrating the standardized AM1.5g solar spectrum  over the EQE without and with filter, yields short-circuit current densities J SC of 13.40 and 13.66 mAcm−2, respectively. Thus, we detect a total gain of 0.26 mAcm−2. Thereof 0.20 mAcm−2 are due to the improvement in the wavelength range 650 nm – 770 nm resulting from the directional selectivity of the filter.
In order to find a measure to quantify the improvement of light trapping, we compare the measured reflectance r(λ) to the prediction of Lambert-Beer’s lawEq. (4) defines the effective (or equivalent) optical path length w opt(λ) (regardless whether or not the actual reflectance is physically described by Lambert-Beer.) The path length enhancement factor k 0/fi(λ) for the solar cell without/with filter is defined by the relation w opt(λ) = k 0/fi(λ)w between the optical path length w opt and the geometrical thickness w. From Eq. (4) we obtainFigure 3(a) depicts these factors obtained with the help of Eqs. (6) and (7) from the reflectance and EQE data in Fig. 2. For 350 nm < λ < 650 nm, κr is above unity due to the reduction of direct reflection by the filter. According to the relatively small increase in the EQE seen in Fig. 2(d), the quantity κEQE is only slightly larger than unity in this spectral range. In contrast for λ > 650 nm both quantities, κr as well as κEQE, increase significantly above unity because of the additional light trapping due to the directional selectivity of the filter. In this range, κr represents a factor quantifying the additional light path prolongation in the device. The peak value κr,max ≈3.5 seen in Fig. 3(a) implies that close to the threshold wavelength λ0 = 767 nm the light path in the device is enhanced by a factor of 3.5 due to the filter. The factor κEQE obtained from the EQE is again below κr and peaks at a maximum value of κEQE,max ≈1.5. The quantity κEQE represents that portion of the light path prolongation that is useful for generating additional short-circuit current density. The large difference between the improvement factor κEQE and κr is due to parasitic absorption in the TCO and at the back contact. Such losses impose limitations on any effort to maximize light trapping in solar cells . At the peak values the light path in the device is prolonged by κr,max-1 ≈250%. However, the useful enhancement is only κEQE,max-1 ≈50%, i.e. only 20% of the additional light confinement is used for generating additional short-circuit current density and 80% is parasitically absorbed.
Figure 3(b) demonstrates that the maximum values for the improvement factors r and EQE depend on the absorber thicknesses and especially on the superstrates (textured SnO2:F on AsahiU glass and etched ZnO:Al on Corning glass). For all thicknesses and superstrates we have achieved a substantial reduction of the re-emission leading to r,max > 2 in all cases. The plotted error bars represent the standard deviation obtained from the number of investigated cells (5-12 cells per data point). The significantly enhanced parasitic absorption of AsahiU glass, however, impedes an improvement of the EQE leading to EQE,max < 1 except for the 420 nm cells. The fact that the values of EQE,max increase for thicker cells on Asahi-U may be due to a better ratio between effective and parasitic absorption.
Figure 4(a) shows the external quantum efficiency EQE fi(θ) measured under various angles of incidence θ. A steeper decrease with increasing θ is observed in the active wavelength range of the filter 650 nm < λ < 770 nm. An additional decrease in EQE fi(θ) at λ ~390 nm occurs due to destructive interference in the multilayer filter. Figure 4(b) shows the quotient EQE fi(θ)/EQE 0(θ) obtained from a cell with filter and a cell from the same preparation run without filter. The ratio EQE fi/EQE 0 drops sharply if θ exceeds the wavelength dependent threshold value. Losses are marked in black. The beneficial effect of the filter is represented by the white area where EQE fi(θ) > EQE 0(θ). The grey area around λ = 650 nm with 1.0 < EQE fi/EQE 0 < 0.9 most probably results from the fact that two different samples are used to generate the plot. The dashed line in Fig. 4(b) is calculated from Eq. (3) with λ0 = 767 nm and λ1 = 600 nm and demonstrates that the directional selectivity of the filter is well described by the simple Bragg characteristic. The spectral range of the improvement corresponds to the upper and lower threshold wavelengths λ0 and λ1 in Eq. (3). The restriction of the directional selectivity of the filter to the relatively small spectral range between λ0 and λ1 as well as the small selectivity close to λ1 explain the relatively small increase in the short-circuit current density. A use of a higher dielectric contrast as provided by the present combination of Ta2O5/SiO2 possibly could provide a larger spectral width for the directional selectivity.
This paper has demonstrated that the use of a directional selective filter can improve light trapping in solar cells and enhance the overall short-circuit current density. For a-Si:H thin-film solar cells the improvement depends on the texture of the front TCO and the thickness of the active absorber layer. A maximum improvement of ΔJ sc = 0.26 mAcm−2 is found when using textured ZnO and an absorber thickness of 322 nm. Here 0.06 mAcm−2 are due to the antireflective effect of the filter and 0.20 mAcm−2 due to its directional selectivity. The demonstrated enhancement of the optical path length up to a factor of κr = 3.5 emphasizes the potential of directional selectivity for improving the light trapping. The full use of this potential is limited by parasitic absorption in the contact layers of the present devices.
Partial funding of this project by the German Federal Ministry of Education and Research (Nanovolt, 03SF0322H) and the German Research Foundation (Nanosun, RA 473/6-1) is acknowledged. We are grateful for valuable discussions with all our project partners and colleagues. Special thank to Andreas Lambertz for providing the samples and to Christoph Zahren, Dirk Erdweg, Wilfried Reetz and Muhammad Tayyib for experimental support.
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