We present a finite-difference time-domain (FDTD) study of an amorphous silicon (a-Si) thin film solar cell, with nano scale patterns on the substrate surface. The patterns, based on the geometry of anisotropically etched silicon gratings, are optimized with respect to the period and anti-reflection (AR) coating thickness for maximal absorption in the range of the solar spectrum. The structure is shown to increase the cell efficiency by 10.2% compared to a similar flat solar cell with an optimized AR coating thickness. An increased back reflection can be obtained with a 50nm zinc oxide layer on the back reflector, which gives an additional efficiency increase, leading to a total of 14.9%. In addition, the patterned cells are shown to be up to 3.8% more efficient than an optimized textured reference cell based on the Asahi U-type glass surface. The effects of variations of the optimized solar cell structure due to the manufacturing process are investigated, and shown to be negligible for variations below ±10%.
© 2013 Optical Society of America
High-efficiency, low-cost solar cells are likely to play a central role in making the world’s energy production sustainable [1, 2]. Amorphous silicon (a-Si) solar cells, along with microcrystalline solar cells, are often said to be well balanced when it comes to price vs. efficiency, compared to the expensive high efficiency gallium arsenide or crystalline silicon cells, and the theoretically cheap, low efficiency polymer cells [3, 4]. The a-Si solar cell is typically a p-i-n structure grown on a glass or metal substrate. The device consists of a metallic back reflector, an a-Si absorber layer, and an anti-reflective (AR) coating, so the materials used to make a thin film a-Si solar cell are common, relatively cheap and well suited for large scale production [3, 5]. As the carrier diffusion length of a-Si is very low, the active layer must be thin to avoid significant electron-hole recombination. This is an advantage in manufacturing, as it reduces the deposition time, but it lowers the efficiency as the absorption is limited by the short light path length. Thus much research focuses on increasing the absorption, especially through the scattering of light inside the absorbing layer.
More generally, absorption enhancement in silicon-based thin film solar cells is approached in one of two ways. One is to introduce light trapping nanoparticles as surface scatterers [6, 7] or back scatterers . The other is to use random surface roughness  or controlled geometrical features such as periodic arrays or gratings on either the back reflector [10–13], or the front contact [14, 15]. In most cells, a transparent conductive oxide, such as ZnO or ITO, is also introduced between the absorbing layer and the metal back contact as it increases the absorption by increasing the back contact reflection [16–18].
The absorption in a-Si solar cells have been studied theoretically by Abass et al., modelling more general dual-interface grating structures . Experimentally, Ferry et al. have imprinted nanoscale patterns on the substrate and shown an enhanced absorption . Production costs can be lowered as well using roll-to-roll processing as shown by Van Aken et al.[20, 21]. A combination of the imprinting and roll-to-roll processes might therefore significantly lower the cost-benefit ratio for a-Si solar cells.
The many absorption enhancement techniques leave a vast set of parameters to tune when trying to achieve the best efficiency in an a-Si solar cell. But in practise, after choosing a cell type and manufacturing method, only a small number of actual production variables remain. For theoretical optimization of cells based on geometrical light trapping, a typical starting point is a one- or two-dimensional grating structure [10, 12, 19, 22]. The absorption is calculated over the absorption range of the solar cell, and optimal grating parameters are determined.
In the present work, we study an imprintable a-Si solar cell grating geometry from a theoretical viewpoint. Our starting point is an imprint master made by anisotropic etching of crystalline silicon. This choice is based on the fact that anisotropic etching generates extremely well defined gratings with highly regular and smooth facets. The geometry of the master is determined by an etch mask that defined the lateral extent of the etched grooves. This leaves a set of geometric parameters, and their influence on the absorption in the a-Si layer is studied using a finite-difference time-domain (FDTD) model. To obtain realistic solar cell performance, the photogeneration yield is optimized for the AM 1.5 solar spectrum. The effect of including a ZnO layer as part of the back contact is studied, as is the influence of manufacturing defects due to the imprinting and deposition processes.
One way of creating nano scale patterns on a silicon wafer is through anisotropic etching. In this process the surface is reduced to having only  facets, forming irregular pyramids if simply etching a  surface , or a controlled pattern by use of an etch mask. The etched pattern can then be transferred to a solar cell through imprinting, either by generating a metallic (Ni) master from it, or by using the etched wafer as a stamp itself, as illustrated in Fig. 1. After imprinting either of the two patterns in a polymer substrate, an a-Si p-i-n stack can be deposited on top by chemical vapour deposition [10, 23].
In the present study, we examine a 2D grating structure as a solar cell substrate, with aluminium as the metallic back reflector, a-Si as the active layer and SiNx as the AR coating. While silver is more commonly used for the back reflector, Al is chosen as it is significantly cheaper than Ag, and has been reported by Naqavi et al. to give close to the same solar cell efficiency. A ZnO or ITO layer of about 100nm thickness is often included between the metal and a-Si layers in order to improve reflection, and this will be treated after an optimal cell has been found.
The master is made by depositing lines of chromium on an (100) Si wafer, and etching away the region in between to get steep grooves with (111) facets. A model of the solar cell to be deposited on the imprinted grating is seen in Fig. 2(a), where the structure 1 geometry of Fig. 1 has been used. The etch mask leaves a plateau between the grooves with a minimal width of about d = 50nm. The groove angle θ = 54.7° stems from the projection of (111) direction onto the (100) surface. This leaves the grating period Λ and the absorber and AR coating thicknesses h1 and h2 as free parameters. For an efficient solar cell, the choice of a-Si layer thickness h2 is a balance between having a large absorption and having enough photo-electrons and - holes reaching the contacts. While a thicker layer will increase absorption, the low electron and hole mobility in a-Si will give large recombination losses in a thicker cell. Thus, the external quantum efficiency (EQE), that is, the ratio of generated carge carriers to incoming photons, will decrease. In an efficient a-Si solar cell, 300nm is a typical distance between contacts . Therefore a contact distance of h2 = 290nm is chosen for the model, corresponding to a vertical (deposited) a-Si layer thickness of 500nm. This leaves Λ and h1 as optimization parameters.
The solar cell is modelled for both geometries illustrated in Fig. 1. In the first, triangular ridges having a flat top are formed whereas a flat bottom section is formed in the second. The absorption in the a-Si layer is investigated for both s- and p-polarizations of the incident light as shown in Fig. 2(b). The absorption is calculated by the finite-difference time-domain (FDTD) method, with a broad band plane wave light source incident perpendicularly on the surface. The materials are modelled by their refractive indices. The Al parameters are those of Palik  while the AR coating is chosen to has a refractive index of n = 2, close to that of SiNx which is often used in solar cell production. The refractive index, ñ = n + ik, of the a-Si layer has been obtained by ellipsometry measurements on a hydrogenated a-Si thin film grown by plasma-enhanced chemical vapour deposition, and can be seen in Fig. 3(a). The inset shows the nearly vanishing values of k above the energy gap wavelength, indicating that we should expect almost no absorption for wavelengths λ > 800nm.
As the photo current is generated in the a-Si layer, the quantum efficiency is calculated from light absorbed in this layer. It is defined as the ratio of the power of the light absorbed in a-Si to the total power of the incoming light, QE(λ) = Pabs(λ)/Ptot (λ). The cell efficiency is described by the integrated quantum efficiency (IQE). This is calculated by weighting QE(λ) with the photon flux Nph of the solar spectrum and integrating over the absorption range . The photon flux is, in turn, calculated from the solar intensity distribution Isun as Nph(λ) = λIsun(λ)/hc, so
The FDTD Solutions package by Lumerical was used for the calculations .
3. Structual optimization
The solar spectrum Isun(λ) is shown in Fig. 3(b) as a black curve. In addition, as a typical example, we show the calculated QE(λ) for a 500nm thick flat solar cell (blue) as well as a grating cell with structure 1 having a period of 600nm (red). An AR coating of h1 = 60nm, and an s-polarized light source have been used for the calculations. As expected, the absorption nearly vanishes above a wavelength of 800nm. The increase in absorption from the grating is clear for the higher wavelengths.
The absorption in the cell varies spatially with the wavelength. At the lower wavelengths the absorption happens immediately at the interface layer (Fig. 4(a) and 4(b)), while at the longer wavelengths the absorption occurs deeper inside the material (Fig. 4(c) and 4(d)). The low wavelength absorption therefore depends on resonances in the AR coating layer, while the high wavelength absorption is also dependent on resonances in the a-Si layer. The internal resonances appear as peaks in the absorption spectrum of a flat cell (Fig. 3(b)), while there is no obvious wavelength dependence in the grating cell. As there is no absorption above 810nm, the IQE will be calculated from the wavelength range of 400nm to 810nm.
The effect of the grating pattern for varying AR coating thickness is seen in Fig. 5. Here, the IQE of a structure 1 solar cell (Fig. 1) with a 600nm period is calculated for both s- and p-polarizations (black and red), and compared to the IQE of two flat cells with a-Si layer thicknesses of 500nm and 290nm (blue and magenta). The flat cells are chosen so that the first has the same a-Si volume pr. area as the grating cell, while the second has the same contact distance. As expected, the thicker flat cell has the higher optimal IQE, at 68.5%, while the thinner has an optimal IQE of 62.7%. As it has the higher IQE, the 500nm flat cell will be used as a reference when comparing to the grating cells even though it might have a smaller EQE. The optimal IQE of the grating cell is seen to be 7–12% higher than the 500 nm flat cell, dependent on polarization.
A complete scan of the AR coating thickness and lattice period for structure 1 is seen in Fig. 6 for both polarizations. The IQE of the s-polarized light is seen to be more sensitive to the choice of parameters than the IQE of the p-polarized light. The IQE of the s-polarized light is slightly better, with a maximum of 76.7% compared to the 73.6% of the p-polarized light. Comparing the two graphs, it is seen that the IQE for the s-polarization has a maximum at a lattice period of Λ = 650nm and a coating thickness of h1 = 55nm, while the maximum is at Λ = 625nm and h1 = 65nm for the p-polarization.
Similar graphs have been calculated for structure 2 from Fig. 1, and are shown in Fig. 7. The difference between the maximal IQEs of s- and p-polarized light is larger in this geometry, with values of 78.1% and 73.9% respectively. The general shape of the graphs is the same as for the first structure, but the maxima of the IQE for the two polarizations are not lying as close to each other in the configuration space. The s-polarization IQE maximum occurs for h1 = 60nm and Λ = 600nm, whereas the p-polarization maximum occurs for h1 = 70nm and Λ = 750nm.
For both geometries, the IQE of the s-polarized light is found to be varying more with the coating thickness than the lattice period in the studied parameter range. The IQE of p-polarized light generally varies less that of the s-polarized, but is more sensitive to the lattice period. Assuming an unpolarized light source, an optimal configuration can be found by averaging the IQE of the two polarizations. This can be seen in Fig. 8. Solar cell structure 1 is found to have a maximal IQE of 75.1% at an AR coating thickness of h2=60nm and a period of Λ = 650nm. Structure 2 has an IQE of 75.5% at the same coating thickness, but with a period of Λ = 600nm. Thus, the grating cells are up to 10.2% better at absorbing light than the flat cell. As the geometry sensitivity is much larger for the s-polarized light than for the p-polarized, the optimal geometry is mainly defined by the s-polarization IQE, with the p-polarization IQE shifting the optimal geometry to a slightly longer period.
4. Production defects
In actual production, the solar cell cannot be expected to follow the model geometry completely. The different layers will likely be deposited slightly unevenly, and the imprinted geometry will have some irregularities. The effects of these modifications will be considered in the following.
During the deposition processes, the a-Si and AR coating will most likely either diffuse towards the bottom of the grooves or adhere more strongly to the protruding grating edges on top, rather than giving a completely uniform layer. A simple model for the a-Si layer variation of the layer thickness is seen in Fig. 9(a), where x = 500nm is the vertical thickness of the layer. A parameter δ is introduced to give a thicker layer of a-Si in the grooves for δ > 0 and a larger deposition on the peaks for δ < 0. In this way, the total deposited amount of a-Si is nearly constant for varying δ, so the IQE values are readily comparable. The effect of this shift is calculated for structure 1 with Λ = 600nm and h1 = 60nm and shown in Fig. 9(b). The graph limits of δ = ±100nm corresponds to a ±20% variation of the layer thickness. It is seen that a variation of 50nm has no significant effect on the average IQE. But when large amounts of a-Si diffuse towards the bottom of the grooves (δ > 50nm), away from the strong absorption regions of Fig. 4(a) and 4(b), the IQE decreases significantly.
A model for the AR coating layer variation is seen in Fig. 10(a), where y =104nm is the optimal vertical thickness of the AR coating layer, corresponding to h1 = 60nm. As there is no need to keep the material amount constant for comparison, the parameter γ simply indicates the filling of the grooves, without subtracting from the AR layer thickness on top. The resulting IQE in Fig. 10(b) indicates that a slight diffusion of the AR coating into the grooves will actually increase the IQE slightly. A 10% decrease of the AR coating thickness in the grooves does not significantly decrease the efficiency of the cell.
A small local variation of the grating due to the imprinting process and polymer elasticity can be modelled using three grating periods as illustrated in Fig. 11(a). Again, structure 1 is used with h1 = 60nm and Λ = 600nm. The length of the three periods is kept constant at 1800nm, while the individual periods w1 and w2 are varied ±60nm corresponding to 10% of the actual period. The resulting IQEs for both polarizations can be seen in Fig. 11(b) and 11(c). The p-polarized light is seen to be better absorbed at the regular geometry, while the IQE of the s-polarized light can be slightly improved by the variation. In both cases, however, the change in IQE is smaller than the changes brought on by variations in the a-Si and AR coating layers.
5. Enhanced back reflection and comparison to a textured reference
For the actual production, a transparent conductive oxide layer should most likely be implemented as part of the bottom contact. A thin ZnO:Al layer between the Al and a-Si layers is known to increase the aluminium reflectivity, and is therefore often included in an actual solar cell . The model including a ZnO layer between the Al and a-Si layers is seen in Fig. 12(a). To investigate the absorption increase stemming from this layer, a thickness parameter h3 is introduced, and the layer is modelled as nanocrystalline ZnO, using the refractive index of Tumbleston et al.. The resulting IQE is seen in Fig. 12(b) for both polarizations as well as an average of the two. A significant increase in IQE is seen over the range of 0–25nm for both polarizations, after which the average IQE becomes fairly constant for h3 in the 50–200nm range.
The IQE as a function of Λ and h1 is calculated for both structures with a ZnO layer of 100nm. The averages over the two polarizations are shown in Fig. 13. New optimal parameters for structure 1 are found to be Λ = 720nm and h1 = 62nm giving an IQE of 80.8%. This is an increase of 7.6% in IQE compared to the optimized structure 1 solar cell without ZnO. For structure 2, Λ = 420nm and h1 = 60nm result in an IQE of 81.4%, giving an increase in IQE of 7.8%.
When studying textured solar cells, a suitable reference is a structure based on Asahi U-type glass [29, 30]. Such a textured reference cell can be modelled from AFM scans of the Asahi U-type glass surface, as described by Ferry et al.. To make an textured reference comparable to the here presented grating cells, The Asahi U-type structure is assumed imprinted onto the solar cell substrate in the manner of Fig. 1, and the final cell is illustrated in Fig. 14(a). As a large surface is needed for a periodic model to behave like something aperiodic, the Asahi-based imprint cell model is limited to two dimensions. To take into account the fact that light incident on a real Asahi-based cell will encounter roughness along both polarization directions, only the IQE of the p-polarization is included in the calculations for the model cell. The IQE is calculated for four different surface profiles, chosen large enough that the effects of periodicity are negligible, and with end points of near-equal height to avoid steps at the periodic interface. To minimize modelling uncertainty, the Asahi reference IQE is calculated as the average IQE of all four models. The surface profiles used for the four models are seen in Fig. 14(b), and are based on AFM surface scans by Vetter et al..
The IQE of the Asahi reference model is calculated for varying AR coating thickness with a 100nm ZnO layer as for the grating cells, and 500nm a-Si as for the the flat reference. A comparison to the flat reference and the the two grating cells, all with 100nm ZnO, is seen in Fig. 15. The maximal IQE of the flat reference with ZnO is found to be 70.4% at an AR coating thickness of 62nm, while the Asahi reference cell has a maximal IQE of 78.4% with 70nm AR coating. The grating cells are still slightly more efficient than the Asahi based reference cell, with structure 1 giving a 3.1% higher IQE and structure 2 a 3.8% higher IQE.
An imprintable a-Si solar cell with a geometry based on imprint stamps produced via anisotropically etched c-Si was presented and studied using finite-difference time-domain methods. The efficiency of the cell was evaluated through the calculation of the integrated quantum efficiency, based on photo-electron generation from the AM 1.5 solar spectrum. The grating-type solar cell was optimized for two geometries, both of which can be produced from the etched master depending on choice of imprinting method. The optimal efficiency was found for gratings with an AR coating thickness of 60nm, and with grating periods of 650nm and 600nm, for the two geometries, respectively. The optimized solar cells were shown to absorb 10.2% more solar photons than a flat solar cell with the same absorber thickness, and the increase in external quantum efficiency is expected to be even higher when taking into account the loss due to the longer contact distance in the flat cell.
Local irregularities in the grating periods and layer thicknesses, expected to appear in the manufacturing process, were investigated. A ±10% local variation of thicknesses and periods did not significantly effect the efficiency of the solar cell. Including a 100nm ZnO:Al layer in the back reflector raised the efficiency by 7.6% and 7.8% for the two cells. A textured reference cell was made based on the surface structure of Asahi U-type glass. The grating cells were found to be slightly better than the textured reference cell, with efficiencies of 3.1% and 3.8% over the reference for structures 1 and 2, respectively. The improvement is, however, still significantly larger than the efficiency losses expected from production irregularities. Thus, a solar cell based on a simple etch and imprint technique was found to be a large improvement over a flat cell, and a slight improvement over a state-of-the-art textured solar cell based on the Asahi U-type glass structure as well.
The authors gratefully acknowledge Søren Vejling Andersen, Dept. of Physics and Nanotechnology, Aalborg University, for the refractive index data on hydrogenated a-Si thin films. This work was funded by the Danish Council for Strategic Research as part of the project “Thin-film solar cell based on nanocrystalline silicon and structured backside reflectors - THINC”.
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