For advanced optical analysis and optimization of solar cell structures with multi-scale interface textures, we applied a coupled modelling approach (CMA), where we couple the rigorous coupled wave analysis method with ray tracing and transfer matrix method. Coupling of the methods enables accurate optical analysis of solar cells made of thin coherent and thick incoherent layers and includes combinations of nano- and micro-scale textures at various positions in the structure. The approach is experimentally validated on standalone single- and both-side textured crystalline silicon wafers, as well as on complete silicon heterojunction (Si HJ) solar cell structures. Using CMA, fully encapsulated bifacial Si HJ solar cells are optically simulated first by applying single- and both-side illumination, and the effects of introducing nano inverted pyramids and random micro-pyramids at front and/or rear interfaces are analyzed. Secondly, an external light management foil with a three-sided pyramidal micro-texture is applied in simulations to the front and/or rear encapsulation glass, and the related improvements are quantified. For the optimal combination of internal textures in the analyzed structure (random micro-pyramids at the front and nano inverted pyramids at the back) and the use of the light management foil on both sides of the device, a 5.6% gain in the short-circuit current is predicted, compared to the reference case with no light management foil and with random micro-pyramids applied to the front and rear internal interfaces.
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In solar cells, light management techniques are used to boost the short-circuit current density and consequently the energy conversion efficiency. In the dominant wafer based silicon photovoltaics (PV), common light management techniques include anti-reflective (AR) coatings or structures on the front encapsulating glass  and micro-scale textures (typically random micro-pyramids) etched into the silicon wafer. These textures help to increase the absorption of light in the cell by minimizing light reflection from the front part of the device and also by refracting the light beams into larger angles of propagation , which in combination with reflective back contacts (reflectors) prolongs the optical paths through the cell. Recent developments in nanotechnology and large area patterning approaches, such as nano-imprint lithography , also enable fabrication and integration of various nano-scale structures to potentially achieve further gains in solar cells’ conversion efficiency.
In the process of design and optimization of PV devices, numerical simulations are of great importance. In this paper we present a coupled modelling approach (CMA) that combines the rigorous coupled wave analysis (RCWA) method  with ray tracing (RT) and transfer matrix method (TMM) . The approach enables involved optical simulation of complex solar cell structures which include both thin coherent and thick incoherent layers and various micro- and nano-scale textures located at different interfaces in the same device, even combined at the same interface (multi-scale textures). Within the CMA, the RCWA method is applied for accurate description of the optical situation in nano-textured stacks of thin layers , RT method is used to describe reflection and refraction of light at microtextures and light propagation through thick incoherent layers, while TMM is applied to optical simulation of (locally) flat thin-film stacks. The coupling of the three methods presents a unique tool for accurate optical simulation of realistic state-of-the-art solar cell devices including all these features in one structure (Fig. 1).
Different combined optical models have been previously reported, such as OPTOS , GenPRO 4 , SETFOS , OPAL  and others . These approaches discretize the scattered light by polar and azimuth angles and produce a single scattering matrix for a partial three-dimensional structure. Then, scattering matrices are non-iteratively coupled in a 1-D simulation. In contrast, our approach iteratively couples matrices in full three dimensional space, which offers (i) greater versatility, shown e.g. in simulation of the combined multi-scale (nano + micro) texture at the same interface , (ii) greater accuracy, e.g. by fully considering the exact trajectories and lateral positions under which the internally reflected light rays return to the micro texture, which is in some cases crucial for proper calculation of light trapping , and also (iii) enables a more realistic description of the optical situation in other cases where structures cannot be approximated as a one-dimensional stack. An example of such structure is a solar cell containing a grid of contacts on both front and rear sides of the solar cell. In this case, 3-D simulations would properly take into account shading by the contacts and enable comparison of aligned and staggered contact grids, while 1-D simulations would be unable to distinguish between these cases. Furthermore, our approach enables calculation of the local absorption in the structure in all individual layers, including in the layers of the nanostructures with full 3-D geometry. In contrast, other approaches calculate absorption for the equivalent 1-D layers, e.g. in .
In the first part of the paper, we describe the CMA method and present the related experimental work for thorough verification of the CMA. CMA was verified first on a standalone textured crystalline silicon wafer and then for a bifacial silicon heterojunction (Si HJ) solar cell as presented in the review paper , which was the investigated structure in the present work. In the second part we apply the verified model to analyze and optimize optical situation in an encapsulated bifacial Si HJ solar cell, which is currently of high interest due to additional collection of reflected light  The optical gains related to introduced nano inverted pyramids and random micro-pyramids applied to the front and rear side of the silicon wafer. To further boost the conversion efficiency of the solar cell, a light management foil (LMF) with the three-sided pyramidal (cornercube) micro texture  is attached to the front, rear and both sides of the simulated device, and its benefits are quantified. We show that the inverted pyramidal nano texture applied to the front side of the c-Si wafer is slightly inferior to the micro texture in the analyzed structure, but it outperforms the micro texture when applied to the rear. Additionally, we show that application of the cornercube LMF significantly improves performance of the solar cell with flat interfaces, whereas its advantage in the micro or nano textured cell is limited mostly to the lower air-glass reflection losses.
In order to validate our modelling approach and the light management concepts related to different texture combinations of the crystalline silicon (c-Si) wafer in Si HJ solar cell structure, various samples were fabricated. In all cases, 200 μm thick mirror-polished n-type wafers with <100> orientation were used as the starting point. All wafers were cleaned with piranha clean – wafers were immersed in H2SO4:H2O2 with 4:1 ratio for 10 minutes, followed by rinsing with deionized water. Wafers were then immersed in dilute HF (0.5%) to remove the grown silicon oxide and rinsed again .
For fabrication of the inverted pyramidal nano texture (Fig. 2(a)) on one side of a wafer, 100 nm thick protective SiO2 was deposited on one side using PECVD. Thermal resist was spin-coated on the SiO2 surface, and a thermal imprint was performed. The nanostructure imprinted into the resist was a periodic pattern of circular holes. Brief O2 reactive ion etch (RIE) was performed to remove the residual resist from the holes, followed by CF4 RIE which selectively etched the SiO2 layer at the holes. Then wet etching using H2O:TMAH:surfactant in 3:2:0.03 ratio was performed at 80 °C for 5 minutes 15 seconds to directionally etch the silicon. After nano texture generation, the protective SiO2 was finally removed using an HF dip to expose the texture. Further details are given in .
For fabrication of the random pyramidal micro texture (Fig. 2(b)), a single step was required – clean wafers were put in H2O:TMAH:surfactant with 20:1:0.1 ratio and the etch was performed at 80 °C for 10 minutes. With this procedure, the random micro-pyramidal texture is realized simultaneously on both sides of the wafer.
In addition to the described single-side nano texturing and double-side random micro texturing, we also created samples with nano texture on one side and micro texture on the other. In the two-step procedure the nano texture was fabricated first, followed by PECVD deposition of a protective layer consisting of 100 nm SiO2 and 100 nm Si3N4 on top of the texture. These layers protected the nano texture during the second step in which the micro texture was fabricated on the opposite side by wet etching. The protective layer was then removed using an HF dip to expose the initial nano texture.
Fabricated textures were imaged with scanning electron microscopy (SEM) and atomic force microscopy (AFM). From these measurements of the inverted pyramidal nano texture, the spread of the periods in both ortogonal directions (P1 and P2) and the corresponding width of the flat parts (W1 and W2) have also been determined (see Fig. 2(a)). The shorter period P1 varied from 880 nm to 900 nm, while the longer P2 varied from 900 nm to 930 nm between different samples as well as different regions of the same sample. The flat part widths W1 and W2 varied from 40 nm to 120 nm and from 70 nm to 150 nm, respectively. The smallest flat parts were observed on the single-side textured sample. We assume that these variations of P and W observed within the same sample are related to the use of a thick soft stamp for the imprint, which deforms under the high imprint force, and also to variations in the depth of the holes after RIE. Variations between different samples are additionally caused by small variations in the manual positioning and orientation of the stamp on top of the wafer and also by uneven soft stamp deformation under the applied force.
An additional descriptive parameter of the inverted pyramidal nano texture is the pyramid fraction (PF) (also called the “fill factor” in ), which is calculated as the ratio of the pyramid area to the total area; . Due to the aforementioned variations of P and W, PF also varied between the samples in the range of 70% to 90%. This parameter is crucial for good optical performance of the nanotexture and should be as high as possible [6,19]; however, over-etching rapidly degrades the structure, making high PF difficult to achieve.
Both, the inverted nano pyramids and (upright) random micro-pyramids have the same 54.7° pyramid angle arising from the slow-etching <111> crystallographic plane.
From standalone textured silicon wafer samples, complete Si HJ solar cell samples were also fabricated. These samples included ITO and hydrogenated amorphpous silicon (a-Si:H) thin layers deposited on both sides of the c-Si wafer. Amorphous silicon layers were deposited first by PECVD using a Roth&Rau AK1000 tool, and then ITO was sputtered using a Leybold A600V7 tool. These layers were subsequently annealed in a nickel furnace in nitrogen atmosphere to assure good passivation and optical properties. The layer sequence and the corresponding thicknesses are specified in section 4. The thicknesses were selected such as to provide good electrical properties in Si HJ solar cells deposited on random pyramidal micro textures and were not optimized for the nano textured case.
Last but not least, deposition of the metal contacts (fingers and busbars) was not considered since our work focuses only on the optical properties of the structures, where the contacts would merely uniformly increase the reflectance of all structures by approximately 4% yet would not change the main trends. Electrical properties are assumed to be equivalent for all cell structures due to the close similarity of the investigated structures (identical angles of the inverted nano pyramids and random micro-pyramids).
Optical characteristics of the samples were measured using spectrometer Lambda 950 (PerkinElmer, USA) with an integrating sphere. Samples were positioned before the integrating sphere for transmittance measurements, with light incident at 0° on the samples. Samples were positioned at the exit of the integrating sphere for reflectance measurements. Angle of incidence was 8°, while for diffused measurements, the 6.6° exit aperture centered around the specular reflectance from the sample was removed.
3. Coupled modelling approach (CMA)
In the developed CMA, we successfully coupled RCWA, RT and TMM optical models. RCWA is briefly outlined first with implementation specifics, followed by the integration of all models under the single CMA framework. While the CMA was already presented in , the model description presented here offers some additional details with respect to the method operation and simulation possibilities.
For rigorous simulation of solar cell structures, the finite element method (FEM) [20,21], the finite difference time domain method (FDTD) , and the rigorous coupled wave analysis (RCWA) [19,23,24] have been used extensively. However, as analyzed and presented in our previous work , they only enable accurate optical simulation of thin-film stacks including nano textures, whereas in the case of micro textures and/or thick layers, their practical applicability and accuracy are severely limited, and coupling with other modelling solutions becomes a necessity. In this respect, we found out that RCWA, also called the Fourier modal method (FMM), is especially appropriate, since its direct output are the intensities and the directions of the diffracted light waves, which can be coupled seamlessly to other models such as RT. Other models, such as FEM, require additional calculations to obtain the far-field light direction and intensities, as in . Therefore, RCWA was chosen also for integration into the developed CMA.
For the CMA purposes, we developed and verified our own three-dimensional RCWA model which mainly builds upon the physics described in . The calculation procedure is performed separately for each wavelength of the simulation wavelength range. It begins by horizontally slicing the (nano)structure of the multi-layer stack to a predefined number of plan-parallel sublayers. The lateral distribution of the refractive index inside each sublayer is then represented in Fourier domain by a predefined number of Fourier spatial frequency components, which correspond to the number of diffraction modes included in the analysis (diffracted light waves). Both the number of sublayers and the number of diffraction modes are the two crucial parameters that heavily influence the accuracy of RCWA and, therefore, need to be carefully chosen and validated for each specific simulation case . At least 5 modes and 30 sublayers were used for all RCWA simulations coupled with CMA, and up to 20 modes with 300 sublayers were used for short wavelengths (below 500 nm) to offer improved simulation accuracy. The resulting matrix of the Fourier components fully characterizes the (nano)structure of the multi-layer stack; in the scope of the CMA this means that, as long as the part of the device handled by RCWA remains unchanged, Fourier expansion is performed only once at the beginning of the CMA simulation.
The main input of the RCWA simulation are the description of the device structure and the incident illumination that defines the boundary condition at the top interface of the simulation domain. In the case of diffused incident illumination, it can also be split into different modes. The main output of the simulation, calculated from the matrix of the Fourier spatial frequency components are the reflection and transmission coefficients for the transverse electric (TE) and magnetic (TM) waves, which are generally diffracted into different directions (diffraction modes). These coefficients can be expressed either in terms of reflected and transmitted power densities (R and T), or in terms of reflected and transmitted fields (r and t). In the latter case, information about the phase of the diffracted waves can also be discerned, however this was not required in the presented CMA simulations where RCWA is coupled primarily to RT model and phase can be discarded. Nevertheless, it should be mentioned that we performed also tests of fully coherent coupling where we split a nanotextured thin-film stack into two parts and then simulated each separately by RCWA. After coupling these two separate simulations together, including the phase information of the waves, the same results were obtained as with a single RCWA simulation of the complete stack, which confirmed the validity of coherent coupling approach. Finally, it is important to point out that during RCWA simulation of three-dimensional structures, special attention has to be paid to possible TE and TM polarization transitions (i.e. TE → TE, TE → TM, TM → TE, TM → TM) that may happen since the incident and the outgoing waves may not share the same plane of propagation. We found out that disregarding these transitions can lead to significant errors of CMA simulation results.
One of the most important additional features of our RCWA implementation is the possibility to calculate also the local light absorption (A) for each individual layer (or sublayer) of the simulated structure by calculation of the local Poynting vectors. This is crucial for enabling an accurate inside view into the optical behavior of the simulated device, and also to properly identify and quantify the individual sources of losses. This feature enables calculation of layer absorptions in arbitrary 3-D nanotextured structures; and arbitrary 3-D structures for CMA, together with full 3-D generation profile to be coupled with electrical simulations. Further on, while RCWA is primarily applicable to periodic nanostructures (diffraction gratings), it can also be extended to the analysis of random nanotextures by assuming proper quasi-periodic conditions , although this was not required for the structures simulated in the scope of this work.
In CMA, the above RCWA simulation procedure should in general be performed each time that light enters any of the substructures in the device that are modelled by RCWA, taking the exact incident direction, polarization, power density etc. into account. However, while this would lead to the greatest accuracy of the final CMA simulation results, it might also lead to unfeasibly long simulation times since the RCWA procedure would need to be performed an enormous number of times.
Therefore, in our CMA implementation, reflection, transmission and absorption of each substructure handled by RCWA in the device are calculated in advance: (i) for each wavelength of the simulation range, (ii) for both TE and TM incident waves, (iii) for illumination from the front and rear side of the substructure, and (iv) for incidence under different angles of propagation, in which case we applied a pre-defined discrete grid of azimuth (θ) and polar (ϕ) incident angles. For simulated structures presented in this work, we found out that angular discretization steps Δθ = 5° and Δϕ = 15° are optimal with respect to simulation accuracy and time yet may need to be changed for other cases and structures. The validation of the chosen discretization angles was performed for selected wavelengths of 400-1200 nm in steps of 200 nm. The most accurate simulation was performed with discretization of 1° for both angles and served as the reference. In final simulations, we employed the coarsest angular discretization that still offered simulation accuracy within 1% of the reference values. Finally, all the relevant input and output values are arranged in the form of a scattering matrix system, which is used for coupling of RCWA with other models. However, unlike the scattering matrices of OPTOS, for each incident plane wave, a separate scattering matrix is generated with exact outgoing angles. Thus, if all the light is incident at the exact angle as prescribed by the scattering matrix, all the simulation results of the nanostructure will be as accurate as if using the standalone RCWA simulation.
Following generation of scattering matrices, RCWA is coupled with the other models in CMA. RT model is applied to the parts where large structures are encountered and optionally for incoherence of thick layers. Ray intensities and their directions are input and output results and can be directly coupled with matrices of RCWA (simple multiplication after remeshing incident angles to the pre-defined grid of applied illumination in RCWA calculations). The nearest calculated scattering matrix with respect to the incident angle is taken, and from it, a single outgoing direction is chosen with the probability of the scattered intensity. Note that the probability depends on the incident ray polarization. The procedure described above repeats until the ray or the plane wave exits the simulation structure (by reflection or transmission), is extinguished inside the structure (by absorption), or the maximum number of iterations is reached. Angles of reflected rays smaller than the threshold of 6.6° (given by the measurement equipment) are considered specular, while larger angles are considered diffused.
For the flat thin layers, TMM was used instead of RCWA in our approach. It is applied to fully or just locally flat thin-film stacks in the structure. Since TMM is extremely fast, it is calculated for each ray. Arbitrary polarization of the ray incident to the partial structure is split to the local TE and TM components as defined by the plane of incidence. The RT & TMM coupling used in our modelling has already been verified experimentally , while this contribution focuses on the complete CMA and its broader functionality.
In many of the other modelling approaches [7–9], the scattering matrices of partial structures are calculated independently in 3-D space, and then they are combined together in form of a 1-D stack and solved non-iteratively in 1-D space. Our approach, on the other hand, iteratively couples all models fully in 3-D, which allows for a much greater versatility in structures we are able to simulate. For example, our approach can be used to simulate double (nano + micro) textures at the same interface (not included in this paper, see ). While the simulation results presented were accurate within 1% with respect to the simulation parameters (number of rays, modes, sublayers etc.), we have not yet validated our model on the experimental samples.
4. Analyzed structures and textures
For CMA verification purposes, we investigated first a simple structure of a standalone freshly etched 200 μm thick n-type c-Si wafer without any other layer. Micro and nano textures were applied to the front and/or rear side of the wafer as explained in the Experimental section. Micro textures were assumed as quasiperiodic in the simulations with the lateral period of 40 μm (directly imported AFM scan), while the lateral period of nano textures was 900 nm.
In the second step, the structure was expanded into the complete Si HJ solar cell, including intrinsic i-a-Si:H layers for passivation, doped hydrogenated amorphous silicon n-a-Si:H and p-a-Si:H layers for the selective charge carrier extraction and the transparent indium-tin oxide (ITO) layers for carrier collection, as shown in Fig. 3 (dimensions not to scale). Metal contacts (fingers and busbars) are not taken into account in optical simulations; they are expected to introduce the offset in device total reflectance by approximately 4%. For further details about the Si HJ solar cell structure and its operation please refer to .
Finally, in the last part of our simulations we considered the complete encapsulated bifacial cell structure, using glass on both sides of the structure, ethyl-vinyl-acetate (EVA) as the encapsulant, and optionally also a light management foil (LMF) applied on top and/or bottom of the device. The LMF featured a micro-scale three-sided pyramidal – cornercube – texture with the cube side length of 6.3 μm and total feature height of 7.3 μm that has already shown to provide efficient light management in different types of solar cells [1,26]. The complete encapsulated cell configuration with individual layer thicknesses is shown in Fig. 3 for the case of front nano and rear micro texturing of the c-Si wafer.
The methods applied for simulation of different parts of the solar cell structure are specified on the right side of Fig. 3. Thick c-Si wafer requires incoherent treatment, as do EVA, glass and the optional LMF. For these layers, RT was used in our coupled approach. On the other hand, thin layers (ITO and various a-Si:H) require coherent treatment. For the locally flat plan-parallel thin layers, which includes also thin layers deposited on large micro textures such as the one on the bottom side of the wafer in Fig. 3, TMM is an efficient choice. For nanotextured thin-film stacks, however, rigorous simulations are required. In our case, RCWA was used for this purpose due to its suitability to be coupled directly with RT. All the models together encompass our CMA, which was used to simulate the complete complex structure of the photovoltaic device. In all CMA simulations, realistic wavelength-dependent refractive indices of all layers were used .
In Fig. 4 we schematically present the applied texture combinations for the case of the standalone c-Si wafer (Fig. 4(a)) and for the case of the LMF applied to the surfaces of the encapsulated device (Fig. 4(b)). For referring to different texture combinations throughout this work, a consistent naming convention in the form of “front texture / rear texture” is used, regardless of the incident light direction. Therefore, for the front side illumination of e.g. micro/nano sample, the side with the micro texture is illuminated, while for the rear side illumination, the nano texture is illuminated. In simulations, fully conformal growth (in vertical direction) of thin layers on top of the textured c-Si interfaces was considered for the case of nano and micro texturing.
The samples with all different c-Si wafer texture combinations were fabricated; both as standalone textured c-Si samples and also as HJ Si cells including ITO and a-Si:H layers with thicknesses shown in Fig. 3. The complete, encapsulated solar cell structure – PV module structure – was not fabricated in this work; the effects of LMF with the cornercube texturing Fig. 4(b) in addition to the Si textures were investigated by means of CMA simulations.
5.1. CMA validation
The validity and accuracy of CMA was first tested on standalone textured c-Si samples. The samples were measured and also simulated by RT alone, by RCWA alone, and finally by CMA. All simulations were performed with light incident as given by the experimental setup described in Section 2. The measured and simulated total reflectance Rtot of the flat/flat and nano/flat samples is shown in Fig. 5(a). Because of anti-reflection (AR) behavior of the nanotexture, reflectance of the nano/flat sample is lower in the majority of the wavelength range. From the simulation point of view, results obtained by RT agree well with the experimental results for the flat/flat sample as expected, but they fail to follow the experimentally observed trends for the nano/flat sample. In this case, RCWA results better follow the experimentally observed behavior up to 900 nm, but then show significant interference effects due to the coherent treatment of light propagation. Smoothing of the RCWA curve can be performed to obtain a better approximation of the experimental trends , although the averaged curve (not shown) still retains some oscillations and predicts too high reflectance from 1050 nm onwards. CMA results, on the other hand, closely match the experimental data and do not show any interferences since the thick silicon layer is treated incoherently in CMA (due to the RT model for thick layers). Disagreement between the simulation and the experiment is observed only in the range of 900-1000 nm, which is likely caused by the overly idealized texture considered in simulations (ideal inverted pyramids with given P and PF) as opposed to the significant texture variability in the experimental samples (Fig. 2 and surrounding text). Agreement would be improved if further texture variations were considered in simulations.
Differences between the accuracy of the various simulators are more apparent in the diffuse reflectance Rdiff of the nano/flat sample (Fig. 5(b)). CMA closely follows measured trends of Rdiff, showing that the intensities of diffraction modes calculated by the method are correct – they match experimental reality. This is especially pronounced near the (weak) oscillations, where some diffraction modes grow much stronger or weaker. On the other hand, RT does not follow any experimentally observed trends and RCWA predicts no diffuse reflectance with wavelengths longer than the maximum structure period (920 nm), as all non-specular reflection modes are evanescent.
Results for the standalone c-Si samples with nano and micro textures on both sides of the wafer (nano/micro and micro/nano) are shown in Fig. 5(c). The front nano texture with 79% PF outperforms the commonly used front random micro texture in the majority of the wavelength range considered by offering superior AR properties. Again, CMA simulation shows very good agreement with the experimentally measured quantities.
Continuing with validation and accuracy testing as well as experimental analysis of the textures, nano/micro and micro/nano texture combinations were tested also in complete HJ Si structures with added thin layers of a-Si:H and ITO. The structure becomes more complex at this stage as it contains more layers. The results for the cases are presented in Fig. 5(d). If we simulate the structure by coupling only RT and TMM, very poor agreement with the experiment is observed when light reaches the nanotexture. By including also RCWA in the complete CMA, on the other hand, results are in very good agreement even for the complex structure.
In terms of optical behavior, it is interesting to note that in contrast to the results of standalone c-Si samples (Fig. 5(a)), the micro texture at the front side now significantly outperforms the nano texture, especially in the crucial wavelength region from 450 nm to 750 nm, while the nano texture performs better from 800 nm onwards, which is around the texture period (~900 nm). The reason for this is twofold: First, the nano texture used in this sample exhibits a relatively low PF of 70%; we found out that with increasing the PF, the performance of the nano texture increases. The low PF is attributed to variation between the samples as described in Section 2. And second, the layer thicknesses used in this sample were optimized for the passivation and contacting of HJ Si cells deposited on micro textured wafers. All these factors suggest that further structure optimization is required for improving the performance of solar cells with front nano textures, for which the developed CMA can play an indispensable role.
5.2. Analysis of bifacial Si HJ solar cell with CMA
In this section CMA is applied to investigate the optical effects in the encapsulated Si HJ solar cells in bifacial configuration (Fig. 3). Different combinations of internal textures are explored first, while the role of the LMF is analyzed in the second part.
For the nano texture, our best experimentally realized inverted pyramidal nano texture with 88% PF (realized on the nano/flat sample) was considered in all simulated structures where required. As the front side illumination, direct light was applied perpendicularly to the solar cell, using AM1.5G spectral distribution. For the rear side illumination, diffused light with Lambertian (cosine) angular distribution was applied, again using AM1.5G spectral distribution, whereas the total intensity was weighted with the albedo factor α = 0.3 . Simulations under front and rear illumination were performed individually, as there is no correlation between them, and then superposition of the corresponding optical effects was considered to obtain the final results.
To calculate the implied short-circuit current density (JSC) from optical simulations, perfect extraction of generated charge carriers from c-Si is assumed, while small contributions from the thin semiconductor layers with lower extraction efficiency are neglected . Therefore, the wavelength dependent absorptance inside the c-Si layer, which is a direct output of optical simulations, is a good approximation of the external quantum efficiency (EQE) of the solar cell and the JSC can be calculated as:
Figure 6(a) shows the absorptance of c-Si layer (EQE) of the solar cell structures with flat/flat, micro/nano and nano/micro internal texture combinations (all structures without LMF). The presented curves correspond to the single side illumination from either front or rear side of the bifacial device. Please note that for the purpose of normalization, the intensity of the front side illumination was considered in both cases. This way, we are able to indicate the actual contributions of stronger front side and weaker rear side illuminations already on the absorptance level. As expected, flat/flat combination, which corresponds to ideally flat solar cell, produces significantly lower A(λ) than the textured cells for both illumination cases. The second general observation is that by applying any combination of the textures (micro/nano, nano/micro) in the analyzed solar cell structure, the performance of the cell is improved significantly, yet both texture combinations result in similar optical performance. However, by looking more closely in the short-wavelength region, A(λ) of the micro/nano combination shows a slight improvement compared to the nano/micro case (observed for front side illumination). The experimental samples (not shown) also exhibit the same trend where the nanotexture performs slightly better for wavelengths until 400 nm, while the micro texture performs better from 400 nm to 600 nm. The analysis of internal optical losses revealed that this is mainly caused by the slightly lower parasitic absorption in the n- and i-a-Si:H front layers arising from the flat parts (PF = 88%) of the nano texture. At longer wavelengths (above 1000 nm), on the other hand, A(λ) of the nano/micro combination is consistently slightly better. Simulations revealed this is primarily caused by scattering to higher angles on the nano texture, while lower initial reflectance and better light trapping also play a role. For the rear side illumination, almost no differences are observed for the analyzed texture combinations.
In the analyzed structure, optical effects of the inverted pyramidal nano texture result in similar gains in absorptance as obtained with the random pyramidal micro texture, although much more significant optical gains in antireflection have been observed for the standalone c-Si wafer in the case of nano front texture (see lower Rtot curve in the short- and long-wavelength range in Fig. 5(c) for the nano/micro case compared to the micro/nano one). Applying thin layers and final encapsulation therefore changes the optical situation significantly, which again calls for careful optimization of layer thicknesses, such as TCO thickness (considering tradeoffs between optical and electrical performances), and further nanotexture optimization (not performed in this paper).
For the structure with micro/nano texture combination, again without LMF, the distribution of light absorption and JSC losses inside the individual layers is presented in Fig. 6(b). Absorptance curves are shown for the front side illumination only, whereas the JSC values are given for both, front and rear illumination. In this representation, the contributions of two layers of the same material, i.e. one at the front and the other at the rear (in the case of glass, EVA, i-a-Si:H and ITO), are joined together. The results show that in the wavelength range up to 600 nm, a significant portion of light is lost by the parasitic absorption in the i-a-Si:H layers and ITO. In the range between 600 nm and 1000 nm, the performance is mainly limited by the reflectance losses at the front interfaces, while reflectance, transmittance and EVA + ITO absorptance are the dominant loss mechanisms from 1000 nm onward. JSC contributions from 300 nm to 1200 nm are shown in the inset of the Fig. for both illumination cases. The most significant contribution to JSC losses comes from reflection, followed by combined a-Si:H absorption, absorption in both ITO layers, transmission, absorption in both EVA layers, and finally absorption in glass (mainly front layers).
To improve light in-coupling and possibly trapping in the encapsulated bifacial cell structures (see Fig. 4 for structures and naming explanation), LMF was applied in simulations. In the presented analysis, the potential of the LMF is studied not only for single side illumination but also for both side illumination of the bifacial cell. Comparison of simulation results of the structures without LMF and of those including LMF on both sides is shown in Fig. 7(a) for combined front and rear illumination with α = 0.3. The total absorptance curves plotted in the figure are constructed from the individual results obtained separately under front or rear illumination, i.e. A(λ)total = A(λ)front + A(λ)rear. Therefore, the limiting level of EQE for both side illumination is 1.3 and 1 for single front side illumination (shown as a dashed horizontal line in the plot). This representation was chosen to clearly show the additional contribution of rear side illumination (A(λ)total > 1) in addition to the front side illumination.
Simulation results show that all structures surpass the EQE = 1 limit for the central part of wavelengths, including the perfectly flat solar cell with no LMF. By adding LMF to both sides of the flat/flat solar cell, the performance is boosted in the entire wavelength range, significantly beyond lowering just the initial reflection at the air-glass interface. This combination surpasses the structures with textured silicon (micro/nano and nano/micro) without LMF in the central wavelength range but lags significantly at both short and long wavelengths. Structures that combine textured silicon with LMF perform best throughout the complete wavelength range. However, detailed analysis of the internal optical situation revealed that the improvement related to the addition of LMF is in these cases limited to lowering the initial reflection from the solar cell, yet does not contribute significantly to internal light trapping as has been reported for the case of planar cells , since this light management function is already performed by the internal textures of the silicon wafer. Additional simulations of devices with internal textures showed that a flat AR foil (coating) matching the AR properties of LMF achieved the same device performance for perpendicular incidence, whereas for oblique incidence LMF performed better.
Finally, JSC for various cases of different texture combinations are shown in Fig. 7(b). The graph reiterates that the addition of the LMF significantly increases the performance of the untextured silicon cell. However, despite the significant improvement offered by LMF, all structures with untextured silicon (flat/flat) are still inferior to any of the samples with textured silicon. Gain offered by LFM for textured silicon cells is smaller, although LMF still offers roughly 0.5 mA/cm2 higher JSC when applied to the rear and 1 mA/cm2 when applied to the front side.
From the studied cases, the highest performance in bifacial operation was observed for the encapsulated cell structure with micro/nano silicon texturization and LMF applied on both sides. This combination achieved JSC = 49.57 mA/cm2, which is 2.6 mA/cm2 (5.5%) higher compared to the same cell without LMF, and 2.63 mA/cm2 (5.6%) higher compared to the conventional micro/micro cell without LMF. For reference, total JSC available in the 350-1200 nm wavelength range is 46.23 mA/cm2 for the single side illumination and 60.09 mA/cm2 when including also the extra 30% illumination from the rear side. All structures with textured silicon surpass the single side illumination maximum, while none of the untextured silicon structures do. The best structure has the potential to extract 81.9% of the total available JSC in bifacial operation with α = 0.3, and 107.2% of the total JSC that is available from the front side illumination.
We have presented and experimentally validated a powerful full 3-D simulation tool named Coupled Modelling Approach, which combines RCWA, RT and TMM, for accurate simulation of complex solar cells that include nano and micro textures and various incoherent thick and coherent thin layers. While the individual simulation methods (RCWA, RT, TMM), and even combination of RT and TMM were found insufficient for reliable simulation of the investigated structures, CMA produced accurate simulation results throughout the wavelength range for various structure and texture combinations, as each individual simulator operated in its own domain where it is accurate and efficient.
We applied the validated CMA to simulate advanced bifacial silicon heterojunction solar cells, including different front/rear c-Si texture combinations, encapsulation and optional light management films on front and/or rear glass. Analysis of loss mechanisms showed that reflection losses are the most significant for the structures without LMF, followed by the parasitic absorption in a-Si:H layers, showing the need for future optimizations. Addition of the cornercube LMF on either side significantly improved the performance of the untextured silicon structure beyond lowering of initial reflection losses due to better light trapping. However, such structure still performed worse than the structures with textured silicon and without LMF. LMF on both sides with micro/nano silicon texture offered a modest performance improvement of 5.6% in JSC compared to the reference micro/micro silicon texture without LMF, mainly by reducing reflection losses.
Slovenian Research Agency (P2-0197 and PhD funding of Z. Lokar); IMEC (industrial affiliation program for silicon photovoltaics).
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