Abstract
Properties of the front textured surface shape and antireflection coating have a great impact on the performance of solar cells. In this paper, the simulation model of the minimum unit cell structure is established and validated, which is based on the framework of Silvaco software and basic parameters of the standard pyramid textures single crystalline silicon PERC solar cell. The effect of the front surface light trapping structures on cell performance is discussed. It is found that the slightly concave pyramidlike textures can improve the response for short wavelengths and the shortcircuit current density of the cell is increased by 0.3 mA/cm^{2}, which is improved by 0.80%. In addition, by properly controlling the preparation process of the antireflection coating, a gradientindex SiO_{x}N_{y}/Si_{3}N_{4} doublelayer antireflection coating (DLARC) can be formed, which can significantly reduce the reflectivity for short wavelengths. And the shortcircuit current density of the cell can be increased by 0.32 mA/cm^{2}, which is improved by 0.86%. Finally, the optimized slightly concave pyramidlike textures and the SiO_{x}N_{y}/Si_{3}N_{4} DLARC can improve the photoelectric conversion efficiency of the PERC solar cell by 0.18% and 0.20%, respectively.
Introduction
PERC (Passivated Emitter and Rear Cell) structure was initially developed in 1989 by University of New South Wales in lab scale [1] and later implemented industrially by the Fraunhofer ISE in 2002 with the pilotline laser fired contact process [2]. Nowadays, PERC technology has become one of the most costeffective solutions of highefficiency cSi solar cells. The advantage of the PERC solar cell is mainly embodied in its low back surface recombination velocity (SRV). As early as 2006, Hoex et al. [3] utilized Al_{2}O_{3} films prepared by lowtemperature plasmaassisted atomic layer deposition (PAALD) to reduce the effective SRVs of ptype cSi to 13 cm/s. Later, Institute for Solar Energy Hamelin (ISFH) reduce the back SRVs of low resistivity ptype cSi PERC cells to less than 10 cm/s with the highly effective back passivation technology of Al_{2}O_{3}/SiN_{x} stacks [4, 5]. With the process of the back side of csi solar cells being perfected [6, 7], researchers try to focus back on the front surface of csi solar cells. In 2011, BakerFinchby et al. [8] studied the light trapping paths of the pyramid texture by identifying discrete paths of reflection and the fraction of the reflected light that follows each of these paths, finding that a regular array of inverted pyramids just outperforms a random array of upright pyramids. In 2013, Kim et al. [9] combined the experiment with Silvaco simulation to study the effect of the texture pyramids size on the emitter performance and the front contact resistance of csi solar cells, and found that solar cells perform better when the pyramids are small. In 2014, Australian National University designed and manufactured an Interdigitated Back Contact (IBC) solar cell with an efficiency of 24.4% using SiO_{x}/SiN_{x} DLARC, and compared with the singlelayer SiN_{x} ARC, the shortcircuit current is increased by 0.4 mA/cm^{2} [10]. In 2015, Bashiri et al. [11] constructed a model of inverted pyramid textures single cSi solar cell and optimized the cell performance by varying the inverted pyramid height, which was found that 5 μm inverted pyramid height leads to a maximum cell efficiency. In 2017, Fraunhofer IS proposed the concept of skins for silicon solar cell modeling, which greatly improved the integrity and accuracy of solar cell device simulation by multiscale modeling [12]. In 2018, Lin et al. [13] improved cell efficiency by approximately 1% through optimizing the pillar texturing of HIT cells.
Textures and ARCs are significant components of solar cells. In high efficiency and industry standard designs, pyramid surface textures play the key role of reducing the reflectivity of the cell surface [8]. Generally, a flat surface has 30% reflectivity, but this can be lowered by texturing the surface [9, 14]. If combined textures with ARCs, a better light trapping effect can be obtained. In photovoltaic industry, the ARC generally consists only of a single layer. Although the single layer ARC, such as Si_{3}N_{4}, is relatively simple in fabrication, its working bandwidth is limited and its antireflection effect is strongly dependent on the incidenceangle [15]. In principle, a multilayer ARC gives the best optical performance [16]. Therefore, constructing a multilayer ARC is another way to improve the front surface light trapping effect. In the case of a doublelayer ARC, the first coating can be used to provide excellent surface passivation and antireflection, while the second coating is used to provide antireflection covering a broader range of solar spectrums.
PERC concept is fully independent from the front side, which means any progress on the front side support the effort to improve cell performance with PERC architecture. Therefore, this paper study the effect of front surface structures based on PERC solar cell. In this paper, TCAD modeling and model verification on the standard (111) pyramid textures single cSi PERC solar cells with the single layer Si_{3}N_{4} ARC are carried out, and then the effect of the texture shape on the front surface light trapping of the cell is explored. Finally, the SiO_{x}N_{y}/Si_{3}N_{4} DLARC is constructed based on the standard pyramid textures to study the gain of the cell performance.
Device structure and simulation model
The twodimensional simulation unit structure of the cSi PERC solar cell is established by using Athena process simulator and Devedit device structure editor of Silvaco Inc., as shown in Fig. 1. Since there is no symmetry between the front contact and the rear local contact array for most PERC solar cells, it is not easy to select an usual geometrically irreducible standard domain [17]. Therefore, in this paper, the front contact and the rear local contact are placed on the central axis of the simulated unit, and the lateral dimension of the simulated unit is determined according to the front contact shielding fraction and the rear groove fraction. The model is validated with the single cSi PERC solar cell parameters in Ref. [18], and the specific standard parameters are shown in Table 1. The contact between the electrode and the semiconductor material are ohmic contact. It is assumed that the silicon surface is an ideal surface. Simulation is implement under the standard test conditions: ambient temperature of 25 °C, AM1.5 spectrum (ASTM G17303 [19]), spectral irradiance of 100 mW/cm^{2}. In ATLAS settings, the light source is at normal incidence. Moreover, the rear internal reflection is considered and the number of reflections is two.
One of the advantages of device simulation is that it can obtain some characteristic parameters of cell that are difficult to measure, such as photogeneration rate, quantum efficiency, etc. ATLAS of Silvaco Inc. predicts the electrical characteristics of physical structures by simulating the transport of carriers through a 2D grid, and it is capable of accurately model a wide range of solar cell operating characteristics [20, 21]. A reliable TCAD simulation is based on the accuracy of the used models. Ray tracing has been regularly used to analyze solar cells. Although it neglects diffraction, ray tracing can account for thillfilm optics, textured surfaces and other complex geometries [22]. For relatively thick bulk devices, such as cSi devices, interference and diffraction effects in the bulk are usually not be concerned about. So ray tracing is useful for planar or textured devices. It is worth mentioning that for textured devices, the texturing must be described explicitly in the device structure when using the Ray tracing method of Silvaco [23]. For textured surfaces, the internal reflection typically requires ray tracing to determine accurately [22]. Setting the refractive index of materials accurately is another crucial part in light propagation model. Optoelectronic device simulation is split into two distinct models that are calculated simultaneously at each DC bias point or transient timestep [23]. Among them, optical ray tracing model use real component of refractive index to calculate the optical intensity at each grid point, while absorption or photogeneration model use the imaginary component of refractive index to calculate a new carrier concentration at each grid point. Since the electrode materials are opaque, the contacts in the model are set to be opaque, namely set the imaginary refractive index of Ag and Al to 1000 to avoid influencing the ray tracing calculations.
The simulation of solar cells can generally be divided into optical and electrical simulation. Good optical design is one of the main approaches for solar cells to achieve high efficiency. It includes reducing the front reflection and enhancing the internal trapping of the cell. The method of optical simulation is to calculate the carrier generation rates in the bulk, and then the three coupled differential equations of the Poisson equation, the electron and hole continuity equations are solved numerically under certain boundary conditions to calculate the electron concentration \(n(x)\), the hole concentration \(p(x)\), the potential \(\phi (x)\) and other internal parameters at the position \(x\) in the semiconductor. In this work, Newton iteration method is selected as the numerical calculation method, and the iterative solution process of the differential equations is completed by Silvaco software. Silvaco ATLAS offers a variety of optional physical models. The concentrationdependent mobility model (conmob), Shockley–Read–Hall recombination model (srh), Auger recombination model (auger), Fermi–Dirac statistic model (fermiairac) and band gap narrowing model (bgn) are chosen as the physical models in the solar cell device simulation process. The Fermi–Dirac statistic model can reduce the carrier concentration in heavily doped regions, which is necessary for high doping(> 10^{18} cm^{−3}) [23]. While the band gap narrowing model is one of the most important physical model for semiconductor devices in medium and high doping conditions [24].
The resistivity losses and the recombination losses are two crucial aspects of solar cell power losses. In this model, they were balanced as follows. First, it is considered that the resistivity losses are mainly caused by the bulk resistance, which is related to the doping concentration, and the top lateral resistance, which is determined by the emitter doping concentration, junction depth and mobility. Second, it is considered that the recombination losses are mainly caused by Shockley–Read–Hall recombination and Auger recombination as mentioned before. It is assumed earlier that the silicon surface which covered with the passivation layer is an ideal surface, namely the interface recombination velocity at the silicon surface is set to zero in the model. In other words, this model ignores the surface recombination losses.
Based on the above device structure description, material model description, numerical calculation method selection and model solving process, the results of the characteristic parameters of the cell are shown in Table 2. The simulation results are in the same level with the real cell performance in Ref. [18]. Note that device simulations normally slightly underestimate J_{sc} and slightly overestimate FF, while the simulated V_{oc} is accurate. This leads to relatively accurate final simulation results [18]. The reason for the underestimation of J_{sc} may be that the twodimensional device simulation overestimates the emitter lateral resistance, while the reason for the overestimation of FF is that the leakage current is neglected in the simulation, namely the shunt resistance is considered to be infinite. The following work will be based on this model. Quantum efficiency, reflectivity, etc. are important evidence for examining the optical behavior of cSi solar cells [22], which will subsequently be used to analyze the optical design of the cell. Moreover, for meaningful comparison, identical device parameters were used, although some of them with default value.
In addition, before using the above model for simulation research, in order to further verify the universality of the model, the single cSi PERC solar cell production data of Hunan Red Solar Photoelectricity Science and Technology CO., LTD. in October 2018 is utilized to conduct a secondary validation. The parameter values in Table 1 are partially replaced according to the process on actual production line, and the corresponding simulation parameters are shown in Table 3. Subsequently, the parameters in Table 3 were used to perform simulation calculations under the same conditions as mentioned before. Finally, the characteristic parameters of the cell are obtained as shown in Table 4. The simulation results are basically consistent with the performance of the PERC solar cell on the actual production line. This also proves once again the accuracy of the device simulation model of the single cSi PERC solar cell in this paper.
Effect of texture shapes on cell performance
First, the superellipse equation [25] is used to design different texture shapes. Construct the superellipse equation as follows:
where the value range of n is set to 0.2–1.8, and the tolerance is 0.2. Figure 2 shows the corresponding texture shapes in these nine cases, where n = 1 corresponds to the (111) crystal orientation pyramid textures formed by the anisotropic etchant on the (100) crystal orientation cSi substrate, the angle of the pyramid is 54.74° [26], and the height is 3 μm. It can be seen from the figure that the texture shape is slightly convex pyramidlike structure when 0 < n < 1 and slightly concave pyramidlike structure when 1 < n < 2. At this time, the front surface of (a)–(i) were covered with a Si_{3}N_{4} ARC with a thickness of 75 nm. Figure 3 shows the shortcircuit current density and efficiency of the cells with different texture shapes. It can be seen that cells with the two curved pyramidlike texture shapes, which are closest to the standard pyramid texture shape, can obtain better shortcircuit current density and efficiency. And the shortcircuit current density and efficiency are 37.68 mA/cm^{2} and 20.87% respectively when n is 1.2, which are increased by 0.3 mA/cm^{2} and 0.18% respectively compared to the reference cell. It is conceivable that the surface area of the slightly concave and slightly convex pyramidlike texture are larger than that of the standard pyramid, so the illumination areas are larger and the light trapping abilities are better.
Figure 4 shows the quantum efficiency of the cells with different texture shapes. As can be seen from the figure, the quantum efficiency of the cell is relatively high in the whole wavelength range when n is 0.8 or 1.2, indicating the spectral response of the cell is good, especially in the short and medium wavelength range of 300–600 nm. In the wavelength range of 600–950 nm, the quantum efficiency of the cells with n of 0.8 and 1.2 are relatively close. While in the wavelength range of 1000–1200 nm, the overall differences of the quantum efficiency between each case begin to narrow slowly. Since the external quantum efficiency refers to the ratio of the available photocurrent (considering the internal recombination process) to the source photocurrent [23, 27], namely:
where the source photocurrent is the amount of current generated by the light source and the available photocurrent is the amount of current absorbed by the semiconductor. In other words, the surface photon reflection losses of the solar cell are not considered. Therefore, the greater the external quantum efficiency, the stronger the light absorption capacity of the cell for the corresponding wavelengths without considering the reflection, also the greater the number of available electron–hole pairs. Meanwhile, it means that the recombination velocity of photogenerated carriers is relatively small. Hence, it can be seen from Fig. 4 that the overall recombination velocity of the cells is comparatively low when n is 0.8 or 1.2. In addition, as the value of n gradually deviates from 1.0, the surface area of the texture increases, and the curvature of texture also increases, resulting in an increase in lattice defects in the emitter region and an increase in recombination, which in turn increases the emitter saturation current. As a result, the performance of the external quantum efficiency is relatively poor when n = 0.2 and 1.8.
Figure 5 shows that reflectivity versus optical wavelength of the cells with different texture shapes. As can be seen from the figure, in the wavelength range of 300–1000 nm, the reflectivity of the cells is both less than 10% when n is 1 or 1.2. In the ultraviolet range, the cell has the lowest reflectivity when n is 1. Meanwhile, noted that in Fig. 4, in the ultraviolet range, the quantum efficiency of the cell is also the lowest when n is taken as 1, indicating that the conventional standard pyramid textures have a lower reflectivity for the ultraviolet range, but the spectral response is relatively poor. In the range of 1000–1200 nm, the reflectivity with n of 1.2 is lower than that with n of 1, indicating that the cell has better light trapping effect on long wavelengths when n is 1.2. In addition to reflectivity and quantum efficiency, the photon flux of the spectrum also affects the performance of the cell [28]. Define the weighted average reflectivity according to Ref. [29]:
where \({text{F}}(\lambda)\) is the photon flux at wavelength \(\lambda\), \({\text{Q}}_{\rm {i}} (\lambda)\) is the internal quantum efficiency at wavelength \(\lambda\), and \(R(\lambda)\) is the reflectivity at wavelength \(\lambda\). The value of \({\text{F}}(\lambda)\) used is extracted from Ref. [29], and \({\text{Q}}(\lambda)\) is given by [29]:
where \(\text{Q}_{\text{e}} (\lambda)\) is the external quantum efficiency of the cell. Finally, the calculated weighted average reflectivity with different values of n is shown in Table 5. The weighted average reflectivity of the cell is 3.50% when n is 1.2, which is almost the same as n of 1. Although the external quantum efficiency of the cell is higher when n is 0.8 as mentioned before, it can be seen from Fig. 5 that the overall reflectivity is higher than n of 1.2, and the calculated weighted average reflectivity is 4.38%. The resulting shortcircuit current density and efficiency of the cell are not as high as n of 1.2, which also illustrates the importance of reducing the reflectivity for improving the cell performance.
Figure 6 shows the internal photogeneration rate contours close to the front surface of the cell with different values of n when the beam is at normal incidence. As the figure inset illustrates, due to optical illumination and absorption, the closer to the surface of the cell, the greater the photogeneration rate, and the photogeneration rate gradually decrease with the beam propagation become deeper. In the local area directly beneath the front contact, the corresponding photogeneration rate is low because the light is difficult to reach there. Meanwhile, the photogeneration rate near the textured surface is large and evenly distributed as shown in Fig. 6d–g, indicating that their light trapping effect are better, which also accounts for the relatively high shortcircuit current density and efficiency of the cell when n is 0.8, 1.0, 1.2, and 1.4.
Effect of the DLARC on cell performance
In the case of stable incident light intensity, the refractive index and thickness of the ARC are the most important factors determining the effect of the antireflection effect. Therefore, it is crucial to match the refractive index and thickness for each of the layers of the DLARC. Currently, the widely used ARC in photovoltaic industry is the silicon nitride coating deposited by PECVD [30]. Note that the deposition of silicon oxynitride can be achieved by simply adding nitrous oxide after inlet silane and ammonia gas during the process of silicon nitride deposition. Moreover, the refractive index of SiO_{x}N_{y} varies widely (1.48–1.88), which is convenient for design. Therefore, we choose SiO_{x}N_{y} and Si_{3}N_{4} films to finish the design of the DLARC. Generally, materials with relative low refractive index are preferred for the top layer of a DLARC, and higher refractive index materials are usually used for bottom layer materials [31, 32], namely \(n_{1}\) is generally smaller than \(n_{2}\). Therefore, Si_{3}N_{4} is chosen as the bottom layer in the simulation, and then the SiO_{x}N_{y} layer was deposited on the top. The optical data of the Si_{3}N_{4} and SiO_{x}N_{y} used in the model are both obtained from SOPRA database. The refractive index of the Si_{3}N_{4} is around 2.00 at the reference wavelength of 632.8 nm [16], while the refractive index of SiO_{x}N_{y} is related to its nitrogen content. The optical data for several kinds of SiO_{x}N_{y} in SOPRA database are shown in Fig. 7 and Table 6. Note that in order to contrast with the reference standard cell model, the subsequent construction and optimization of the DLARC are based on the standard pyramid texture.
Next, the design of the SiO_{x}N_{y}/Si_{3}N_{4} DLARC is completed by two plans. First, consider applying the singlelayer ARC design rule to DLARC circumstances to finish the design of the DLARC (hereinafter referred to as Plan 1). As we known, a quarter wavelength thickness of ARC layer effectively reduces the reflection to minimum at normal incidence. The required optimal single layer thickness for minimum reflection at central wavelength \(\lambda\) is defined by the Eq. 5:
where \(n\) is the refractive index of the ARC. If it is applied to the DLARC thickness design, then:
where \(d_{1}\) and \(d_{2}\) are the optimal thicknesses of the top and bottom layers, respectively. When the central wavelength \(\lambda\) is selected to be 600 nm [33], the optimal thickness of the bottom Si_{3}N_{4} with a refractive index of 2.00 is 75 nm, which is consistent with the abovementioned reference standard cell model parameters. On this basis, SiO_{x}N_{y} with different refractive indices were deposited as the top layer respectively. As a result, five groups of SiO_{x}N_{y}/Si_{3}N_{4} match schemes were formed. The results are shown in Table 7. It can be seen that when the refractive index gradient between SiO_{x}N_{y} and Si_{3}N_{4} layers are small, the shortcircuit current density and efficiency of the cell are greatly improved. Figures 8 and 9 show the external quantum efficiency and reflectivity versus optical wavelength of the five groups of schemes respectively. As the figure inset illustrates, the fourth and fifth schemes have relatively poor spectral responses in the ultraviolet range, but their reflectivity for the ultraviolet range is also relatively low. The weighted average reflectivity is calculated to be 3.49% and 3.44%, respectively. The resulting shortcircuit current density and efficiency are inversely higher, which demonstrates again the importance of reducing reflectivity for improving cell performance. In addition, combining Fig. 8 and Table 6, it can be known that as the nitrogen content of the top SiO_{x}N_{y} film increases, the overall external quantum efficiency of the cell slightly decreases, which indicates that the recombination of the cell slightly increases, but the overall change is not obvious. The reason may be that the top SiO_{x}N_{y} film does not have direct contact with the silicon surface, so it has less effect on the emitter saturation current.
Second, consider adjusting the thickness allocation of the bottom layer and the top layer with fixed total ARC thickness to finish the design of the DLARC (hereinafter referred to as Plan 2). Fix the total ARC thickness of the top SiO_{x}N_{y} layer and the bottom Si_{3}N_{4} layer to 75 nm. For each of the above SiO_{x}N_{y} with different refractive index in Sopra database, five groups of simulation experiment schemes with different SiO_{x}N_{y}/Si_{3}N_{4} thickness allocation (45/30 nm, 50/25 nm, 55/30 nm, 60/15 nm, 65/10 nm) are set. Figures 10 and 11 show the simulation results of the shortcircuit current density and efficiency in Plan 2, respectively. On one hand, it can be seen from the figure that the shortcircuit current density and efficiency reach the maximum value when the thickness of SiO_{x}N_{y}/Si_{3}N_{4} of each group is 60/15 nm. This shows that when the total thickness of the SiO_{x}N_{y}/Si_{3}N_{4} DLARC is a constant, there is an optimal Si_{3}N_{4} bottom film thickness of 15 nm, which maximize the cell performance. Figure 12 shows the external quantum efficiency of the cell with each SiO_{x}N_{y}/Si_{3}N_{4} DLARC in Plan 2 (both with SiO_{x}N_{y} refractive index of 1.88) versus optical wavelength. It can be seen that in the ultraviolet range, the spectral response of the cell is better when the thickness of SiO_{x}N_{y}/Si_{3}N_{4} is 60/15 nm, while in the other wavelength range, the spectral response of the five groups are with little difference. This also shows that the reason why the optimal thickness of the Si_{3}N_{4} bottom film is 15 nm is that the SiO_{x}N_{y}/Si_{3}N_{4} DLARC has a better spectral response for the ultraviolet band at this time. On the other hand, for different groups, the greater the refractive index of the SiO_{x}N_{y} top layer, the better the performance of the cell, which demonstrates again that the smaller the refractive index gradient of the DLARC, the higher the shortcircuit current density and efficiency of the cell. Therefore, Fig. 13 shows the reflectivity of the cell with each SiO_{x}N_{y}/Si_{3}N_{4} DLARC in Plan 2 (both with SiO_{x}N_{y}/Si_{3}N_{4} thicknesses of 60/15 nm) versus optical wavelength. It can be seen that in the wavelength range of 300–1000 nm, the higher the refractive index of SiO_{x}N_{y}, the lower the reflectivity of the cell. This trend can also be seen from the results of the weighted average reflectivity of each group shown in Table 8. Hence, the smaller the refractive index gradient of the DLARC, the lower the weighted average reflectivity, and the better the performance of the cell. Combined with the two design plans, it can be found that the SiO_{x}N_{y}/Si_{3}N_{4} DLARC has a great influence on the solar radiation in the ultraviolet range, which is mainly determined by the reflectivity characteristics of SiO_{x}N_{y}/Si_{3}N_{4} DLARC for short wavelengths. In contrast, Plan 2 shows better results with a shortcircuit current density of 37.70 mA/cm^{2} and an efficiency of 20.89%. Compared to the reference standard cell, the shortcircuit current density is increased by 0.32 mA/cm^{2} and the efficiency is increased by 0.20%.
Conclusion

(1)
A device simulation model, in which the surface recombination is neglected, based on Silvaco Atlas was constructed and validated, which is suitable for exploring the front surface structure characteristics of the single cSi PERC solar cell.

(2)
Compared with the standard pyramid textures, the slightly concave pyramidlike textures can further enhance the light trapping ability of the PERC solar cell due to the larger illumination areas.

(3)
The SiO_{x}N_{y}/Si_{3}N_{4} DLARC with suitable match of refractive index and thickness can significantly reduce the reflectivity for short wavelengths and consequently improve the shortcircuit current density of the cell.

(4)
The optimal slightly concave pyramid textures increase the shortcircuit current density of the reference standard cell by 0.30 mA/cm^{2} and the efficiency by 0.18%. The optimal SiO_{x}N_{y}/Si_{3}N_{4} DLARC increases the shortcircuit current density of the reference standard cell by 0.32 mA/cm^{2} and the efficiency by 0.20%.
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Acknowledgements
We acknowledge Hunan Province Science and Technology Department for funding (Grant No. 2017GK5002) and Central South University for funding (Grant No. 2018zzts492). Also, we acknowledge B.X. Zhao, Y.M. Chen, Y.Y. Wang and Y.Q. Ren for helpful discussions.
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Zhou, J., Tan, Y., Liu, W. et al. Effect of front surface light trapping structures on the PERC solar cell. SN Appl. Sci. 2, 799 (2020). https://doi.org/10.1007/s4245202026084
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Keywords
 PERC solar cell
 Light trapping
 Texturing
 Antireflection coating
 Device simulation