Insights in light trapping for new generation silicon solar cell: optical characterization of plasmonic nanostructures beside anti-reflection layer

Designing light-trapping is one of the requirements for new generation silicon solar cells. Herein, the optical properties of front-based plasmonic nanoparticles besides the anti-reflection layer on new-generation silicon cells were investigated by the 3D-FDTD method. The simulated results were compared with some experimental kinds of literature. In addition to a perfectly periodic structure, the nearly regular structure (closer to the experimental one) was also modeled. Along with the conventional far, near-field effect, generation rate, and ideal Jsc, enhancement in quantum efficiency (g-curve) and integrated quantum efficiency (G-value) were used as suitable characterizing sets. The g-curve result of the sample with the anti-reflection layer showed superiority compared to the standard cell in the ~ full wavelength range. Moreover, the thickness engineering of the anti-reflection layer can significantly increase cell performance (G = 1.4). In contrast, the plasmonic structure was not more effective according to the g-curve of some optimum plasmonic samples for wavelengths below 500 nm. The best G-value among plasmonic samples was 1.3. Also, using both anti-reflection with the plasmonic design did not significantly improve the optical performance. The results determined that the plasmonic system can lead to a considerable decrease in spectral reflectance, consistent with some reported experimental ones. Moreover, the simulations clarified the cause of the lack of necessary plasmonic enhancement in some experimental studies could be attributed to the lateral trap of the light. In other words, this reduction in reflection does not lead to notable transit near and far-field into the active layer.


Introduction
It is estimated that single-crystal silicon (C-Si) solar cells make up about 90% solar photovoltaic market. These solar cells are the most adopted technology than any other solar cells (Płaczek-Popko 2017). The C-Si cells are stable, have long lifetimes, and are made of abundant and non-toxic materials. As the C-Si technology is related to electronic systems, the prior high investment in the electronic industry can be another advantage for C-Si cells. These benefits are not the case for another competitive solar cell (SC) technologies. Due to its indirect band-gap, the optical absorption of C-Si cells is poor, necessitating significantly higher wafer thickness than other thin-film solar cells (Yang 2019). In a C-Si solar cell, the conventional thickness of C-Si is ~ 180 µm, which accounts for more than 50% of the SC fabrication cost (Mir-Artigues and Río 2016). Moreover, the Si surface is responsible for reflecting in the 35-50% range. It also suffers from inevitable losses due to non-radiative recombination and the relatively long path of carriers to electrical contacts. In this regard, reducing surface reflection with the help of the passivation-antireflection layer and trapping light with surface texturization has been studied (Eisenlohr 2017;John 2018;Shanmugam et al. 2020). Nevertheless, more cost reduction for C-Si solar cells is still being pursued seriously. One straightforward solution is to significantly reduce the thickness of the active layer in what is known as the new generation (or thin-film) C-Si cell. For new generation C-Si cells, the Si has a thickness on the order of only a few micrometers and is deposited on external substrates like plastic, glass, ceramics, or metal for mechanical backing (Eisenlohr 2017). Now, the efficiencies of such new generation cells are low compared to wafer-based ones because of the mainly poor light absorption (Andreani et al. 2019). Based on theory and practice, it is also possible to achieve a suitable efficiency (> 10%) for an SC with a thickness of about 1 µm (Shah 2010). Since thin-film solar cells have a thickness of about a few microns, typical methods of increasing the light absorption, which uses surface textures with dimensions around ~ 10 µm, cannot be used (Fashina et al. 2015). Moreover, plasma etching techniques that can be used to etch submicron-sized features may damage the Si, thereby decreasing the efficiency. Another alternative method to direct texturing is the texturing of the substrate. But this also results in increased recombination loss by increasing surface area. In this regard, unique innovations involving a wide range of optical features have been studied (Fonash 2014). These innovations are mostly based on nanoscale structures to use new light trapping to overcome the original weak optical absorption of a variety of thin-film solar cells like the C-Si one. Optical characteristics based on nanolithography, plasmonics, and other nanostructures have amplified the opportunities for the greatest utilization of the photovoltaic potential of a 1 to 20 µm layer of mono-multi crystalline silicon on low-cost substrates. Spinelli et al. studied the effect of periodic dielectric cylindrical nanoparticles on thin-film Si (Spinelli and Polman 2014). Bhattacharya et al. have increased the efficiency of a thin-film cell through a photonic crystal structure (Bhattacharya and John 2019). Moreover, different plasmonic nanostructures (PNSs) have been studied to increase the efficiency of diverse thin-film cells (Huang 2017). Improved forward scattering from metal nanostructures placed on top of the C-Si cell is one of the main plasmonic light-trapping approaches due to the angular redistribution of the scattered light. This is more straightforward than using a PNS at the rear surface and enhances silicon absorption due to light coupling into photonic modes (Shah 2010). The PNS presence on the top of Si cells can be significant because they can be relatively separate from the stage of initial cell production. Therefore, undesirable changes such as an increase in bulk-surface defects are not associated with adding PNSs. Zhang et al., more by the simulation, analyzed the effect of adding periodic spherical PNSs at the top and hemispherical ones at the rear surface (Zhang et al. 2014). There are various physical and chemical methods for making PNSs. Thermal evaporation with specifications such as wellcontrolled and reproducible is one of the most effective of them (Saylor and Irby 2018). Pillai et al. studied thermally evaporated nanoparticles at a front-based light-trapping structure for 1.25 µm silicon on insulator and double-sided polished 300 µm Si wafer-based cells (Pillai et al. 2007). In their study, for several sizes of particles, they deposited different mass thicknesses of silver thin-films, the light trapping potential was studied by measuring the wavelength-dependent current for visible to IR wavelengths. They stated a relative increase in photocurrent for a device with the best-optimized nanoparticle structure compared to without nanoparticle-based devices. Toward investigating best-optimized nanoparticles on front-based light trapping geometry, Spinelli et al. explored Ag nanoparticle arrays formed using electron beam lithography (Spinelli et al. 2011). They only emphasized reducing the spectral reflectance of the plasmonic sample. In addition, El Daif et al. have examined metal nanoparticles by hole-mask colloidal lithography for thin (2-12 µm) C-Si solar cells toward employing the scattering property of PNS at the front (Daif et al. 2012). But, a relative decrease in efficiency was observed compared to a standard cell. Saravanan et al. e simulated the various photonic and plasmonic nanostructures used on the front side of the very thin silicon layer (Saravanan et al. 2022). According to their findings, the best performance did not belong to the plasmonic structure. So, proper improvements in solar cells due to PNSs are still less reported.
Furthermore, some frontside plasmonic simulations have relied on the calculation of absorption enhancement only through reflection (Tharwat et al. 2021;Winans et al. 2015). But the less reflected light may not pass to the active layer due to optical loss of PNS, so the active layers' absorption should be studied more carefully. The absorbing, scattering, and lateral trapping of light by PNS is very sensitive to the metal nanoparticles' size and shape, the surrounding medium, and the surface coverage on the substrate (Duan et al. 2018). As a result, improving the integrated SC efficiency is still a significant challenge. For that reason, one should design frontside PNS to diminish loss and lateral trapping of the light and boost the scattering across the desired frequency regime. Moreover, it is worth noting that obtaining reproducible PNS with the desired size, shape, and distribution is often challenging from a technical point of view. Therefore, knowing the physic of plasmonic solar cells requires further study and investigation.
In this study, the elliptical-spherical metal PNS were investigated by 3D-FDTD simulation. Simulations were performed for both Ag and Al metals. Far and near field factors were simulated and analyzed. To more precisely determine PNS's effect on SC performance, it doesn't seem sufficient to use just absorption and reflection curves. Therefore, the net spectral plasmonic impact on the absorption enhancement of the active layer compared to the standard C-Si cell (i.e., 3 µm Si thickness without PNS and Si3N4 anti-reflection layer) was considered by presenting spectral g-curve. Also, the numerical G-value was presented by considering the AM 1.5 solar spectrum on the "g-curve" and integrating it into the whole range. In other words, the g-curve gives a spectral positive or negative impact of the added structure compared to the standard one, and the G-value indicates that in a given sample (like a plasmonic sample or one using an anti-reflection layer or both), the cell is better than the standard one or not.
In other words, a greater G-value than one is associated with a more positive optical effect. This information can describe how plasmonic nanoparticles are effective and help to understand their physics better. The impact of perfectly periodic and nearly periodic plasmonic samples was studied and compared with anti-reflection monolayer samples to complete the study. In addition, only emphasizing the spectral reflection in justifying the usefulness of the frontside plasmonic structure or computing the absorption of the active layer by reflectance (i.e., 1-Reflectance-Transmittance) was examined. In this regard, the simulation results were compared and evaluated with some experimental results.

Method and simulation
In the SC layer, the absorption per unit volume can be calculated from (Eq. 1) El-Bashar et al. 2021): where is angular frequency, E 2 is electric field intensity, and Ɛ is the permittivity. Therefore, the electric field intensity and the imaginary part of the permittivity are just needed to calculate the absorption as a function of frequency and space. Both quantities are easy to measure in an FDTD method (Houle and Sullivan 2020).
The quantum efficiency of a solar cell, QE (λ), can be proportional to (Eq. 2): where P in ( )∕ℏ and P abs ( )∕ℏ is the number of photons per unit volume of the incident light and absorbed light within the cell, at a wavelength λ, respectively, and ℏ is the reduced Planck's constant. Since no recombination mechanism is considered, the ideal integrated quantum efficiency, IQE (or equivalently as spectral absorption rate, A (Bo et al. 2017) can be defined as Eq. 3: where h is Plank's constant, c is the speed of light in the free space, and AM1.5 solar spectrum.
In the above equation, the numerator and denominator indicate the number of photons absorbed by the SC and that coming into the solar cell. To study how added structure such as plasmonic structure or anti-reflection layer can improve the performance of the SC compared to a bare (standard) C-Si cell, the following quantities are defined (Rassekh et al. 2021) (Eqs. 4): where g( ) and G are enhancement in quantum efficiency and integrated quantum efficiency, respectively (i.e., the normalized spectral enhancement and it's weighted to AM 1.5 with spectral integrated to the standard cell, respectively). The subtitle "Standard structure" is related to the case that the basic (bare) structure used in the simulation, and the subtitle "Added structure" is associated with a new design such as an anti-reflection layer or plasmonic nanostructure (or both) is added to the SC. Enhancement factors more significant than one mean that the number of photons absorbed in the Si is increased with the added structure compared to a bare Si cell. In other words, the overall performance of (1) the structure over the entire solar spectrum can be evaluated by considering the integrated absorption enhancement (G).
If it is assumed that all electron-hole pair contributes to photocurrent, the short circuit current density (Jsc) is provided by (Eq. 5): where e is the electron charge.
The Lumerical simulator is used for FDTD simulation (www. lumer ical. com). The plane-wave source and the FDTD region with the perfectly matched layer (PML) in the Y-direction and periodic or Bloch boundary condition (BC) in the XZ surface are used. In the model, one flux monitor is placed on the top outside of the structure to measure reflected light (backward scattering) at numerous wavelengths. Moreover, two others are located between the C-Si layer for absorption measuring. To consider the metallic nanostructure in the simulation, the override mesh setting (2 × 2 × 2 nm 3 Yee cell) was applied to this section of the C-Si model (Fig. 1). . 1 Schematic view of the 3D-FDTD region of the simulation Several sample groups (Qi, i = 0 till 5) were considered for simulations and study. In these groups, two structures that can be added alone or together are the mono anti-reflection layer (MARL) and the plasmonic nanostructure (PNS). The periodic PNS (PPNS) was considered an entirely or somewhat periodic structure (the second model is closer to the experimental one). Their specifications are given in Table 1.

Mono anti-reflection layer (MARL)
In the first step, the cell performance was studied by just MARL, which can passivate the surface, too. The simple theory of the optical layer can be used to make an initial guess. For a MARL (refractive index n 2 on a silicon substrate (n s ) in the air (n 1 )), the Si 3 N 4 can be chosen according to this formula: √ n 1 * n s . Then the thickness of Si 3 N 4 (d) as a factor for the less reflection can be determined by min = 4n s d MARL (MacLeod 2001). But the standard cell structure comprises several thin films ( Fig. 1), which do not entirely follow the above formulas for a thin layer on a thick substrate. Therefore, the FDTD simulation can be used for this purpose. FDTD can calculate the dependence of the total reflection of the cell on the Si 3 N 4 thickness at a specified wavelength of the source (400 nm, 600 nm, and 800 nm separately). The simulated thicknesses that provided the least reflection at the selected wavelengths are 47 nm, 75 nm, and 95 nm, respectively (Fig. S1 of supporting information). Based on coherent constructive and destructive interference, the reflection changes with the thickness of the Si 3 N 4 layer. Figure 2 shows the spectral g-curves of a C-Si cell with different thicknesses (d) of Si 3 N 4 (the Q 1 group). The corresponding G-values are given in the figure, too. For better comparison, these absorption and reflection spectra are also shown in Fig. S2 and S3. According to Fig. S1, the Si 3 N 4 layers with a thickness of 47 nm and 75 nm show the least reflectance (~ 0) at a wavelength of 400 and 600 nm, respectively.
In contrast, the thickness ability to decrease the reflection for a single wavelength source with 800 nm is weaker than two other wavelengths (400 nm and 800 nm). The G-value is similar to an average "g-curve" over the absorption spectrum that also considers the AM 1.5. So, it accurately indicates the improvement in cell performance compared to the standard cell.
As can be understood from different parts of Fig. 2, the presence of the MARL can significantly improve cell performance. Due to the Fabry-Perot-like structure, sharp fluctuations at the g-curve are mainly observed at wavelengths greater than 600 nm. By comparison, the enhancement of the sample with the 47 nm anti-reflection (AR) (the sample in the Q 1 group) is very effective up to 500 nm wavelengths. But at longer wavelengths in g-curve, the amplitude of the oscillations is less than others. To evaluate the enhancement in performance, the final assessment cannot be done by looking at the reflectance and absorptance curves (Fig. S2 and S3). But, the g-curve provides spectral evaluation, and the G-value indicates that d = 75 nm is an optimized value of Si 3 N 4 thickness for these samples. In other words, the g-curve and G-value have been used as two important simulated factors. The G-value is similar to an average "g-curve" over the absorption spectrum that also considers the AM 1.5. So, it accurately indicates the improvement in cell performance compared to the standard cell.

Al and Ag PNS
In the second part, the impact of entirely periodic PNS (PPNS) was investigated. The scattering and absorption of metallic nanostructures depend on their size or shapes, relative positioning, and environment. Metallic particles significantly smaller than the wavelength of light tend to absorb more; hence, extinction is dominated by absorption. Absorption dissipates heat, and this property is utilized in applications like solar glazing, nanoscale lithography, and therapeutic applications (Barbillon 2019). But, as the size of the particles increases, extinction is dominated by scattering, and this property for light trapping is helpful. But, beyond certain limits, increasing the particle size leads to risen retardation effects and higher-order multipole excitation modes, which reduces the efficiency of the scattering part. Based on performed simulations (they are not presented here) and also according to some studies (Zhang et al. 2014;Pillai et al. 2007;Spinelli et al. 2011), two types of periodic arrays of Al and also Ag particles (elliptical one with 200 nm width and 130 nm height as well as spherical one with 200 nm diameter) with a pitch of 450 nm were selected. Figure 3 shows the g-curves and G-values of these plasmonic samples (Q 2 group). It seems that up to ~ 600 wavelengths, Al PNS is more effective in improving cell performance than Ag due to their less loss absorption. While at wavelengths above 600 nm, Ag PNS are more prevalent due to their higher scattering strength (Haidari 2022). Moreover, based on G-values, oblate PNS (H = 120) are more geometrically efficient for both materials. To emphasize the importance of g and G, the reflectance curves (Fig. S4) show that all PPNSs can reduce the backward reflection. But, by comparing the reflection curves, it is not easy to find the exact influence of PNSs on the optical performance of C-Si cells and compare them with each other. In other words, once again g-curve and G-value showed that they could be helpful in a more detailed investigation of the optical effect of PNS and their comparison. According to Figs. 2 and 3, using optimized plasmonic and monolayer structures can improve the value of G by up to 30% and 40%, respectively.

Combining ARML and PPNS
Pillai et al. showed a 33% increment in current generation potential for a 12 nm thermally evaporated plasmonic cell compared to a standard one (1.25-µm-thick silicon-oninsulator-based solar cell) (Pillai et al. 2007). This improvement, like the 30% improvement in G here for the Q 2 group, may not be comparable with the alone AR sample (for example, the 40% improvement in G for the Q 1 group). The comparison of Figs. 2 and 3 shows that the monolayer alone sample improves G-value at all wavelengths (especially for d = 47 nm). But, the PPNS cell in wavelengths less than 500 nm (unlike larger wavelengths) does not appear very practical. In other words, improvements are also observed at larger wavelengths close to the silicon band gap, similar to experimental studies. Therefore, it can be guessed at this stage that both MARL and PNS may increase more the g-curve and G-value. However, this assumption needs further investigation.
In the first case at this step, PPNS was placed on the top surface of the anti-reflective layer (Q 3 group). The spectral g-curves and G-values for this case are shown in Fig. 4. Figure 4 shows that the simultaneous use of PPNS on MARL improves the g-curves in the whole absorption spectrum. For further comparison among different groups, the g-curves of samples of other groups simultaneously are shown in Fig. S5. In the second case at this step for the Q 4 group, PPNS was placed directly on the top surface of the Si layer among the MARL (the g-curves and G-values are shown in Fig. 5). By comparison, two samples in the Q 3 and Q 4 group offers the best enhancement. They lead to the highest value of G-value (1.43) among different samples in Table 1. This value is about 2.2% better than the MARL alone (Q 1 group) and about 10% better than the just PPNS (Q 2 group). A relative peak at ~ 450 nm is seen in plasmonic g-curves, especially for Ag samples (Q 3 and Q 4 group). To determine the reason for this peak, the maximum amount of field intensity (E 2 max ) on XZ surfaces in the active layer (this XZ cross-section is shown in Fig. S6) was recorded at each wavelength and shown in Fig. 6. As can be seen, due to the PPNS and plasmonic behavior of Ag in this range, a relative guided mode peak is observed because of the relative forward scattering at wavelength ~ 450 nm. Fig. 3 The g-curves and G-values of C-Si cell for plasmonic samples (Q 2 group). The inset shows the cell structure Contrary to the apparent difference in the g-curves of different groups (Fig. S5), no significant growth for Q 3 and Q 4 groups was observed for G-value compared to the Q 1 group. One of the reasons may depend on the spectral form of AM 1.5 and the reduction of the g-curve at wavelengths below 600 by PPNS compared to MARL. Due to the plasmonic wavelength(s) of PPNS and parasitic loss, especially in the visible range for Ag (Figs. 7,8,9), the positive effect of PNS on the g-curve may be limited. By comparing the results (Fig. 4), this limitation can be lower for the Al structure, whose plasmonic wavelength is probably outside the visible range (Haidari 2022). Nevertheless, the influence of the material and the geometric characteristics of the design is evident (for example, the effect of changing the H parameter from 130 to 200 nm). Therefore, more investigation for a more optimal structure can be suggested.  Toward examining best-optimized nanoparticles on front-based light trapping geometry, Spinelli et al. investigated Ag nanoparticle arrays made by electron beam lithography (Spinelli et al. 2011). Their test samples were 300 µm C-Si layer. The reflection coefficients, which were measured, showed the reduced reflection clearly. The Plasmonic geometry in that study is very close to our model of PPNS specification. As mentioned before, Fig.  S4 shows the simulated reflectance curve of a number of our samples. The reflectance reduction in the samples that used both PPNS and MARL is quite apparent and relatively similar to the mentioned experimental samples. In this experimental study, only the reflectance curve was measured for the non-thin C-Si sample. Therefore, it may be reasonable to expect it to be very effective in improving cell operation. Although our results show a reasonable decrease in reflectance, at the same time, they present a relatively small increase in simulated C-Si cell performance, too.
Besides, El Daif et al. have examined metal nanoparticles by hole-mask colloidal lithography for thin (2-12 µm) C-Si solar cells toward employing the scattering property of PNS at the front (Daif et al. 2012). But, a relative decrease in efficiency was observed compared to a standard cell, which is somewhat consistent with some samples of our simulation. This cast doubt on the applicability of a similar PNS to improve the cell. To more clarify the causes of failure to improve performance despite the effective reduction of backward reflection (far-field result), cross-section surfaces that includes the XY axes were also selected for typical monitoring of the near-field (XY cross-section is shown in Fig. S6). Simulation shows there are strong near-field effects in the monitor for samples with PPNS (for wavelength 400 nm, 600 nm and 800 nm and for Q 2 , Q 3 and Q 4 that they are shown in Fig. 7 till 9). These effects mainly occur at the interface of the plasmonic surface and cell structure. It is true that PPNSs, like the MARL, contribute to an acceptable decrease in reflection, but this decrease in reflection does not mainly increase the light transition into the active layer. In other words, the lateral trap of the field intensity instead of penetrating the field inside the layer may be an optical reason for the decrease in SC performance. As a result, our calculations suggest that in using PNS on the frontside surface, relying only on reflectance to calculate the absorption (1-Reflectance-Transmittance) (Tharwat et al. 2021;Winans et al. 2015) and noting its reduction as a reason for increasing the performance of the cell (Spinelli and Polman 2014), cannot seem very appropriate. Therefore, the plasmonic effects could either facilitate or bother the performance. Another thing that can be significant is the distance between the PPNS and the active layer. Considering this case, the nanoparticles can be placed adjacent to the active layer, besides the MARL, or on the MARL. Despite the placement of nanoparticles on the C-Si surface in Q 2 , the best G-value (1.43) did not result for this group. But the other two groups (Q 3 and Q 4 ) had the best G-value result. Therefore, the near-field pattern shows its complexities in design.
For a complete study, generation rate curves and the ideal Jsc values of different samples of various groups are shown in Figs. 10 and 11, respectively. Studying Figs. 10 and 11 along with ّ Fig. 7 till Fig. 9 show that despite the strong near-field effects, near-fields penetration into the active layer are different for various samples. In contrast to group Fig. 10 Optical generation rate of carriers as a function of depth in the C-Si for different samples Fig. 11 The ideal Jsc for different samples of different groups Q 2 , for group Q 4 where the environment of Ag PPNS changed, near-field effects led to a significant increase in the Generation rate near the silicon surface (or near depth zero in C-Si). The same Jsc values for Al samples of group Q 3 and Q 4 , with the lower amount of Jsc for Al compared to Ag of group Q 2 , suggest that cannot be significant near-field effects for Al in this spectral region. In other words, the most considerable contribution of the Al samples can be due to the scattering. Since the plasmonic resonance wavelengths for Al samples are generally not in the visible range.
Lastly, the perfectly PPNS in the simulation may be considered somewhat unrealistic because the experimental samples may not be made precisely periodic. A unit cell with the nine particles was considered and repeated to evaluate this aspect with the Bloch periodic boundary condition along the XY surface (Q 5 group). For nine PNS, different lengths of nanoparticles were somewhat randomly selected, which could result in a pre-determined average particle size (averaged height = 130 nm, an average of both lateral dimensions = 200 nm, and the standard deviation for each size = 15 nm). The g-curves and G-values for this case are shown in Fig. 12. This can be considered a more suitable model for an experimental issue. Moreover, the near field intensity image at 600 nm wavelength is also shown in Fig. S7.
Comparing Fig. 4 and Fig. 12, it can be seen that the enhancement of the PNS decreases by moving away from the perfect PPNS. This decrease in plasmonic efficiency becomes more apparent as it moves from the oblate PNS to more prolate PNS, too (or average H moves from 130 to 200 nm). Another notable change is the lack of a relative peak at 450 nm in the g-curves of this model. In other words, this relative peak, which existed in a perfectly PPNS, is no longer observed when the structure is somewhat away from the ideal state.

Conclusion
Conventional optical trapping approaches seem not easily generalizable to the new generation (thin film) silicon cells. Therefore, PNSs can be considered suitable candidates. Some experimental study on the use of PNS has not stated effective improvement. In the number Fig. 12 The g-curves and G-values of C-Si cell for plasmonic samples with MARL (Q 5 group). The inset shows the cell structure (Index "i" in W 1i , W 2i, and H i refer to the particle number) of other references, only an effective reduction in the reflection curve has been reported. This study has precisely determined the effect of front-based PNS and tried to clarify the physics of the problem properly. For this purpose, in addition to the usual characterization of near, far-field effects, generation rate and ideal Jsc, spectral g-curve and numerical G-value were used by the 3D-FDTD method. Initially, a completely periodic structure whose geometric characteristics follow the near-optimal one was selected. The plasmonic effect was combined and compared with an anti-reflective layer to complete the study. Firstly, the impact of MARL thickness on cell improvement was investigated (Q 1 group), and then the maximum of G (1.4) was obtained for the 75 nm MARL thickness.
Moreover, the 47 nm thickness also had the most positive impact at a wavelength of less than 600 nm. In contrast, the perfect PPNS alone (Q 2 sample) yielded a maximum G = 1.3 and, by g-curve, didn't show a significant impact at wavelengths below 500 nm. The combination of MARL and perfect PPNS (Q 3 and Q 4 group) increases the G-value to 1.43. In more forward realistic modeling (Q 5 group), in the nearly periodic case (the PPNS with a narrow size and location distribution), the improvement rate of the G-value decreases. One reason for this could be eliminating guided peaks in forwarding scattering due to the absence of an entire periodic structure. Besides, though there is a significant reduction in backward reflection in some experimental references, no significant improvement has been reported for the PNS with a geometry close to our simulations. To clarify the reason, the simulation results offer that these PNSs sometimes do not provide much ability to transfer near and far-field light into the active layer.
In other words, reduced reflection from the surface in plasmonic samples is due to the change of light's direction to the lateral dimension. The simulated results with a comprehensive characterization method for considering its physics showed that merely reducing the reflection cannot be referred to as the improved efficiency of the front plasmonic structure in the solar cell. This simulation showed that although nanostructure can be a suitable candidate for optical trapping, this topic requires considering careful aspects in designing, particularly for considering near-field effects.