Refractory plasmonics enabling 20% efficient lead-free perovskite solar cells

Core-shell refractory plasmonic nanoparticles are used as excellent nanoantennas to improve the efficiency of lead-free perovskite solar cells (PSCs). SiO2 is used as the shell coating due to its high refractive index and low extinction coefficient, enabling the control over the sunlight directivity. An optoelectronic model is developed using 3D finite element method (FEM) as implemented in COMSOL Multiphysics to calculate the optical and electrical parameters of plain and ZrN/SiO2-modified PSCs. For a fair comparison, ZrN-decorated PSCs are also simulated. While the decoration with ZrN nanoparticles boosts the power conversion efficiency (PCE) of the PSC from 12.9% to 17%, the use of ZrN/SiO2 core/shell nanoparticles shows an unprecedented enhancement in the PCE to reach 20%. The enhancement in the PCE is discussed in details.

The promising efficiency and affordable cost are the driving forces pushing the research on lead (Pb)-based perovskite solar cells (PSCs) over the past decade [1][2][3][4][5] . The latest power conversion efficiency (PCE) certified by the National Renewable Energy Laboratory (NREL) for PSCs is 24.2% as reported by KRICT/MIT 6 , competing that of Si-based photovoltaic and surpassing CdTe solar cells 7,8 . However, the toxicity concerns of Pb were proved to be a serious flaw and can hurdle the path of PSCs towards commercialization [9][10][11][12] . Partial replacement of Pb with lower toxicity cations has been reported and proposed as Ge 13 , Sb 14 , and Sn 15,16 . Among those candidates, Sn has shown a close similarity to Pb 17 with a remarkable enhancement in PCE from 6% 16 to 10% 18 . However, this PCE is much lower than that reported for Pb-based PSCs, leaving a room for improvement. Generally, the lack of light absorption is the major concern hindering the achievement of high PCE for thin film solar cells (TFSCs) due to the small thickness of the active layer used. In this regard, the use of plasmonic light trapping nanoparticles has emerged as a means to enhance the PCE of TFSCs [19][20][21][22] . Plasmonic nanoparticles act as nanoantennas that couple near field electromagnetic waves (sunlight) to sub-wavelength area, enhancing the nanoscale light-material interactions [23][24][25] . The geometry, dielectric permittivity, surface roughness, and surrounding medium are the factors determining the plasmonic near-field intensity. To this end, noble metal nanoparticles (Au, Ag, etc.) have been reported to enhance the efficiency of TFSCs 26,27 due to their ability to couple electromagnetic waves at air/metal interactions using surface plasmon guided modes and control the direction of scattered light 28,29 . However, noble metals are expensive, exhibit narrow-band scattering and absorption spectra, thermally unstable, and CMOS incompatible. As alternatives, refractory plasmonic metal nitrides such as TiN and ZrN have been investigated with promising results being reported that were ascribed to their highly tunable optoelectronic characteristics [30][31][32][33][34] Of special interest, plasmonic/dielectric core/shell nanostructures have attracted recent attention mainly due to the fact that dielectrics are transparent to sunlight and enjoy high refractive index that enables the control over light coupling 35 and the possibility of tuning the surface plasmon resonance 36 . The use of core-shell structure provides both electrical and chemical protection isolation to the plasmonic core as it prevents the metal diffusion contaminant into the solar cell structure.
Herein, we show the opportunity to boost the efficiency of Pb-free perovskite solar cells (PSCs) to reach up to 20% upon the implantation of ZrN/SiO 2 core/shell nanoparticles in the active layer. For comparison, ZrN and TiN-decorated PSCs have also been investigated and discussed.

Optoelectronic Modeling Details
Four 3D electromagnetic wave (EMW) models have been constructed based on finite element method (FEM). The first model is used to calculate the interaction of sunlight electromagnetic radiation (AM 1.5 G) with solar cell active layers based on Maxwell's equations of light propagation: where H is the magnetic field, E is the electric field, μ is the permeability, ℇ is the electric permittivity, and σ is the electric conductivity. This model is used to develop the full field of the proposed design in Fig. 1a of planar www.nature.com/scientificreports www.nature.com/scientificreports/ perovskite solar cell in order to obtain the generation rate and short circuit current (Jsc). The optical carrier generation rate (G opt ) per wavelength over the active layer volume is calculated using Eq. 3 37 .
where the optical carrier generation depends on the complex permittivity imaginary part (ε″) and the electric field intensity. Upon integrating the optical carrier generation over the simulated wavelength (λ), the total generation rate (TGR) can be estimated using Eq. 4. =

Normalized Absorption
Absorption of nanostructured film Absorption of planar film (5) The fourth model proposes a novel design of ZrN nanoparticles with different radii (50 nm, 75 nm) as a plasmonic core and SiO 2 as a dielectric shell of thickness 40 nm. The proposed design is shown in Fig. 1d.
The external quantum efficiency (EQE) was calculated for the planar, TiN, and ZrN nanostructured solar cells using Eq. 6 38 assuming single-path absorption and unit internal quantum efficiency (IQE). www.nature.com/scientificreports www.nature.com/scientificreports/ = * EQE IQE Absorption (6) The optical refractive indices and extinction coefficients of Au, MASnI 3 , TiO 2 , Spiro-OMeTAD, ITO, TiN, and ZrN were taken from previously published data [39][40][41][42][43][44][45] . The electrical model was based on the use of the G opt as an input parameter. The current-voltage characteristics were obtained by solving the drift-diffusion and 3D Poisson's equations. Series and Shunt resistances were used as fitting parameters from previously measured data 46 . The J sc was calculated using Eq. 7 47 .
sc hc 1 2 where q is the elementary charge, d is the thickness of the active layer, and α is the absorption coefficient calculated using Eq. 8.
where k(λ) is the extinction coefficient for each simulated wavelength. As J sc is directly proportional to the total carrier generation rate and have the same dimensions of the planar model, Eq. 9 can be used to calculate any enhancement in J sc 48 .   The COMSOL Multiphysics software package was used with AM 1.5 G as an input power port and a wavelength in the range 100-1300 nm was swept over with 10 nm step size in order to cover the UV, visible, and IR regions to obtain the greatest possible plasmonic enhancement over the whole possible simulated bandwidth because TiN and ZrN nanoparticles have an increasing extinction coefficient in the IR bandwidth 44,45 . The optoelectrical model was applied on a cell surrounded by perfectly matched layers (PMLs) in all directions and periodic boundary conditions (PBCs) in x-y direction. However, there were some hurdles in the optical

Results and discussion
Nanoparticles-decorated PSCs. To construct the optoelectrical model of the TiN or ZrN-decorated PSCs, the optoelectrical model for plain (planar) solar cell is developed first to calculate the G opt and J sc for planar PSC for better comparison. The proposed design is shown in Fig. 1a, where the thicknesses of Au, Spiro-OMeTAD, MASnI 3 , TiO 2 , and ITO layers are 100 nm, 200 nm, 40 nm, 350 nm, and 150 nm, respectively with 600 nm width   www.nature.com/scientificreports www.nature.com/scientificreports/ and 600 nm depth. The electric field profiles are investigated at selected wavelengths that represent the UV, visible, and IR bandwidths (i.e. full bandwidth scan). The electric field profiles of the planar perovskite solar cell are shown in Fig. 2.
TiN-decorated PSCs. TiN nanoparticles were implanted on-top of the PSC active layer as discussed in model 2 and shown in Fig. 1b. Figure 3 shows the electric field profiles upon implanting TiN nanoparticles and their electromagnetic radiation resonance coupling enhancement to the solar cell active layers, which glows the most in the IR range compared to the planar PSCs counterparts. For each simulated TiN nanoparticles' size, the corresponding G opt is calculated using Eq. 3 and plotted in Fig. 4a. TiN acts as an absorber in the bandwidth range 300 nm − 580 nm with the absorption coefficient being significantly decreasing at wavelengths greater than 780 nm. Note that the TiN nanoparticles that are 100 nm in radius have their plasmonic resonance peak at a wavelength of 880 nm, indicating the high scattering capability of TiN in the IR range 45 . While the 75 nm radius TiN nanoparticles showed two plasmonic resonance peaks at 1000 nm and 1280 nm, the 50 nm radius counterparts showed a resonance peak at 840 nm. The TGR is calculated using Eq. 4 and listed in Table 1, indicating a maximum enhancement of 36.7% for the PSC decorated with 75 nm TiN particles compared to the planar PSC counterpart. Figure 4b shows the normalized absorption calculated using Eq. 5 for the simulated PSCs. TiN nanoparticles function as nano-antennas with their surface plasmon resonance (SPR) modes coupled to the PSC active layers due to the increase of the near field sunlight in the IR region (> 800 nm). This absorption enhancement, especially in the IR bandwidth, due to the plasmonic nanoparticles effect to act as wave guide to direct sunlight by means of localized SPR, forming surface plasmon polaritons (SPP) at the air/TiN nanoparticle interface that couple sunlight into sub-wavelengths active area.    www.nature.com/scientificreports www.nature.com/scientificreports/ The corresponding J-V and P-V characteristics of the simulated PSCs are shown in Fig. 5 and listed in Table 1. Note that the series and shunt resistances are tuned based on the reports in literature taking into account the recombination mechanisms in PSCs 46 . The optimized series resistance is found to be 50 Ω and the shunt resistance is 400 Ω. The J sc shows a pronounced enhancement upon TiN-decoration compared to that of the planar PSC. The maximum enhancement in PEC is observed for the PSC decorated with the 100 nm TiN nanoparticles as it is increased from 12.9% for the planar PSC to 18.2%, achieving ca. 41% enhancement in the overall solar cell efficiency. Figure 5c shows the EQE enhancement for each of the TiN-decorated PSCs. Note that the 100 nm TiN has an EQE of 85% due its high electric field directivity as shown in Fig. 2, where the localized surface plasmonic resonance of TiN nanoparticles is shown at 840 nm, in agreement with Shalaev et al. 33 .
ZrN-decorated PSCs. ZrN is another very promising refractory plasmonic material. The electric field profile for ZrN nanoparticles implanted onto the active layer of PSCs is shown in Fig. 6. Also, the G opt and the normalized www.nature.com/scientificreports www.nature.com/scientificreports/ optical absorption (NOA) are shown in Fig. 7. Note that the PSC decorated with 100 nm ZrN particles showed significant plasmonic resonance enhancement at the wavelengths of 1000 nm and 1250 nm. Upon integrating the G opt over the swept simulated wavelength using Eq. 4, it was possible to calculate the total generation rate enhancement as listed in Table 2. Note that the 100 nm ZrN particles showed 25.8% enhancement in the TGR compared to planar PSC with an increase in the PCE from 12.9% (planar) to 16.6%. Moreover, a maximum EQE of 84.63% at 840 nm, compared to 72% for the planar PSC at the same wavelength, is observed, Fig. 8.
Novel ZrN/SiO 2 core/shell-decorated PSCs. ZrN/SiO 2 core/shell structure has been tested as a novel structure to enhance the efficiency of PSC using two different radii of ZrN of 50 nm and 75 nm core surrounded by 40 nm of silica (SiO 2 ) shell. The core/shell structure is used as a means to tune the LSPR of ZrN, which depends on the surrounding dielectric medium. Figure 9 shows the electric field profiles, indicating a great enhancement in the sunlight coupled to the solar cell active layer. Figure 10 shows a tremendous enhancement in the G opt and optical absorption in the active layers of the PSCs upon the use of ZrN/SiO 2 . Moreover, a 13.3 mA/cm 2 increase in J sc , 55% enhancement in the TGR, and an increase in the PCE from 12.9% to 20% are observed as listed in Table 3 and Fig. 11a,b. The EQE is 87% at 840 nm as recorded for the PSC decorated with 115 nm ZrN/SiO 2 , see Fig. 11c. Table 4 summarizes the calculated optical and electrical parameters of the PSCs-decorated with different refractory plasmonic nanoarchitectures. Note that the generation rate of ZrN/SiO 2 (75 nm core and 40 nm shell) increases by 19.8% and 15.7% compared to ZrN alone with 75 nm and 100 nm in radius, respectively. This can be ascribed to the enhancement in the plasmonic surface plasmon directivity by the dielectric shell.

Conclusion
In summary, refractory plasmonic materials (RPMs) have been investigated as a promising replacement to noble metals as nano-antennas to boost the photoconversion efficiency of lead-free perovskite solar cells. This was mainly based on the light trapping ability of the BPMs. The use of ZrN leads to a total generation rate enhancement of 25.8% with an increase in the PCE from 12.9% to 17%. On the other hand, replacing ZrN with TiN shows a noticeable enhancement in the total generation rate of 18.2% with a PCE of 18.2%. Tremendous enhancement in the optical and electrical characteristics of the PSCs are observed upon the use of ZrN/SiO 2 core/shell nanoparticles with a total generation rate enhancement of 55% and an overall PCE of 20%, which is yet to be achieved for any Pb-free PSC. We hope our study opens a new avenue towards the realization of high efficiency Pb-free PSCs.