1.Introduction

One of the most important events of 1991 was the report on a new low-cost chemical solar cell by the successful combination of nanostructured electrodes and efficient chargeinjecting dye technology, known as dye-sensitised solar cell (DSSC) or Grätzel cell, which belongs to the third generation of efficient and inexpensive photovoltaic cells ¹. Besides Perovskite and tandem solar cells, DSSCs are considered among photovoltaic (PV) devices with the most potential. This led to remarkably increased interest in DSSCs as an alternative technology for the production of future renewable energy because of their high solar power conversion efficiencies (PCE) ². DSSC consists of a mesoporous (Titania) TiO₂ layer adsorbing a monolayer of dye molecules, an electrolyte based redox system for charge transport, and counter electrodes to collect photogenerated carriers ³, which has high power-conversion efficiency ⁴. To optimise the performance of DSSCs, research universities and institutes are now working on TiO₂ photoanodes fabrication with different forms of nanostructure morphologies ^5-7. Because of their advantages, which include abundantly available inexpensive materials and potentially lower costs of fabrication, DSSCs offer a promising alternative to thin-film silicon solar cells ⁸. The PCEs of existing DSSC photovoltaic devices-up to this time at their development stage-reach around 15 percent, which exceeds the efficiency of conventional amorphous silicon solar cells ⁹. However, this efficiency level is still far below the efficiencies offered by crystalline silicon solar cells, Perovskite solar cells, and tandem thin-film solar cell technologies ^10,11.

Over the two decades, since Grätzel introduced mesoporous TiO₂ nanoparticle films as photoanodes in DSSCs, much of the research efforts have focused on the design of photoanodes and counter/reference electrodes, in addition to dyes and electrolytes, to achieve higher efficiencies of DSSCs ¹². Among these, the photoanode contribution plays a vital role in improving the performance of DSSCs ¹³. However, the investment of maximum conversion efficiency is not easy to achieve. The loss in efficiency is because of insufficient absorption and an internal quantum efficiency smaller than unity at long wavelengths (>350 nm) of visible light ^14,15. The intensity and amount of trapped light are directly proportional to the PCE, which means that a DSSC photovoltaic device’s efficiency can be further boosted by introducing light trapping management ^16-18. Generally, the light-harvesting capacity of a DSSC photovoltaic device is determined by the amount of dye adsorption via the photoanode surface and the spectral response of the dye molecules ¹². Enhancing the visible light absorption is one of the approaches to increase the PCE of DSSCs. Another convenient way is to optimize the TiO₂ thin layer’s thickness for light-harvesting because the number of dye molecules adsorbed on the TiO₂ layer is increased. However, the PCE of DSSCs is a function of the photovoltaic cell length, implying that this approach may reduce the efficiency because it assists the recombination rate of photoelectron-hole pairs to travel all the increased distance to reach the collecting electrode ¹⁹. Several approaches are available to increase the PCE of the DSSCs further, including external coatings ^20,21, carrier collection, photonic structures ^22-24, and diffractive layer ^25,26. However, such enhancements might come at a cost, negatively affecting other electrical properties, such as separate pairs of charge carriers, and, consequently, reducing the PCE ²⁷.

The nanophotonic technology for light-harvesting management inside a photovoltaic device has been suggested as another approach to achieve high PCEs ¹⁹. The applications of modern surface plasmon in photovoltaic technology are not recent, having possibly been first reported in 1998 by Stuart et al, ²⁷. Thus, surface plasmonics has become a global target for photonic development studies. It was found that by increasing the concentration of metallic nanoparticles, the photocurrent (electrical properties) of the photovoltaic cell device was improved 20 times at the long-wavelength (800 nm). So far, using metallic nanostructures for surface plasmonic effect has been one of the best ways to enhance light harvesting and PCE of DSSCs ²⁸. The plasmonic phenomenon in nanomaterials could help harvest more light from sub-wavelength antennas or generate plasmon polaritons from scattering or incident light by trapping light energy on metal NPs in a constant thickness of the TiO₂ thin layer ^29,30. As a result, the PCE would be improved because this leads to an increase in the overall short circuit current density (J _sc ) in the solar cells ²⁷. In recent years, the concept of plasmon resonance has been introduced to the DSSCs using noble metal nanoparticles such as gold (Au) or silver (Ag) because of their low reactivity. Plasmon resonance is one of the approaches adopted for further improvement of PCE of DSSCs. The light-harvesting efficiency is substantially enhanced with the localised surface plasmon resonance (LSPR) phenomena of metal nanoparticles ^30,31. The phenomenon of LSPR refers to the resonance between the oscillation of free electrons and the electromagnetic light field. The LSPR amplifies the electromagnetic light field near the metal nanoparticles and resonant oscillations of electronic clouds ^27,32. This improves the plasmonic effect via extending absorption and harvest of visible light by dye sensitisers in DSSCs ^16,32.

The introduction of metallic nanoparticles (NPs) in appropriate places inside the active layer to confine visible light could provide superior performance due to improved absorption in the organic semiconductor film and enhance photocurrent generation via the effect of LSPR ^1,33. Metal NPs with sharp edges are highly desired due to the high electronic conductivity and their applications as interconnections in the bottom-up self-assembly approach towards future nanodevices. Moreover, the branched structure of Metal NPs such as star-shaped enhance the electric field around the nanoparticles and have multiple plasmon resonances resulting in polarization-dependent scattering with multiple spectral peaks and strong dielectric sensitivity into a single structure ^34,35.

For these potential features of the metal nano-star particles, in this research, different star-shaped GNPs were prepared and applied to TiO₂ (possibly for the first time) to improve its optical absorption using FDTD software as described in a previous article by ²⁹. Multiple sizes of GNPs were applied to study the multiple plasmon-enhanced effects in the structure of the TiO₂ layer. The effects of the size of GNPs on the scattering of light were investigated systematically. We have also studied the correlation between the light source incident angle and the optical absorption characteristics of the TiO₂ thin layer to obtain an optimum angle for enhancing the photovoltaic performance of DSSCs. Clearly, more extensive measurements on the fully packaged DSSC (including electrodes) are required in future work.

2.Result and discussion

The FDTD (Yee’s FDTD algorithm) technique was chosen from among the various available methods to report our results. This modeling technique is applied to solve and represent Maxwell’s equations over a grid-based domain in the differential form. Given that the FDTD simulation calculates the magnetic (h) and electric (e) fields everywhere as they evolve in time in the computational domain, it is straightforward to simulate and calculate the propagation of electromagnetic light field by using this model ³⁶. In the simulation technique, the results of TiO₂ and Au optical constants were taken from the reports of ³⁷ and ³⁸, individually. We chose three GNPs embedded in TiO₂ thin layer films using the Lumerical FDTD simulation technique. The mesoporous TiO2 active layer thickness was used as 100 nm, depending on Shanmugam’s experiment report ³⁹. Also, choosing this specific thickness of the TiO₂ layer in this simulated study is to decrease the simulation time and space of the PC drive.

The monitors in the simulation were located at proper places to precisely calculate the absorbance (A), reflectance (R), and transmittance (T). In the z-axis direction, perfectly matched layer (PML) absorbing boundary conditions were used on the upper and lower boundaries, while periodic boundary conditions (PBC) were used on both sides for the x- and y-axis. For the structure’s dimensions under simulation, we selected a length of 0.1 μm, a width of 0.1 μm, and a height of 1 μm for each shape. The Lumerical FDTD Solution was performed over the visible light region in the solar spectrum. This FDTD simulation software was used to calculate the absorption rate as a function of the visible wavelength for a flat spectrum. This was done automatically by means of continuous wave (CW) normalisation in FDTD, and the visible sunlight was modeled with a source of a plane wave. The calculation of power absorption was performed by solving Maxwell’s equations, i.e., the absorbed power L (r→λ) per unit volume at each wavelength. In this study, we theoretically investigated the effect of introducing metallic Ag nanoparticles in thin-film CuPc on their optical absorption efficiency.

The combinations of NP shapes in the absorber layer were studied to explore the effect of nanostructures on the absorption efficiency of the TiO₂ layer. Moreover, different sizes of NPs were investigated to exploit the ultimate efficiency potential in this simulation. The optical properties of TiO₂ and star-shaped GNP@TiO₂ thin layer in the visible spectral range of 300 to 800 nm were then studied.

Figure 1 shows the effect of the size of GNPs on the reflection spectra of embedded GNP@TiO₂ thin films with star shapes. Here, r represents the radius of the GNPs. It is clear from the figure that NPs of different sizes have different effects on the TiO₂ reflection spectra.

Figure 1 Reflection spectra of TiO₂ layer with different size of Au nanoparticles. 

Similarly, it is evident from Fig. 2 that GNPs of different sizes have different effects on the TiO₂ thin film transition spectra. Furthermore, the absorption spectra of GNP@TiO₂ thin films are significantly enhanced compared to those of pristine TiO₂ thin films, as shown in Fig. 3. This is clearly noticeable in the visible wavelength range of 350 to 700 nm. The results are close and comparable to the nano-star absorption spectrum of a known experimental reference ³⁵. The wide range and the multiple spectral peaks are because the gold nano-star particles have two plasmon resonance modes. One of them being localized at the range of 375 nm to 525 nm in the visible spectrum due to central core dipolar resonance of the GNPs. On the other hand, broad absorption spectra of star-shaped GNPs between 550 to 775 nm due to localized plasmon phenomenon at the tips and edge of GNPs. Rodriguez et al. suggested that the number of branches is of minor importance for determining the red-shifted band’s spectral position ^34,40.

Figure 2 Transition spectra of TiO₂ layer with different size of Au nanoparticles. 

Figure 3 Absorption spectra of TiO₂ layer with different size of Au nanoparticles. 

In this simulation study, the effect of the size of NPs on the amount of scattered light was investigated with various sizes of GNPs. As shown in Fig. 4, the different sizes of GNPs have different scattering range of the visible spectrum. Gold nanoparticles with a radius of 85 nm were seen to have a broader and maximum scattering spectrum compared to the other sizes. The different sizes of GNPs have different absorption spectra in the visible wavelength range of 300-800 nm, as shown in Fig. 5. This investigation revealed that the change in the size of the particles from r = 85 nm to r = 15 nm gradually reduces the absorption spectrum.

Figure 4 Scattering spectra of different size of Au nanoparticles. 

Figure 5 Absorption spectra of different size of Au nanoparticles. 

Bloch Boundary Conditions (BBCs) are similar to PBCs and are essentially required for a phase change across each period. The BBCs for a plane wave source were set at a non-zero injection angle. However, the zero-injection angle refers to the normal incidence of light on the layer of TiO₂ thin film.

To demonstrate the effect of a non-zero injection angle source on the improvement in absorption, a volume of the simulation was selected with a length of 0.1 μm, a width of 0.1 μm, and a height of 1 μm. It was evident that by increasing the plane wave angle injection source, light absorption significantly increased in the GNPs@TiO₂ thin film, as shown in Fig.8. However, in the case of reflection of light, the changes were not considered in GNPs@TiO₂ thin-film except for the injection angle of 40 that showed an increase, as can be seen in 6. On the contrary, it is clear from Fig. 7 that the decreasing light transition above 450 nm of wavelength with increasing in the angle of injection source. It is worth mentioning that at the light source injection angle of 70 absorption reaches almost 100% between 450≤λ≤800 nm in GNPs@TiO₂ thin film. This implies that the best injection angle to achieve high performance of DSSC devices based on embedding GNPs on TiO₂ thin film is 70.

Figure 6 Reflection of Au@TiO₂ thin layer of non-zero injection angle source. 

Figure 7 Transition of Au@TiO₂ thin layer of non-zero injection angle source. 

Figure 8 Absorption of Au@TiO₂ thin layer of non-zero injection angle source. 

3.Conclusion

Increased optical absorption of a TiO₂ semiconducting layer by embedding star-shaped GNPs in DSSCs was verified. A simulation was also performed to interpret the improvement of photocurrent by means of FDTD solution. The effects of the size of GNPs on light absorption and non-zero injection angle on the TiO₂ layer were presented. The investigation of the size of GNPs has shown that the best optimum size for absorption is GNPs with a radius of 85 nm, with an injection angle of 70. This has revealed that these GNPs have multiple plasmon resonances resulting in polarization-dependent scattering with multiple spectral peaks, which correspond to the star-shaped structure’s tips and branches. The quantum of light scattered and absorbed by the various sizes of GNPs, along with their effects, was also presented. This study indicates that the size of NPs in TiO₂ thin film influences the level of light scattering and absorption. It is believed that DSSC with star-shaped GNPs embedded TiO₂ layer records more PCE than traditional DSSC. Future research will focus on extending the model to a full DSSC package. Coupling of the optical model to an electrical charge transport model would enable a complete DSSC device optimization.

Conflict of Interest

The authors declare no conflict of interest.