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Multiscale Science and Engineering

, Volume 1, Issue 2, pp 161–166 | Cite as

Geometric Effect of Grating-Patterned Electrode for High Conversion Efficiency of Dye-Sensitized Solar Cells

  • Hee Chul Lee
  • Wooju Lee
  • Jun Hyuk Moon
  • Dongchoul KimEmail author
Original Research
  • 142 Downloads

Abstract

Photovoltaic devices that convert solar energy into electrical energy are a promising solution to resolve environmental problems the world is facing today. Among the various photovoltaic system, dye-sensitized solar cells (DSSCs) has been regarded as a new generation of the photovoltaic device due to the low cost and simple fabrication process. However, the current design of DSSCs shows insufficient conversion efficiency. To solve this problem, we increase the optical path length by trapping the incident light using a diffraction grating with high reflectance. We numerically investigate the effect of geometric parameters on the reflectance of diffraction gratings in DSSC system. Based on the simulation results, we propose an optimized geometry of diffraction grating that reflects the outgoing light and traps the incident light. The optimized geometry of the diffraction grating increase in the reflectance about 80% when it is compared to that without the diffraction grating.

Keywords

Dye-sensitized solar cell Diffraction grating Optics simulation Reflectance 

Introduction

Dye-sensitized solar cell (DSSC) is one of the simplest systems of the photovoltaic devices because it composed of only electrodes, consist of four main components, namely, photo-electrode, counter-electrode, dye, and electrolyte. The photo-electrode generally employs TiO2 due to their high surface area that maximizes dye loading and high chemical stability [1, 2, 3, 4, 5, 6, 7]. Although TiO2-based DSSCs have various advantages such as low cost, simple fabrication process and feasibility of large-scale production [8, 9, 10], the lower conversion efficiency as compared to the other photovoltaic devices based on silicon and GaAs still remains challenging issue [11, 12].

In order to improve the lower conversion efficiency, the amount of light absorbed by the dye should be increased. There have been many efforts to increase the optical path length of the light in the electrode by trapping the incident light. As the optical path length of the light is increased, the amount of the optical energy absorbed by the dye must be increased. A quasi-solid-state gel electrolyte has been proposed to reflect the light and increase the optical path length [13, 14]. The high reflectance of the quasi-solid-state gel reflects the transmitted light that passes through the electrode back into the electrode. In the same way, the optical path length can be increased by attaching the high reflective film on the counter electrode [15, 16]. These methods can increase the optical path length of the incident light but there is some energy loss in the electrolyte. To resolve the energy loss in the electrolyte, the electrode containing a micro-tube structure has been developed which enhances the optical path length by scattering the incident light in the electrode [17]. However, the electrode with the micro-tube structure is hard to fabricate and it not meet the purpose of DSSCs.

Diffraction gratings have become one of the solutions to effectively enhance the optical path length for the high conversion efficiency without energy loss. To design the optimal geometry of the diffraction grating with respect to the materials employed in the DSSCs, the geometric effects on the reflectance of diffraction grating should be fully understood. The diffraction grating has been studied to increase the absorbance of the incident light for the Si-based standard solar cells [18, 19, 20, 21, 22]. These studies ignored the geometric effects of the diffraction grating on the optical path length and only focused on the enhancement of the absorption of the incident light [18, 19, 20]. There are few studies that increase the optical path length by using the diffraction grating in the standard solar cells [21, 22]. However, the optimized design of the diffraction grating of the standard solar cells does not valid to the DSSCs systems due to the different selection of the electrode and the electrolyte. A recent study proposed the DSSC system that employs the diffraction grating to improve the conversion efficiency [23, 24, 25]. However, they only focused on the methods of fabricating diffraction gratings, not the optimal design of diffraction gratings.

In this study, we calculate reflectance based on a previously fabricated design of the diffraction gratings by using a numerical simulation. The reflectance of the non-optimized diffraction grating is around 10% when the wavelength of the incident light is selected to be a maximum absorbance–wavelength of the dye. In this study, we present the effect of geometries (e.g. pitch, depth, filling factor and slanted angle) of diffraction gratings on reflectance at the maximum absorption wavelength of dye with consideration of electrolyte. The interference of transmitted light with respect to geometries of diffraction gratings is also analyzed to understand the high reflectance phenomenon.

Method

In order to investigate the effect of diffraction gratings on the reflectance at the maximum absorbance-wavelength of dye with consideration of electrolyte, a wave-optic simulation is carried out with respect to geometries of diffraction gratings using commercial software (COMSOL Multiphysics 5.0; Comsol, Inc.). The Maxwell’s equations are solved to calculate the electromagnetic field around the diffraction grating. Figure 1a shows the absorbance of N-719 dye having maximum absorbance-wavelength at 540 nm. Figure 1b represents a schematic illustration of the simulation model. The geometries of diffraction gratings are defined by geometric parameters including pitch (P), depth (D), filling factor (w/P) and slanted angle (\(\theta\)). The filling factor is the ratio of grating width to pitch. A transverse electric (TE: electric field direction parallel to the pattern lines) polarized light having 540 nm of wavelength (λ) is incident from the bottom to the top of the simulation domain. The refractive index of TiO2 electrode is 2.03 [26]. The refractive index of the electrolyte is changed from 1 to 1.35 which is regarded as the refractive index of iodine electrolyte [27]. Because we only focus on the reflectance at electrode–electrolyte interface, the energy loss by absorption in TiO2 electrode is not considered in this simulation, the sum of reflectance and transmittance is 100%. From the simulations, we measure the reflectance on the bottom and transmittance on the top of the simulation domain. We analyze the reflectance with respect to geometric parameters to derive optimal geometric design for the highest reflectance. We also analyze the transmitted light according to geometric parameters to understand the high reflectance phenomenon.
Fig. 1

The schematic illustration of dye-sensitized solar cells (DSSC) and simulation model. The incident light is path through the DSSC system from bottom to top. The dye attached on the electrode enhance the absorbance of the light. a Absorbance spectrum of N-719 dye attached on the electrode. b Geometric parameters of the simulation model

Results and Discussions

The effect of pitch of diffraction gratings on the reflectance

Figure 2 shows the reflectance of the diffraction grating as a function of the normalized grating pitch. Other geometric parameters including the depth (D), the filling factor (F), and the slanted angle (θ) were set to be 800 nm, 0.5, and 90° respectively. The pitch is normalized by the wavelength of incident light (λ) which is same with the maximum absorbance–wavelength of dye to consider absorbance of dye with respect to wavelength. As shown in Fig. 2a, optimal pitch (P) for maximum reflectance is changed in inverse proportion to the refractive index of the electrolyte (n1), \(P /\lambda = 1/n_{1} .\) The maximum reflectance at the optimal pitch is decreased as the refractive index of the electrolyte is increased. The reflectance can be increased up to 100% only when the refractive index of electrolyte is unity.
Fig. 2

The effect of pitch of diffraction gratings on reflectance and the analysis of diffracted light: a the reflectance with respect to normalized grating pitch when refractive index of electrolyte is from 1.00 to 1.35. b The directions of transmitted lights at the interface region 2 and region 3 on the condition of \(P /\lambda = 1 /n_{1} .\)c The directions of transmitted lights at the interface region 2 and region 3 on the condition of \(1 /n_{1} < P /\lambda < 2 /n_{1}\)

In order to understand the high reflectance phenomenon, we analyze the interference of diffracted light. The intensity of the diffracted light at the interface is related with the refractive indices of the electrode and the electrolyte. Because the refractive index of electrode is always higher than that of electrolyte, the intensity of reflected light is always higher compared to transmitted light at the electrode–electrolyte interface. In this study, the interference of transmitted light is analyzed. Figure 2b presents the direction of transmitted light according to diffraction orders at the interface of region 2 and region 3 on the condition of \(P /\lambda = 1/n_{1} .\) The maximum diffraction orders are ± 1, which means transmitted light has been diffracted with 3 directions. As shown in Fig. 2b, the direction of transmitted lights having ± 1st order diffractions is parallel with the interface of region 2 and region 3. The lights having ± 1st order diffractions only propagate laterally not forward. Only the light having 0th order diffraction propagate forward. Figure 2c presents the direction of transmitted light according to diffraction orders at the interface of region 2 and region 3 on the condition of \(1 /n_{1} < P /\lambda < 2 /n_{1} .\) The maximum diffraction orders are ± 1, which means transmitted light has been diffracted with 3 directions. As shown in Fig. 2c, all transmitted lights propagate forward. The amount of propagated light reached at the interface of region 3 and region 1 on the condition of \(P /\lambda = 1 /n_{1}\) is smaller than that on the condition of \(1 /n_{1} < P /\lambda < \lambda /n_{1} ,\) even smaller than that on the condition of \(P /\lambda < 1 /n_{1}\) or \(2 /n_{1} < P /\lambda\).

The effect of depth of diffraction gratings on reflectance

Figure 3a shows the effect of depth of diffraction gratings on reflectance. Other parameters such as pitch (P), filling factor (F), and slanted angle (θ) were constant \(\lambda /n_{1}\) nm, 0.5, and 90°, respectively. Depth is normalized by wavelength (λ) of incident light that is same as maximum absorbance-wavelength of dye to consider absorbance of dye with respect to wavelength. As shown in Fig. 3a, regardless of the refractive index of the electrolyte, optimal depth (D) for maximum reflectance is regarded as 1.5 λ. The maximum reflectance at optimal depth is decreased as the refractive index of the electrolyte is increased. 100% of maximum reflectance can be reached only as the refractive index of the electrolyte is unity. In order to understand the high reflectance phenomenon, we analyze the interference of diffracted light. Figure 3b presents the phase difference of two lights passing through electrode (bold yellow line) and electrolyte (bold blue line) on the condition of \(D /\lambda = 1.5.\) Only the light having 0th order diffraction propagates forward due to optimal pitch. The phases of two lights passing through the electrode and the electrolyte are opposite-phase at the interface of region 3 and region 1. The light passing through electrode has been transmitted and diffracted in 3 directions at the interface of region 3 and region 1. The lights having ± 1st orders diffraction (bold red line) propagate laterally and interfere with light passing through the electrolyte. As shown in Fig. 3c, if the lights passing through the electrode and the electrolyte reach with opposite-phase at the interface of region 3 and region 1, the transmitted light having ± 1st orders diffraction destructively interferes with the light passing through the electrolyte. Figure 3d describes the interference of reflected light and transmitted light. The light passing through electrode has been reflected and diffracted with 5 directions at the interface of region 3 and region 1. The reflected light having ± 1st orders diffraction (bold green line) might interfere with the transmitted light having 0th order diffraction (bold yellow line) at the interface of region 3 and region 1. In other words, the transmitted lights disappear, which means high reflectance, due to destructive interference on the conditions \(P /\lambda = 1 /n_{1} ,D /\lambda = 1.5, F = 0.5, \theta = 90^\circ .\)
Fig. 3

The effect of depth of diffraction gratings on reflectance and the analysis of diffracted light: a the reflectance with respect to normalized grating depth when refractive index of electrolyte is from 1.00 to 1.35. b The phase difference of two lights passing through electrode (bold yellow line) and electrolyte (bold blue line) at the interface region 3 and region 1 on the condition of \(D /\lambda = 1.5.\)c The destructive interference of two lights, the one passes through electrolyte (bold blue line) and the other propagates laterally at the interface region 3 and region 1 (bold red line) on the condition of \(D /\lambda = 1.5.\)d The destructive interference of two lights, the one passing through electrode transmits at the interface region 3 and region1 (bold yellow line) and the other reflecting at the interface region 3 and region1 has ± 1st orders diffraction (bold green line) on the condition of \(D /\lambda = 1.5\) (color figure online)

The effect of filling factor of diffraction gratings on reflectance

Figure 4a shows the effect of filling factor of diffraction gratings on reflectance. Other parameters such as pitch (P), depth (D), and slanted angle (θ) except filling factor (F) were constant (\(\lambda /n_{1}\) nm, 1.5 λ nm, and 90°, respectively) and chose based on previous simulation results and researches. Filling factor is defined by the ratio of grating width to pitch. When the refractive index of the electrolyte is less than 1.25, the two maxima are observed around 0.25 and 0.5, respectively. The first peak of the reflectance is shifted to the right as the refractive index of the electrolyte increases. When the refractive index of the electrolyte is increased over 1.25, two peaks of the reflectance are merged into a single maximum and the maximum reflectance is decreased. The simulation shows that a complete reflectance can be reached only as the refractive index of the electrolyte is unity. In order to understand the high reflectance phenomenon, we analyze the amount of destructive interference of diffracted lights. Figure 4b presents the amount of difference of two lights passing through electrode (bold yellow line) and electrolyte (bold blue line) on the condition of F =0.1 or smaller than 0.1. The transmitted light having ± 1st orders diffraction (bold red line) propagates laterally at the interface of region 3 and region 1 and interferes with the light passing through the electrolyte. The amount of light passing through the electrode, which contributes to the amount of transmitted light interfering with light passing through the electrolyte, is much smaller than that of light passing through the electrolyte. Therefore, the amount of destructive interference between transmitted light having ± 1st orders diffraction and light passing through electrolyte is smaller compared to the condition of F = 0.5. Likewise, the amount of destructive interference on the condition F is bigger than 0.5 is much smaller compared to the condition of F = 0.5. The amount of destructive interference between transmitted light having ± 1st orders diffraction and light passing through electrolyte on the condition of F = 0.5 is greater compared that F is smaller than 0.1 or bigger than 0.5.
Fig. 4

The effect of filling factor and slanted angle of diffraction gratings on reflectance and the analysis of diffracted light: a The reflectance with respect to filling factor when refractive index of electrolyte is from 1.00 to 1.35. b The amount of two lights passing through electrode (bold yellow line) and electrolyte (bold blue line) on the condition of F = 0.1 or smaller than 0.1. c The destructive interference of two lights, the one passes through electrolyte (bold blue line) and the other propagates laterally at the interface region 3 and region 1 (bold red line) on the condition of F = 0.1 or smaller than 0.1. d The reflectance with respect to slanted angle when refractive index of electrolyte is from 1.00 to 1.35 (color figure online)

The effect of slanted angle of diffraction gratings on reflectance

Figure 4c shows the effect of slanted angle of diffraction gratings on reflectance. Other parameters such as pitch (P), depth (D), and filling factor (F) except slanted angle (θ) were constant (\(\lambda /n_{1}\) nm, 1.5 λ nm, and 0.5, respectively) and chose based on previous simulation results. As shown in Fig. 4c, the maximum reflectance is observed at 90° of slanted angle when the refractive index of electrolyte is less than 1.25. The maximum reflectance at the optimal slanted angle is decreased as the refractive index of the electrolyte is increased. A complete reflectance can be obtained only as the refractive index of the electrolyte is unity. Based on analysis of interference of diffracted light, the amount of destructive interference on the condition θ = 90° is greater than any other conditions.

The improvement of reflectance compared to previous researches

Figure 5 shows calculated reflectance according to wavelength on the condition that electrolyte and dye are iodine redox whose refractive index is 1.35 and N-719 whose maximum absorbance-wavelength is around 540 nm. The purple line shows calculated reflectance of optimal gratings \((P = 400 {\text{nm}},D = 810 {\text{nm}}, F = 0.5, \theta = 90^\circ )\) determined by simulation results. The blue and green lines show calculated reflectance of the diffraction grating in the previous researches, Kim [23] and Na [24]. Due to the selective reflectance of the diffraction grating what we designed, the transparent characteristics of DSSC make them suitable for outdoor applications, particularly for use as building integrated photovoltaic devices, where power supplying device replace conventional building materials such as window glass.
Fig. 5

The reflectance according to wavelength with optimal grating (purple line), without grating (black line), with diffraction grating developed by Kim [23] and Na [24] (color figure online)

The black line shows calculated reflectance of without gratings. The optimal gratings have maximum reflectance, 83%, at 540 nm of wavelength. The reference 1, 2 and without grating have only 8, 10 and 4% reflectance, respectively. The improvement of calculated reflectance with optimal grating at maximum absorbance–wavelength of N-719 dye is around 925, 783 and 1975% compared to previous researches and without gratings.

Conclusion

In summary, we have demonstrated an effective design of diffraction gratings of DSSCs consist of TiO2 photo-electrode, iodine redox electrolyte, and N-719 dye. The optimal diffraction gratings can enhance the reflectance of incident light, which allows elongation of the optical path length of incident light. As a result, as the amount of light absorbed by the dye is increased, the conversion efficiency is improved. The geometries of diffraction gratings such as pitch, depth, filling factor, and slanted angle have an effect on the diffraction and interference of incident light, respectively. The pitch determines the number and the direction of diffracted light. The depth determines the constructive or the destructive interference of diffracted light. The filling factor can affect the amount of constructive or destructive interference of diffracted light. The optimal diffraction gratings for reflectance is that \(P = 400 {\text{nm}},D = 810 {\text{nm}}, F = 0.5, \theta = 90^\circ\) on the condition of TiO2 photo-electrode, iodine redox electrolyte, and N-719 dye. The reflectance with optimal diffraction gratings is improved by up to 925, 783, and 1975% compared to previous researches and without gratings, respectively. It is believed that our work presented here offers insight and guidance to the design of diffraction gratings of various solar cells for high conversion efficiency.

Notes

Acknowledgements

This research was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea, funded by the Ministry of Science and ICT (NRF-2016R1D1A1A09916859).

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Copyright information

© Korean Multi-Scale Mechanics (KMSM) 2019

Authors and Affiliations

  • Hee Chul Lee
    • 1
  • Wooju Lee
    • 1
  • Jun Hyuk Moon
    • 2
  • Dongchoul Kim
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringSogang UniversitySeoulSouth Korea
  2. 2.Department of Chemical and Biomolecular EngineeringSogang UniversitySeoulSouth Korea

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