Simple dynamic energy core equivalent rays method to design freeform surface for extended source

Abstract

A simple method is proposed to design freeform surface for Lambertian extended source. In this method, it can take advantage of the designing method for point source via substituting each incident ray with a dynamically calculated equivalent ray. For each facet on the freeform surface, the equivalent ray emits from the energy weighted average-emitting-position for the corresponding incident beam, and redirects into the direction which is determined by a source-to-target mapping. The results of the designing examples show that the light distributions’ uniformities can be improved by this method, e.g., even the improvement of 59% can be achieved.

Keywords

nonimaging optics / illumination design / light emitting diodes (LEDs)

1 Introduction

Dye-sensitized solar cells (DSSCs) developed by Grätzel have attracted considerable interest as a low-cost alternative to silicon solar cells [1]. However, it is necessary to further improve the energy conversion efficiency and reduce the cost of DSSCs for successful commercialization.

One important way to improve the efficiency of DSSC is broadening the absorption spectra of dyes. Many attempts have been carried out, including tandem DSSCs, hybrid DSSCs, and co-sensitized DSSCs [2-14]. The tandem and co-sensitized methods improved the efficiencies of DSSCs to a certain extent. However, the problem is that tandem DSSCs require a strict adjustment of the transmittance of the top cells and restrictions on the short circuit current density (J_SC) and open circuit voltage (V_OC) of the two cells [2]. Although co-sensitized DSSCs avoid the disadvantages of tandem DSSCs, undesirable competitive adsorption and interactions between dyes can easily cause a decrease in the conversion efficiency of DSSCs [3]. To solve these problems, a new type of hybrid DSSC with a multilayer photoanode prepared by a simple and low-cost film-transfer technique has been developed. The results showed that the hybrid structure achieved a panchromatic response and a superposed J_SC by using two complementary dyes AP and ZnPc without the significant decrease in V_OC.

Semiconductor oxide photoelectrode is known to be one of the key components that affect the energy conversion efficiency of DSSCs. TiO₂ is a typical semiconductor oxide material for photoelectrodes. However, oxygen deficiencies found in the pure TiO₂ crystal structure may cause the shortened lifetime of DSSCs [15-18]. To solve this problem, we have developed a DSSC system based on N-doped TiO₂, which successfully achieved high energy conversion efficiency [19]. In this paper, a simple method was used to prepare the needle-like N-doped TiO₂ nanocrystals from commercial TiO₂ powders. The DSSC fabricated by the N-doped photoanode prepared by our approach achieved a high conversion efficiency of 10.10%, which is much higher than the value of 8.90% for the undoped-DSSC. Furthermore, the electron injection, electron transport time and electron lifetime were studied and the details will be available in a future paper.

To reduce the cost of DSSCs, it is important to explore substitutes for Pt to make DSSCs more competitive among various photovoltaic devices. One approach is to replace Pt with abundant, non-precious materials not susceptible to price inflation during high demand. Carbon materials attract the most attention due to their high catalytic activity, low cost, and excellent corrosion resistance against the redox couple among non-Pt catalytic materials. We synthesized a well-ordered mesoporous carbon (Com) with a modified one-pot chemical method. The DSSC using Com counter electrode (CE) yielded an efficiency of 7.50%, which is similar to the value of DSSCs using Pt CE (7.47%). We also compared the performance of several kinds of carbon materials used as CE catalytic materials with the traditional Pt CE in the DSSC system. They activated carbon (Ca), carbon black (Cb), and multi-wall carbon nanotube (MWCNT, Cn).

2 Experiment

2.1 Fabrication of DSSCs

Dye-sensitized hybrid electrodes (area: 0.16 cm²), N-doped and undoped TiO₂ electrodes (area: 0.16 cm²) were assembled with platinized counter electrodes.

Photoanodes for the carbon CEs were prepared from the TiO₂ films (8 μm, area: 0.2 cm²) of 20 nm-sized particles (Degussa, Germany) followed by a sintering process at 500°C and then cooling to 80°C. The TiO₂ films were immersed in a 5 × 10^-4 M solution of N719 dye (Solaronix SA, Switzerland) in acetonitrile/tert-butanol (v∶v= 1∶1) for 16 h.

The photoanodes and corresponding CEs were assembled to form a solar cell by sandwiching a redox $({\mathrm{I}}^{-}/{\mathrm{I}}_{\mathrm{3}}^{-})$ electrolyte solution. The electrolyte was composed of 0.03 M I₂, 0.06 M LiI, 0.6 M 1-butyl-3-methylimidazolium iodide (BMII), 0.1 M guanidinium thiocyanate, and 0.5 M 4-tert-butylpyridine (TBP) in acetonitrile.

2.2 Characterization

The UV-Vis-NIR absorption spectra were recorded using UV–550 (Japan) UV–Vis spectrophotometers. The current-voltage curves were conducted by a Keithley digital source meter (Keithley 2601, USA). The intensity of the incident light was 100 mW·cm^-2. The instrument was equipped with a 300 W solar simulator (Solar Light Co., INC., USA) that served as the light source. The photon flux was determined by a power meter (TES–1333R, Taiwan) and a calibration cell (BS–520, s/n 019, Bunkoh-Keiki Co., Ltd., Japan).

3 Results and discussion

3.1 Hybrid DSSC

The new type of hybrid DSSC with a multilayer photoanode developed by our group was prepared by a simple and low-cost film-transfer technique. The structure of the multilayer photoanode consists of an adhesive TiO₂ bottom layer/Dye 1/, a transferred porous P25 layer/Dye 2/, and a scattering layer (ST41). The sintered adhesive bottom layers that lie on the F-doped SnO₂ glass (prepared by the doctor-blade technique) were first sensitized with Dye 1 (AP) [20]. The hybrid photoanode was fabricated using the bottom layer sensitized with Dye 1 (AP) to transfer the porous P25/ST41 scattering layer under friction [21,22]. After compression, the obtained anode was then dipped into the solution of Dye 2 (ZnPc).

AP and ZnPc are two model dyes with independent spectral absorption in the visible and near-IR (NIR) region. Figure 1 shows the absorption spectra of AP, ZnPc, and hybrid of AP/ZnPc absorbed onto the TiO₂ films. The absorption band in the range of 300-580 nm is assigned to AP. On the other hand, the absorption band of ZnPc is observed to be between 500 and 800 nm. The absorption spectra of the hybrid photoanode showed the sum adsorption of the AP and ZnPc as comparable to a panchromatic response in the range of 300-800 nm. Through an investigation of photoelectrical performances, the J_SC of the hybrid cell was found to be 10.73 mA·cm^-2, almost equivalent to the sum value of 10.74 mA·cm^-2 for the AP cell (8.65 mA·cm^-2) and ZnPc cell (2.09 mA·cm^-2). The V_OC of the hybrid cell was between the values of two single devices, but closer to the larger one. The photoelectric characteristics can be interpreted in Eqs. (1) and (2):

(1)$$J_{\mathrm{S}\mathrm{C}\mathrm{h}\mathrm{y}\mathrm{b}\mathrm{r}\mathrm{i}\mathrm{d}}=J_{\mathrm{S}\mathrm{C}\mathrm{1}}+J_{\mathrm{S}\mathrm{C}\mathrm{2}},$$

(2)$$V_{\mathrm{O}\mathrm{C}\mathrm{2}}<<V_{\mathrm{O}\mathrm{C}\mathrm{h}\mathrm{y}\mathrm{b}\mathrm{r}\mathrm{i}\mathrm{d}}<V_{\mathrm{O}\mathrm{C}\mathrm{1}}.$$

Fig.1 UV-Vis absorption spectra of AP, ZnPc, hybrid of AP/ZnPc absorbed onto the TiO2 films

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The developed film-transfer technique is also simple, convenient, low-cost and highly efficient. It is very easy to fabricate the multilayer-structured hybrid photoanode by using three or more dyes to further broaden the absorption spectrum of DSSC, thus breaking restrictions on the semiconductors and dyes in conventional DSSCs.

3.2 N-doped photoanode

N-doped and undoped photoanodes were prepared by a simple method from commercial TiO₂ powders. Commercially-available ST-01 (Ishihara Sangyo Kaisha, Ltd.) was used to prepare N-doped TiO₂ through a simple dry method. In brief, nanocrystalline N-doped ST-01 was prepared by sintering pure TiO₂ powders at 500°C for 3 h under dry N₂ and NH₃ gas flow. For comparison, pure ST-01 was also treated under the same conditions without nitrogen source and the obtained sample was denoted as undoped ST-01. The screen-printable N-doped and undoped TiO₂ colloidal pastes were prepared according to the procedure developed by our group [23]. A screen-printing technique was used to fabricate the films. Then, the obtained films were sensitized with N719.

The photoelectrical performances of DSSCs based on the N-doped and undoped TiO₂ electrodes are shown in Table 1. The DSSC fabricated by the N-doped photoanode prepared by our approach achieved a high conversion efficiency of 10.10%, which is much higher than the value of 8.90% for the undoped DSSC. Our results show that the N-doped DSSCs possess higher photocurrent and enhanced open circuit photovoltage. Finally, the synergetic effect of higher dye uptake, faster electron transport and higher photovoltage contributes to a higher conversion efficiency of N-doped DSSCs. The details will be shown in a future paper.

Tab.1 Performance of the DSSCs based on N-doped and undoped TiO2 electrodes

titania electrode	VOC/mV	JSC/(mA·cm-2)	FF/%	η/%
N-doped ST-01	778±10	19.05±0.07	0.68±0.01	10.1±0.2
undoped ST-01	756±13	17.40±0.10	0.68±0.01	8.9±0.3

Notes: FF: fill factor; η: conversion efficiency

3.3 Carbon CE

Among the four kinds of carbon materials, Ca, Cb, and Cn were purchased. The Com was synthesized with a modified one-pot chemical method [24,25]. The experimental details will be shown in another paper. The transmission electron microscopy (TEM) images in Fig. 2 showed that the Com powder was well-ordered and built by rows of carbon walls with accumulated small-sized carbon particles. Figure 2(b) showed the cross-section of the ordered carbon walls presenting a mesoporous structure. The well-ordered mesoporous structure provide the Com a large surface area. Such a configuration was beneficial to diffuse the redox couple in the electrolyte.

Fig.2 TEM images of the well-ordered Com. (a) Top view; (b) cross-section

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We investigated the impact of the sprayed carbon paste sprayed onto the performance of carbon CEs and determined the proper spray time duration. Under optimal conditions, the energy efficiencies of the DSSCs using the four carbon CEs and traditional Pt CE are 6.57% (Ca), 6.25% (Cb), 7.02% (Cn), 7.50% (Com) and 7.47% (Pt). The I-V curves are shown in Fig. 3. We conclude that the Com CEs show excellent catalytic activity for triiodide reduction among the four carbon materials, which can match the performance of Pt CE.

Fig.3 I-V curves for DSSCs using the four kinds of CEs and the Pt electrode

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4 Conclusions

In conclusion, we successfully developed a new type of hybrid photoanode and the N-doped photoanode for high-efficient DSSCs as well as the carbon CEs for low-cost DSSCs. The hybrid DSSCs with multilayer photoanodes by the film-transfer technique achieved a panchromatic response and a superposed J_SC by using two complementary dyes without the significant decrease in V_OC.

The DSSC fabricated by the N-doped photoanode of our simple approach achieved a high conversion efficiency of 10.10%, which was much higher than the value of 8.90% for the undoped-DSSC. Moreover, N-doped DSSCs possess higher photocurrent due to a higher dye uptake. Furthermore, an enhanced open circuit photovoltage was obtained in N-doped DSSCs. Therefore, N-doped TiO₂ nanocrystals prepared by our approach are ideal semiconductor materials for DSSCs.

We synthesized a well-ordered Com with a modified one-pot chemical method. Com CE was used in the DSSC system, as well as other three kinds of carbon CEs. The high performance of DSSC using Com CE yields an efficiency of 7.50%, comparable to that of Pt CE (7.47%). This demonstrates its promising potential for replacing Pt.

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Acknowledgements

This work was supported by the National Key Basic Research Program of China (Nos. 2015CB351900, 2011CB301902 and 2011CB301903), the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (No. 2012BAE01B03), the Science and Technology Planning Project of Guangdong Province (No. 2011A081301003), the Opened Fund of the State Key Laboratory on Integrated Optoelectronics (No. IOSKL2012KF09), the High Technology Research and Development Program of China (Nos. 2011AA03A112, 2011AA03A106 and 2011AA03A105), the National Natural Science Foundation of China (Grant Nos. 61307024, 61176015 and 61176059).

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