Full solar-spectrum power-generation system based on high efficiency and wide spectral splitter film and Fresnel lens

Based on high efficiency and wide spectral splitter film and Fresnel lens, we have theoretically investigated a full solar-spectrum power-generation system. Designed nano-multilayers are fabricated on Fresnel lens. Then short wavelengths (400 nm ~ 1100 nm) of solar-spectrum can be transmitted 95% to the solar cell, and long wavelengths (1100 nm ~ 2500 nm) of solar-spectrum can be reflected 90% and focused to the thermoelectric cell. This system can combine the efficiency of solar cells and thermoelectric cells to generate electricity across the entire solar spectrum. In theory, the limit for total conversion efficiency is η = 56.64%.


I. INTRODUCTION
Solar-energy conversion usually takes one of two forms: the quantum approach, which uses the large per-photon energy of solar radiation to excite electrons, as in photovoltaic cells, or the thermal approach, which uses concentrated sunlight as a thermal-energy source to indirectly produce electricity using a heat engine.
In a photovoltaic (PV) cell, solar photons with energies above the semiconductor's bandgap excite electrons into the conduction band, which diffuse to electrodes and generate current. In high-performance solar cells, charge separation and collection are very efficient. However, the quantum approach of PV cells places intrinsic limitations on single-junction conversion efficiency. Photon energy in excess of the bandgap is lost as heat, known as thermalization loss, and sub-bandgap photons are not absorbed at all, known as absorption loss. In silicon solar cells, thermalization and absorption losses account for approximately 50% of the incident solar energy [1]. In principle, these losses could be reclaimed by using this waste heat from the PV cell to power a secondary thermal cycle. Combinations of PV and thermal engines are predicted to have efficiencies greater than 60% [2], yet fail in practice because PV cells rapidly lose efficiency at elevated temperatures [3], whereas heat engines rapidly lose efficiency at low temperatures [4].
Thermionic energy converters (TECs) are less wellknown heat engines, which directly convert heat into electricity. A simple thermionic converter consists of a hot cathode and cooler anode separated by a vacuum gap. In the TEC cathode, fractions of the electrons have sufficient thermal energy to overcome the material's work function and escape into vacuum, generating current between the two electrodes. The thermionic current density is dictated by the cathode work function and temperature according to the Richardson-Dushman equation: , where C  is the cathode work function, C T the temperature and * C A the materials-specific Richardson constant [5]. Thermionic converters were first proposed and fabricated in the 1950s, with experimental conversion efficiencies eventually reaching 10-15% [5,6]. Both NASA and the Soviet space programme funded the development of TECs for deep-space missions and other applications requiring high-power autonomous generators, but the technology was never commercialized. Thermionic conversion's main challenges relate to the very high temperatures and substantial current densities required for efficient operation [7,8].
These years, there is an increasing need for hybrid technologies for solar power generation. Photon-enhanced thermionic emission (PETE) combines photovoltaic and thermionic effects into a single physical process to take advantage of both the high per-quanta energy of photons, and the available thermal energy due to thermalization and absorption losses [9,10]. Furthermore, the concept of solar thermophotovoltaic (STPV) system is introduced [11,12], in which an intermediate element is placed between the sunlight and the solar cell. The intermediate element includes a black absorbera material that can absorb the entire solar spectrumon the side that faces the Sun. When exposed to sunlight, the element heats up and generates thermal radiation that is emitted through the other side, which is directed towards the photovoltaic cell. The fundamental advantage of this design is that virtually allsolar energy could be converted into electricity. However, despite their conceptual simplicity, STPV devices have performed below expectations and efficiencies have struggled to reach 3.2%.
Solar spectral splitting is a strategy to optimize the extraction of exergy from sunlight through the separation of incident photons by energy levels (or wavelengths). This approach generally implements any combination of thermal, electrical, or chemical processes that can increase the efficiency of a device [13][14][15][16].
Concentrated solar photovoltaic and photo-thermal conversion strategies each have their unique benefits and disadvantages, and the limiting efficiencies of both strategies have been discussed extensively. In order to take advantage of both technologies simultaneously, hybrid converters have been of great interest. The design of a number of these converters have been reported [17][18][19][20].
In this article, we have theoretically investigated a full solar-spectrum power-generation system based on high efficiency and wide spectral splitter film and Fresnel lens, which can combine the efficiencies of solar cells and thermoelectric cells to generate electricity across the entire solar spectrum. The characteristic of our system is the high efficiency and wide spectral splitter film. For short wavelength from 400 nm to 1150 nm, the transmittance is above 95%. For long wavelength from 1150 nm to 2500 nm, the reflectance is above 90%.

II. PRINCIPLE
As shown in Fig. 1, it is the diagram of our full solarspectrum power-generation system. The splitter film is evaporated on the Fresnel lens. Therefore, short wavelengths (400 nm ~ 1100 nm) of solar-spectrum can be transmitted to the solar cell, and long wavelengths (1100 nm ~ 2500 nm) of solar-spectrum can be reflected and focused to the thermoelectric cell.
In the next sections, we shall further study the specific structure of the splitter film and Fresnel lens. A high efficiency and wide spectral splitter film is of great concern, and is difficult to design in technically and scientifically.

III. SPLITTER FILM
In this section, the theory of thin film optics (TFO) [21] is applied to design the splitter film, which can be used to design various functions of films. Based on FTO, we have studied quantum tunneling transparent conductive films [22] and anti-reflection nano multi-layers [23,24].
These kind of nano multi-layers can be fabricated by low cost techniques, for example magnetron sputtering, electron beam evaporation, and thermal deposition process. Commercial software based on TFO is widely used to guide the industrial production of optical film, such as optical film design on lenses or glasses. Full solar-spectrum is shown in Fig. 2. The dotted line is the solar spectrum at the top of the atmosphere, and the solid line is the solar spectrum at the sea level after being absorbed by H2O vapor and CO2.
In our system as shown in Fig. 1, the splitter film should have the following function, that short wavelengths (400 nm ~ 1100 nm) of solar-spectrum are transmitted, and long wavelengths (1100 nm ~ 2500 nm) of solar-spectrum are reflected.
In TFO design, low and high index materials are necessary to achieve the desired optical target. The materials should have low chromatic dispersity and no absorption. In this study, the low index material is MgF2, and the high index material is Ta2O5. It's worth noting that the other low index material (such as SiO2) and the other high index material (such as TiO2) can also be used to design the splitter film. Once the material is selected, the thickness of every layer will determine the optimized result. Encouragingly, these thicknesses can be obtained by optical target optimization simulation of Essential Macleod or other commercial software. In this work, the film design and following results are obtained by Essential Macleod. Firstly, in Edit Generate window of Targets button, optimization goals can be set, i.e. transmittance and reflectance at different wavelength with different weight coefficients. Secondly, in Optimac Parameters window, Merit Function Power and Maximum Number of Layers can be set. Thirdly, press Refine button, and then Essential Macleod can optimize the layer number and thickness to meet the pre-set targets. Here, the transmittance target from 400 nm to 1150 nm is set to be 99% with weight 2, and the transmittance target from 1150 nm to 2500 nm is set to be 1% with weight 1. Finally, the number of layers and every layer thickness in Table 1 are automatic optimization by Essential Macleod for three months. Optical target optimization simulation requires the knowledge of optical parameters of the materials. The refractive index N and extinction coeffificient K dependence on the wavelength (nm) for all the materials in this study can be obtained from the pioneer published works [24][25][26][27], as shown in Fig. 3. However, every different fabrication method with different condition will inflfluence the optical parameters of material, and then inflfluence the final designs. If researchers want to compare the experimental data with the theoretical results, they must obtain the optical property of every layer material in their experiment condition by ellipsometer.
Firstly, we should introduce the mathematical basics of energy transfer through the medium based on TFO. For the general case of assembly of q layers, the expression is where the subscripts i-s and o-s means the physical quantities at the input surface boundary and the output surface boundary, respectively. In addition, k0 is the wave where zin and zou are the impedances of the input port medium and the output port medium, respectively. The net irradiance I is defined as   Here we have ignored the magnetic effect, and the relative permeability of all above materials is assumed to be 1. However, there are many kinds of glass, for example white glass, electron-grade glass, and so on. Optical properties of these glasses are different. To simplify the problem, the substrate glasses in our following study are white glass. Generally, the relative permittivity of air is 1.
The detailed design of splitter film is in Table 1 of supplemental document by Essential Macleod, which has 189 layers of Ta2O5 and MgF2, and the total thickness is 13.76 μm. The substrate is glass, and the incidence medium is air. Therefore, the material of Fresnel lens should be glass, which will be studied in detail in the next section.
The transmittance and reflectance properties of the splitter film are obtained, as shown in Fig. 4. The blue and red dotted lines are transmittance and reflectance, respectively. The wavelength varies from 350 nm to 2500 nm. For short wavelength from 400 nm to 1150 nm, the transmittance is above 95%. For long wavelength from 1150 nm to 2500 nm, the reflectance is above 90%. Therefore, this design of splitter film with high efficiency and wide spectral can meet our requirement for the full solar-spectrum power-generation system.

IV. FRESNEL LENS
The above splitter film has high efficiency and wide spectral. However, in order to reduce the occlusion of incident light and enhance the light thermal effect with a small size of the system structure, a flat and focusing device is also required. A large solar cell can be placed at the flat side, and the small thermoelectric cell can be placed at the focusing side. Therefore, Fresnel lens can meet our requirements. In this section, we should use geometrical optics to design the Fresnel lens. Fresnel lens is widely used to concentration light because of its flat and focusing characteristics [28][29][30][31][32][33].
In our full solar-spectrum power-generation system, the Fresnel lens should present reflectance and focusing peculiarities. Therefore, the Fresnel lens uses concave surface design, and the previously mentioned splitter film is fabricated on the concave side. In addition, for geometrical optics the reflectance angle is independent of wavelength. Hence, the position of the reflected focal point depends only on the geometry. However, for more sophisticated applications (for example super-resolution imaging), we need to consider diffractive optics, i.e. Fresnel diffraction formula, to study Fresnel lens. As shown in Fig. 5, it is the diagram of design from concave lens to Fresnel lens. Sub-figure A is a concave lens (denoted as green pattern), which is a circle combined with the axis outside the paper 2D surface. Sub-figure B shows that the concave lens is divided into a lot rings, and each ring is removed from the part of the parallel plane (denoted as red pattern). Finally, the remaining parts constitute the Fresnel lens, as shown in sub-figure C. In geometrical optics, parallel plane cannot change the direction of light, nor can concentrate or diffuse light. Consequently, the remaining parts (in Fig. 5(C)) not only keep the reflectance and focusing peculiarities of concave lens (in Fig. 5(A)), but also has thinner structure, which can be easier to integrate smaller systems. Here we use Geometrical Optics module of COMSOL Multiphysics (a commercial software based on finite element method) to study the Fresnel lens and obtain the following results. For more accuracy requirement, aspheric concave surface should be used to design the Fresnel lens. However, considering the cost and the accuracy of our experimental system, the spherical concave surface is adopted to design the Fresnel lens, as shown in Fig. 6(A).
The radius of the spherical concave surface is 150 mm. The diameter and thickness of our Fresnel lens are 190 mm and 12.5181 mm, respectively. There are eight order reflectors, which are the 1 st reflector, the 2 nd reflector, the 3 rd reflector, etc., as denoted in Fig. 6(A). These reflectors are on a 5 mm thickness disk. The 1 st reflector is a concave disk with diameter 50 mm and thickness 2.098 mm. The 2 nd reflector is a concave doughnut with inner diameter 50 mm, outer diameter 70 mm, and thickness 2.0425 mm. The 3 rd reflector is a concave doughnut with inner diameter 70 mm, outer diameter 90 mm, and thickness 2.7686 mm. The 4 th reflector is a concave doughnut with inner diameter 90 mm, outer diameter 110 mm, and thickness 3.5379 mm. The 5 th reflector is a concave doughnut with inner diameter 110 mm, outer diameter 130 mm, and thickness 4.368 mm. The 6 th reflector is a concave doughnut with inner diameter 130 mm, outer diameter 150 mm, and thickness 5.281 mm. The 7 th reflector is a concave doughnut with inner diameter 150 mm, outer diameter 170 mm, and thickness 6.312 mm. The 8 th reflector is a concave doughnut with inner diameter 170 mm, outer diameter 190 mm, and thickness 7.5181 mm.  As shown in Fig. 6(B), it is the 3D simulation results of incident ray reflection on Fresnel lens. It can be found that not all of the reflected rays will converge. A few rays at certain characteristic incidence points will be diffused by multiple reflections. In order to further investigate the convergence characteristics of rays, Poincare Maps is adopted. Generally, a cross section (called the Poincare cross section) is used to cut the track of continuous motion. Then, according to the situation of the track passing through the cross section, the shape of the motion can be simply judged, and the resulting image is called the Poincare Map. Fig. 7(A) is Poincare Map of x-z plane with y=0 mm, Fig. 7(B) is combined Poincare Map of x-y plane with z = 48 mm (black points), 50 mm (blue points), 52 mm (cyan points), 54 mm (gray points), 56 mm (green points), and 58 mm (magenta points). What's more, Figs These results show that the focus point is at z = 54 mm and the diameter of the focal spot is 20 mm. It means that thermoelectric cell should be placed at the 54 mm above the Fresnel lens, and physical size should be about 20 mm. Combined with the splitter film in section III, long wavelengths (1100 nm ~ 2500 nm) of solar-spectrum can be reflected and focused to the thermoelectric cell, which is placed at a height of 54 mm; short wavelengths (400 nm ~ 1100 nm) of solar-spectrum can be transmitted to the solar cell. In this section we analyze the integration of the splitter film and Fresnel lens. As shown in Fig. 9, it's the diagram of the integration with the actual system. The main body of the system is an octahedral scaffold, which is convenient for large area parallel power generation. The upper and lower faces are a small circle and a large hexagon, respectively. The hexagonal frame with the side as 95mm holds a hexagonal Fresnel lens in place. Structural parameters of eight order reflectors for the hexagonal Fresnel lens are the same as that in section IV. Single crystalline silicon solar cell is nestled beneath the Fresnel lens, which is denoted by green color. The circle frame with the diameter as 20 mm is about 54 mm above the hexagonal frame, and holds a thermoelectric cell in place, which is denoted by red color. The splitter film in section III is evaporated on the upper surface of Fresnel lens.

V. FULL SOLAR-SPECTRUM POWER-GENERATION SYSTEM
The splitter separates incident photons based on their frequency. Low energy photons and high energy photons are directed towards the thermoelectric cell and solar cell, respectively.
The net heat gained can be determined by calculating the integral [14]           0 2 cos sin , where b  and c  are 1150 nm and 2500 nm, respectively.
A blackbody source at Tsun = 5777 K (the thermodynamic temperature of the sun) generates a spectrum of electromagnetic radiation following the Planck distribution, denoted as () s G  , as shown in Fig. 2.
  r F  is the reflection splitter function of the splitter film, as shown in Fig. 4.  is the zenith angle, and QBB is the blackbody spectrum characterized by TH, which has the same functional form as Gs. This heat is then coupled to a thermal engine with a hot-side temperature equivalent to the absorber temperature and the cold-side temperature set at Tamb = 300 K. In the limiting case, thermodynamic work, Wtherm, is extracted based on the Carnot efficiency between these two temperatures.
Meanwhile  (7) where IQE is the internal quantum efficiency, q is the elementary charge, and kb is the Boltzmann constant.
  t F  is the transmission splitter function of the splitter film, as shown in Fig. 4. The corresponding electrical power that the cell may extract from these carriers can be determined by The sum of the output work from the thermal engine and the output work from the photovoltaic cell divided by the input sun power to the system is defined as the efficiency   100%.
For our full solar-spectrum power-generation system, the bandgap of a typical Si solar cell is EG = 1.1 eV, and the thermal collector temperature is TH = 666 K (the dissociation temperature of one of the most common solar thermal heat transfer fluids, Therminol, VP-1 [34]). Therefore, the limit for total conversion efficiency is 56.64%   .

VI. CONCLUSION
We have theoretically investigated a full solar-spectrum power-generation system based on high efficiency and wide spectral splitter film and Fresnel lens, which provides a new way of thinking for the comprehensive utilization of all spectrum solar energy. Short wavelengths (400 nm ~ 1100 nm) of solar-spectrum can be transmitted 95% to the solar cell, and long wavelengths (1100 nm ~ 2500 nm) of solarspectrum can be reflected 90% and focused to the thermoelectric cell. In theory, the limit for total conversion efficiency is 56.64%   . Our system is simple and cheap to manufacture and convenient for mass production. It makes sense not only in science but also in business. In the future, we will work on implementing our full solarspectrum power-generation system, experimentally.
Supplemental Document