Does micro-scaling of CPV modules improve efficiency? A cell-to-module performance analysis

Solar Energy 173 (2018) 789–803

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Review

Does micro-scaling of CPV modules improve efficiency? A cell-to-module performance analysis

T

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Arnaud Ritoua,b, Philippe Voarinoa,b, , Olivier Raccurta,c a

Univ. Grenoble Alpes, INES, F-73375 Le Bourget-du-Lac, France CEA, LITEN, DTS, Concentrators Photovoltaic Laboratory, F-38054 Grenoble, France c CEA, LITEN, DTBH, Solar Thermal Systems Laboratory, F-38054 Grenoble, France b

A R T I C LE I N FO

A B S T R A C T

Keywords: Micro-CPV Cell-to-module losses Concentrating optics Multijunction solar cell

The actual trend of Concentrator PhotoVoltaic (CPV) development is going into micro-scaled CPV modules (micro-CPV) to optimize the balance between cost and efficiency. The compactness and high efficiency of modules constitute distinct advantages for solar farms or residential applications but the module efficiency can still be improved. While the cell efficiency is higher than 40%, the module efficiency is still below 35%. Based on a complete analysis of the Cell-To-Module (CTM) loss chain in micro-CPV, this article aims to question if the micro-scaling of CPV modules tends to improve their efficiency. Optical, mechanical and electrical losses are identified and analyzed according to data reported in the literature. It appears that the same loss mechanisms are identified in CPV and micro-CPV CTM but their impact order differs on a few points. The surface reflections and bulk absorption are the most important losses in both cases. Then, the surface shape quality which is quantified by either roughness or slope errors varies a lot as function of the manufacturing processes and module technology. These two losses have to be determined specifically for each concentrator. With the size reduction of modules, the losses due to mechanical misalignment become non-negligible, pushing a micro-CPV assembly into tighter mechanical tolerances. In contrast, the non-uniform light profile which is not yet well known for microCPV, seems to be a less impacting loss mechanism. The CTM ratio, which sums every loss mechanisms, goes from 71% to 86% for micro-CPV modules while stays between 65% and 75% for CPV modules. Finally, with an improvement of manufacturing accuracy by the implementation of micro-electronics assembly processes, the micro-scaling of CPV modules could increase the CTM efficiency without added manufacturing costs.

1. Introduction Photovoltaic cells have seen an important increase in efficiency with the appearance of III–V multijunction solar cells (MJSC) (Asim et al., 2012). First, the efficiency is boosted by stacking several PV junctions with various energy bandgaps: a larger fraction of the solar spectrum can be converted, compared to single bandgap case (Vos, 1980). Second, solar cell efficiency increases logarithmically with the light intensity. While MJSC are orders of magnitude more expensive than widely used silicon cells, the concentrated photovoltaic (CPV) technology still offers a competitive Levelized Cost Of Electricity (LCOE), thanks to the MJSC small size and high efficiency. These two principle are the main motivations of concentrated photovoltaic (CPV) technology. Indeed, a large fraction of sun-facing CPV modules surface is composed of low-cost concentrating optics which focus the light on small MJSC, thus decreasing the expensive materials consumption and

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balance the overall cost of the module (Philipps and Bett, 2017). Concentrating optics can be mirrors or lenses and MJSC are often triple junction solar cells which absorb solar spectrum in three different wavelength ranges to maximize the harvested energy (Kazmerski, 1997). The first commercial CPV modules were made with large concentrating optics and centimetric sized MJSC (Philipps and Bett, 2017). Typically, the concentrating optics were squared Fresnel lenses (Kumar et al., 2015) of dozens of centimeters wide and module’s thickness were also dozens of centimeters, as shown in Fig. 1.1(a). The solar irradiance collected by the primary lens is focused on the receiver composed of the MJSC, eventually covered by a secondary optic; in case of large primary lens, a heat sink is also used on the back side of the module (Collin et al., 2013). However, the current trend in CPV technology is to create more compact modules (see Fig. 1.1(b)), with simplified manufacturing processes. This trend inspired by micro and nanotechnology is driven by several research program like Mosaic from the ARPA-E (Haney et al.,

Corresponding author at: Univ. Grenoble Alpes, INES, F-73375 Le Bourget-du-Lac, France E-mail address: [email protected] (P. Voarino).

https://doi.org/10.1016/j.solener.2018.07.074 Received 6 June 2018; Received in revised form 12 July 2018; Accepted 24 July 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

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Fig. 1.1. From concentrated photovoltaics (CPV) to Micro-concentrator photovoltaics (micro-CPV). (a) Typical large concentrator photovoltaic with Fresnel lens and heat spreader (IEC 62108:2016 RLV). (b) Schematics of a micro-CPV cross-section without heat spreader (Jared et al., 2014).

compose the CTM ratio. This study is based on values taken in the literature of CPV and micro-CPV. In order to find the best compromise between cost and manufacturing accuracy, the most impactful defects of micro-module which reduce electricity production are identified and compared with CPV losses. For the moment, the studies about CPV losses were managed for specific losses without giving a clearly quantified global loss chain. A brief review of micro-CPV modules technologies has also been published (Domínguez et al., 2017), giving an overview of manufacturing processes developed in micro-CPV. As complement to these previous works, this paper offers a quantitative comprehension of loss chain in micro-CPV modules, identifies the main technological locks in module manufacturing and qualifies the CTM enhancement in a module size reduction context. First, a state-of-the-art of micro-CPV systems will be presented to introduce the different technological solutions for light concentration on sub-millimetric solar cells. Then, the light conversion chain will be detailed and sorted out by physical phenomenon to obtain an exhaustive list of occurring losses, and quantify their impact in the CTM ratio.

2015). This decrease in CPV module dimensions implies a decrease in focal length and cell size to conserve a high concentration ratio. Consequently, it reduces material consumption needed to build the CPV module chassis. In addition, the reduced area of light collection per solar cell limit the heat power to spread out. In this extent, heat spreader is not necessary in micro-CPV. Finally, miniaturization of CPV modules is interesting both economically and technically (Algora et al., 2005). On another hand, the integration of high efficiency solar cells into concentrating modules introduces important losses. The Cell-to-Module ratio (CTM), which is the fraction of the module efficiency with respect to the cell efficiency, is within the between 65% and 75% for the commercial CPV modules (Philipps and Warmuth, 2018). Indeed, the Fig. 1.2, taken in (Philipps and Bett, 2017), shows that the evolution of both cell and module efficiency increase with a quite constant gap which is quantified by the CTM. With the recent apparition of microscaling trend in CPV modules, we may wonder if their CTM can be enhanced. This article aims to identify and quantify every losses that

2. State of the art of micro-concentrator photovoltaic 2.1. Generalities about micro-concentrators Micro-CPV modules are not compliant with standardization. As mentioned in reference (Domínguez et al., 2017), the concentration ratio, the cell dimensions, the concentrating optic setup (reflective, refractive, single or multiple optical elements, etc.) and the cell technology can be totally different from one module to another. Despite the lack of standardization, the electricity produced by such systems can be characterized by one figure of merit: the Levelized Cost Of Electricity (LCOE), which shall be as low as possible (Kost et al., 2013). In other words, micro-CPV actors have to obtain the best compromise between manufacturing costs and module efficiency. A basic approach to quantify the module manufacturing quality is to calculate the CTM which we define here with the following ratio of efficiencies: Fig. 1.2. Efficiency evolution of CPV cells, modules and systems (Philipps and Bett, 2017).

CTM =

790

Module Efficiency Cell Efficiency

(2.1)

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2.2. Main micro-CPV components of the state-of-the-art

The CPV measurement standard IEC 62670-3 specifies efficiency measurement conditions of both cell and module efficiencies (IEC 62670-3, 2017, p. 62170). This standard fixes the environmental measurement conditions as the spectrum, the sunlight irradiance, the wind speed and the ambient temperature. For the sake of clarity, each efficiency measurement or CTM in this article is measured in standard conditions. In addition, cell efficiency is measured for the concentration ratio corresponding to the module. The CTM sums all the losses in the conversion chain from cell to manufactured module in micro-scale CPV systems studied. With this figure of merit, a state-of-the-art of the main micromodules are compared as function of module efficiency and concentration ratio in Fig. 2.1 and in Table 1 below. The sample selected is composed of modules with sub-millimetric MJSC, with various concentration ratios and measured in similar light conditions close to the AM1.5D standard spectrum (IEC 60904-3, 2016). The module and cell efficiency data published in the articles in Table 1 were uses to calculate the CTM ratios. This table sums up the main characteristics of each module on the graph. In the following paragraphs, different optical design solutions, mechanical assembly and particularity of solar cells are depicted for every kind of micro-concentrators referenced here. The graph in Fig. 2.1 shows the module efficiencies from Table 1 as a function of their CTMs and their concentration ratio. Independently of the cell efficiency together with the concentration ratio, it appears that the most efficient modules are the modules with the highest CTMs.

In this section, each component of typical micro-CPV module, represented in Fig. 2.2, will be described with its role in the conversion chain underlined.

2.2.1. Concentrating micro-optics 2.2.1.1. Optical designs. Concentrating optics are designed according to non-imaging designing technics (Winston et al., 2005a). Concentrating optics goal, as its name suggests, is to concentrate the sun light impinging on module aperture area to cell surface (Born and Wolf, 2000a). Instead of flat PV cells, most of CPV cells are MJSC which require a good spectral balance to maximize electrical performances (Domínguez et al., 2013). In addition, concentrating optics must obtain an angular acceptance higher than tracking errors. This acceptance angle is defined by the IEC 62670-3 standard as “The minimum full angle through which the module can be rotated (with respect to the sun) while continuing to produce 90% of its DNI normalized maximum power” (“IEC 62670-3“, 2017, p. 62170). To put CPV optics goal in a nutshell, the light must be concentrated without modifications of the solar spectrum and the acceptance angle of the optics must be higher than the average angle tracking error of the tracker (typically ± 0.1°) (Singh et al., 2018). The detailed optical designing methods, which are based on the

Fig. 2.1. CPV micro-module efficiency as a function of CTM ratio and concentration ratio for a sample of micro-concentrators representative of the state-of-the-art.

Table 1 CPV micro-modules of the state-of-the-art compared by their electrical performances, concentration ratio, CTM and basic dimensions. Reference

Module name

Concentration (Suns)

Cell-to-module ratio (%)

Module efficiency (%)

Cell aperture (mm2)

Number of cells

Year

Hayashi et al. (2015) Chinello et al. (2017) Ritou et al. (2016) Itou et al. (2014) Price et al. (2017) Ritou et al. (2017) Ghosal et al. (2016) Sheng et al. (2014)

Panasonic 2015 Micro-tracking Insolight µ-X 275X CEA-INES Panasonic 2014 Micro-tracking Pennsylvania µ-X 1000X CEA-INES Semprius commercial Semprius Ilinois 4J

150 190 275 277 743 1000 1111 1111

83.7 86.7 79.8 81.8 71.4 78.8 85.1 83.1

35.5 36.4 29.7 34.7 30 33.4 34.9 36.5

0.672 0.6x0.6 0.9x0.9 0.6x0.6 0.65x0.65 0.6x0.6 0.6x0.6 0.6x0.6

5x5 7 4x4 5x5 1 1 22x30 1

2015 2016 2016 2014 2017 2017 2016 2014

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homogenizes the irradiance distribution on the cell and improves the acceptance angle. Several types of SOE are used (either refractive, reflective or TIR) and they differ by their angular acceptance and/or irradiance uniformity (Victoria Pérez, 2014). Double stage concentrating optics are used both for low concentration ratio for instance, see the IRDEP research work in Jutteau (2016) and Jutteau et al. (2016) as for high concentration ratio as it is shown by CEA-INES in references Ritou et al. (2017, 2016), Suncore in Huang et al. (2018) and Semprius in Furman et al. (2010), Gu et al. (2015), and Menard et al. (2011). The last type of optical design displayed in Fig. 2.4(c), is called RX concentrator. The RX notation describes the type of optical surfaces: the refractive primary surface is noted “R”, and the reflective secondary surface is noted “X” (Miñano et al., 1995a). This configuration allows thin concentrators with high concentration ratio with solar cell located in the middle of the lens bulk. This kind of concentrator is developed for example by Morgan Solar (Morgan et al., 2017; Sinclair et al., 2014) or Pennsylvania State University (Grede et al., 2016; Price et al., 2017, 2015). Finally, the concentrating optics can be refractive, or reflective. The direct sunlight is focused on cells through at least one optical surface. More than optical efficiency, solar spectrum conservation and uniform irradiance distribution on the cell are targeted by optical designers. The following paragraphs will detail how losses mechanisms disturb the light flux management.

sun light

Fig. 2.2. Schematic of micro-CPV module cross section.

étendue conservation, are beyond the scope of this article and thus will not be developed here; we present here only the most common results of these methods. In Fig. 2.3, a schematic representation of the three rays deviation phenomena intervening in optical train are shown (Mohedano and Leutz, 2016). Whether it is refraction, reflection or total-internal-reflection (TIR) used in concentrating optics, Fig. 2.3 shows that the direction of transmitted/reflected ray depend on angular incidence of impinging rays. In case of refraction, the refractive index also determines the transmitted ray direction (Saleh and Teich, 2007). Based on these optical principles, concentrator design methods determines the slope profile of optical surfaces in order to concentrate light on MJSC with a minimum acceptance angle and maximum of uniformity. The number of optical surfaces can vary between one and three and combination of refraction and reflection are also used. The concentrating optics shown in Fig. 2.4 below, corresponding to the three micro-modules (Hayashi et al., 2015; Ghosal et al., 2016; Price et al., 2017) listed in Table 1, represent the main designs implemented in the micro-CPV field. Single stage refractive optics directly fixed to the cell as shown in Fig. 2.4(a) are generally used for low concentration ratio (< 300X). This kind of micro-concentrators are used by Panasonic for instance. Double stage refractive optics, as shown Fig. 2.4(b), are based on typical CPV configuration: a primary optical element (POE) and a secondary optic element (SOE) as shown in the standard schema of Fig. 1.1. While Fresnel lenses are used as POE in CPV (Xie et al., 2011), double stage micro-CPV uses conventional lenses, in order to improve the optical efficiency (losses related to draft angles and facet corner rounding are suppressed Gupta, 1981). In case of double stage optics, the POE concentrates the sunlight on the SOE, which

2.2.1.2. Mechanical structures. To maintain focal spots of concentrating optics in cells active area, mechanical structure of modules must respect optical tolerances. For each kind of optics described previously, the mechanical structure need to be adapted and a compromise between cost and reliability has to be found. Optical tolerances are quantified by determining optics misalignment acceptance (Menard et al., 2011) which is the maximum lateral shift, angular tilt or shape deflection that ensures a certain percentage of maximal electrical power production. And as shown in reference (Ritou et al., 2017), the constraints on micro-concentrator mechanical tolerances become more stringent with increasing concentration ratio. Thus, the mechanical structure of high concentration modules is more expensive than for low concentration ones (Lin, 2013). In addition, concentrators must accept sun tracking angular errors. Some micro-CPV system developed in Price et al. (2017) or Insolight (La jeune pousse Insolight multiplie par deux le rendement des panneaux solaires, 2016) incorporates sun tracking mechanism in the module structure itself. The module integrated tracker is an interesting way to

Fig. 2.3. Light deviation phenomena used in concentrating optics: from left to right, schematic representation of refraction, Total Internal Reflection (TIR) and metallic reflection. (Mohedano and Leutz, 2016). 792

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Fig. 2.4. State-of-the-art representative concentrating micro-optics example. (a) Simple stage of 277X concentrating lens (Hayashi et al., 2015). (b) Two-stage 1111X Concentrator (Ghosal et al., 2016). (c) RX 743X concentrator (Price et al., 2017).

Fig. 2.5. Examples of three integrated tracking systems: (a) rotary system with a circular mirror, (b) bi-axial planar tracking, (c) tracking using liquid crystal (LC) chemico-optical properties (Duerr et al., 2013).

the bottom cell (often made of germanium) converts the low energy photons transmitted through the cells above. These three subcells are monolithically integrated and connected in series, by mean of tunnel junctions. The multi-junction device has a standard front/back 2terminal contacting scheme as shown in Fig. 2.6(b) (Nishioka et al., 2003). In this electrical schematics, Rs represent the series resistance of the cell and Ip1 to Ip3 are the current generated by each subcell. Thus, the photogenerated current by the entire cell is limited by the smallest current of the three subcells. In Fig. 2.6(b), each junction are modelled by the single junction equivalent electrical circuit as described in references (Galiana et al., 2005; Rodrigo et al., 2013). To study more precisely the behavior of MJSC, more accurate three dimensional MJSC electrical models can be defined. The 3-D lumped model principle is represented in Fig. 2.7. The elementary units represented in Fig. 2.7(b) are composed by the twodiode model of a single junction and every junction is connected by resistors to simulate series, parallel and sheet ohmic losses. A tunnel junction is also present at every junction interface; the specific currentvoltage (IV) characteristics and function of tunnel junction are explained in following Section 3.3 (Jordehi, 2016). By computing these electrical models in circuit simulators (Espinet González, 2012), the behavior of MJSC under particular light conditions can be studied. For instance, Baig et al. reviewed the electrical loss studies due to nonuniform light distribution based on 3-D lumped model simulations and experiments (Baig et al., 2012). In the electrical equivalent circuit of a triple-junction solar cell above, the resistors and diodes parameters are inherent to the cell architecture and current generation. For every subcell, it depends on light

reduce CPV system size and costs. Such technologies can be used for instance in Building Integrated PV (BIPV) or rooftop application for example (Duerr et al., 2013) or (Xuan et al., 2017). In such systems, the lenses are movable as shown in Fig. 2.5: For other non-integrated sun tracking micro-CPV, optical stages are fixed and trackers are usually angularly precise within ± 0.1° (Singh et al., 2018). To ensure a perfect collection of the ± 0.27° sun light cone, concentrator’s acceptance angle must be higher than ± 0.37°. Tracking losses are not taken into account in the CTM loss chain but angular acceptance of module is an important figure of merit in the module performances. Modules defects that impact the acceptance angle of modules are presented in the third section together with the optical losses. 2.2.2. Multijunction solar cell (MJSC) CPV and micro-CPV panels are based on the principle that MJSC and concentrated light boost efficiency (Si et al., 2017). Multijunction cells are composed of multiple “subcells” absorbing different part of the solar spectrum (Alharbi and Kais, 2015). In Fig. 2.6(a), the energy conversion principle of III-V triple junction solar cell is represented. Every subcell is absorbing different part of the solar spectrum, related to their bandgaps specified on the schematics. The spectral irradiance for AM1.5, which is the standard solar spectrum on earth, is represented in power density unit (W/m2/nm), together with the fractions that can be converted by each subcell in the detailed balance efficiency limit (Yastrebova, 2007). The top cell (typically GaInP) is absorbing high-energy photons, the middle cell (typically GaInAs) is absorbing the intermediate part of the solar spectrum, and 793

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Fig. 2.6. (a) AM1.5D spectrum (black) as function of wavelength, together with the maximum theoretical fraction (color shaded areas) that can be converted by each subcell with a triple-junction GaInP/GaInAs/Ge device (Yastrebova, 2007). (b) Simple electrical equivalent circuit of a triple-junction solar cell with a one-diode model for each subcell (Nishioka et al., 2003).

i.e. between the sunlight power collected by the primary optics and the output electrical power produced by the micro-module. First, the optical losses are detailed with particular attention to power losses. Then, the losses due to mechanical assembly defects are studied. The electrical losses happening in the CPV module are described and a study of light non-uniformities impact on cell performance is performed. For the sake of clarity, the temperature influence on each losses described in this article is not studied. The CTM module ratio is calculated from standard efficiency measurement at 25 °C.

intensity and wavelength distribution. Current distribution, ohmic losses and temperature are linked to the light distribution on the whole cell volume. 2.2.3. Conclusion on micro-concentrators components Based on concentrating optics principles, micro-CPV optical designs are not compliant with a standard configuration. Concentrating optics can be reflective, refractive or both together but, reduced size allows simpler geometrical profile. For instance, Fresnel patterns, which generate corner rounding and draft angle losses, are not necessary to reduce lens thickness in micro-concentrators. Moreover, the short focal length implies thinner modules and chassis integrated sun tracking mechanisms are implemented in some micro-CPV systems. This integrated tracking systems are very compact which is interesting for rooftop or BIPV applications. With a reduced aperture area, typically below 1 mm2, the micro-MJSC have the same electrical characteristics than usual MJSC. Analyzing the behavior of each micro-CPV component, the following section describes the losses composing the CTM ratio.

3.1. Optical losses Low cost concentrating optics are subject to manufacturing defects or imperfections. Considering an input sunlight flux impinging on a concentrator optical aperture, a non-negligible part of this flux will simply not reach the cell surface aperture due to optical losses. In this section, only the power losses due to flux leaks are described. For the sake of clarity, the losses induced by the light distortion in the cell plane is discussed later in Section 3.3. The Fig. 3.1 below represents the main power losses in concentrating optics. The optical efficiency of a concentrator is defined as the fraction of light power impinging on the entrance aperture which is effectively received by the cell (Victoria et al., 2016). This section of the

3. Loss mechanism in micro-CPV systems We present here an exhaustive list of loss sources in the CTM ratio;

Fig. 2.7. (a) Top view 3-D electrical lumped model of MJSC principle (“Photovoltaic Devices – SUNLAB Solar Research Lab,” 2018). (b) Elementary unit model of a triple-junction solar cell cross section (Espinet González, 2012). 794

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Fig. 3.1. Schematic representation of main optical power losses along the light path in a micro-concentrator.

The absorption coefficient α depends on refractive index and attenuation index (Born and Wolf, 2000c). This coefficient is also a function of material properties and wavelength. For instance, a low-iron glass coefficient is α = 0.0074 mm−1 (Rubin, 1985), α = 0.0097 mm−1 for PMMA (McIntosh et al., 2011) and α = 0.0021 mm−1 for silicone (McIntosh et al., 2009). In terms of visible light power losses, absorption represents respectively 3.6%, 4.7% and 1.0% of losses for a 5 mm thick layer of the three above-mentioned materials. Applying the Beer’s law to state-of-the-art micro-concentrators, the best module with thinner and least absorbent optics have only 0.87% of power losses instead of 7.6%, measured on thick PMMA lens.

article details the surface reflection losses, the bulk absorption and the miscellaneous losses. 3.1.1. Reflection and absorption losses The surface reflection shown in Fig. 3.1 depends on the refractive indexes and the rays incident angles, according to the Fresnel Formulae (Born and Wolf, 2000b) in Eq. (3.1). The angles θi and θt are respectively formed between the incident and transmitted ray together with the surface normal direction. The parameters ni and nt correspond respectively to the refractive indexes of the incident and the transmitted media.

Rf =

nicos(θi )−ntcos(θt ) nicos(θi ) + ntcos(θt )

2

3.1.2. Miscellaneous optical losses The other optical losses, represented in Fig. 3.1, concern all the nonreflected and non-absorbed light that does not reach the solar cell aperture area. This power loss results of the combination of several defects that highly depends on concentrator technology and manufacturing quality. In fact, dispersion, scattering and surface shape error modify spatial and spectral light distribution in the focal plane and may lead to power losses if the light overflows the cell surface. In this article, light non-uniformities on the cell aperture area are dissociated from lost rays and described later in Section 3.3. Here, the three origins responsible of rays losses are the high dispersion of material, large scattering effect and surface shape defects (Hornung et al., 2012; Victoria et al., 2013; Victoria Pérez et al., 2016).

(3.1)

This reflection happens at each material interface of the system and reach 4% or 5% for Air-Glass interface with nglass = 1.5 and normal incidence. This well know phenomenon could be treated with anti-reflective coating (ARC) that decrease the reflection to 1% or 2% depending on the wavelength range (Fresnel, 1819). For instance, Panasonic micro-module is constitute by a single optic directly attached to the cell with an ARC on the top surface. This module, the best to minimize the surfaces reflection losses in the stat-of-the-art, generates only 2.2% losses (Hayashi et al., 2015). In contrast, micro-modules with two-stage concentrating optics have three reflective surfaces and, according to the Fresnel formulae, generate around 10% of losses. The light absorption phenomenon takes place in continuous media. Even if the materials used for lenses such as glass or silicone are transparent, a percentage of energy is absorbed according to the Beer’s law in Eq. (3.2). The value Pn+1 is the power at the exit of the media separated by two surfaces, Pn is the power at the entrance, α is absorption coefficient of the media and L is the length of passing light in the media.

Pn + 1 = Pn e−αL

3.1.2.1. Dispersion. First, the dispersion is quantified by the material dispersion formula (Born and Wolf, 2000d) which models the refractive index variation as function of the wavelength generally given in the material datasheet. Dispersion, also known as chromatic aberration, in case of dispersion angle larger than angular aperture of the concentrator can lead to power losses. However, even if material is highly dispersive, the effect of chromatic dispersion generates only power density disparities between different wavelengths. In all cases of

(3.2) 795

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LReflected (θr ; λ; Ei ) = BRDF (θi ; θr ; λ ) Ein (θi ; λ )

(3.4)

LTransmitted (θt ; λ; Ei ) = BTDF (θi ; θt ; λ ) Ein (θi ; λ )

(3.5)

To estimate the angular distribution of the scattered light as a function of the roughness of surface, dozens of models have been identified in the review (Elfouhaily and Guérin, 2004). They found a lot of particular cases but no universal method to quantify the influence of surface roughness on BSDF. The most speaking example is the comparison of Beckmann-Kirchhoff (Beckmann and Spizzichino, 1963) and Rayleigh-Rice (Rice, 1951) theories that differs particularly from the ratio σ/λ which is ≈1 in the former and ≪ 1 in the latter. Due to the various optical designs used for micro-concentrating optics, calculus of flux lost due to scattering must be done separately. The adequate scattering model corresponding to the optical design and surface roughness range must be chosen to estimate the effect of surface roughness on scattering losses for each system. For the moment, there is no specific study of power losses induced by rough surface scattering but it is taken into account in the optical efficiency measurements (Victoria Pérez et al., 2016).

Fig. 3.2. Rough surface profile characterized by σs, the standard deviation of the height distribution of roughness. The height h is on the order of the wavelength (Harvey et al., 2012).

this article, the losses due to large dispersion can however be neglected (Bunthof et al., 2018; Yeh, 2010). Dispersion, or chromatic aberration, is only impactful on non-uniformity losses presented in Section 3.3. Thus, direct power losses due to dispersion are neglected in this study.

3.1.2.2. Scattering. Secondly, due to manufacturing process, the surfaces of the optics are not perfectly smooth and generates light scattering. In scattering studies, both roughness measuring and scattering analysis are complicated to estimate. In one hand, Bennett et al. studied roughness of diamond-turned optics in Bennett and Decker (1981) which is the most common way to manufacture molds for polymeric optics or precise mirrors. Surface roughness can be measured by several techniques with mechanical contact or optical sensing and quantified by statistical values as shown in Fig. 3.2. The roughness is typically quantified by the RMS roughness average (Ra), also defined by the standard deviation σs of height distribution. The height of the surface roughness is on the order of the wavelength, typically σs is below few hundred of nm in concentrating optics. With various POE and SOE manufacturing technics from micro-CPV and LED litterature, the measured Ra varies from few nanometers to hundreds of nanometers (Chakrabarti et al., 2016; Hayashi et al., 2011; Schmid and Manley, 2014). In another hand, the surface roughness magnitude influences the light scattering behavior in reflected and transmitted half-space. This behavior is explained by either the Bidirectional Reflected Distribution Function (BSDF) or the Bidirectional Transmitted Distribution Function (BTDF) like represented in the Fig. 3.3 (Davies, 1954; Fest, 2013; Harvey et al., 2007). The BRDF gives the angular scattering distribution in the reflected half-space (Eq. (3.4)) and the BTDF, in the transmitted half-space (Eq. (3.5)). The BRDF and BTDF are given in sr−1 units, the radiance LReflected/Transmitted is in W/m2/sr−1/nm and the irradiance Ein is in W/m2/nm. θi is the angle of incident beam; θr the angular direction of reflected light; θt the angular direction of transmitted light and λ is the wavelength. Fig. 3.3 shows that a fraction of transmitted light is scattered in every direction while the specular beam is following the reflection or refraction geometric laws. In concentrating optics, large angle scattered light spreads the light spot in the focal plane, making it overflowing the cell.

3.1.2.3. Surface slope defects. In the miscellaneous loss sources depicted in Fig. 3.1, the third component concerns losses due to large surface shape errors. In contrast with the surface roughness error, the surface slope errors have a spatial frequency much higher than the wavelength and generates light rays deviation and then, power losses. The slope errors can be measured by non-contacting technics, or with mechanical profilometer (Fang et al., 2013). Then, their impact on flux losses is either determined by ray tracing simulations or stochastic approach based on surface accuracy measurements (Leutz et al., 2010). The slope errors induce ray direction errors which lead to power losses if light miss the cell. Finally, flux losses depend on magnitude of angular slope error which is quantified by σslope. In the same way σs is the RMS roughness average, σslope is the RMS average of angular errors in optical surface profile of optical components of the module. Simulations show that slope errors in the profile between the perfect theoretical lens from design and the real lens decreases the acceptance angle of the concentrators. Fig. 3.4 gives an example of this effect by showing the case of a 34X XR concentrator (such as that shown in Fig. 2.4(c) (Winston et al., 2005b). In Fig. 3.4, transmissions of XR concentrators as function of angular direction of incident rays are simulated by ray-tracing software. Each curve is plotted by either simulations or experimental measures for different values of σslope in mrad. It appears clearly that the acceptance angle decreases with the slope error. We can also note that, for high deviation of slope (> 4 mrad), power losses appear at normal incidence. Contrary to the angular curves of Fig. 3.4, theoretical models can calculate the maximum slope error σslope tolerated to ensure a specific acceptance angle. For example, Fig. 3.5 compares the maximum σslope

Fig. 3.4. Transmission of a 34X concentrating optic with various slope error values as function of angle of incident rays. σslope is the RMS average of slope errors given in mrad. The errors are measured for spatial frequencies much higher than the wavelength (Winston et al., 2005b).

Fig. 3.3. Light scattering due to surface reflection and transmission. BRDF and BTDF function represent the angular distribution of reflected and transmitted light (Fest, 2013). 796

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b)

a)

Fig. 3.5. Maximum slope errors of various concentrators which ensure at least ± 0.75° of acceptance angle. (a) Values for 5X concentrators. (b) Values for 50X concentrators (Winston et al., 2005b).

concentrators, preferring the use of lenses with continuous shape. In this particular case, the losses induced by manufacturing defect of Fresnel patterns are avoided, while the thin lenses with continuous shape introduce negligible absorption. Concerning the miscellaneous losses depicted in Section 3.1.2, each loss of this section is affected differently by size reduction. The dispersion is reduced as function of the focal length of concentrators. Thus, losses due to dispersion are always neglected. The surface scattering losses, independently of the lens sizes, are linked with the manufacturing quality process, quantified by the RMS surface roughness average. In contrast, the surface shape errors are more impactful on micro-concentrators performances, particularly at high concentration ratio. The optical mismatch, which is the difference of light power received by two optic/MJSC couple, is reported in the current mismatch losses described in Section 3.3.

values tolerated by different concentrators which ensures an acceptance angle of ± 0.75°. “Parabola” is a parabolic reflective concentrator. “CPC” mean Compound Parabolic Concentrator. The first “CPC” is purely reflective while the “solid CPC” is TIR reflective in a dielectric media (Gordon and Rabl, 1992). The others concentrators XR/RXI and RX are constitute by combination of reflective and refractive optical surfaces as described respectively in references (Miñano et al., 1995b, 1995a; Zhang et al., 2013). The “X” in first position in the name designs a reflective primary optic and “R” in second position mean a refractive secondary optic. For every concentrator, the σslope in mrad unit is applied for every surface with the same amplitude. Another important remark about Fig. 3.5 is that the slope error tolerance of concentrator decrease with the concentration ratio (Shanks et al., 2018). This effect is clearly visible when comparing Fig. 3.5(a) and (b) diagrams. To conclude about surface shape defects, every concentrating optic technology provides its typical acceptance performances and need to be calculated separately. However, there is two clear trends in surface slope error studies. First, the acceptance angle decreases when the slope error increases. Second, the maximum slope errors allowed by a concentrator to obtain a high acceptance angle drops with the concentrating ratio. For the CTM study in this paper, the worst scenario of surface shape error is taken for the highest slope standard deviation found in the literature. At normal incidence with σslope = 8 mrad, the XR concentrator loses 4% of the flux, and this value is taken as the worst case scenario in this study.

3.2. Mechanical losses In manufacturing of micro-CPV modules, discrepancies appears in positioning of the cells and in mechanical parts dimensions. Due to these discrepancies, each lens/cell couple can be misaligned respectively to the mechanical degrees of freedom as represented in Fig. 3.6 (González-Correa et al., 2015). These mechanical misalignments decrease the acceptance angle (Herrero et al., 2015), like the surface shape defect does in Fig. 3.4. Each movement of the optical train possible must be limited by the mechanical structure. This limitation in optics displacement defines the mechanical tolerances calculated by ray-tracing simulations. Due to the high number of degrees of freedom and the intercorrelation between the mechanical displacements, sensitivity analysis are needed to quantify the mechanical tolerances of an optical train (Drew et al., 2014; Herrero et al., 2017; ur Rehman et al., 2018). These studies reveals that the mechanical displacements mainly impact the acceptance

3.1.3. Optical losses in micro-concentrators In the micro-concentration case, the effect on Fresnel reflection is unchanged because the number of diopter is the same than in classical CPV systems. Absorption is smaller because of the smaller optics thicknesses. In particular, for the Fresnel lens case, the Fresnel patterns implemented to reduce the lens thickness can be removed in micro-

Fig. 3.6. Optical losses due to mechanical parts misalignments. Most impactful assembly error in concentrating optics (González-Correa et al., 2015). 797

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angle (AA). Power losses, at normal irradiance, may not be impacted if AA drop is limited, as represented for small slope errors in Fig. 3.4. In micro-concentrators, the mechanical tolerances may have the same behavior on the acceptance angle. However, two categories of micro-concentrators can be studied separately: the micro-tracking structures and the fixed structure. In micro-tracking micro-CPVs, the misalignment of the POE rather than the receiver is voluntarily created to track the sun like represented in Fig. 2.4(c) for the Pennsylvania State University micro-CPV system (Price et al., 2015). With another optical architecture, Insolight microCPV system also moving laterally the POE plane rather than the receiver plane in order to track the sun (Chinello et al., 2017). For fixed structure micro-concentrators, the impact of micro-module misalignment highly depends on optical architecture. With higher concentration ratio, the misalignment impact on the acceptance angle is more pronounced. In a recently published study on mechanical misalignment, it is demonstrated that the secondary optics shift in the focal plane direction is the most important cause for misalignment (Ritou et al., 2017). In this study, realized for a double stage refractive 1000X concentrator, shifting the cell laterally of 70 µm decreases the acceptance angle from ± 0.7° to ± 0.5°. In another study on a similar concentrator with slightly higher concentration ratio (1111X) shown in Fig. 2.4(b), a lateral shift between secondary optic and cells induces 0.7% of power losses for 50 µm shift and 3% for 75 µm (Menard et al., 2011). For the sake of simplicity, 3% power loss is the figure taken in loss chain comprehension as the worst case scenario expected. The concentration ratio of 1111X is the highest reported for a micromodule, and the cell positioning precision at the micron-level also define the state-of-the-art for this technology (Maeda et al., 2015).

Fig. 3.8. 1D two-diode electrical model of a triple junction solar cell in passing tunnel diode mode (Rodrigo et al., 2013).

peak tunneling current of the tunnel junction (Andreev et al., 2006). Indeed, since the current density of a solar cell depends linearly on the concentration ratio, a too high concentration ratio will create a current density exceeding the tunnel diode peak current (Jpeak), and thus create a drop in the I-V curve of the MJSC, as shown in the Fig. 3.7(b) (Espinet et al., 2011). However when the tunnel diode is operating at J < Jpeak, thus in passing mode, the tunnel junction behave as a simple wire (negligible voltage drop), as shown in Fig. 3.8 below. The ohmic losses are in this case integrated in the series resistance components of the concerned subcell. The series and shunt resistances are respectively noted Rs,x and Rp,x in Fig. 3.8 with “x” replaced by the junction name (Rodrigo et al., 2013). These two parasitic resistances, but also the subcell current and two-diodes parameters vary with the light spectrum, light intensity and the local temperature (Ben Or and Appelbaum, 2013; Domínguez et al., 2010; Segev et al., 2012; Wanlass et al., 1989). The intrinsic cell losses due to parasitic resistances already affect the solar cell efficiency itself, therefore do not appear in the CTM. In contrast, the electrical losses due to non-uniform light distribution generates losses in the CTM but this point will be described in the following Section 3.4. Moreover, the electrical losses due to cells connections in a module influence the CTM ratio. First, interconnection resistive losses vary as function of the series-parallel combinations chosen and the contact

3.3. Electrical losses Based on the electrical models described in Section 2.2.2, the electrical losses in micro-concentrators and concentrators are described below. Fig. 2.7 in Section 2.2.2, represents a complete model of a triple junction solar cell (TJSC). In this electrical model, a particular expression of Jtj as function of voltage between two subcells is leaded by the tunnel junction current behavior. Indeed, stacking several PV cells with different bandgaps in a monolithic device enforces the use of tunnels junctions which have the I-V characteristic is represented in Fig. 3.7(a) below. The tunnel junction ensures a low resistance ohmic current path between subcells in a MJSC (Yamaguchi et al., 2006). In the intermediate voltage range, the tunnel junction may limit the total current density of the device. This happens at high concentration ratios when the current density produced by the solar cell is higher than the

Fig. 3.7. (a) Tunnel junction J(V) characteristic. In the intermediate voltage range, the so called valley region, the current density is limited. (Hong and Yu, 2011). (b) I(V) characteristic of a MJSC for 3 different concentration ratios. For the highest concentration, the curve shows a pronounced drop in the intermediate voltage range, related to a limited peak tunneling current of the tunnel junction (Espinet et al., 2011). 798

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Fig. 3.9. Effect on MJSC electrical characteristic of different Peak-to-Average Ratio (PAR) in case of non-uniform light distributions (Herrero et al., 2012).

cells (Belghachi and Khelifi, 2006). However, concentrating the light on cells mitigate the decrease in Voc, Fill Factor and efficiency as function of perimeter/area ratio (Fidaner et al., 2014). Anyhow the electrical disadvantages of micro-cells compared to larger cells, already measured in the cell efficiency, does not appear in the CTM ratio. In this extent, the smaller lens aperture reduces the photogenerated current, decreasing the RI2 losses in the series resistances. On another hand, tunnel junction current limitation is considered as extremely rare and is neglected. Ohmic losses are less impacting in micro-modules than classical CPV modules, therefore we will assume that cell stringing ohmic losses are negligible in micro-concentrators (García Vara, 2010). Finally, in the electrical losses category, only the current mismatch between different cells series-connected is responsible of 1% power losses in the best scenario case instead of 5% in the worst case. 3.4. Cell electrical losses due to optical non-uniformities

Fig. 3.10. Simulated effect of chromatic aberration on 3J MJSC (Araki and Yamaguchi, 2003).

As a combination of non-homogeneous light distribution and MJSC architecture, the light-solar cell coupling is responsible for non-negligible losses (Baig et al., 2012; Li et al., 2018). More than dispersion and scattering described in Section 3.1, concentrating optics inherently introduce spatial and spectral non-uniform light distributions which lead to losses in the cell (Baig et al., 2012). Depending on material properties and optical design (concentration ratio, refractive or reflective optics), the amplitude of spatial or spectral non-uniformity varies from one system to another. Non homogenizing concentrators optical distribution profiles are assimilated to a Gaussian profile as verified experimentally by Franklin and Coventry (2002) or Herrero et al. (2012). The quantification of the spatial non-uniformities degree is based on the peak-to-average ratio (PAR) figure of merit. PAR is defined as the ratio of the highest light power density (or concentration) divided by the average power density in the cell aperture area. Many simulations based on lumped model diode of MJSC were validated with experiments in order to estimate the impact on MJSC as function of this PAR (Espinet-González et al., 2015; Galiana et al., 2005; Korech et al., 2007; Sharma et al., 2017). The main results proved that an increase in PAR raises the losses like it is showed in the Fig. 3.9 (Herrero et al., 2012). The IV experimental curve of 1 cm2 dual-junction III-V cell shows that high amplitude Gaussian light distribution (i.e. high PAR) lead to a decrease in Fill Factor (FF) of the curve. This decrease in fill factor is observed for MJSC on both lumped models and experimental measures

quality (Wang and Xuan, 2018). These losses directly impact the module power production by adding extra series and shunt resistances (Das et al., 2017). Nevertheless, the resistive losses due to cell interconnection in CPV modules are always considered as negligible compared to the resistive losses arising from current transport in the cells structure (Mizuno et al., 2012). Second, the current mismatch losses are directly impacting the module power: the spreading of cells performances together with various optical efficiency of various mono-concentrators can be responsible of 2% power losses (Kaushika and Rai, 2007). Hopefully in CPV applications, the space saved by concentration allows the use of by-pass diode for each and every cells; in addition, adapted cells interconnection design (maximizing the parallel connection) can be used to reduce these mismatch losses to 1% from a cell performance variance of 5% (Steiner et al., 2011). Finally, the electrical losses in CPV module influencing the CTM ratio for a few percent (1–2%) of power losses due to current mismatch with cell performance disparities. 3.3.1. Conclusion on electrical losses in micro-concentrators The most common cells used in micro-concentrators photovoltaic modules are Triple Junction Solar Cells (TJSC). Their performances does not differ as function of size but, the perimeter/area ratio increases and perimeter recombination losses can become significant for micro799

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Fig. 4.1. State-of-the-art micro-concentrator cell-to-module loss chain. The minimum and maximum values of loss are given in percentage of cell efficiency.

are summarized in Table 2. For each loss, a fraction of lost power is given in percentage of CTM ratio. For the losses not clearly quantified, as the surface scattering and the non-uniformity losses which are specific to each concentrator, most impactful parameters and trends are identified and represented in Table 2. Other losses, like dispersion, tunnel junction current limit and electrical interconnection losses are negligible. By comparing each step of CTM loss chain between CPV and micro-CPV modules, it appears that modules micro-scaling presents definite advantages on few losses while mechanical tolerances become more stringent. Implementing mass market manufacturing processes of micro-electronics into micro-module factories, the mechanical accuracy can be easily enhanced without incurring additional costs. Then, losses are reduced naturally with the micro-scaling of modules. The Fresnel reflection which is the predominant loss should be limited by a reduction of refractive surface number instead of adding anti-reflective coating on every surface. Typically the reflection losses goes from 2.2% to 10%. Absorption, which is the second predominant loss (from 0.9% to 7.6%), highly depends on lens thickness and absorptivity. Then, the refractive surface number should not be reduced at the expense of absorption. In contrast with reflection and absorption which are conception dependent losses, the quality dependent losses are more difficult to quantify. Rough surface scattering and surface shape error losses must be analyzed specifically for each micro-concentrator module. For instance, the shape error is quantified for a couple of low concentration micro-CPV modules from 0% to 4%, depending on the shape error. However, the standard optical efficiency measurement of CPV and micro-CPV modules gives an accurate value of cumulated optical losses. Mechanical misalignment losses, which are also leaded by manufacturing accuracy, have a particular effect on acceptance angle value. The effects on the CTM are perceptible for important misalignment of micro-CPV components and the micro-CPV state-of-the-art values goes from 0.7% to 3%. This observation shows that micro-CPV modules are more sensitive to micro-module assembly quality than CPV and processes must be more accurate. Hopefully, the micrometric size of MJSC are compliant with widespread LED manufacturing process which are highly accurate and cheap. In contrast, the non-uniformity loss phenomenon, which is well known in CPV literature, is not enough studied for micro-CPV and no loss values were founded. However, MJSC reduced size present an advantage to balance

(Espinet González, 2012). The voltage at the maximum power point is also decreasing with increasing PAR. In fact, non-uniform light creates non-uniform current density in the cell and lateral current flows are created. These lateral current generate ohmic losses in the distributed series resistances represented in Fig. 2.7 which is responsible of FF decreasing (Franklin and Coventry, 2002). Thus, solar cells with small distributed series resistance are less impacted by light spatial non-uniformities. Non-uniform light distribution also lead to non-uniform temperature distribution on cell which lead to a decrease of Voc (Li et al., 2018). Those electrical and thermal effects on FF and Voc are magnified in high concentrated PV. The spectral non-uniformities, also called chromatic aberrations (CA), lead to a loss in efficiency as well (Araki and Yamaguchi, 2003; Garcia et al., 2008). Araki and Yamaguchi proved that the spectral nonuniformities have different effect than the spatial ones within the Fig. 3.10 observation. In this study, a Gaussian flux is applied to each junction with a fixed PAR and different level of CA. Resulting I-V curves are calculated from a distributed 2D numerical model of TJSC. It clearly appears that high CA lead to high short-circuit current decrease. Finally, the effect of light non-uniform distribution on MJSC depends on light Peak-to-Average ratio together with CA level in one hand. In the other hand, distributed series resistances, cell technology (inverted metamorphic, lattice matched, number of junctions, etc.) play an important role in the losses due to non-uniformities. The power losses induced by non-uniformities in cell are due to lateral current flows in the cells that generate ohmic losses. For the moment, apart from the 330X micro concentrator from Hayashi et al. (2016) which treats only CA effects, no study have published yet to deal with the impact of non-uniformities on micro-cells performances; it is likely that a smaller cell size will reduce this impact. Finally, non-uniformity losses are depending on cell size, cell technology, Cg, PAR and CA. 4. Conclusion This article studies every point in the CTM loss chain with a quantification of maximum and minimum values based on published data. For the first time in CPV literature, a quantified loss chain diagram is compiled. Experimental data or empirical models found in the literature 800

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out the lateral ohmic losses created by light non-uniform power density. Then, each loss described previously have various values from a monomodule to another. Together with the various electrical performances of series connected in a complete module, the current mismatch losses is also not negligible with values from 1% to 5%. Finally, the micro-CPV loss sources does not differ a lot from CPV but levels are different. Higher manufacturing accuracy is needed but few losses are avoided in micro-CPV technologies. Implementing widespread micro-electronics assembly processes into micro-CPV is interesting to improve CTM ratio while keeping low costs by using large scale processes.

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Table 2 Quantification of Cell-to-Module (CTM) power losses, as found in literature, for various loss sources. Loss name

Minimum of the state-of-the-art (%)

Maximum of the state-of-the-art (%)

Fresnel reflection Absorption Dispersion Surface scattering Shape error Mechanical misalignment Tunnel junction losses Electrical interconnexion Current mismatch Non-uniformities

2.2 0.9 Negligible f (θi , σs, λ ) 0 0.7

10 7.6 Negligible f (θi , σs, λ ) 4 3

Negligible

f (C g) for Cg > 4000X

Negligible

Negligible

1 f (Cg , λ, PAR)

5 f (Cg , λ, PAR)

Each value is a fraction of the cell efficiency in percent. As summarized in Table 2 above, scattering and non-uniformities losses could not be quantified based on literature knowledge. Thus the two min/max CTMs ratio reported in Fig. 4.1, respectively 71.4% and 86.7%, correspond to min/max experimental values found literature, as shown in Fig. 21. Compared to the CPV CTM comprised between 65% and 75% (Philipps and Warmuth, 2018), micro-CPV modules present a greater potential. Moreover, the maximum CTM of micro-CPV modules reachable is 93.2% if every loss is minimized and the two unquantified losses are estimated at 1%. Finally, the micro-scaling of CPV modules already improves the CTM and can afford even better results. Acknowledgements This work has been released with the precious help of all the CPV laboratory team at CEA-INES and particularly with Romain Cariou. References Algora, C., Rey-Stolle, I., Galiana, B., González, J.R., Baudrit, M., García, I., 2005. III-V concentrator solar cells as LEDs. III-Vs Rev. 18, 40–42. https://doi.org/10.1016/ S0961-1290(05)71233-3. Alharbi, F.H., Kais, S., 2015. Theoretical limits of photovoltaics efficiency and possible improvements by intuitive approaches learned from photosynthesis and quantum coherence. Renew. Sustain. Energy Rev. 43, 1073–1089. https://doi.org/10.1016/j. rser.2014.11.101. Andreev, V.M., Ionova, E.A., Larionov, V.R., Rumyantsev, V.D., Shvarts, M.Z., Glenn, G., 2006. Tunnel diode revealing peculiarities at I-V measurements in multijunction III-V solar cells. In: Presented at the 2006 IEEE 4th World Conference on Photovoltaic Energy Conference, pp. 799–802, doi:10.1109/WCPEC.2006.279577. Araki, K., Yamaguchi, M., 2003. Extended distributed model for analysis of non-ideal concentration operation. Sol. Energy Mater. Sol. Cells, PVSEC 12 PART III 75, 467–473. https://doi.org/10.1016/S0927-0248(02)00203-9. Asim, N., Sopian, K., Ahmadi, S., Saeedfar, K., Alghoul, M.A., Saadatian, O., Zaidi, S.H., 2012. A review on the role of materials science in solar cells. Renew. Sustain. Energy Rev. 16, 5834–5847. https://doi.org/10.1016/j.rser.2012.06.004. Baig, H., Heasman, K.C., Mallick, T.K., 2012. Non-uniform illumination in concentrating solar cells. Renew. Sustain. Energy Rev. 16, 5890–5909. https://doi.org/10.1016/j. rser.2012.06.020.

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