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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 8136–8147
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Antireflective coatings for multijunction solar cells under wide-angle ray bundles

Marta Victoria, César Domínguez, Ignacio Antón, and Gabriel Sala  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 8136-8147 (2012)
http://dx.doi.org/10.1364/OE.20.008136


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Abstract

Two important aspects must be considered when optimizing antireflection coatings (ARCs) for multijunction solar cells to be used in concentrators: the angular light distribution over the cell created by the particular concentration system and the wide spectral bandwidth the solar cell is sensitive to. In this article, a numerical optimization procedure and its results are presented. The potential efficiency enhancement by means of ARC optimization is calculated for several concentrating PV systems. In addition, two methods for ARCs direct characterization are presented. The results of these show that real ARCs slightly underperform theoretical predictions.

© 2012 OSA

1. Introduction

Antireflection coatings (ARCs) have been widely investigated since the beginning of photovoltaics [1

1. A. Luque, Solar cells and optics for photovoltaic concentration (Adam Hilger, 1989).

]. The high refractive indexes of semiconductors (n~4) will lead to unacceptable reflection losses if no ARC is used. Multijunction (MJ) solar cells have shown the highest efficiency for a photovoltaic device ever measured at 43.5% [2

2. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (Version 38),” Prog. Photovolt. Res. Appl. 19(5), 565–572 (2011). [CrossRef]

]. ARC design for III-V semiconductor MJ solar cells is especially challenging as these cells are typically sensitive to a wider spectral bandwidth than silicon. In addition, their subcells are connected in series. Hence, if the ARC performs worse in a particular region of the spectrum, photogenerated current for the corresponding subcell will be limited and, as a consequence, total cell efficiency will significantly decrease. In terrestrial applications, MJ solar cells are only economically viable when used in concentrator systems. Concentration implies that the bundle of rays impinging the cell consists of a cone with large interior angle, in some systems as wide as ± 70°. Hence, besides considering the wide spectral sensitivity and the series connected structure, the angular distribution of the incident light over the cell must be taken into account to properly design an ARC for a concentrator cell.

When using optics to concentrate light, the product of concentration and acceptance angle, known as CAP, is the most significant figure of merit as it indicates how close a real concentrator is to ideality [3

3. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

]. Attainable CAP is limited by the étendue conservation theorem. In rotationally symmetric optical systems in air it can be stated as:
Xgeomsin2(θentrance)n22sin2(θcell)
(1)
where Xgeom represents the ratio of the optical input area to the exit area, or concentration ratio and θentrance represents the system acceptance angle. The acceptance angle is the angle of incidence of the extreme light ray: the most inclined ray that continues to reach exit of the optical system. Symbols n2 and θcell stand respectively for the refractive index and the extreme ray’s angle at the system exit. To maximize attainable CAP, the refractive index at the exit must be higher than unity, for example by using a dielectric SOE over the cell, but this is not the scope of this article. Furthermore, the angle at the exit of the optical system, that is, over the cell, must be as wide as possible, ideally 90°. Nevertheless, it must be considered that reflection losses at the cell aperture increase with θcell and, in point-focus systems the largest incident angles contain the majority of the energy. Therefore, as CPV systems approach ideality, this necessarily translates into higher CAPs and wider ray-bundles, and therefore a need for an ARC design which takes into account these angular light distributions.

This paper aims to apply the optimization of ARC to real CPV systems taking into account simultaneously the restriction imposed by MJ solar cells and the angular light distribution created by concentrators which illuminate the solar cell with wide-angle ray bundles. Although specific aspects of the problem have been previously considered by other authors, as summarized above, we believe that the current combination of new CPV system with ever-increasing concentration levels together with new MJ solar cell architectures with more restrictive current matching conditions [8

8. S. Wojtczuk, P. Chiu, X. Zhang, D. Derkacs, C. Harris, D. Pulver, and M. Timmons, “InGaP/GaAs/InGaAs 41% concentrator cells using bi-facial epigrowth,” in Proceedings of the 35th IEEE Photovoltaic Specialists Conf. (2010) pp.1259–1264.

] requires a global ARC optimization procedure.

The paper is organized as follows: Section 2 discusses basic ARC theory and also summarizes the available materials to manufacture ARC. Section 3 includes a brief description of ARC transmittance modeling. The definition of the figure of merit to evaluate each ARC is presented and the numerical optimization procedure is described. The optimization procedure is applied to several real CPV systems and the transmission enhancement when the actual angular distribution is considered compared with ARC optimized for normal incidence is calculated for each optical system. As it will be shown later, ARC performance sensibility to manufacturing errors is non-negligible and, as a consequence, a method to experimentally analyze the ARC once it has been manufactured is desirable. Section 4 presents two such methods to spectrally and angularly characterize ARC when the solar cell is illuminated by the particular CPV system the ARC has been designed for.

2. Approach

Creating an antireflection coating consists of depositing layers of materials with specific indices of refraction. As a general guide, wider incidence angles require thicker layers. Consider, for example, the well-known quarter-wave ARC design based on building a layer which refractive index is obtained as the square root of the product of the refractive indexes of the two medium adapted (i.e., solar cell and air). The layer thickness must fulfill the condition of creating destructive interference for the design wavelength, λ. In the case of oblique incidence (θ≠0) that condition leads to a thickness (d*) greater than when incidence is normal (d).
nARC=nmediumncell
(2)
d*=λ4nARCcos(θr)d
(3)
sinθr=nmediumnARCsinθi
(4)
where θi and θr are the incidence and refracted angles at the ARC entrance [9

9. A. N. Matveev, Optics (Mir, 1988)

].

From the theoretical point of view, an ideal ARC would be one in which refractive index will change smoothly from that of the solar cell to that of the surrounding medium [10

10. J. S. Rayleigh, “On the reflection of vibrations at the confines of two media between which the transition is gradual” in Proceedings London Math. Soc.11 (1880) pp. 51–56.

-11

11. D. Poitras and J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. theory,” Appl. Opt. 43(6), 1286–1295 (2004). [CrossRef] [PubMed]

]. Different experimental processes have been proposed to obtain ideal or quasi-ideal ARC, including depositing very thin alternating layers of high-index and low-index materials to create an intermediate refractive index [12

12. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24(4), 457–460 (1985). [CrossRef] [PubMed]

-13

13. D. J. Aiken, “High performance anti-reflection coatings for broadband multi-junction solar cells,” Sol. Energy Mater. Sol. Cells 64(4), 393–404 (2000). [CrossRef]

], depositing materials with oblique angle which causes self-shadowing and consequently porous materials whose refractive index will be between that of the air and that of the bulk material [14

14. M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express 16(8), 5290–5298 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-8-5290. [CrossRef] [PubMed]

-15

15. D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009). [CrossRef] [PubMed]

] or co-sputtering of different materials [14

14. M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express 16(8), 5290–5298 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-8-5290. [CrossRef] [PubMed]

]. Those processes, which aim to accurately control the refractive indexes of the deposited layer, are usually expensive and time-consuming, and furthermore are currently not used on an industrial scale. In this work we seek not to improve ARC coating technology, but to optimize the ARC for concentration applications using current deposition procedures and materials, and therefore obtain efficiency increases at no extra cost.

In industry, step-down coating structures with several layers are used. In them, refractive indexes for each layer decrease progressively from that of the cell to that of the air. A rule of thumb [7

7. C. E. Valdivia, E. Desfonds, D. Masson, S. Fafard, A. Carlson, J. Cook, T. J. Hall, and K. Hinzer, “Optimization of antireflection coating design for multijunction solar cells and concentrator systems,” Proc. SPIE 7099, 709915, 709915-10 (2008). [CrossRef]

] can be expressed as: for an N-layers ARC, the layer-i ideal refractive index ni can be obtained as:

ni=nmedium(N+1iN+1)ncell(iN+1)
(5)

Table 1

Table 1. Ideal Refractive Indexes for 1, 2 and 3 Layers ARC When the Solar Cell Is Surrounded by Air and by a Material with n = 1.5. Dielectric Materials Which Refractive Indexes Are Close To the Ideal Values Are Also Indicated

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summarizes the ideal refractive indexes for an ARC composed of one, two or three layers when a MJ solar cell is surrounded by air and by a medium with n = 1.5 (for example, a BK7 glass secondary or encapsulating silicone). It also shows materials whose refractive index is close to the theoretical values and are currently used by the industry [1

1. A. Luque, Solar cells and optics for photovoltaic concentration (Adam Hilger, 1989).

].

3. Antireflection coating numerical optimization

The general process of the ARC optimization for a given concentrator can be described as follows. First, the number of layers to be used is chosen, then available materials whose refractive indexes are closest to the ideal values are selected and finally a numerical optimization process is followed to obtain the optimum thickness for each layer.

The optimization figure of merit, Tweighted, is the ARC transmittance weighted by the actual distribution of angles and wavelengths found at the entrance of the solar cell, compared by the ideal. First, the ARC transmittance T (λ, θ, d), for each wavelength and incidence angle is calculated by multiplying the transmission matrix for each layer [1

1. A. Luque, Solar cells and optics for photovoltaic concentration (Adam Hilger, 1989).

]. The transmission matrix is mainly dependent on the layer thicknesses and material refractive indexes [16

16. E. D. Palik, Handbook of Optical Constant of Solids (Academic Press, 1997).

-17

17. Sopra materials database, www.sopra-sa.com.

] (not only the real part but also the imaginary part is considered to account for absorption). Secondly, using ray-tracing simulations the optical transmittance Topt (λ, θ), of the concentrator optics under study is obtained. The angular distribution of the light impinging the solar cell L(θ), the reference spectral distribution of the light B(λ), and the MJ solar cell spectral response for each subcell, SRj (λ), are also used to weight the integrand. As the three subcells are series–connected, the minimum of the three photogenerated currents is selected. To summarize, Tweighted is a measure of how close is the actual short-circuit current in the cell compared to what it will be if the transmittance at the cell entrance were perfect, similar to the solar weighted transmittance SWR, that has been proposed previously [4

4. D. J. Aiken, “Antireflection coating design for series interconnected multi-junction solar cells,” Prog. Photovolt. Res. Appl. 8(6), 563–570 (2000). [CrossRef]

,7

7. C. E. Valdivia, E. Desfonds, D. Masson, S. Fafard, A. Carlson, J. Cook, T. J. Hall, and K. Hinzer, “Optimization of antireflection coating design for multijunction solar cells and concentrator systems,” Proc. SPIE 7099, 709915, 709915-10 (2008). [CrossRef]

,18

18. D. Redfield, “Method for evaluation of antireflection coatings,” Solar Cells 3(1), 27–33 (1981). [CrossRef]

].

Tweighted=JscJscideal=min[λ1λ20π2T(λ,θ,di)Topt(λ,θ)L(θ)B(λ)SRj(λ)dθdλ]j=1Nmin[λ1λ20π2Topt(λ,θ)L(θ)B(λ)SRj(λ)dθdλ]j=1N
(6)

The evaluation of the figure of merit at each point is time consuming and the presence of local minima makes convergence difficult. A two-steps convergence algorithm has been implemented using brute force approach in a first step to determine the starting point for a simple nonlinear optimization method to determine the combination of layer thicknesses that maximize weighted transmittance.

3.1 Case Example: Optimized ARC for the FluidReflex concentrator

The optimization procedure described above has been used to optimize the ARC of a cell to be used in FluidReflex concentrator. A detailed description of this concentrator can be found in [19

19. M. Victoria, C. Domínguez, S. Askins, I. Antón, and G. Sala, “Optical characterization of FluidReflex concentrator,” in Proceedings of Int. Conf. on Concentrating Photovoltaic Systems (2010) pp. 118–121.

]. It consists of a reflective paraboloid that illuminates the cell creating an incident cone of light with a semi-angle of 65°. All the volume between the mirror and the cell is surrounded by a fluid dielectric whose refractive index is 1.47 (at 550 nm). Taking into account the ideal materials to be used and their availability, the selected materials are TiO2 for the monolayer, Al2O3/TiO2 for the bilayer and SiO2/Al2O3/TiO2 for the trilayer. Optimized thicknesses are summarized in Table 2

Table 2. Thicknesses and Weighted Transmittances When the Optimized Monolayer, Bilayer and Trilayer Are Used in a MJ Solar Cell Under FluidReflex Concentrator

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. As it was expected, the optimum thickness (75 nm) of the TiO2 monolayer is greater than the optimum when incidence is normal (64 nm). The same general conclusion applies for to the bilayer and trilayer coatings.

The sixth column of Table 21) shows the efficiency benefit obtained for each extra layer, for example, adding a monolayer coating compared to no ARC increases Tweighted by 16.9 absolute percentage points, going from one to two layers increases transmittance by 2.9 absolute percentage points, and only 0.3 is gained by adding the third layer. As a general conclusion, we can state that the cost of adding up to two layers will be compensated by the efficiency improvement, while adding the third layer may or may not be justified depending on the additional cost incurred.

Figure 1
Fig. 1 Transmittance for different wavelengths and incidence angles on a solar cell when no ARC is used (up-left), the optimized monolayer is used (up-right), the optimized bilayer is used (down-left) and optimized trilayer is used (down-right). Monolayer shows one maximum in transmittance, bilayer clearly shows two maximum, trilayer improves transmittance mainly at high incidence angles. Only wavelengths useful for top and middle subcells in typical MJ solar cells are shown as bottom subcell generates an excess of current making the ARC transmittance at higher wavelengths not very critical.
shows transmittance as a function of wavelength and incidence angle for different ARC structures, it can be observed how the number of layers the ARC is composed of is equal to the number of transmittance maximums that can be observed in the figures. As a general rule, an ARC with a number of layers equals to the number of junctions the cell is composed may be justified in terms of efficiency improvement. Although customary Ge-based MJ solar cells are composed of three subcells, only two of them are matched (top and middle) while the other (bottom) has an excess of photogenerated current under the standard spectrum. Hence, a two-layers ARC is clearly justified for these cells, but a trilayer is most likely is not. This is in agreement with previously reported results [13

13. D. J. Aiken, “High performance anti-reflection coatings for broadband multi-junction solar cells,” Sol. Energy Mater. Sol. Cells 64(4), 393–404 (2000). [CrossRef]

].

Table 2 seventh column (Δ2) shows efficiency enhancement when the ARC has been optimized for the particular concentrator light distribution, compared to the case when only normal incidence has been considered in the optimization. Both bilayer and trilayer ARCs show an efficiency increase higher than 2 percentage points if the particular FluidReflex light distribution is taken into account.

An additional remark need to be made regarding ARCs: values shown in Table 2 will represent average transmissions when the layers thicknesses as manufactured perfectly match the optimized ones but in reality manufacturing processes have certain tolerances that will influence the ARC performances. Figure 2
Fig. 2 Average transmission losses when due to manufacturing errors the different ARC layers optical thickness (physical thickness multiplied by refractive index) are not the optimized values. For this configuration, the higher the refractive index of the layer the more sensitive the transmission is to manufacturing errors in the layer.
shows the losses in the average transmission values for the trilayer ARC when two of the layers have been evaporated correctly but an error was committed in the third layer optical path. That is, either the evaporated thickness or the material refractive index resulted different to what it was intended. From the graph we conclude that performance sensitivity to manufacturing errors is not the same for all layers. In fact, for this particular configuration, the average transmission is far more sensitive to errors in the layer closer to the cell. This is in agreement with a similar two-layer ARC tolerance analysis reported in [20

20. I. Rey-Stolle and C. Algora, “Optimum antireflection coatings for heteroface AlGaAs/GaAs solar cells-Part II: The influence of uncertainties in the parameters of window and antireflection coatings,” J. Electron. Mater. 29(7), 992–999 (2000). [CrossRef]

]. An accurate control of the evaporated thickness must be guaranteed since, if for example, an error of −50 nm happens in the optical thickness (physical thickness multiplied by refractive index) deposited for the TiO2 layer, average transmission will decrease by 2 relative points (which is similar to the advantage that it has been obtained by designing the ARC for the specific angular light distribution created by FluidReflex concentrator).

3.2 Case example: Optimized ARC for a concentrator composed of a Fresnel lens and a secondary optical element

Table 3

Table 3. Al2O3/TiO2 Bilayer ARC Optimized Results for a MJ Solar Cell To Be Illuminated By a System Composed of a Fresnel Lens Plus Different SOEs

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presents a summary of the ARC optimization results obtained assuming an Al2O3/TiO2 bilayer, the non-optimized thicknesses account for the optimization results if only normal incidence is considered while for the optimized thicknesses each particular light angular distribution has been taken into account. For the majority of SOEs the maximum incidence angle reaching the cell is lower than 45°, and as a consequence optimized and non-optimized results are very similar and the potential efficiency enhancement by a SOE-specific ARC design is negligible. However, for the dielectric CPC (Compound Parabolic Concentrator), which is a more ideal concentrator that creates a wider cone of light impinging the cell, the optimized thicknesses differ from the non-optimized values and an efficiency increase of 0.7 percentage points can be obtained by an optimized ARC. For an ideal concentrator that illuminates the cell isotropically an efficiency increase of 3.1 percentage points will be obtained by optimizing a bilayer ARC.

In addition to a different angular light distribution over the cell, every SOE creates an irradiance distribution that is not uniform either spatially nor spectrally. This may translate into significant efficiency losses due to increment of effective series resistance and a subcells currents mismatch. The real effect of a particular non-uniform profile strongly depends on the sheet resistance between subcells. This aspect has been an active area of research recently [22

22. S. R. Kurtz and M. J. O’Neill, “Estimating and controlling chromatic aberration losses for two-junction, two-terminal devices in refractive concentrator systems,” in Proceedings of the 25th IEEE Photovoltaic Specialists Conf. (1996) pp. 361–364.

26

26. M. Victoria, R. Herrero, C. Domínguez, I. Antón, and S. Askins andG. Sala, “Characterization of the spatial distribution of irradiance and spectrum in concentrating photovoltaic systems and their effect on multi-junction solar cells,” Prog. Photovolt: Res. Appl. (2011) published online DOI: . [CrossRef]

], but is outside the scope of this article.

4. Antireflection coating characterization

To analyze the performance of an ARC once it has been manufactured different techniques can be used. It is of interest to characterize ARC performance not only spectrally but also angularly. A direct way of characterizing ARC behavior at different wavelengths could be to measure reflectance by using a spectrometer. For measuring the ARC performance at different angles of incidence, a simple experiment consists on measuring short-circuit current of the solar cell when light strikes the cell with different angles can be carried out by using a goniometer and a cavity that only admits collimating light [27

27. J. Jaus, P. Nitz, G. Peharz, G. Siefer, T. Schult, O. Wolf, M. Passig, T. Gandy, and A. W. Bett, “Second stage reflective and refractive optics for concentrator photovoltaics,” in Proceedings of the 33rd IEEE Photovoltaic Specialist Conf. (2008) pp. 1–5.

-28

28. V. Díaz, J. M. Ruíz, C. Algora, and J. Alonso, “Outdoor characterization of GaAs solar cell under tilted light for its encapsulation inside optic concentrator,” in Proceedings of the 27th Eur.Photovoltaic Sol. Energy Conf., (2001).

].

In this section, we propose a method to analyze the spectral and angular aspects of ARC performance when the cell is illuminated by the actual light field created by the concentrator system with which it is to be used, which provides results that accurately predict the efficiency gain produced by the ARC in the intended application. In our experiments, we illuminate the concentrator with collimated light produced by the Helios 3198 Solar simulator [29

29. C. Domínguez, I. Antón, and G. Sala, “Solar simulator for concentrator photovoltaic systems,” Opt. Express 16(19), 14894–14901 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-19-14894. [CrossRef] [PubMed]

], although measurements could also be done under real sun if adequate tracking and temperature and spectrum controls are used.

In our method, the spectral and angular characterization is carried out separately. First, a set of band-pass filters is used to measure the concentrator optical efficiency at different wavelengths, including the ARC. Optical efficiency ηopt, is defined as the ratio between the effective concentration Xeff, and the geometrical concentration Xgeom, which in turn is obtained dividing the concentrator aperture area Aentrance by its exit area Aexit, this is, the area of the solar cell. The measurement of the short-circuit current with the set of filters gives an estimate of the system spectral response. This response is used to obtain a discrete measurement of the spectral optical efficiency, this is, the optical efficiency at a set of particular wavelengths, ηopt,λi. Every sample can be calculated using the following expression:
ηopt,λi=Xeff,λiXgeo=IscDUT,λiIscDUT(1)IscREF(1)IscREF,λiXgeo
(7)
Xgeom=AentranceAexit
(8)
where IscDUT,λ represents the short-circuit current of the cell in the concentrator when it is illuminated by light filtered with a band-pass filter centered at λi, IscDUT(1) stands for the cell short-circuit current under 1 sun uniform illumination using the entire reference spectrum, and IscREF,λ represents the reference cell short-circuit current when it is illuminated by the same band-pass filter. Figure 4
Fig. 4 Total optical efficiency for different wavelengths measured using 80 nm-wide band-pass filters (dots, right vertical axis). Simulated averaged transmission for the same ARC structures (solid lines, left vertical axis).
shows the result for two cells with different ARC structures (monolayer and bilayer) under the FluidReflex concentrator system. The available materials instead of the ideal ones where used to manufacture the ARC. ARCs to be analyzed were evaporated over a single junction GaAs since subcell current limitation when using multijunction solar cell will prevent the measurement. Solid lines represent simulated transmission for each particular wavelength. Dots represent the measured spectral total optical efficiency ηopt,λi. As 80 nm band-pass filters were used in the measurements, an 80 nm-wide moving-average filter has been applied to the spectral transmittances predicted by simulation in order to equal data resolutions. For each band pass filter, the total optical efficiency depends on the ARC transmission for that bandwidth and on the spectral behavior of the rest of the concentrator (fluid transmittance, mirror reflectance, etc.). Then, although ARC simulated averaged transmission and measured total optical efficiency do not represent exactly the same magnitude, the fact that display a very similar tendency (Fig. 4) proves the effectiveness of the proposed method results spectrally characterize ARC performance within a concentrator. For the monolayer ARC, transmission is lower in the wavelengths region useful for the top cell than in those useful for the middle cell. If the photogenerated current for each subcell is calculated using the expression shown in Eq. (6) and assuming a matched MJ solar cell under the reference spectrum, the top subcell will generate 6% less current than the middle one, reducing significantly the total cell efficiency.

The second proposed method consists on masking the aperture of the CPV system to analyze the optical efficiency when the angular distribution reaching the cell varies. For the FluidReflex system when circular masks with different radii are used, it directly translates into the cell being illuminated by cones of light with different semi-angles. For other more complex systems, ray-tracing simulation must be used to study the angular light distribution over the cell that will create each particular mask. Figure 5
Fig. 5 Efficiency for cells with three different ARC structures (bare cell, bilayer and trilayer ARCs) under FluidReflex concentrator system. Masks with several radii are used to reduce the semi-angle of the incidence light cone.
shows optical efficiency measurements for the FluidReflex system under different semi-angles of incidence of the light cone. As was expected, for almost normal incidence (cone semi-angle < 30°), trilayer and bilayer ARCs transmittances increase significantly with respect to bare cell. Transmittance for the bare cell decreases for semi-angle cones wider than 52°, while for the bilayer ARC transmittance remains almost constant up to 58 ° semi-angle cones. Trilayer ARC not only performs better than the others but its transmittance peaks for a cone with 58° semi-angle, close to the 65° design semi-angle. Note that even coatings optimized for large semi-angles, may show higher transmittances at lower angles because lower incident rays always exhibit lower reflection.

The greatest discrepancy between our experimental and simulated results is the fact that the trilayer ARC transmittes 6 absolute points more than bilayer (Fig. 5), whereas the expected increment when going from a bilayer to a trilayer predicted by numerical simulation (that is Δ1 in Table 2 but calculated for the materials and thicknesses of Fig. 5) was only 2 absolute points. Figure 5 suggests that this is due to underperformance of the bilayer ARC, which is possibly due to manufacturing tolerances. As Fig. 2 showed if an error is committed in one or a combination of several of the layers optical thicknesses ARC performance will considerably decrease. As the bilayer optical thicknesses are lower, manufacturing tolerances of a given magnitude will represent higher relative layer optical thickness changes, and cause greater performance variations in the coating as a whole. Also, the silicon oxide deposition process has been shown to have higher variability than other materials [30

30. C. Stevenson, P. R. Denton, G. Sadkhin, and V. Fridman, “Stability and Repeatability of 2-Layer Anti-Reflection Coatings,” Denton Vacuum technical paper, http://www.dentonvacuum.com/PDFs/Tech_papers/stab.pdf

], and since the bilayer depends more on the SiO2 layer, this further increases the susceptibility of this coating system to manufacturing errors.

5. Conclusions

A numerical model to optimize MJ-cell antireflection coatings (ARCs) has been presented. It takes into account the characteristics of MJ solar cells (broad spectral response and increased spectral sensitivity due to series connection between subcells) and the angular light distribution created by the particular concentration system that will be used to illuminate the cell.

If the angle of incidence of the light reaching the cell under a concentration system is lower than 45°, ARC optimized for normal incidence can be used without expecting significant reflection losses at the cell entrance. However, for systems with wider angles of incidence over the cell an accurate ARC optimization can lead to significant efficiency improvement. A concentrator system composed of a Fresnel lens and a dielectric CPC (Compound Parabolic Concentrator), with an f-number equals to 1.1, may benefit of additional 0.7 percentage points of efficiency increase due to ARC optimization. In the case of reflective systems such as the FluidReflex, where light reaches the cell contained in a 65° semi-angle cone the efficiency increase can be up to 2.9 absolute points.

Furthermore, two experimental methods for characterizing ARC performance by means of illuminating the concentrator have been presented, allowing spectral and angular characterization of the ARC performance to be obtained directly.

Acknowledgments

This work has been partially supported by European commission within the project NACIR (226409-2) under the VII Framework Program. M. Victoria work is directly supported by Spanish Ministry of Science and Innovation under an FPI grant. Authors would like to acknowledge comments and suggestions by S. Askins that have significantly contributed to clarify the objectives and approaches followed in this work.

References and links

1.

A. Luque, Solar cells and optics for photovoltaic concentration (Adam Hilger, 1989).

2.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (Version 38),” Prog. Photovolt. Res. Appl. 19(5), 565–572 (2011). [CrossRef]

3.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

4.

D. J. Aiken, “Antireflection coating design for series interconnected multi-junction solar cells,” Prog. Photovolt. Res. Appl. 8(6), 563–570 (2000). [CrossRef]

5.

C. Algora and V. Díaz, “Modelling of GaAs solar cells under wide angle cones of homogeneus light,” Prog. Photovolt. Res. Appl. 7(5), 379–386 (1999). [CrossRef]

6.

V. Dı́az Luque and C. Algora del Valle, “On the effects of tilted light in a global prediction of AlGaAs/GaAs solar cell performance,” Solar Energy & Solar Cells 57(4), 313–322 (1999). [CrossRef]

7.

C. E. Valdivia, E. Desfonds, D. Masson, S. Fafard, A. Carlson, J. Cook, T. J. Hall, and K. Hinzer, “Optimization of antireflection coating design for multijunction solar cells and concentrator systems,” Proc. SPIE 7099, 709915, 709915-10 (2008). [CrossRef]

8.

S. Wojtczuk, P. Chiu, X. Zhang, D. Derkacs, C. Harris, D. Pulver, and M. Timmons, “InGaP/GaAs/InGaAs 41% concentrator cells using bi-facial epigrowth,” in Proceedings of the 35th IEEE Photovoltaic Specialists Conf. (2010) pp.1259–1264.

9.

A. N. Matveev, Optics (Mir, 1988)

10.

J. S. Rayleigh, “On the reflection of vibrations at the confines of two media between which the transition is gradual” in Proceedings London Math. Soc.11 (1880) pp. 51–56.

11.

D. Poitras and J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. theory,” Appl. Opt. 43(6), 1286–1295 (2004). [CrossRef] [PubMed]

12.

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24(4), 457–460 (1985). [CrossRef] [PubMed]

13.

D. J. Aiken, “High performance anti-reflection coatings for broadband multi-junction solar cells,” Sol. Energy Mater. Sol. Cells 64(4), 393–404 (2000). [CrossRef]

14.

M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, and E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express 16(8), 5290–5298 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-8-5290. [CrossRef] [PubMed]

15.

D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, and J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009). [CrossRef] [PubMed]

16.

E. D. Palik, Handbook of Optical Constant of Solids (Academic Press, 1997).

17.

Sopra materials database, www.sopra-sa.com.

18.

D. Redfield, “Method for evaluation of antireflection coatings,” Solar Cells 3(1), 27–33 (1981). [CrossRef]

19.

M. Victoria, C. Domínguez, S. Askins, I. Antón, and G. Sala, “Optical characterization of FluidReflex concentrator,” in Proceedings of Int. Conf. on Concentrating Photovoltaic Systems (2010) pp. 118–121.

20.

I. Rey-Stolle and C. Algora, “Optimum antireflection coatings for heteroface AlGaAs/GaAs solar cells-Part II: The influence of uncertainties in the parameters of window and antireflection coatings,” J. Electron. Mater. 29(7), 992–999 (2000). [CrossRef]

21.

M. Victoria, C. Domínguez, I. Antón, and G. Sala, “Comparative analysis of different secondary optical elements for aspheric primary lenses,” Opt. Express 17(8), 6487–6492 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-8-6487. [CrossRef] [PubMed]

22.

S. R. Kurtz and M. J. O’Neill, “Estimating and controlling chromatic aberration losses for two-junction, two-terminal devices in refractive concentrator systems,” in Proceedings of the 25th IEEE Photovoltaic Specialists Conf. (1996) pp. 361–364.

23.

L. W. James, “Effects of concentrator chromatic aberration on multi-junction cells,” in Proceedings of the 24th IEEE Photovoltaic Specialists Conf. (1994) pp. 1799–1802.

24.

I. García, C. Algora, I. Rey-Stolle, and B. Galiana, “Study of non-uniform light profiles on high concentration solar cells using quasi-3D distributed models,” in Proceedings of the 33rd IEEE Photovoltaic Specialists Conf. (2008) pp. 1–6.

25.

K. Nishioka, T. Takamoto, and W. Nakajima, “Analysis of triple-junction solar cell under concentration by SPICE,” in Proceedings of the 3rdWorld Conf. on Photovoltaic Energy Conversion (2003) pp. 869–872.

26.

M. Victoria, R. Herrero, C. Domínguez, I. Antón, and S. Askins andG. Sala, “Characterization of the spatial distribution of irradiance and spectrum in concentrating photovoltaic systems and their effect on multi-junction solar cells,” Prog. Photovolt: Res. Appl. (2011) published online DOI: . [CrossRef]

27.

J. Jaus, P. Nitz, G. Peharz, G. Siefer, T. Schult, O. Wolf, M. Passig, T. Gandy, and A. W. Bett, “Second stage reflective and refractive optics for concentrator photovoltaics,” in Proceedings of the 33rd IEEE Photovoltaic Specialist Conf. (2008) pp. 1–5.

28.

V. Díaz, J. M. Ruíz, C. Algora, and J. Alonso, “Outdoor characterization of GaAs solar cell under tilted light for its encapsulation inside optic concentrator,” in Proceedings of the 27th Eur.Photovoltaic Sol. Energy Conf., (2001).

29.

C. Domínguez, I. Antón, and G. Sala, “Solar simulator for concentrator photovoltaic systems,” Opt. Express 16(19), 14894–14901 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-19-14894. [CrossRef] [PubMed]

30.

C. Stevenson, P. R. Denton, G. Sadkhin, and V. Fridman, “Stability and Repeatability of 2-Layer Anti-Reflection Coatings,” Denton Vacuum technical paper, http://www.dentonvacuum.com/PDFs/Tech_papers/stab.pdf

OCIS Codes
(220.1770) Optical design and fabrication : Concentrators
(310.1210) Thin films : Antireflection coatings
(350.6050) Other areas of optics : Solar energy

ToC Category:
Thin Films

History
Original Manuscript: February 15, 2012
Revised Manuscript: March 17, 2012
Manuscript Accepted: March 19, 2012
Published: March 22, 2012

Citation
Marta Victoria, César Domínguez, Ignacio Antón, and Gabriel Sala, "Antireflective coatings for multijunction solar cells under wide-angle ray bundles," Opt. Express 20, 8136-8147 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-8136


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References

  1. A. Luque, Solar cells and optics for photovoltaic concentration (Adam Hilger, 1989).
  2. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop, “Solar cell efficiency tables (Version 38),” Prog. Photovolt. Res. Appl. 19(5), 565–572 (2011). [CrossRef]
  3. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).
  4. D. J. Aiken, “Antireflection coating design for series interconnected multi-junction solar cells,” Prog. Photovolt. Res. Appl. 8(6), 563–570 (2000). [CrossRef]
  5. C. Algora, V. Díaz, “Modelling of GaAs solar cells under wide angle cones of homogeneus light,” Prog. Photovolt. Res. Appl. 7(5), 379–386 (1999). [CrossRef]
  6. V. Dı́az Luque, C. Algora del Valle, “On the effects of tilted light in a global prediction of AlGaAs/GaAs solar cell performance,” Solar Energy & Solar Cells 57(4), 313–322 (1999). [CrossRef]
  7. C. E. Valdivia, E. Desfonds, D. Masson, S. Fafard, A. Carlson, J. Cook, T. J. Hall, K. Hinzer, “Optimization of antireflection coating design for multijunction solar cells and concentrator systems,” Proc. SPIE 7099, 709915, 709915-10 (2008). [CrossRef]
  8. S. Wojtczuk, P. Chiu, X. Zhang, D. Derkacs, C. Harris, D. Pulver, and M. Timmons, “InGaP/GaAs/InGaAs 41% concentrator cells using bi-facial epigrowth,” in Proceedings of the 35th IEEE Photovoltaic Specialists Conf. (2010) pp.1259–1264.
  9. A. N. Matveev, Optics (Mir, 1988)
  10. J. S. Rayleigh, “On the reflection of vibrations at the confines of two media between which the transition is gradual” in Proceedings London Math. Soc.11 (1880) pp. 51–56.
  11. D. Poitras, J. A. Dobrowolski, “Toward perfect antireflection coatings. 2. theory,” Appl. Opt. 43(6), 1286–1295 (2004). [CrossRef] [PubMed]
  12. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24(4), 457–460 (1985). [CrossRef] [PubMed]
  13. D. J. Aiken, “High performance anti-reflection coatings for broadband multi-junction solar cells,” Sol. Energy Mater. Sol. Cells 64(4), 393–404 (2000). [CrossRef]
  14. M. F. Schubert, F. W. Mont, S. Chhajed, D. J. Poxson, J. K. Kim, E. F. Schubert, “Design of multilayer antireflection coatings made from co-sputtered and low-refractive-index materials by genetic algorithm,” Opt. Express 16(8), 5290–5298 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-8-5290 . [CrossRef] [PubMed]
  15. D. J. Poxson, M. F. Schubert, F. W. Mont, E. F. Schubert, J. K. Kim, “Broadband omnidirectional antireflection coatings optimized by genetic algorithm,” Opt. Lett. 34(6), 728–730 (2009). [CrossRef] [PubMed]
  16. E. D. Palik, Handbook of Optical Constant of Solids (Academic Press, 1997).
  17. Sopra materials database, www.sopra-sa.com .
  18. D. Redfield, “Method for evaluation of antireflection coatings,” Solar Cells 3(1), 27–33 (1981). [CrossRef]
  19. M. Victoria, C. Domínguez, S. Askins, I. Antón, and G. Sala, “Optical characterization of FluidReflex concentrator,” in Proceedings of Int. Conf. on Concentrating Photovoltaic Systems (2010) pp. 118–121.
  20. I. Rey-Stolle, C. Algora, “Optimum antireflection coatings for heteroface AlGaAs/GaAs solar cells-Part II: The influence of uncertainties in the parameters of window and antireflection coatings,” J. Electron. Mater. 29(7), 992–999 (2000). [CrossRef]
  21. M. Victoria, C. Domínguez, I. Antón, G. Sala, “Comparative analysis of different secondary optical elements for aspheric primary lenses,” Opt. Express 17(8), 6487–6492 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-8-6487 . [CrossRef] [PubMed]
  22. S. R. Kurtz and M. J. O’Neill, “Estimating and controlling chromatic aberration losses for two-junction, two-terminal devices in refractive concentrator systems,” in Proceedings of the 25th IEEE Photovoltaic Specialists Conf. (1996) pp. 361–364.
  23. L. W. James, “Effects of concentrator chromatic aberration on multi-junction cells,” in Proceedings of the 24th IEEE Photovoltaic Specialists Conf. (1994) pp. 1799–1802.
  24. I. García, C. Algora, I. Rey-Stolle, and B. Galiana, “Study of non-uniform light profiles on high concentration solar cells using quasi-3D distributed models,” in Proceedings of the 33rd IEEE Photovoltaic Specialists Conf. (2008) pp. 1–6.
  25. K. Nishioka, T. Takamoto, and W. Nakajima, “Analysis of triple-junction solar cell under concentration by SPICE,” in Proceedings of the 3rdWorld Conf. on Photovoltaic Energy Conversion (2003) pp. 869–872.
  26. M. Victoria, R. Herrero, C. Domínguez, I. Antón, S. Askins andG. Sala, “Characterization of the spatial distribution of irradiance and spectrum in concentrating photovoltaic systems and their effect on multi-junction solar cells,” Prog. Photovolt: Res. Appl. (2011) published online DOI: . [CrossRef]
  27. J. Jaus, P. Nitz, G. Peharz, G. Siefer, T. Schult, O. Wolf, M. Passig, T. Gandy, and A. W. Bett, “Second stage reflective and refractive optics for concentrator photovoltaics,” in Proceedings of the 33rd IEEE Photovoltaic Specialist Conf. (2008) pp. 1–5.
  28. V. Díaz, J. M. Ruíz, C. Algora, and J. Alonso, “Outdoor characterization of GaAs solar cell under tilted light for its encapsulation inside optic concentrator,” in Proceedings of the 27th Eur.Photovoltaic Sol. Energy Conf., (2001).
  29. C. Domínguez, I. Antón, G. Sala, “Solar simulator for concentrator photovoltaic systems,” Opt. Express 16(19), 14894–14901 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-19-14894 . [CrossRef] [PubMed]
  30. C. Stevenson, P. R. Denton, G. Sadkhin, and V. Fridman, “Stability and Repeatability of 2-Layer Anti-Reflection Coatings,” Denton Vacuum technical paper, http://www.dentonvacuum.com/PDFs/Tech_papers/stab.pdf

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