Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

phys. stat. sol. (a) 205, No. 12, 2811–2821 (2008) / DOI 10.1002/pssa.200880456 p s sapplications and materials science

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Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies

Jan Christoph Goldschmidt*, 1, Marius Peters1, Liv Prönneke2, Lorenz Steidl3, Rudolf Zentel3, Benedikt Bläsi1, Andreas Gombert1, Stefan Glunz1, Gerhard Willeke1, and Uwe Rau4

1 Fraunhofer Institute for Solar Energy Systems, Heidenhofstr. 2, 79110 Freiburg, Germany 2 Institut für Physikalische Elektronik, Universität Stuttgart, Pfaffenwaldring 47, 70569 Stuttgart, Germany 3 Institut für Organische Chemie, Universität Mainz, Duesbergweg 10–14, 55128 Mainz, Germany 4 IEF-5 Photovoltaik, Forschungszentrum Jülich, 52425 Jülich, Germany

Received 9 July 2008, revised 17 September 2008, accepted 21 September 2008

Published online 18 November 2008

PACS 42.15.Dp, 42.15.Eq, 42.79.Ek, 42.79.Nv, 81.16.Dn, 84.60.Jt

* Corresponding author: e-mail [email protected], Phone: +49 761 4588 5475, Fax: +49 761 4588 9250

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Fluorescent or luminescent concentra-tors are a concept well known since the late seventies [1, 2]. These devices allow concentrating sunlight without track-ing systems. In addition, they not only utilize direct radia-tion from the sun but also the diffuse part of the solar radiation. In a fluorescent concentrator dye molecules em-bedded in a dielectric matrix absorb the incident radiation and emit light with a longer wavelength in random direc-tion. Total internal reflection traps most of the emitted light and guides it to solar cells which are optically cou-pled to the edges or the bottom of the concentrator. In a stack of fluorescent concentrators, each concentrator with a different dye collects a different part of the solar spectrum. These different parts can be used by solar cells which are especially efficient in the spectral region of the concentra-tor they are attached to. The solar cells can be intercon-nected with a high degree of freedom, which is a clear ad-vantage over tandem cell concepts with a forced serial in-terconnection and the need for tunnel diodes and current matching of the different solar cells.

Fluorescent concentrators were investigated intensively in the early eighties [3, 4]. Research in those days aimed at cost saving by using the concentrator to reduce the need for expensive solar cells. However, several problems led to reduced research interest. First, the used organic dyes had only relatively narrow absorption bands. Secondly, al-though the organic dyes showed high quantum efficiencies of the absorption and reemission process above 95% in the visible range of the spectrum, quantum efficiencies re-mained at 50% and lower in the infrared. Furthermore, the dyes which were sensitive in the infrared were unstable under long-term illumination. Reabsorption of the emitted light due to overlapping absorption and emission spectra further reduced efficiencies [3]. Based on conceptual pro-gress and new materials several groups (see e.g. Refs. [5–15]) are currently reinvestigating the potential of fluo-rescent concentrators. These new concepts aim especially at the suppression of the escape cone losses. Figure 1 shows a standard fluo-rescent concentrator where all light which is emitted by the

In this study we present a theoretical and experimental analy-

sis of the application of photonic band stop filters on top of

photovoltaic fluorescent concentrators in order to increase the

photon collection efficiency. The light guiding effect of the

fluorescent concentrator relies on total internal reflection. The

escape cone of total internal reflection is their major loss

mechanism. Our ray tracing simulation allows to calculate

the beneficial effect of photonic band stop reflection filters,

which reduce these losses, and to simulate the angular distribu-

tion of the light trapped in the concentrator. We present simula-

tions of the optical properties of 1D and 3D photonic structures

and how 3D structures are realized with colloidal opals. We

also show that the application of a 1D photonic structure in-

creases the efficiency of a real system by 20% relative.

2812 J. C. Goldschmidt et al.: Photonic structures for fluorescent concentrators

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Figure 1 (online colour at: www.pss-a.com) Escape cone of total

internal reflection is the major loss mechanism of a fluorescent

concentrator. Light impinging onto the surface with an angle

smaller than the critical angle θc is lost. For PMMA about 26% of

the light is lost after every emission process. Because of reab-

sorption and reemission, total losses are considerably higher than

26%.

dyes and impinges on the internal surface with an angle smaller than the critical angle θc leaves the collector and is therefore lost. The critical angle is given by θc = arcsin (1/n), with n being the refractive index of the matrix material. The light which impinges with greater an-gles is totally internally reflected. Integration gives a frac-tion

F = (1 – n–2)1/2 . (1)

of the re-emitted photon flux that is trapped in the collector [16]. For PMMA (Polymethylmethacrylat) with n = 1.5 this results in a trapped fraction of around 74%, which means that a fraction of 26% is lost. Since this loss occurs after every re-absorption and re-emission process, the ef-fective loss due to this mechanism is considerably higher than 26% especially for large collector sizes. To reduce these losses the application of hot mirrors was proposed in Ref. [5] and the application of photonic structures in Ref. [10]. Figure 2 depicts that such a photonic structure should act as a band stop reflection filter which allows radiation with energy in the absorption range

Figure 2 (online colour at: www.pss-a.com) A photonic structure

reduces the escape cone losses. The photonic structure acts as a

band stop reflection filter. It allows light in the absorption range

of the dyes to enter the collectors, but reflects light in the emis-

sion range.

of the dye to enter the collector but reflects photons in the spectral emission range of the dye. Thus, the collector traps an increased amount of light which is guided to the solar cells at the rims. In this paper, we concentrate on how the escape cone losses can be reduced by using selectively reflective photonic structures. We examine theoretically and experi-mentally the increase of solar cell efficiency coupled to fluorescent collectors under applied photonic structures. In section two a Monte-Carlo ray-tracing simulation predicts a significant increase of the photon collection probability due to a photonic band stop filter. Section three presents optical simulations of one and three dimensional photonic structures. In section four we set a starting point for exam-ining the effect of photonic structures on the angular distri-bution of light guided to the collector sides. Section five outlines our results in producing three dimensional photonic crystals. Finally, in section six we prove that a photonic structure raises the efficiency of a solar cell cov-ering a fluorescent collector side by 20% relative. 2 Ray tracing simulations of fluorescent con-centrator systems with idealized photonic struc-tures To understand and quantify the effect of the photonic structure and to optimize the fluorescent concen-trator system, we developed a Monte-Carlo ray-tracing simulation of the fluorescent concentrator [17]. The fluo-rescent concentrator is modelled with all edges fully cov-ered with solar cells and the back side with a mirror. Fig-ure 3 depicts the dye properties modelled in this paper: The absorption constant α increases stepwise from zero at en-ergies E < E2 to α2 for E2 < E < E1 and to α1 for energies E > E1. The emission results from Kirchhoffs law

r bb( ) ( ) ( ) ,e E E n Eα φ= (2)

where φ bb is the black body spectrum and nr the refractive index of the collector material. Throughout this section, we

Figure 3 Absorption and emission scheme of the fluorescent dye

in the ray tracing model. The absorption constant rises step like

from zero to α2 at energy E2 and again to α1 for energies E > E1.

Because of Kirchhoff’s law (Eq. (2)), the emission coefficient e2

at E2 is higher than e1 at E1. The energy selective photonic band

stop (PBS) reflects all the light between E1 and E2 and therefore

keeps emitted light in the fluorescent concentrator.

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Figure 4 Fluorescent collector geometry modelled in this paper:

solar cells cover all four sides of the collector fully. Therefore,

increasing normalized collector length l/d decreases coverage

fraction f = 4ld/l 2. Mirror covers the back side of collector. A

photonic band stop (PBS) filter can be placed on top of the con-

centrator optionally.

assume E1 = 2.0 eV, E2 = 1.8 eV and absorption coeffi-cients α1 = 3/d, α2 = 0.03/d where d denotes the thickness of the, fluorescent concentrator. That definition means that the concentrator absorbs the same amount of light during one light path independently from its thickness. A thicker fluorescent concentrator would have a lower dye density per volume. The fluorescent concentrator emits most likely photons with energy E2, whereas the emission for energies E > E1 is significantly lower. With this absorption/emission behaviour, we consider the detailed balance limit of fluo-rescent concentrators with a continuous spectral photo-voltaic action [10, 11, 18]. Figure 3 also features the func-tionality of an idealized photonic band stop (PBS) filter, which transmits rays with E > E1 into the collector and blocks the emitted photons with energy E < E1 in order to keep them in system. Figure 4 shows the geometry of fluorescent collectors in the photovoltaic system analyzed in this paper. Every increase of the collector length l in x- and y-direction, nor-malized to the collector thickness d, leads to a decreased coverage fraction

2

cell coll/ 4 / 4 / ,f A A dl l d l= = = (3)

with the cell area Acell and the collector aperture Acoll. Figure 5 shows the dependence of the photon collec-tion probability pc on the normalized collector length l/d calculated for side-mounted solar cells with PBS (full symbols) and without PBS (open symbols). Aside from the radiative limit, we also consider non-radiative recombina-tion in the dye by assuming different probabilities for non-radiative processes after the absorption of a photon of pnr = 0.1, 0.5, 0.7, and 0.95. Most importantly, applying a PBS leads to a consid-erably higher photon collection. The reason lies in the sup-pressed emission from the top surface as shown in Fig. 2. This radiative loss occurs in the uncovered system when-ever a photon falls into the critical angle θc of total internal reflection. In the system with PBS the photon additionally must be emitted at an energy E ≥ E1, which happens with a low but, for reasons of detailed balance, non-zero probabil-

Figure 5 Dependence of the collection probability pc of a fluo-

rescent collector fully covered with solar cells at its sides on the

collector length l normalized to the thickness d. A perfect mirror

covers the back side. In systems with a photonic band stop (PBS,

full symbols) pc is higher than in those without PBS (open sym-

bols). For a system with PBS in its radiative limit (pnr = 0) a col-

lection probability pc close to unity remains up to a normalized

collector length l/d ≈ 500. In contrast, the system without PBS

has a maximum pc only slightly above 80%. With increasing col-

lector length l/d, which means a decreased coverage fraction f

(top axis) the collection probability pc decreases immediately.

Considering non-radiative recombination in the dye (pnr > 0) de-

teriorates pc in all cases.

ity. The suppressed emission also results in high photon collection probabilities pc of systems with PBS at larger collector lengths l/d. The systems without PBS collect con-siderably less photons already for slight increases of l/d. With increased l/d the number of photons that are absorbed by the dye more than once increases. Each absorption event leads to θ-randomization of the re-emitted photon and, in consequence, to a certain probability that the pho-ton is lost by emission from the collector surface. The loss through the top surface, as mentioned above, is much more likely for the systems without PBS than for those with PBS. Therefore, the deterioration of pc by large scales is higher in the uncovered systems. Figure 5 also shows the impact of non-radiative re-combination in the dye (pnr = 0.1, 0.5, 0.7, and 0.95). The system covered with PBS is especially sensitive to non-radiative recombination at l/d > 100. Before a photon reaches the solar cell at the collector side, it is most likely only absorbed once in small-scaled systems. Here, the maximum of pc decreases proportionally to (1 – pnr). But in large-scaled systems, the repeated re-absorption of photons leads, aside from more radiative losses, to a higher risk of non-radiative recombination. Whereas in the non-radiative case a value of pc > 90% remains up to a normalized col-lector length l/d ≈ 500, for pnr = 0.1 the systems achieve pc ≈ 90% only for l/d ≤ 10. A further increase of pnr leads

2814 J. C. Goldschmidt et al.: Photonic structures for fluorescent concentrators

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to collection probabilities significantly lower than 90% (e.g. 50% for pnr = 0.5 and 30% for pnr = 0.7). As radiative losses are low in the systems with PBS the relative impor-tance of non-radiative losses is much more important. In contrast, the radiative emission losses are already high in the systems without PBS. Therefore, the deterioration in pc caused by non-radiative recombination is not as significant over the whole range of l/d as in the systems with PBS. A larger pnr diminishes the differences in pc for the systems with and without PBS. However, applying a PBS is always advantageous, especially for the retardation of reaching the large scale limit. 3 Simulation of the optical properties of realis-tic photonic band stop filters In the previous section we have shown, that an idealized photonic structure has a huge beneficial impact on the collection efficiency of the fluorescent concentrator. In this section, we will simulate the optical properties both of one-dimensional (1D) and three-dimensional (3D) photonic structures, which could serve as photonic band stop (PBS) reflection filter. The de-sired filter characteristics are high transmittance in the absorption range of the dye and high reflectance in its emission range. As we are interested in solar application no polarisation effects have been considered and all data given are (TE + TM)/2. 3.1 One dimensional photonic structures A pos-sible realization of the PBS filter are 1D photonic crystals; systems in which the refractive index is varied in one di-rection only. The stop gap of these structures is matched to the emission characteristic of the dye by choosing the characteristic dimension of the structure accordingly. Typically, these structures are produced by depositing thin layers of different discrete refractive indices. To simulate the 1D photonic structures we use the formalism of charac-teristic matrices [21]. An example for such a structure is the rugate filter. In a rugate filter the refractive index is varied sinusoidally. Fig-ure 6 shows the simulation results for the angular character-istics of such a filter. The special feature of the rugate filter is that only a single stop gap between 500 nm and 650 nm exists. Undesirable harmonic stop bands are suppressed. As the simple rugate structure still shows sidelobes and un-wanted reflection with a high magnitude outside the stop gap an optimization process [19] is used to fit the rugate filter to our purpose. However, these structures also have some dis-advantageous aspects: First, the Fresnel reflections on a simple surface show an enhanced reflectance for an increas-ing angle of incidence of the light. This is a general aspect of surfaces and happens as well for the surface of the fluores-cent concentrator as for the one of the 1D photonic crystal. Figure 6 points out this increased reflection with higher an-gles of incidence. This effect results in a diminished use of the diffuse light for the system with filter. Furthermore, a blue shift occurs for the stop gap of the photonic structure that is caused by the Bragg effect [20].

Figure 6 (online colour at: www.pss-a.com) Simulation of the

angular dependent reflectance of the rugate filter. With increasing

angles of incidence the reflectance of the filter outside the stop

gap increases. The stop gap is shifted towards smaller wave-

lengths (blue shift). The period of the rugate filter shown is

160 nm, the refractive index is varied sinusoidally between

n = 1.6 and n = 2.0. An optimization is used to suppress side

lobes. This effect is very detrimental, because the stop gap is shifted into the absorption range of the dye. To overcome this problem, there are several strategies. Even with 1D fil-ters it is possible to suppress the blue shift. For this pur-pose the numerical needle method has been proposed [22, 23]. Other possibilities lie in the use of higher dimensional photonic crystals that feature omni-directional filters [24]. However, these filters show an undesirable broadening of the reflection peak. One of the future tasks will be to evaluate the angular characteristics of these filters with re-gard to their application on fluorescent concentrators. 3.2 Three dimensional photonic structures To overcome the disadvantages of the 1D photonic structures 3D photonic crystals might be a solution. To investigate and optimize these structures we have set up routines to simulate 3D photonic crystals. We use a code based on the rigorous coupled wave analysis (RCWA) method [25] that was developed at the University of Paris [26]. This method calculates the electromagnetic field within the structure rigorously. With this information we obtain the optical characteristics like transmission, reflection and absorption.

A first example of a 3D photonic crystal considered for the application on a fluorescent concentrator is the opal. Opals consist of spheres ordered in a closest package, typi-cally assumed to be the face centred cubic (fcc) structure This structure was chosen because with the vertical deposi-tion [27] a method exists with which the crystal can be pro-duced on large areas. A RCWA simulation of an opal is shown in Fig. 7. For our application the stop gap between the 2nd and the 3rd band in the ΓL-direction, the direction in which the opal typically growth is used for the spectral selectivity. The spectral selectivity of the opal was tuned to our test system by adjusting the size of the spheres accord-ingly. With the opal it is in principle possible to overcome the high reflectance for high angles of incidence. The reason

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Figure 7 (online colour at: www.pss-a.com) z-component of the

electric field inside an opal simulated with the RCWA method.

The wavelength of the light for illumination is λ = 550 nm. The

method gives all six components of the electromagnetic field

separately. From the EM field the optical properties of the struc-

ture are obtained. The simulated opal consists of spheres with a

radius r = 150 nm and a refractive index n = 1.5. The opal con-

sists of 12 layers of sphere of which the top six layers are dis-

played. While the opal has a finite thickness of 3 µm, the expan-

sion into the x- and y-direction is infinite.

for this lies in the diffractive behaviour of the opal. Orders of diffraction higher than the 0th order occur that allow an incoupling of the light even for angles of incidence close to 90°. A simulation of this effect for our test system is shown in Fig. 8. In this figure a polar–azimuth plot of the reflection of an opal is displayed. The r-component gives the polar angel, the ϕ-component the azimuth angle. The

Figure 8 (online colour at: www.pss-a.com) Polar–azimuth plot

of the simulated reflectance of an opal. The opal consists of

21 layers of spheres. The spheres have a radius r = 254.7 nm and

a refractive index n = 1.5. The wavelength of the light used for

illumination is λ = 540 nm. The red encircled space marks the

angular range for which light is coupled into the fluorescent con-

centrator because of diffractive effects.

opal shown consists of 21 layers of spheres with a radius of r = 254.7 nm and a refractive index of n = 1.5. The plot shows the angular dependant reflection for a single wave-length λ = 540 nm. This plot shows that it is principally possible to couple light into the fluorescent concentrators even if it impinges under very high angles. The area is red encircled and shows a considerably low reflectance for an-gles of incidence close to 90°. As in the simulation no ab-sorption was assumed, this is equivalent to a high trans-mission. This effect originates from the diffractive nature of the opal. In the encircled area the first order of diffrac-tion is coupled into the crystal. The angular selective re-flectance of the opal is also given by the Bragg formula [20]

eff

2 2

111 111( ) 2 sin ( ) ,d nλ θ θ= ◊ ◊ - (4)

with the wavelength λ111 of maximum reflection under the angle θ and the distance d111

between the crystal planes of the opal in 111 direction. Taking into account the filling fraction of the opal, that is the volume actually filled with material, we derive the effective refractive index. A typical opal consists of spheres with a refractive index of n = 1.5 and a filling fraction of 74%. The remaining volume con-sists of air voids. The typical effective refractive index of an opal is therefore neff = 1.37 and thus lower than the typi-cal effective refractive index of a rugate filter which is in the range of neff = 1.7. From Eq. (4), a lower effective re-fractive index results in a more pronounced blue shift of the position of the reflectance peak. This is disadvanta-geous regarding the fluorescent concentrator as the reflec-tance peak is shifted into the absorption range of the dye and therefore especially diffuse light is blocked. This problem may be solved by the application of other three dimensional structures. First considerations show that the diamond structure is a possible candidate here. Simula-tions show, that the reflection peak of the diamond struc-ture changes only weakly with the angle of incidence, be-cause of the different crystal structure. Another possibility is the application of inverted or coated opals to increase the effective refractive index and therefore reduce the blue shift. However, to our knowledge there is no possibility to produce diamond structured crystals on large areas and in-verted opals used in the experiments yielded severe scatter-ing losses because of their poor quality. 4 Angular distribution of the trapped and col-lected light According to the previous section we can ex-pect a pronounced angular characteristic from real photonic structures. To be able to understand the effect of the photonic structure on the light guiding in the concentra-tor we are therefore interested in analyzing the angular dis-tribution of the light which is trapped in the concentrator and subsequently guided to the edges. Figure 9 sketches the experimental setup. An index-matched half cylinder is optically coupled to the edge of the concentrator such that at this edge no total internal reflection occurs. If the cylin-

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Figure 9 (online colour at: www.pss-a.com) Experimental setup

to measure the angular distribution of the light which is coupled

out at the edges of the fluorescent concentrator.

der is large in comparison to the thickness of the concen-trator, the light impinges on the outer surface of the cylin-der perpendicularly. The light leaves the cylinder without significant refraction and the intensity is measured accu-rately at every angle θ . The concentrator material consisted of an organic dye from BASF embedded in a PMMA ma-trix. The material was produced during the first research campaign in the Eighties [3] and shows excellent stability since. The concentrator was 3 mm thick and 5 × 5 cm in size. The half cylinder was also made from PMMA and is 2 cm thick. The surroundings of the half cylinder were covered with blinds, so only light leaving the concentrator directly into the half cylinder was detected. As shown in Fig. 10, the intensity drops significantly at angles θ ≈ 50° and 130°, which correspond to the critical angle of total internal reflection. That is, only the photons with angles θ < 50° or θ > 130° which are emitted close to the edge of the concentrator and therefore can reach the cylinder without a reflection at the top or the back surface

Figure 10 (online colour at: www.pss-a.com) Measured angular

distribution of the light which is coupled out at the edges of a

5 × 5 × 0.3 cm fluorescent concentrator.

Figure 11 Path of different rays in the fluorescent concentrator.

(a) Definition of ray angle θ and ray section element dw, needed

in Eq. (3). (b) Rays coming with angle θ > 90° pass by a lot of

sources for emitted photons, but traverse at last through the bot-

tom area of the concentrator, where only little light is emitted,

because of the absorption profile in the concentrator. (c) Rays

with angle slightly less than 90° collect only few photons on their

short way through the collector but they pass through the stronger

emitting front of the concentrator. (d) In this case the rays experi-

ence the same distance as in case b), but traverse the top section

in the end.

of the fluorescent concentrator are detected. Additionally the angular distribution shows an unexpected anisotropic dip around θ = 90°. We explain this dip and asymmetry around θ = 90° as follows: Because of the absorption of the incoming light in the concentrator the intensity of the incoming light drops with increasing distance from the front surface. Thus, also less light is emitted further away from the front surface. Additionally, because of re-absorption, the region close to the edge contributes more to the measured intensity than the region further away. Figure 11a–d show that light detected with an angle <90° originates partly from the area close to edge and close to the front surface; an area were a high flux of light is emitted. In contrast, the light which is detected with an-gles >90° stems either from regions where less light is emitted (close to the bottom of the concentrator) or has to travel longer distances in the concentrator, which means higher re-absorption losses. Therefore, the spatial distribu-tion of the absorption of the incident light and the resulting re-emission profile is responsible for the anisotropy in the angular distribution in Fig. 10. For a more quantitative analysis we use an analytical approach. In our model, we consider one ray for each angle θ . This ray collects or looses photons on its path through the entire concentrator. Figure 11a defines the angle θ and the path element dw of the ray. The change in the photon flux Φ along the path w of the ray is

Re

d,

dG A

w

Φ= - (5)

with the generation G and re-absorption ARe of photons in the collector. The generation G results from incoming pho-tons which the dye absorbs with an absorption constant α1

and emits with a probability of unity. Because the incom-ing light is preferentially absorbed close to the top surface of the concentrator, the re-emission profile decreases with

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increasing distance from the top surface. Thus, for a ray which runs from the top surface to the bottom the genera-tion at a certain distance w is

1 cos

e ,w

Gα θ

γ-

= (6)

with a proportionality factor γ. For the whole generation along the path of a ray with multiple reflections the contri-butions from the single passes have to be added up. Note that for the path with the ray running from the bottom to the top of the concentrator, the sign in the exponent of Eq. (6) changes. Emitted photons are re-absorbed with the absorption constant α2 and therefore, the re-absorption

Re 2,A α Φ= (7)

acts as a drain for photons. Depending on its starting point and angle θ every ray experiences a certain amount of re-flections. As we can see in Fig. 11, rays (b) and (c) both experience the same numbers of reflections. Since their ways through the collector have the same lengths they ex-perience the same loss due to re-absorption. The difference causing the anisotropy in Fig. 10 is due to ray (d) travers-ing the top section of the collector in the end, where the generation rate is high. Therefore on its way from the last reflection through the collector it collects more photons than ray (b) in Fig. 11 whose last segment comes from the back side where the generation rate is low. Ray (c) with an angle slightly lower than 90° sees only a few sources, but these are close to the top surface, where the generation rate is high. Such, this ray collects more photons on its way than a ray detected with an angle slightly higher than 90. Inserting Eqs. (6) and (7) in Eq. (5) and integrating the change in the photon flux along the ray path provides the photon flux Φ of photons for every angle. This calcu-lated photon flux Φ should correspond to the measured in-tensity for every angle. Figure 12 presents the results from a fit of the analytical approach to the experimental data. In addition, we have entered the optimized parameters (ab-

Figure 12 (online colour at: www.pss-a.com) Experimental data

are fitted with an analytical approach. The optimized parameters

of absorption constants α1, α2 and the refractive index nr are en-

tered into the Monte-Carlo simulation.

Figure 13 (online colour at: www.pss-a.com) Angular distribu-

tion at the collector sides remains mostly unchanged for an as-

sumed dipole characteristics of the photon emission of the dye in-

stead of a random emission that is uniform in all spherical angles.

sorption constants α1 = 0.185 cm–1, α2 = 0.078 cm–1 and the refractive index nr = 1.28) into the Monte-Carlo ray-tracing simulation described in Section 2. Both, the analytical fit and the numerical results show good agreement with the experimental data at the drop in intensity for the angle of total internal reflection θc. Unfortunately, this holds only for an assumed refractive index which is lower than the re-fractive index of the dielectric material. Both approaches also form the peak before θ = 90°, but fail to shape accu-rately the experimental data for 100° < θ < 120°. We be-lieve that this discrepancy is caused by the simplifying assumption of a two-level absorption coefficient in the analytical as well as in the Monte-Carlo model. A more detailed absorption behavior should lead to a more quanti-tative reproduction of the experimental data. However, our modelling results unveil the basic mechanism of the aniso-tropy. Figure 13 analyzes the effect of an increased α1 and an assumed dipole moment in the emission characteristic of the dye. Increasing the absorption coefficient α1 of the in-coming light leads to a higher generation rate close to the top surface. Therefore, the anisotropy in the angular distribution is more obvious for α1 = 1 cm–1 than for α1 = 0.3 cm–1. We have further analyzed the effect of a di-pole like emission characteristics of the dye instead of a random emission that is strictly uniform into all spherical angles. As can be seen from Fig. 13, the differences be-tween dipole and uniform emission are almost negligible. Therefore, we can conclude that the physically more realis-tic dipole emission characteristic has only little influence on the randomization of the light and the resulting angular distribution of the light trapped in the concentrator. 5 Production of photonic band stop filters with polymer opals As discussed in Section 3 3D photonic crystals with an opal like crystal structure are a promising option to realize the desired band stop reflection filters. In this section, we describe how such structures can be real-ized as colloidal opals. Such colloidal photonic opals con-

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sist of SiO2 or polymer spheres which are crystallised into a face centered cubic (fcc) lattice. As mentioned before the reflectance of such an opal depends on the size of the crys-tallised beads as well as the angle of incidence and are de-scribed by the modified Bragg equation (see Eq. (4)). The higher the ordering in these colloidal crystals the more distinct is the Bragg reflectance and the lower is the rate of diffuse scattering. Hence, the preparation of a good opal reflector requires (1) the preparation of monodisperse colloids with controlled size to fit the desired reflectance wavelength and (2) an appropriate method for bead crystal-lization to achieve a well-ordered crystal structure. To address these requirements monodisperse PMMA colloids were prepared by surfactant-free emulsion polym-erization (SFEP) whereby the size of the colloids was con-trolled by adjusting the monomer to water ratio at a given initiator concentration and temperature [28]. By crystalliz-ing these beads opaline films of high quality can be pre-pared. For the build-up of the opal reflectors on the fluo-rescent concentrator there are two possible approaches: On the one hand thin opal films can be crystallized directly on PMMA, which is the material of the fluorescent concentra-tor, on the other hand we tried to create free standing opal films, which can be attached to the substrate in a second step. With these approaches reflector films, which are ei-ther directly attached to the fluorescent concentrator or with an air gap in between can be produced. 5.1 Crystallization on PMMA Many techniques have been designed for the assembly of colloidal spheres into ordered structures including vertical deposition by lift-ing the substrate out of suspension of dispersed colloids, the usage of flowing cells or most simply the slow drying of a colloidal dispersion on a flat substrate [29]. Regardless of the method hydrophobic substrates (like PMMA) are not preferable for two reasons. First, the build-up of a ho-mogenous opal film is almost impossible during horizontal drying due the insufficient wetting of the substrate, which results in opal films of low quality. Secondly, the forces on the interface between the substrate and the suspension, which are driving the crystallization in a moving meniscus are not acting at a hydrophobic substrate. This leads to no film formation at all in case of a vertical deposition [30]. Therefore, 2 × 2 cm PMMA substrates were hydrophi-lized by an oxygen plasma treatment. The effect of this pre-treatment was followed by contact angle measurements. Figure 14A–C show the result of such a measurement.

Figure 14 Contact angle measurements (water on PMMA). (A)

without pre-treatment, (B) after 3 min of oxygen plasma, (C)

15 min after the treatment.

Figure 15 (online colour at: www.pss-a.com) Reflection peak of

an opaline film from 256 nm PMMA-beads (size calculated with

Eq. (4)) compared to the emission and absorption spectrum of the

fluorescent concentrator. The overlap of the opal reflection and

the dye emission is observable.

Partial oxidation of the polymer chains on the surface by the oxygen plasma results in a lowering of the contact angle from 80° to approximately 35° showing the increased hydrophilicity. However, during annealing in a hydrophobic environment (air) the oxidized polymer chains move back into the bulk material and the contact angle increases again. Hence, the effect of the plasma pre-treatment is vanishing rather quickly and an immediate use of the treated substrate for the crystallization experiment is necessary. Although opal films of high quality could be prepared on these substrates by vertical deposition we concentrated on a horizontal crystallization approach. This was done be-cause horizontal crystallization is the easiest way to cover just one side of the substrate with an opaline film and the method is not limited by the size of the PMMA device. As a result of these experiments opaline films of high quality on PMMA substrates with a reflectance well above 70% could be prepared. Figure 15 shows that the film reflectance peak overlaps with the emission band of the dye used in the fluorescent concentrator. In addition, these films show high brilliance and a strong reflectance. Furthermore, it seems possible to increase the height of the reflectance further by increasing the crystal quality. This will also reduce scattering, which contributes to the broadband reflection visible in the spec-tral region from 350 nm to 525 nm. This reflection should be reduced, so that no light which can be used by the dye is prevented to enter the collector. 5.2 Preperation of free standing opal films The preparation of a free standing opal film involves (i) the crystallization of the colloids, (ii) the removal of the opaline film from the substrate and (iii) the transfer of the opal film to the fluorescent concentrator. Since the opal film has to be of several cm2 in size a general problem arises from the low stability of colloidal photonic crystal. The colloids of the opals are negatively charged, which is

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Figure 16 (online colour at: www.pss-a.com) (A) Photo of an

opaline film swimming on a water surface. (B) SEM image after

transfer to glass showing a fragment on the opal surface.

advantageous for the crystallization process since the beads are prevented from coagulation and they form a well ordered structure; but this leads to weak attractive forces between the beads in the resulting opal as well. A strong stabilization ef-fect can be achieved if the beads are chemically linked to each other. This is possible by the use of core-shell colloids, which can be synthesized with a slightly modified SFEP-method. The beads consist of a PMMA-core and a shell of a functional monomer (glycidyl methacrylate – GMA) which can be crosslinked upon heating [31]. Opaline films prepared from such core-shell beads show a strongly enhanced mechanical stability [32]. How-ever, chemical links between the beads and the surface strongly connect these opal films to the substrate. This complicates the transfer process and the preparation of a free standing film. We solve this problem with a fluid sub-strate, from which we lift the stabilized film. The crystalli-zation of polymer opals on fluid metals has already been shown [33]. The removal of traces of gallium, which is sticking to the opaline film, is however a problem. Figure 16A and B show the results for the alternative approach we developed: the colloids are crystallized on a sacrifice layer, which is removed after the stabilization of the opal. For this approach a tert-Butylmethacrylate (t-BMA) film containing 15 wt% of acid (p-toluene sul-fonic acid) was spun on a glass slide and hydrophilized using oxygen-plasma treatment. On this thin film a colloi-dal photonic crystal from PMMA-co-GMA core-shell colloids was grown. Thereafter, the glass slide was heated to 110 °C on a hot-plate. This resulted simultaneously in a chemical cross-linking of the beads as well as the acid catalyzed cleavage of the t-BMA ester bond in the sacrificial layer, which transforms to polymethacrylic acid (PMA). Since PMA is soluble in aquous base the spin-coated film is removable. Figure 16A presents opa-line films floating freely on water. Such films can – later on – be transferred to any other substrate. Figure 16B shows the SEM image of the opaline film after transfer to a glass substrate. Some fragments, which broke off during the transfer process, are found on the surface of the opal. In summary, well-ordered opaline films on PMMA substrates as well as free-standing opaline films with con-

trollable reflection wavelength are achievable. The usage of the presented approaches for the preparation of colour-selective reflectors either directly attached to the fluores-cent concentrator or with an air gap in between will be the next steps of our work. 6 Fluorescent concentrator systems with pho-tonic structures For an experimental validation of the beneficial effect of the photonic structures we also realized a complete system of fluorescent concentrator with at-tached solar cell and photonic band stop filter. We pre-pared a system with a 5 mm thick, 5 × 10 cm big fluores-cent concentrator to which we optically coupled one GaInP solar cell with silicone. The fluorescent concentrator was made from the same material as described in Section 4. The GaInP solar cell has a bandgap of around 1.85 eV (670 nm). The solar cell is equipped with a single layer an-tireflection coating of 65 nm Ta2O5, which is optimized for the emission range of the dye in the fluorescent concentra-tor between 550 nm and 650 nm. The solar cell was bonded to a copper base to give mechanical stability. The solar cell has an active area of 5 × 49 mm, so the relation between illuminated fluorescent concentrator area and so-lar cell area constitutes a geometric concentration ratio of 20×. We used white Teflon as bottom reflector and also as reflector at the three edges, which were not covered by so-lar cells. There was an air gap between the concentrator and the reflectors. Photonic band stop filters were placed on top of the fluorescent concentrator without optical coupling. We used two commercially available filters (5 × 5 cm) from mso-Jena optimised for the used fluorescent concentrator mate-rial. The filters have an antireflection coating optimised for the absorption range of the dye in the concentrator. Fig-ure 17 displays the reflection of the filter, the absorption and the photoluminescence of the fluorescent concentrator. We see that the filter shows high transmission in the ab-sorption range of the dye and high reflection for the emit-ted light. We determined the emission characteristics of the dye via photoluminescence (PL).

Figure 17 (online colour at: www.pss-a.com) Absorption and

photoluminescent emission of the fluorescent concentrator and

reflection of the used photonic structure.

2820 J. C. Goldschmidt et al.: Photonic structures for fluorescent concentrators

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

ph

ysic

ap s sstat

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Figure 18 (online colour at: www.pss-a.com) Line scans of the

fluorescent concentrator system, with and without the photonic

structure on top. Close to the solar cell the photonic structure de-

creases the collection efficiency, because it reflects light, which

could have reached the solar cell directly. However, over most of

the concentrator the collection efficiency is increased, resulting

into an efficiency enhancement of the system by 20% relative.

We measured the I–V characteristic and the efficiency of the system with and without the photonic band stop fil-ters under AM 1.5 g illumination with a sun simulator. The system has an efficiency of 2.6 ± 0.1% in reference to the 50 cm2 area of the system, without the filter. The filters in-crease the efficiency to 3.1 ± 0.1%, which constitutes an efficiency increase of around 20% relative. (The given ac-curacies reflect uncertainty for relative comparison, not the absolute uncertainty.) We also performed light beam induced current (LBIC) scans of the system in order to investigate the effect of the photonic structures with a spatial resolution. Figure 18 dis-plays the average of several linescans made starting from the solar cell over the whole length of the fluorescent con-centrator with and without the photonic structures. Close to the solar cell the collection efficiency is lower with the

Figure 19 External quantum efficiency measurement of a fluo-

rescent concentrator system with and without the photonic struc-

ture. The illumination spot was 1 cm away from the solar cell.

The efficiency is increased over a broad spectral range. Only in

spectral regions where the photonic structures reflects light which

could have been used (below 350 nm) the efficiency decreases.

photonic structure. This is because the structure reflects light, which could reach the solar cell without any absorp-tion/emission event directly or by reflection from the dif-fuse bottom reflector. However, further away from the so-lar cell the photonic structure effectively traps the emitted light and the collection efficiency is increased significantly. This results in the measured efficiency increase of 20%. Figure 19 illustrates the increase in collection effi-ciency with a spectral resolution. For a smaller system with an area of 2 × 6 cm and 3 mm thickness from the same ma-terial as mentioned above we measured the external quan-tum efficiency (EQE) of the system, with and without the filters on top of the fluorescent concentrator. A GaInP solar cell with an active area of 21 mm × 3 mm was at-tached to one short side of the concentrator. The other pa-rameters of the solar cell were equal to those mentioned before. Again white reflectors were placed around the free edges and at the bottom of the concentrator. The system was illuminated with a spot of 1 mm diameter white light in 1 cm distance to the solar cell. Obviously, the filter in-creases efficiency significantly over a broad spectral range. Only where the filter is reflective the collection efficiency is reduced. 7 Summary In this study we presented a detailed theoretical and experimental analysis of the application of photonic structures to increase the collection efficiency of fluorescent concentrators. Our simulations show that a photonic band stop filter increases the efficiency of a photovoltaic system with a fluorescent concentrator sig-nificantly. With optical simulations we determined the properties of 1D and 3D photonic structures. Our results suggest that the angular characteristics of 3D photonic structures would allow a better use of diffuse radiation while retaining the positive effect on the concentrator’s ef-ficiency. We investigated the angular characteristics of the light trapped and guided to the edges of the fluorescent concentrator. We offered an explanation for the asymmet-ric form of the angular distribution and developed a ray-tracing model, which was able to reproduce our results qualitatively. Further work has to be done to implement a more realistic absorption model into the simulation. We showed how first 3D photonic structures were realized on the basis of colloidal opals, which showed a nice reflection peak in the emission region of the dye. Research is on the way to enable applying these structures to fluorescent con-centrators. Finally, we demonstrated that 1D photonic structures increased the efficiency of a real 5 × 10 cm fluo-rescent concentrator system by 20% relative.

Acknowledgements The authors would like to thank the

German Science Foundation DFG for their financial support in

the project Nanosun (Pak88). J. C. Goldschmidt gratefully

acknowledges the scholarship support from the Deutsche Bundes-

stiftung Umwelt, and the ideational support from the Heinrich-

Böll Stiftung and the German National Academic Foundation.

We thank G. Glasser from the MPI for Polymer Research for

SEM measurements and Dr. Birger Lange for helpful discussions.

phys. stat. sol. (a) 205, No. 12 (2008) 2821

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We would also like to thank the III–V group at Fraunhofer ISE

for the preparation of the GaInP solar cells. We thank C. Ulbrich

and T. Kirchartz for interesting discussions and J. H. Werner for

continuous support.

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