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Analysis of Optical Losses in High-Efficiency CuInS-Based Nanocrystal Luminescent Solar Concentrators: Balancing Absorption vs Scattering Ryan Sumner, Steven Eiselt, Troy B. Kilburn, Christian S. Erickson, Brian Carlson, Daniel R. Gamelin, Stephen McDowall, and david L Patrick J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12379 • Publication Date (Web): 23 Jan 2017 Downloaded from http://pubs.acs.org on January 24, 2017

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The Journal of Physical Chemistry

Analysis of Optical Losses in High-Efficiency CuInS2-Based Nanocrystal Luminescent Solar Concentrators: Balancing Absorption vs Scattering Ryan Sumner1, Steven Eiselt1, Troy B. Kilburn2, Christian Erickson2, Brian Carlson1, Daniel R. Gamelin2, Stephen McDowall3, David L. Patrick1,* 1

Department of Chemistry, Western Washington University, 516 High St., Bellingham, WA, 98225 Department of Chemistry, University of Washington, Seattle, WA 98195-1700 3 Mathematics Department, Western Washington University, 516 High St., Bellingham, WA, 98225 2

*corresponding author: [email protected] Abstract. Luminescent solar concentrators (LSCs) use down-converting luminophores embedded in a waveguide to absorb sunlight and deliver high irradiance, narrowband output light for driving photovoltaic and other solar energy conversion devices. Achieving a technologically useful level of optical gain requires bright, broadly absorbing, large-Stokes-shift luminophores incorporated into low-loss waveguides, a combination that has long posed a challenge to the development of practical LSCs. The recent introduction of giant effective Stokes shift semiconductor nanocrystal (NC) phosphors for LSC applications has led to significant performance improvements by increasing solar absorption while reducing escape cone and nonradiative losses compounded by re-absorption, placing increased emphasis on the importance of minimizing parasitic waveguide losses caused by scattering from NC aggregates and optical imperfections. Here, we report a detailed analysis of optical losses in polymer-NC composite waveguide LSCs based on CuInS2/CdS NC phosphors, which have been shown to provide best-in-class performance in large-area, semitransparent concentrators. A comprehensive analytical optical model is introduced enabling quantification of parasitic waveguide, scattering, escape-cone, and non-radiative relaxation losses on the basis of distance-dependent edge-emission measurements. By examining the effect of NC loading we show that NC clustering in polymer composite waveguides leads to light scattering losses that ultimately limit efficiency at large geometric gain. By optimizing NC concentration, optical power efficiencies up to 5.7% under AM1.5 illumination are demonstrated for devices having a geometric gain 𝐺 = 6.7×, with limiting achievable efficiencies predicted to exceed 10%.

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Introduction Solar collectors capable of simultaneous spatial and spectral optical concentration can open new avenues for improving solar conversion efficiency, scalability, and cost by providing high brightness, narrow-bandwidth light optimized for photovoltaic (PV) or photochemical conversion. Luminescent solar concentrators (LSCs), which concentrate light in an inexpensive dielectric waveguide by active frequency shifting, have emerged as one of the most promising approaches for practical solar concentration (Fig. 1A).1-3 LSCs employ down-shifting luminophores to increase the spectral power of photons trapped in a waveguide by total internal reflection, theoretically enabling conversion efficiencies superior to other concentrator designs.4,5,6 PV cells or other converters coupled to the concentrator edges receive intense, bandgap-matched light, while excess energy from above-bandgap light is dissipated over the full area of the LSC. LSCs can concentrate diffuse as well as direct sunlight, are tolerant to partial shading, and can be semi-transparent, making them particularly useful for building-integrated PV applications such as energyharvesting window layers. Because some energy is sacrificed in the absorption, downshifting, and transport of sunlight by an LSC, achieving the required high levels of efficiency has long been an obstacle for practical concentrators. The theoretical performance limits of an LSC are established thermodynamically by the optical properties of the luminophores. The upper energy efficiency obeys the single-bandgap Shockley-Queisser limit,7 and the limiting energy concentration ratio (CRlim) depends on the Stokes shift. For visible to near-IR luminophores, thermodynamically limited theoretical energy concentrations of CRlim > 104 are predicted at room temperature for a Stokes shift of ~500 meV, corresponding to >103 Wm-2 of narrowband output.4-6 In

Fig. 1. In an LSC, broadband sunlight is absorbed by luminophores and emitted into a waveguide, traveling to the edge of the collector to provide concentrated narrowband light for driving conversion processes. With each emission, a fraction of light is lost to non-unity PL quantum yield or out the escape cone. Subsequent reabsorption of guided photons by other luminophores compounds these losses, causing efficiency to fall with concentrator size. Further optical losses results from parasitic waveguide attenuation. 2 ACS Paragon Plus Environment

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practice, however, the performance of LSCs falls far below these thermodynamic limits,9 mainly because of four dominating loss factors:8-12 (1) only a fraction of incident sunlight is absorbed, determined by the luminophore absorption spectrum, device thickness, and concentration; (2) only a fraction of absorbed sunlight is re-emitted, depending on luminophore photoluminescence (PL) quantum yield (Φ); (3) only a fraction of this emitted light is captured in guided modes (e.g. ~75% in a planar waveguide with refractive index n ~ 1.5),13 with the remainder lost to escape cones defined by Snell’s Law; and (4) a fraction of guided light is lost during transport to the concentrator edges by parasitic waveguide losses. For most LSC luminophores, mechanisms (2) and (3) account for the greatest losses because they occur repetitively, since waveguided photons may be re-absorbed/re-emitted repeatedly before reaching an edge (Fig. 1A). Long optical pathlengths in a large area LSC cause even the smallest overlap between absorption and emission spectra to result in compounding self-absorption losses.14 This situation has recently begun to change with the introduction of a new generation of broadly absorbing, giant effective Stokes shift phosphors based on semiconductor nanocrystals (NCs). Compared to previous generations of LSC luminophores based primarily on organic and organometallic dyes, the large Stokes shift (≥ ~500 meV) of NC phosphors such as “giant shell”15-17 and “dot-in-rod”18 heteronanocrystals, “doped” NCs including Mn2+:CdxZn1-xSe and Cu+:CdSe,19,20 and ternary III-VI2 NCs such as CuInSe2 and CuInS2 21-25 dramatically reduce self-absorption. Consequently, when these phosphors are incorporated into large area, high-geometric-gain LSCs, mechanisms (1) and (4) can take on more prominent roles, requiring careful design to balance all four loss mechanisms in order to optimize efficiency. Here, we report a detailed study of optical losses in polymer-NC composite waveguide LSCs incorporating CuInS2-based NC phosphors, which have been shown to provide best-in-class performance in large-area, semitransparent concentrators.21-25 Particular attention is given to understanding and quantifying parasitic waveguide losses, which are found to ultimately limit concentrator performance in high-geometric-gain LSCs prepared using these latest generation giant effective Stokes shift luminophores (geometric gain, 𝐺 is defined as the ratio of concentrator facial to edge area). We find that scattering from NC aggregates is the largest contributor to parasitic losses. Using a new analytical optical model, we predict and then demonstrate experimentally that maximizing concentrator efficiency requires balancing optical density (i.e. solar absorption) with aggregation-induced turbidity. By optimizing NC concentration, we demonstrate LSCs with optical power efficiencies up to 5.7% under AM1.5 illumination for devices having a geometric gain G = 6.7×, among the highest performance reported so far in large-𝐺 NC-polymer composite LSCs. These results underscore the importance of balancing all loss mechanisms in order to optimize performance in LSCs based on large Stokes shift NC phosphors.



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Experimental Methods Nanocrystal synthesis and characterization. CuInS2/CdS NCs were synthesized following the procedure outlined in Ref. 26 with small modifications. Briefly, CuInS2 cores were prepared by adding indium acetate (0.292 g, 1 mmol), copper iodide (0.190 g, 1 mmol), and dodecanethiol (5 mL) to a 50 mL three-neck round-bottom flask. The solution was degassed three times at room temperature by evacuating the flask and refilling with nitrogen. After degassing, the reaction was heated to 110˚ C under nitrogen for 10 minutes until the solution turned optically clear pale yellow. The reaction was then elevated to 230˚ C for 10 minutes, during which time the solution turned from yellow to dark red. After 10 minutes, the reaction was quickly cooled to room temperature. A portion of the crude reaction solution (1.0 mL) was added to 1octadecene (4.0 mL) in a clean 50 mL three-neck round-bottom flask. The cores were degassed with three pump-purge cycles using nitrogen at room temperature, and were then heated to 210˚ C. A shelling solution was prepared by heating and sonicating cadmium myristate (0.272 g), sulfur (0.013 g), 1-octadecene (4 mL), and n-trioctylphosphine (0.4 mL) under a nitrogen atmosphere to form a uniform white dispersion. The shelling solution was injected into the reaction at 0.2 mL/min. After all of the shelling solution was added, the reaction was cooled gradually to 60˚ C. Oleic acid (1 mL) and toluene (1 mL) were added, and the mixture was stirred for 10 min. The resulting CuInS2/CdS core/shell nanocrystals were purified with several cycles of precipitation upon addition of ethanol followed by resuspension in toluene. Typical NCs prepared by this method were pseudo-spherical with diameters of d ~ 3-4 nm (Fig. 2B). X-ray diffraction data (Fig. 2C) are consistent with CuInS2/CdS NCs in the chalcopyrite phase, with diffraction angles shifted slightly due to the thin CdS shell layers. NCs from several similar syntheses were then used to prepare LSCs. For most data reported here, the original colloidal NCs had Φ ~ 75% in toluene. Several defect-based PL mechanisms have been proposed to explain the PL of CuInS 2 and related NCs.

27,28

Recent results are consistent with rapid trapping of photogenerated holes at lattice Cu+ ions,

followed by "free-to-bound" recombination of conduction-band electrons with these trapped holes.29-31 Hole localization is fast and efficient, leading to formation of a luminescent mid-gap excited state (Fig. 2A) that displays a large effective Stokes shift, small self-absorption, and a high Φ. Although absorption/emission overlap in CuInS2 NCs is slightly greater than in some other actived NCs,21 it is far smaller than in organic dyes, and this feature combined with its high Φ and broadband absorbance enables higher overall LSC performance. Its emission is also size- or composition-tunable over a wide wavelength range (600 ~ 900 nm),32-34 enabling matching to many important inorganic and organic semiconductor materials used in PV and photochemical conversion applications.35


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Fig. 2. CuInS2/CdS Nanocrystals. (A) Schematic summary of the luminescence mechanism in CuInS2 nanocrystals. Photon absorption excites the nanocrystal from its ground state to band-to-band excited states (1). These excited states relax to a mid-gap state that has been described as a self-trapped exciton (STE) (2). This mid-gap state emits a photon, returning the system to the ground state (3). In the STE description, this emission involves a "free-to-bound" recombination of a delocalized conduction-band electron with a self-trapped hole. (B) A TEM image of representative CuInS2/CdS nanocrystals. (C) Xray diffraction data collected for a representative CuInS2/CdS NC sample, consistent with nanocrystals in the chalcopyrite crystal structure. The peaks are shifted to slightly lower diffraction angles than the reference CuInS2 (black bars) because of the thin CdS shell layers.

Nanocrystal luminescent solar concentrators. The LSCs prepared in this work consisted of a 75mm × 75 mm × 1 mm thick NC-containing poly(laurylmethacrylate-co-ethyleneglycol) (PLMA) layer sandwiched between 0.90 mm thick B270 glass sheets, for an overall device thickness of 2.8 mm. The glass layers provide a low autofluorescence, low roughness, and low loss cladding with low water and oxygen permeability.36 Empty glass shells sealed around the perimeter by a transparent elastomeric spacer were filled with mixtures of monomer, polymer, CuInS2 NCs, cross-linker, and photoinitiator, and polymerized under UV light (refer to ESI for details). NC loading was measured by thermogravimetric analysis (Fig. S3A) and completeness of polymerization was probed by Fourier-transform infrared spectroscopy (Fig. S3B). Transfer of NCs from toluene to the monomer mixture results in a ~80 meV bathochromic shift of the NC PL (Fig. S2); the absorption spectrum remains unchanged, increasing the already large effective Stokes shift of these phosphors. The origin of this small shift is unclear, but it does not come from reabsorption

losses.

Instead,

it

may

relate

to

a

size-dependence


of

the

reduction

in

d (mm) 17.8 22.8 27.8 32.8 42.8 52.8 62.8

(B) Absorbance

0.4

PL

0.2

ABS

0.0 400

PL Intensity (Rel. Quanta nm-1)

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500

600 700 Wavelength (nm)

800

PL Intensity (Rel. Quanta nm-1)


900

(C)

17.8 mm

62.8 mm

500

600

700 800 Wavelength (nm)

900

Fig. 3. Optical properties of a representative CuInS2 LSC. (A) A 75×75×2.8 mm LSC (geometric gain 𝐺 = 6.7×) based on CuInS2/CdS NC phosphors in a poly(laurylmethacrylate-co-ethyleneglycol) waveguide with glass cladding. (B) Absorption spectrum of a typical LSC device. Edge-harvested PL spectra of the same device, collected as a function of distance 𝑑 between the excitation spot and the LSC edge. (C) Normalized PL intensity, illustrating the progressive loss of higher-energy photons with increasing optical pathlength caused by overlap with the absorption tail. PL intensities are reported in units of relative number of quanta per wavelength interval. 6 ACS Paragon Plus Environment

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quantum yield upon polymer incorporation: Transfer to the polymer is also accompanied by an up to 30% (absolute) decrease in PL quantum yield relative to that measured in toluene (Φ ~ 75%). Other possible origins may involve surface polarization upon reduction in the NC surface ligand density, or the effect of changing the dielectric of the surrounding material.

Results and Analysis Experimental characterization of CuInS2 LSCs. Absorbance and edge-emitted PL spectra for a representative CuInS2 LSC are presented in Fig. 3. The first absorption feature is a broad band centered at ~2.1 eV, with an absorption tail that weakly overlaps the PL band centered at ~1.6 eV, measured here under 475 nm excitation. Emission spectra were measured by illuminating 5 mm diameter areas of the device located at various distances 𝑑 from the waveguide edge and collecting edge-emitted light through a 7 mm aperture into an integrating sphere (inset, Fig. 5a). Three replicate measurements were performed on two orthogonal edges and the results averaged. Outside the collection aperture, all remaining waveguide perimeter was blackened to eliminate edge reflections. As shown in Fig. 3B, the small overlap between absorption and PL bands results in the gradual loss of guided photons on the high-energy side of the PL peak with increasing optical pathlength. We find that in devices prepared using a high NC loading, scattering begins to make a contribution to total extinction. This observation is illustrated in Fig. 4, which shows the measured extinction for an LSC containing 2.6 wt% CuInS2:PLMA, having a total extinction of 0.36 mm-1 at 𝜆 = 575 nm, corresponding to the first absorption feature. Below we show this scattering arises mostly from NC aggregation occurring

2.0 ANC () + B / 4 + C toluene NC () toluene

1.5

Extinction

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B / 4 + C Measured LSC

1.0

0.5

0.0 400

600 Wavelength (nm)

800

Fig. 4. At high NC loadings (> ~2 wt%) scattering begins to contribute significantly to total extinction. To separately determine their contributions, spectra are fit to an extinction function accounting for both components. 7 ACS Paragon Plus Environment


at high NC concentrations. To determine the contributions from NC absorption and scattering individually, we make use of the fact that the absorption spectra were virtually unchanged going from toluene to PLMA 𝑁𝐶 (𝜆) + 𝐵/𝜆4 + 𝐶. Here (Fig. S2), and we fit the measured spectra using the function, 𝜀𝑡𝑜𝑡𝑎𝑙 (𝜆) = 𝐴𝜀𝑡𝑜𝑙𝑢𝑒𝑛𝑒 𝑁𝐶 𝜀𝑡𝑜𝑙𝑢𝑒𝑛𝑒 is the normalized absorption spectrum measured in toluene, and 𝐴, 𝐵, and 𝐶 are fitting constants.

The first term accounts for NC absorption, the second for scattering, and the third for Fresnel reflections at the glass/air and glass/polymer interfaces. At low concentrations scattering losses are well-described by 𝜆−4 wavelength dependence, consistent with a Rayleigh scattering mechanism (see below). In the following, for devices exhibiting measureable scattering, reported optical densities are based on the best𝑁𝐶 (𝜆). fit value of 𝐴𝜀𝑡𝑜𝑙𝑢𝑒𝑛𝑒

Integrating the areas under the absorption and emission spectra in Fig. 3A gives the fraction of photons absorbed by the LSC that reach the collection aperture as a function of excitation distance, or optical quantum efficiency, 𝑂𝑄𝐸𝑎𝑝 (𝑑) (Fig. 5, solid points). 𝑂𝑄𝐸𝑎𝑝 decreases with 𝑑 due to both a geometric effect (the collection angle subtended by the edge aperture decreases as tan−1 (1/𝑑)) and compounding escape-cone, non-radiative relaxation, and waveguide attenuation losses. The latter can be expressed as an optical pathlength-dependent loss such that 𝑃 = 𝑃𝑜 𝑒 −𝛼𝜉/4.34, where 𝑃/𝑃𝑜 is the fraction of power remaining after a propagation distance 𝜉, 𝛼 (dB cm-1) is an attenuation coefficient, and the factor 4.34 arises from converting dB cm-1 to Naperian units (cm-1). For reference, an attenuation coefficient of 𝛼 = 0.1 dB cm-1 results in a loss of ~2% of guided photons per centimeter pathlength. The attenuation coefficient accounts for absorbance and scattering by the polymer, as well as scattering from NCs,

2.0

OQEap (%)

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1.5 1.0 0.5

 = 0.46 dB cm-1  = 75%

0.0 20 30 40 50 60 70 Distance of Illumination Spot from LSC Edge, d (mm)

Fig. 5. LSC characterization and projected performance. Solid points give the optical quantum efficiency measured at the small edge aperture. Line is a fit to eq 2. Inset: geometry used for LSC characterization. 8 ACS Paragon Plus Environment

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polymer/glass, and glass/air interfaces. We treat 𝛼 as wavelength-independent over the emission band of the phosphor. In the following sections we show how device absorption and emission spectra, along with edge emission measurements performed at a series of illumination spot positions like the example in Fig. 5, enable complete quantification of LSC optical properties. Such measurements were performed on eight devices, based on CuInS2 NCs possessing very similar absorption and emission spectra, but different NC loadings, varying from 0.4 to 6.1 wt%. From these data the optical power efficiency (𝑂𝑃𝐸), flux gain, edge-emission irradiance, and other characteristics are found for each experimental device, and can be projected for any device configuration having a specified geometry, size, and NC loading. 𝑂𝑃𝐸 is defined as: 𝑂𝑃𝐸 = (Edge output irradiance × LSC edge area) / (Solar irradiance × LSC major area)

(1)

The best performing device is measured to have 𝑂𝑃𝐸 = 5.7% at a geometric gain 𝐺 = 6.7×, with a narrowband edge output irradiance of 385 W m-2 centered at 760 nm, among the highest performance yet reported in a large-𝐺 LSC. Achieving this level of performance requires minimizing waveguide attenuation losses while maximizing solar absorption, which as described in the following, trend in opposite directions with NC loading. Below, we provide a detailed analysis of the principle optical loss mechanisms, and use the results to project the performance of fully optimized LSCs. Analytical model of LSC performance. To determine attenuation and other losses individually, we introduce a new analytical optical model taking as inputs only the measured absorption and emission spectra, fitting 𝑂𝑄𝐸𝑎𝑝 (𝑑) to determine the best {𝛼, Φ}. Once these parameters are known it becomes possible to compute for any 𝐺 the impact of each loss mechanism, as well as the optical power efficiency and edge output irradiance. Details of the model are given in the SI, and are summarized here briefly as follows: For a photon absorbed at a location (𝑥, 𝑦) to reach the integrating sphere, it must be emitted into a guided mode whose path of propagation meets the aperture. During propagation the photon might be reabsorbed, with probability determined by the photon’s wavelength and the NC absorption spectrum, and it may be attenuated, with probability determined by 𝛼. For this situation, all photons that are re-absorbed even once can be treated as lost, even if potentially they could have been re-emitted in a direction allowing them to reach the edge aperture; in the SI we show that the probability of such photons being measured at the integrating sphere is very small and does not affect the estimation of Φ and 𝛼. Let 𝐷 be an illumination window within which solar absorption occurs, and |𝐷| denote the area of this window. Let Θ(𝑥, 𝑦) be the part of the unit sphere corresponding to guided modes intersecting the aperture. Let 𝑙(𝑥, 𝑦, 𝜃, 𝜙) be the pathlength of propagation within the full LSC from (𝑥, 𝑦) to the measurement aperture in the direction (𝜃, 𝜙), given in spherical coordinates. Along this path, attenuation is possible from scattering, absorbance by the polymer matrix, and other parasitic loss mechanisms. Since 9 ACS Paragon Plus Environment


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only the central composite layer of the LSC contains NCs, and the glass cladding is relatively lossless (see below), attenuation is considered in the composite layer only and the distance traveled subject to attenuation 𝑁𝐶 (𝜆) and 𝐸𝑚(𝜆) denote the absorption is less than 𝑙. Let 𝜉(𝑥, 𝑦, 𝜃, 𝜙) be this distance. If 𝐴𝑏𝑠(𝜆) = 𝐴𝜀𝑡𝑜𝑙𝑢𝑒𝑛𝑒

and emission spectra of the NCs, then Φ

1

𝑂𝑄𝐸𝑎𝑝 = |𝐷| ∬𝐷 4𝜋 ∬Θ(𝑥,𝑦) 𝑒 −𝛼 𝑙(𝑥,𝑦𝜃,𝜙) ∫ 𝐸𝑚(𝜆)𝑒 −𝐴𝑏𝑠(𝜆)𝜉(𝑥,𝑦,𝜃,𝜙) 𝑑𝜆 sin 𝜃 𝑑𝜃 𝑑𝜙 𝑑𝐴(𝑥, 𝑦). (2) In fact, we also take into account the angle-dependent Fresnel reflection coefficient at the measurement aperture, where the refractive index changes at the LSC / air interface, but omit it here for brevity. We assume that scattering losses from the polymer-glass and glass-air interfaces are negligible, consistent with previously reported measurements on poly(methylmethacrylate)-glass waveguide LSCs.37 To determine NC PL quantum yield and the waveguide attenuation rate, measurements of 𝑂𝑄𝐸𝑎𝑝 (𝑑) are fit using Eq. 2 with a least-squares procedure. The solid line in Fig. 5 gives the result of this fitting process for a representative device. For the example shown, Φ = 75% and 𝛼 = 0.46 dB cm-1. Having estimated the Φ and 𝛼, we proceed to compute the expected OQE for LSCs of other dimensions when illuminated uniformly over the whole LSC, now considering photons that reach any point on the concentrator perimeter. From this, we can then compute the optical power efficiency and the edge output irradiance. For these computations, the model presented above is no longer appropriate because reabsorbed photons have a non-negligible probability of reaching an edge, possibly even after more than one re-absorption/re-emission event. Given initial absorption that is uniformly distributed over the full LSC, we assume that first-time re-absorbed photons are again uniformly distributed over the LSC, an assumption that is borne out in ballistic Monte Carlo simulations. In the SI, we present a complete derivation of the proportion of emitted photons that are lost to attenuation before reaching an edge or being re-absorbed (𝒮), and the proportion that are re-absorbed exactly once before reaching an edge or being lost to attenuation (𝒜). If ℰ is the proportion lost out the escape cone, then 𝒞 = 1 − 𝒜 − 𝒮 − ℰ is the proportion of initially emitted photons that reach an edge without being absorbed nor attenuated. To obtain the proportion of incident solar irradiance absorbed by the LSC, and the output edge irradiance, we integrate the AM1.5 spectral irradiance against the LSC absorbance. From these, of all initially absorbed photons, we obtain the total proportions: lost out the escape cone, ℰΦ(1 − 𝒜Φ)−1 ; lost to attenuation, 𝒜Φ(1 − 𝒜Φ)−1; lost due to sub-unity luminescence quantum yield, (1 − Φ)(1 − 𝒜Φ)−1 ; and reaching an edge, 𝒞Φ(1 − 𝒜Φ)−1 . In Fig. 6 we apply this treatment to project how performance varies with 𝐺 for the device in Fig. 5. The circled points correspond to the measured LSC. 𝑂𝑃𝐸 decreases with increasing 𝐺 as reabsorption and waveguide attenuation losses grow with concentrator size; simultaneously the collection area increases, increasing the solar irradiance absorption rate. The output irradiance approaches a limiting value of ~770 W m-2 at 𝐺 ≥ 100, corresponding to a square LSC with an edge length ≥ 2.8 m. Under full area illumination 10 ACS Paragon Plus Environment

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the efficiency of the best performing device was 𝑂𝑃𝐸 = 5.7% (𝐺 = 6.7×). The same parameters project 𝑂𝑃𝐸 = 4.8% at 𝐺 = 10×. The latter represents a 50% relative efficiency improvement over the next-best performing nanophosphor in this category, also based on CuInE2 (E = S, Se) NCs,16 for a device of the same geometric gain. 7 2.5

6 5

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Fig. 6. Dependence of optical power efficiency and flux gain on concentrator size. The circles indicate experimental results for the device of Fig. 5. The projected flux gain is computed for amorphous Si PVs coupled to all four edges of a square LSC. Photoconverters such as PVs or photoelectrodes that are optically coupled to LSCs receive high irradiance,

narrowband

light,

producing

an

enhanced

photocurrent

density

𝐽=

𝐼𝐴𝑀1.5𝐺 𝐺(𝐸𝑄𝐸𝜆 )(𝑂𝑃𝐸)(𝜆𝑒𝑚 /ℎ𝑐𝑛𝐶 ), where 𝐼𝐴𝑀1.5𝐺 is the solar irradiance, 𝐸𝑄𝐸𝜆 is the photoconverter external quantum efficiency at the NC peak emission wavelength 𝜆𝑒𝑚 , ℎ is Planck’s constant, 𝑐 is the speed of light, and 𝑛𝐶 is the number of electrons per Coulomb. For 𝐸𝑄𝐸𝜆 = 1, the projected limiting photocurrent density 𝐽𝑜 = 24 mA cm-2 for the LSC in Fig. 6 neglecting coupling losses, increasing to a maximum of 𝐽𝑜 ≈ 47 mA cm-2 for 𝐺 ≥ 100. The latter represents a nearly two-fold increase in current density for an ideal single-junction photoconverter based on a bandgap matching 𝜆𝑒𝑚 . For LSC-coupled PVs, the corresponding flux gain 𝐹, defined as the ratio of the power produced by edge-attached PVs to the power produced by the same PVs under AM1.5 illumination, is proportional to the ratio of the short-circuit currents: 𝐹 = (𝐸𝑄𝐸𝜆 )𝐽𝑜 /𝐽𝐴𝑀1.5𝐺 , where 𝐽𝐴𝑀1.5𝐺 is the photocurrent under direct AM1.5G exposure. Taking high-performance a-Si PVs as an example,38 the right-hand axis in Fig. 6 shows the projected flux gain increases from ~1.3× at 𝐺 = 6.7× to ~2.6× in the large-𝐺 limit. Examination of loss processes. The impacts of non-radiative relaxation, parasitic attenuation, and escape-cone losses and their dependence on geometric gain are shown in Fig. 7, again computed for the device in Fig. 5 as an example. The dominant loss mechanism is found to depend on concentrator size. For 11 ACS Paragon Plus Environment

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Quantum Efficiency / Loss (%)


50

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Attenuation loss

40

Non-radiative loss

30 20

Escape-cone loss

10

Optical Quantum Efficiency

0 0

20

40 60 80 Geometric Gain, G

100

Fig. 7. Optical loss mechanisms. The statistical fate of absorbed solar photons depends on geometric gain, with losses dominated by non-radiative relaxation at small 𝐺, and waveguide attenuation at large 𝐺. Results are computed for the device in Fig. 5. small devices (𝐺 ≤ 10), nonradiative relaxation presents the largest loss, followed by escape cone loss. This conclusion is consistent with the measured PL quantum yield, which gives a 1 − Φ = 25% nonradiative loss each time a photon is absorbed. Since emission is directionally isotropic, escape-cone 2 2 losses are Φ (1 − √1 − 𝑛𝑎𝑖𝑟 /𝑛𝐿𝑆𝐶 ) ≈ 17% each time a photon is absorbed, where 𝑛 is the refractive index.

For larger devices however, attenuation losses become limiting. This surprising finding is a direct result of the high LQY and large effective Stokes shift of the CuInS2/CdS phosphors employed in these LSCs, and emphasizes the importance of waveguide transparency for large area, high performance concentrators. In the majority of LSCs studied to date, such losses have typically been either neglected (as being relatively small compared to non-radiative and escape cone losses) or not separately analyzed and determined. It is noteworthy that the LSCs reported here appear almost entirely clear to the unaided eye (see Figs. 3A and S1), requiring careful analysis of optical data to identify waveguide losses as distinct from non-radiative and escape-cone losses compounded by self-absorption. To investigate the origins of these parasitic losses further, we prepared a series of LSCs having different NC loadings and measured their attenuation loss rates; the results are summarized in Fig. 8, which shows a small, nearly concentration-independent attenuation coefficient up to an optical density of ~0.25, beyond which attenuation increases rapidly with increasing NC concentration. The data in Fig. 8 are fit using the attenuation function 2/𝐷 −𝐷/2

𝛼 = 𝛼𝑜 + 𝛽𝑐𝑜 + 𝛾𝑐𝑜3 (1 + 𝛿𝑐𝑜

)

(3)


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0.0 Attenuation Coefficient,  (dB cm-1)

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Nanocrystal Loading (wt%) 1.8 3.6 5.4

2

1

0 0.00

0.25 0.50 0.75 Optical Density at 575 nm (mm-1)

Fig. 8. Dependence of waveguide attenuation on NC loading. The points represent experimental attenuation coefficients measured for individual LSCs. The line results from fitting eq 3. derived assuming particle aggregation produces clusters with fractal geometries and a size distribution related to NC concentration (details are given in the SI). Here, 𝑐𝑜 represents NC concentration, 𝐷 is the fractal dimension of NC clusters postulated to form at high NC concentrations by aggregation, and 𝛼𝑜 , 𝛽, 𝛾, and 𝛿 are constants. The first term in eq 3 accounts for intrinsic propagation losses in the absence of NCs, and arises from absorption and scattering by the polymer, impurities, and at interfaces and imperfections. The second and third terms describe scattering from single NCs and aggregates, respectively. For 𝐷 = 1.8 we find an intrinsic attenuation rate 𝛼𝑜 = 0.16 dB cm-1 and negligible single-particle scattering losses (𝛽 = 0.02 dB cm-1 wt%-1). The latter is consistent with an estimate of the Rayleigh scattering cross section, which indicates that scattering from individual NCs is 1-2 orders of magnitude too small to account for the observed attenuation, and also with the observations of Knowles et al. who found no significant scattering for similar CuInS2 NCs in toluene at even greater volume fractions and over a pathlength of 1.2 m.21 At low NC loadings, 𝛼 is dominated by intrinsic waveguide losses. The intrinsic attenuation of opticalgrade methacrylate polymers in this wavelength range is39 ~1×10-3 dB cm-1, and that of the glass cladding is even lower36 (1.810-4 dB cm-1), suggesting it should be possible to reduce 𝛼𝑜 further through improved purification or fabrication methods. At high NC concentrations 𝑐𝑜 ≥ ~2 wt%, the analysis indicates that scattering losses from NC aggregates begin to dominate, as evidenced by the signature cubic scaling of attenuation rate with NC concentration. This result can be understood by the fact that, although aggregation reduces the number density of scattering objects by a factor 𝑛−1 (where 𝑛 is the number of NCs per aggregate), the scattering cross section of such aggregates scales as 𝑛2 .40



1.4

NC Loading (wt %) 2.9 4.3 5.8

7.2

60

(A) 400

40

300

200 20 100 0 8

Absorbed Irradiance (W m-2)

Optical Quantum Effic. (%)

0.0

Optical Power Effic. (%)

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(B)

6

4

2 0.0

0.2 0.4 0.6 0.8 Optical Density at 575 nm (mm-1)

1.0

Fig. 9. LSC performance normalized to 𝚽 = 1. (A) Absorbed solar irradiance increases, and optical quantum efficiency decreases, with increasing optical density. (B) Consequently, the optical power efficiency reaches a 𝐺-dependent maximum at an optical density equal to ~ 0.3 mm-1. Solid points correspond to individual LSCs, normalized to Φ = 1 to enable comparison between devices with varying luminescence quantum yields. Lines are computed using the model in section 4 of the SI. Since both scattering losses and solar flux absorbed by the LSC increase with increasing NC concentration, there exists for a given 𝐺 an optimal NC concentration that maximizes the 𝑂𝑃𝐸. The opposing effects of increasing absorption and attenuation are illustrated in Fig. 9A, and the consequence for 𝑂𝑃𝐸, in Fig. 9B. To compare devices prepared using NC samples having different values of Φ, 𝑂𝑄𝐸 and 𝑂𝑃𝐸 are normalized by setting Φ = 1, but otherwise using identical properties to the experimentally measured devices (𝛼, absorption, and emission spectra). The maximum 𝑂𝑃𝐸 is predicted to occur at an optical density at 𝜆 = 575 nm equal to ~0.3 mm-1, corresponding closely to the LSC analyzed in Figs. 5-6, which was in fact the best performing device studied here. In Figure 10 we show how concentrator performance depends on both NC loading and polymer waveguide layer thickness, computed for a 1 m2 LSC, which is representative of the size of a typical window in a commercial building. NC concentration is expressed in terms of the optical density at the first


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3.4 OD mm-1 0.05 2.5 0.08 0.10 0.17 1.7 0.2

750

500

0.3 0.4 0.5 0.6

250

0

Flux Gain

1000 Edge Output Irradiance (W m-2)

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0.8

0.0 0

2 4 6 8 polymer layer thickness (mm)

10

Fig. 10. Projected performance of 1 square meter LSCs. Edge irradiance and flux gain computed for large area concentrators as a function of optical density at 575 nm and polymer thickness using Φ, absorbance, and emission spectra of the device in Figure 5. The projected flux gain is computed for amorphous Si PVs coupled to all four edges of a square LSC. absorbance feature (575 nm), where OD = 1.0 mm-1 equates to 7.2 wt% NC loading. The attenuation coefficient is calculated using eq 3 and all other properties (Φ, absorbance, and emission spectra) correspond to the device in Figure 5. The results in Figure 10 show that, for a 1 m2 LSC, a polymer layer thickness of 1.7 mm produces the largest flux gain, using 1.2 wt% NC loading. This concentrator achieves a projected output irradiance of nearly 1000 W m-2 with a thin waveguide geometry minimizing photoconverter area and weight, satisfying important requirements for practical solar energy harvesting window layers. Comparison of best-performing and idealized NC LSCs. Finally, we apply these results to examine the performance of CuInS2 NC LSCs if further improvements can be made to 𝛼 and Φ. As noted, the NC PL quantum yield falls by up to 30% upon polymer incorporation, and the observed parasitic attenuation loss rate is 10 – 100 times greater than the intrinsic attenuation limits imposed by the PLMA waveguide, polymer, or single-NC scattering. Since these factors limit performance in small and large devices, significant further improvements should be possible. The host CuInS2 bandgap can also be reduced via anion alloying or growth of larger diameter NC cores, improving solar spectrum matching. Figure 11 projects the impacts on performance from improvements in these areas for devices with 𝐺 = 10×. The dashed lines assume Φ = 86%, the highest value we have obtained for these CuInS2 NCs in toluene,21 along with complete solar absorbance up to the indicated bandgap, and show 𝑂𝑃𝐸 for a range of 𝛼. The solid line shows the limiting case corresponding to Φ = 1, 𝛼 = 0, 500 meV Stokes shift, and zero self-absorption, i.e. an ideal CuInS2 LSC with a single escape-cone loss. These calculations indicate efficiencies exceeding 15 ACS Paragon Plus Environment


4.1 Optical Power Efficiency (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.1

2.5

Energy (eV) 2.1 1.8 1.5

0.04 dB/cm 0.1 dB/cm 0.2 dB/cm

15

5

1.2

0.0 dB/cm

20

10

1.4

Page 16 of 21

Mn:CdxZn1-xSe

Mn:ZnSe

0 300

400

CuInS2 CuInSe2 500 600 700 800 Wavelength (nm)

900 1000

Fig. 11. Theoretical and actual performance of nanophosphor LSCs. Dashed lines: predicted performance at 𝐺 = 10× for CuInS2 LSCs with Φ = 86% and 𝛼 = 0.2, 0.1, or 0.04 dB cm-1 as labeled. Solid line: predicted performance of an ideal LSC with a single escape-cone loss, 500 meV Stokes shift, zero self-absorption, Φ = 100%, and 𝛼 = 0 dB cm-1. Calculations assume complete absorption of all solar irradiance up to the bandgap. Bars indicate best-in-class performance for four nanophosphor LSCs. Experimental data are projected to a uniform size 𝐺 = 10× using the model in the text. Horizontal axes give the host bandgap. Vertical dashed line shows the bulk bandgap of CuInS2. 10% should be achievable for CuInS2 NC LSCs. Also shown are representations of experimental NC LSCs prepared using Mn2+:ZnSe/ZnS,19 Mn2+:CdxZn1-xSe/CdS,20 CuIn(S1-xSex)2/ZnSe,23 and CuInS2/CdS (this work), all extrapolated from experiment to the same G = 10× for comparison purposes. The CuInS2 concentrators prepared here achieve the highest performance reported so far in this class of materials, and among the best performance for any reported LSC at comparable 𝐺. Although the smaller-bandgap CuIn(S1xSex)2/ZnS

NCs studied Ref. 23 enable absorption over a slightly greater spectral range than the CuInS2/CdS

NCs studied here, the latter’s higher PL quantum yield (up to 75% in LSC devices vs. 40%) and optimized NC loading result in substantially improved efficiency in the present LSCs.

Conclusion In summary, we report NC-polymer composite waveguide LSCs based on CuInS2/CdS NC phosphors demonstrating record high performance in large geometric gain, semi-transparent concentrators, with optical power efficiencies up to 5.7% under AM1.5 illumination for 𝐺 = 6.7×. A new analytical framework is introduced enabling quantitative analysis of each principle loss mechanism on the basis of straightforward luminophore concentration- and excitation distance-dependent measurements without the need for ray-tracing or Monte Carlo simulation. Application of this model shows that waveguide losses grow in proportion to NC loading, leading to an optimal concentration corresponding to an optical density of ~0.3 mm-1 at the first absorbance maximum, equivalent to ~2 wt% NC content. An analysis of optical 16 ACS Paragon Plus Environment

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losses shows that non-radiative relaxation losses dominate at small geometric gain, but scattering losses from NC aggregates become limiting in larger devices. These results demonstrate the importance of understanding and balancing each optical loss mechanism in order to maximize performance in LSCs based on large Stokes shift NC phosphors.

Acknowledgments This work was supported by the National Science Foundation through DMR-1035512 (S.M. and D.L.P.) and DMR-1505901 (D.R.G.) and the Environmental Protection Agency EPA-SU835704 (D.L.P). Part of this work was conducted at the University of Washington NanoTech User Facility, a member of the NSF National Nanotechnology Infrastructure Network (NNIN).

Supporting Information. Experimental details of NC synthesis and device fabrication. Derivation of the optical model. Thermogravimetric analysis of NC loading. Fourier transform infrared spectroscopy measurements of the degree of polymerization. Derivation of the light scattering model.

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