Performance Limits of Luminescent Solar Concentrators Tested with

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Performance Limits of Luminescent Solar Concentrators Tested with Seed/ Quantum-Well Quantum Dots in a Selective-Reflector-Based Optical Cavity Hyung-Jun Song, Byeong Guk Jeong, Jaehoon Lim, Doh C. Lee, Wan Ki Bae, and Victor I. Klimov Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04263 • Publication Date (Web): 11 Dec 2017 Downloaded from http://pubs.acs.org on December 13, 2017

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Performance Limits of Luminescent Solar Concentrators Tested with Seed/Quantum-Well Quantum Dots in a Selective-Reflector-Based Optical Cavity Hyung-Jun Song†, Byeong Guk Jeong†,‡,!, Jaehoon Lim†, Doh C. Lee!, Wan Ki Bae‡, Victor I. Klimov†* †

Center for Advanced Solar Photophysics, Chemistry Division, Los Alamos National

Laboratory, Los Alamos, New Mexico 87545, USA ‡

Photoelectronic Hybrids Research Center, Korea Institute of Science and Technology, Seoul

02792, Republic of Korea !

Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of

Science and Technology, Daejeon 34141, Republic of Korea * Address correspondence to [email protected]. Telephone: 505-665-8284.

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ABSTRACT Luminescent solar concentrators (LSCs) can serve as large-area sunlight collectors for photovoltaic devices. An important LSC characteristic is a concentration factor (C), which is defined as the ratio of the output and the input photon flux densities. This parameter can be also thought of as an effective enlargement factor of a solar cell active area. Based on thermodynamic considerations, the C-factor can reach extremely high values that exceed those accessible with traditional concentrating optics. In reality, however, the best reported values of C are around 30. Here we demonstrate that using a new type of high-emissivity quantum dots (QDs) incorporated into a specially designed cavity, we are able to achieve the C of ~62 for spectrally integrated emission and ~120 for the red portion of the photoluminescence spectrum. The key feature of these QDs is a seed/quantum-well/thickshell design, which allows for obtaining a high emission quantum yield (>95%) simultaneously with a large LSC quality factor (QLSC of ~100) defined as the ratio of absorption coefficients at the wavelengths of incident and reemitted light. By incorporating the QDs into a specially designed cavity equipped with a top selective reflector (a Bragg mirror or a thin silver film), we are able to effectively recycle reemitted light achieving light trapping coefficients of ~85%. The observed performance of these devices is in remarkable agreement with analytical modeling, which allows us to project that the applied approach should allow one to boost the spectrally integrated concentration factors to more than 100 by further improving light trapping and/or increasing QLSC. Keywords: Luminescent solar concentrator, LSC, quantum dot, concentration factor, LSC quality factor, selective reflector


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Luminescent solar concentrators (LSCs) have attracted considerable attention as lowcost sunlight collectors for photovoltaic cells (PVs) in both small (residential)- and utility (solar farm)-scale PV installations, as well as space-based systems.1-6 These devices are especially attractive for implementing ideas of building integrated PVs using “solar windows” that in addition to providing a programmable degree of shading would also serve as a source of electricity. This concept can be further extended to building sidings that could be based on flexible, strongly absorbing LSC sheets. A combination of these approaches represents a viable pathway towards an important goal of zero-energy-consumption buildings.3-10 An LSC is comprised of a large-area slab of a transparent material containing highly emissive fluorophores and supplemented by edge and/or bottom mounted smaller size PV cells (Figure 1a). Sunlight incident onto a device (input photon flux !1, input area A1) is absorbed by the fluorophores, re-emitted at a lower energy (longer wavelength), and then a portion of it trapped by waveguide modes of the slab is guided towards the PV cells (output photon flux !2, output area A2), where it is converted into electricity. If the LSC area is considerably greater than the area of edge-installed PVs and the device efficiency is sufficiently high, the use of the LSC light collector can boost the photocurrent, and hence, the power output of the coupled LSC-PV system compared to that of a stand-alone PV device. Since the LSC cost can, in principle, be considerably lower than that of a complex PV module, this approach can potentially lead to a significant reduction in the cost of solar electricity, which has been one of the motivations for the LSC research.7,8,11 Two important parameters of LSCs are external (!ext) and internal (!int) quantum efficiencies. The first quantity is defined as the ratio of the output and the input photon fluxes (!ext = !2/!1), while the second as the ratio of the output photon flux and the portion of the incident flux absorbed by the LSC (!abs), that is, !int = !2/!abs. !abs can be related to the 3 ACS Paragon Plus Environment

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total incident photon flux by !abs = !abs!1. Here, !abs is the device absorptance, which can be

(

)

(

calculated from !abs = T1 1" e"#1d = (1" R1 ) 1" e"#1d !!"# ! !! ! ! ! !!! ! ! ! !! ! !!! !

)

or

! !! ! !! ! ! ! ! !!! ! ! ! !! ! !!! !

(1)

for devices without and with a back reflector, respectively. In the above expressions, "1 is the absorption coefficient at the wavelength of incident light, R1 and R2 are the reflection coefficients of, respectively, the front and the back LSC surfaces, and T1 = 1 – R1 is the transmittance of the top surface. Another important characteristic of an LSC is a concentration factor (C). This quantity is defined as the ratio of the output ("2 = !2/A2) and the input ("1 = !1/A1) photon flux densities, and it can be thought of as the effective expansion (if C > 1) or contraction (if C < 1) factor of an active PV area due to a light-collecting effect of the LSC. Based on this definition, C = "2 /"1 or C = G!ext, where G = A1/A2 is the geometric gain factor. For smaller LSC dimensions, the concentration factor scales linearly with the geometric gain factor. However, at larger LSC dimensions, the C-vs.-G dependence becomes progressively more sub-linear and eventually reaches saturation (C = Csat), as illustrated in Figure 1b (see also a quantitative analysis of the C-vs.-G dependence later in this work). Past the saturation, any further increase in G does not lead to any appreciable increase in "2 or the output power.12 As was shown in refs 13 and14, the ultimate thermodynamic concentration limit (Cth) of an LSC based on ideal fluorophores with a 100% photoluminescence (PL) quantum yield (QY; !PL) is directly linked to the energy lost by the incident photon during the downconversion process. This energy is often referred to as a Stokes shift and defined as #S = hv1 – hv2, where hv1 and hv2 are the energies of the absorbed and the reemitted photons. Based on


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3 thermodynamic arguments, Cth = (! 2 / !1 ) exp(! S / kBT ) , where kB is the Boltzmann constant,

and T is the temperature. This expression suggests that, for example, for a fluorophore emitting at hv2 = 1.5 eV and having a Stokes shift #S = 0.3 eV, Cth is ~65,000, which is higher than the maximum concentration factor achievable for direct sunlight with traditional concentrating optics (C of ~46,000). In practice, however, the concentration factors achieved with LSC devices are considerably lower than the thermodynamic limit, and at best are just slightly above 30.15 The reason for the underperformance of practically realized LSC is a number of loss mechanisms not considered in the ideal thermodynamic model including nonradiative recombination of photoexcited LSC fluorophores,16 nonunity light trapping efficiency into waveguided modes, and propagation losses due to light scattering at imperfections with the LSC slab11,17,18 and its surfaces as well as reabsorption by the fluorophores themselves.19,20 Even in the case of an ideal fluorophore with !PL = 1, the latter mechanism can still lead to a considerable reduction in the overall LSC efficiency due to randomization of the light propagation direction following each reabsorption event, which increases photon losses due to emission into the escape cone defined by the angle 2#esc (Figure 1a). In the case of an isotropic emitter, the efficiency of light trapping into waveguide modes (!trap) is defined by the probability of photon emission outside the escape cone, which can be calculated from !trap = cos" esc . In a standard waveguide without a photonic reflector, #esc is equal to the angle

of total internal reflection, and be hence, can be found from !esc = arcsin(1/n), where n is the refractive index of the slab material. For the glass slab (n = 1.5), #esc = 41.8° and !trap = 0.75.3 The practical concentration limits of LSCs have been previously analyzed using analytical and numerical approaches that account for various loss mechanisms existing in 5 ACS Paragon Plus Environment

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real-life devices.12,21,22 One such model developed for planar LSCs23 has demonstrated that the maximum concentration factor (C0) realizable in these devices in a large-G limit is directly linked to a so called LSC quality or Q-factor (QLSC) defined as the ratio of fluorphore’s absorption cross-sections ($) or absorption coefficients (") at the absorption and emission wavelengths ("1 and "2, respectively): QLSC = $(%1)/$( %2) = $1/$2 = "1/"2 (Figure 1c). Specifically, in the case of an ideal emitters (!PL = 1) dispersed in a glass slab (n = 1.5), C0 is approximately equal to QLSC.23 Thus, in addition to a high emission efficiency, a key prerequisite of a high-performance LSC fluorophore is a specially shaped (e.g., step-like) absorption spectrum, which features a large absorption coefficient for incident radiation (solar spectrum in the case of PV applications) and a very small " at the reemission wavelength, that is, "1 >> "2. Previous efforts on tailoring optical spectra of LSC emitters for optimal performance (often referred to as “Stokes-shift engineering”) explored specially engineered molecules or molecular mixtures wherein effects such as emission from a weakly absorbing triplet state or cascaded energy transfer have been utilized to downshift the PL spectrum versus the onset of strong absorption.24-27 Many recent works have also explored colloidal quantum dots (QDs) for implementing ideas of Stokes-shift engineering via a number of methods including heterostructuring for separating the light absorption and emission functions between different spatial domains of the nanocrystal (e.g., an extra-thick shell and a small quantum-confined core),15,17 introduction of highly emissive intra-gap defects (e.g., Mn2+ ions),20,28 the use of indirect-gap (e.g., Si) QDs with intrinsically weak absorption at the emission wavelength,29 application of QDs emitting through native intra-gap states (e.g., CuInSexS2-x QDs),18,30 and the use of specially designed dye-QD hybrids.31-33 One such approach applied to demonstrate high-concentration devices is based on 6 ACS Paragon Plus Environment

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thick-shell CdSe/CdS QDs known as “giant” or g-QDs.17,34-37 Due to a large ratio between the overall volume of the QD and the volume of the emitting CdSe core (approximately defines the $1/ $2 ratio), these QDs exhibit high LSC quality factors (QLSC > 100) for excitation with blue light (see typical absorption and emission spectra of g-QDs in Figure 1c). Recently, gQDs were used to demonstrate record-high concentration factor of 30.3 by incorporating them into specially designed cavities supplemented by a top photonic mirror for improved trapping of reemitted light.15 As illustrated in Figure 1b (dashed black line), this value is close to Csat estimated from the analytical model of ref 23 for the parameters of the experiments of ref 15 and assuming G = 10,000, which is equal to the LSC/PV area ratio used in these measurements.38 The high concentration factors were obtained despite only moderate emission efficiencies of g-QDs used in this work (!PL = 0.6), suggesting a considerable room for improvement by simply increasing the !PL. Based on the modelling, for example, by increasing !PL to 0.95 and keeping all other parameters of experiments of ref 15 the same, it should be possible to push Csat to more than 140. Here, we practically demonstrate the concentration factors of more than 60 using a new generation of thick-shell nanocrystals wherein the quantum-confined CdSe emitter is incorporate into the structure not as a core but a thin strained layer deposited on top of the CdS seed and overcoated with the thick CdS shell (inset of Figure 2a). These nanocrystals, recently introduced in ref 39 combine the quantum-well and QD motives in the same structure, and therefore have been termed seed/quantum-well QDs or sqw-QDs. Application of strained-layer-epitaxy helps alleviate the large lattice mismatch at the CdSe/CdS interface by coherently stressing the CdSe layer, which allows for virtually dislocation-free growth of the final thick CdS shell. As a result of elimination of defects in the shell region, sqw-QDs exhibit nearly ideal PL quantum yields of >95%. In addition, as g-QD, they have a large 7 ACS Paragon Plus Environment

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apparent Stokes shift between the PL band and the onset of strong optical absorption due to a dominant role of the thick CdS shell in the light-absorption process. As a result, sqw-QDs feature high QLSC in excess of 100 for illumination in the blue. Based on these properties, they are ideally suited for testing “ultimate” concentration limits attainable with QDs. By incorporating sqw-QDs into LSC cavities equipped with two different types of selective reflectors, we achieve the concentration factors of up to 62.2 for spectrally integrated PL and ca. 120 for the red portion of the PL spectrum. For these studies, we synthesize sqw-QDs comprising a 1.3-nm radius CdS core, a 1.2 nm-thick CdSe emitting layer and a final CdS shell of a 5-nm thickness as schematically depicted in Figure 2a; see detailed characterization of these dots in Figure S1a-d.39 The PL spectrum of these QDs peaks at 636 nm (Figure 2b), and the emission QY evaluated by both integrating sphere measurements and a comparison to a reference dye (Rhodamine 101 in ethanol with !PL = 97%)40 is from 95% to 100% (Figure S1b), as was previously observed by us for similar structures.39 These values are considerably higher than those for more traditional CdSe/CdS g-QDs for which !PL is typically limited by 60 - 70%, due to detrimental effects of misfit dislocations formed at large shell thickness as a means to relax the stress accumulated in the CdS layer. In sqw-QDs, the emitting CdSe layer is coherently strained to adopt the crystal lattice of the CdS seed, and hence, the growth of the outer CdS layer occurs virtually stress-free, which greatly reduces the abundance of misfit dislocations and allows for obtaining near unity PL quantum efficiencies.39 As in g-QDs, the absorption edge of sqw-QDs is defined by the onset of the CdS-shell absorption, which is around 520 nm (Figure 2b). This value corresponds to the effective Stokes shift of 435 meV, which is considerably greater than the PL bandwidth (195 meV), and thus, allows for obtaining high QLSC for excitation wavelengths shorter than 520 nm. For 8 ACS Paragon Plus Environment

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example, assuming excitation at 455 nm, and using "2 at the peak of the PL band, we find QLSC = 78.2. To account for the change in the absorption coefficient across the PL spectrum, we introduce a spectrally averaged QLSC () calculated from

!!"# ! !! !

where !! ! !

!! !! !!!

!!" !!!!! !" !!" ! !"

,

(2)

and SPL(") is the spectral shape of the emission band undistorted by

reabsorption. Using this definition, we find that for 455-nm excitation, is 105. This value is higher than that at the PL peak wavelength due to the quick drop of the absorption coefficient on the red side of the emission band. For a quantitative analysis of concentration limits, we apply the analytical model of ref 23. In its original version, it considered a planar waveguide with two openings at the left and the right sides of the LSC (Figure 1a). In the context of calculations of internal efficiencies, this scheme is analogous to one with a single opening but for a device length (L) that is reduced by half and one of the device edges terminated with a perfectly reflecting mirror (see Figure 1a). Based on this analogy and using derivations from ref 23 we can present !int of the planar LSC with a single exit aperture as follows:

!int =

!PL!trap

(

1+ 2 "# 2 L 1$ !PL!trap

)

,

(3)

where & is the constant factor, which accounts for elongation of the average photon propagation path in a three-dimensional LSC slab versus a model one-dimensional waveguide. In ref 23, & was derived from the fit of the exact analytical solution for !int in the absence of reemission1 to eq 3, and then, validate using Monte Carlo modeling. Based on this analysis, & ranges from 1.4 to 1.8, where the larger values provide a closer description for 9 ACS Paragon Plus Environment

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longer LSCs or greater geometric gain factors.23 Since in the studied devices, G is much greater than unity, in our modeling we use & = 1.8. We further re-write eq 3 by expressing the absorption coefficient at the PL wavelength via the LSC Q-factor and the absorption coefficient at the wavelength of incident light, and further, presenting the device length as the product of the geometric gain factor and the thickness of the waveguide (d), which leads to

!int =

!PL!trap . !1 G (1 ! !PL!trap ) 1 + 2 ! ("1d)QLSC

(4)

While in experimentally studied LSCs, the exit aperture is located not at the device edge as in Figure 1a, but at its bottom (Figure 2a; discussed later in this work), eq 4 still allows for an accurate description of internal efficiencies, as indicated by good agreement with the results of numerical Monte Carlo simulations, as was previously observed for LSCs with edgecoupled PVs.23 As we mentioned earlier, the above analytical model allows one to accurately describe experimental observations for both large-area, practical-size devices11 as well as small-size models designed to test the limits for luminescent concentration.22 For example, the record-concentration structures studied in ref15 are characterized by the following set of parameters: QLSC = 230, "1d = 1.5, !abs = 0.94, !trap = 0.82, !PL = 0.6, and G = 10,000. Using these values in eq 4, we obtain !int = 0.0041. Further, by multiplying !int by G and !abs, we obtain C = 38.5 (see Figure 1b; dashed black line), which provides an upper estimate for concentration factors that could in principle be achievable in experiments of ref15. This value is indeed close to (but higher than) the concentration observed in that work for lowerscattering devices that showed C = 30.3. We can also use this model to estimate the highest concentration factors that can be 10 ACS Paragon Plus Environment

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achievable with the sqw-QDs. Specifically, our calculations indicate that while their QLSC is lower than that in ref15, their high !PL (= 0.95) allows for obtaining Csat greater than 36 even without a selective reflector. Specifically, using QLSC = 105 and

trap

= 0.75, we estimate Csat

= 36.5 (solid red line in Figure 1b) for "1d = 1.84 and !abs = 0.93 (these parameters are close to those of our experiments as discussed below). It should be possible to further boost Csat to ~62 with a selective reflector having !trap = 0.85 (solid blue line in Figure 1b), and then, to ~136 by increasing QLSC to 230 (solid green line in Figure 1b). In high-performance LSCs characterized by near-unity !PL and !trap, the originally generated photon can experience multiple reabsorption/reemission events whose number (nre) increases with increasing the geometric gain factor. To calculate nre, we introduce a waveguiding efficiency !wg = !int/(!PL!trap). This quantity is defined as the ratio of the number of the photons collected at the LSC output and the number of the first-generation, waveguide-trapped PL photons.23

Using eq 3, we can present !wg as follows: !wg = [1 +

2#G($2d)(1 ! %PL%trap)]-1. Alternatively, !wg can be expressed via nre using following considerations. After each reabsorption/reemission event, !wg is attenuated by a factor of (!PL!trap); hence if the total number of reabsorption/reemission events is nre, !!" ! !!!" !!"#$ !!!" . Combining the two expressions for !wg, we obtain [1 + 2#G($2d)( 1 ! %PL%trap)]-1 =!!!" !!"#$ !!!" or nre = !ln[1 + 2#($2d)G(1 ! %PL%trap)]/ln(!PL!trap). (5) Using eq 5, we can estimate nre for the parameters used in our earlier estimations of the concentration factors ("1d = 1.84, QLSC = 105, and !PL = 0.95), and specifically evaluate the effect of !trap on nre, which provides a quantitative measure of the efficiency of “photon recycling” in the LSC waveguide. Using, for example, !trap = 0.75 (standard glass/air 11 ACS Paragon Plus Environment

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interface), we obtain that nre changes from ~1.8 to ~11.3 as G is increased from 47 to 2500; this corresponds to the range of geometric gain factors explored in our experiments (see later in this work). If !trap is boosted to 0.85, nre remains almost unchanged for G = 47 (nre = 2.1). However, it shows a considerable increase (up to 16.1) for G = 2500, which is a direct result of improved “photon recycling” due to more efficient light trapping in the LSC waveguide. It is also instructive to separate contributions from nonradiative decay and photon escape from an LSC waveguide to overall losses arising from reabsorption of propagating light. During each reabsorption/reemission event, the fractional loss (fnr) in !wg due to a nonunity PL QY in given by (1 – !PL), while the loss due to photon escape (fesc) is proportional to !PL(1 – !trap). This yields the total loss coefficient f = fnr + fesc = (1 – !PL!trap) per single reabsorption/reemission event. Thus, relative contributions from nonradiative decay and photon escape to the overall photon losses can be found from fnr/f = (1 – !PL)(1 –

!PL!trap)-1 and fesc/f = !PL(1 – !trap)(1 – !PL!trap)-1, respectively. Using again parameters from previous estimations, we find fesc/f = 0.83 and 0.74 for !trap = 0.75 and 0.85, respectively. As expected for the high-emissivity QDs, the dominant efficiency loss mechanism in an LSC without a photonic reflector (or with an imperfect reflector) is photon escape from the LSC waveguide. In order for the escape losses to become lower than the nonradiative-decay loss, the light trapping coefficient should satisfy the condition !trap > 2 – 1/!PL, which yields !trap > 0.947 for the case of !PL = 0.95 considered in our estimations. To study the effects of luminescent concentration with sqw-QDs, we load them as a 3

toluene solution into an optical quartz cell with dimensions 5™4™1 cm (L™W™d); see Figure 2a. The larger 5-by-4 cm2 side of the cell is considered as a top, light collecting LSC surface. In our experiments, it is covered either with a standard quartz slide or a specially 12 ACS Paragon Plus Environment

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designed “selective” reflector based on either a thin silver (Ag) film or a Bragg mirror, as discussed later in this work. To improve recycling of PL photons escaping from the waveguide, we have examined two types of back/edge reflectors: diffuse vs. specular.41,42 As a diffuse reflector, we have tested polytetrafluoroethylene (PTFE) plates, while as a specular, a commercial metal film (Solar Mirror Film 1100; 3M Company); see optical characteristics of both reflectors in Figure S2a-c. A side-by-side comparison of two types of devices indicates a considerably poorer performance of LSCs with the PTFE reflectors (internal LSC efficiency is reduced by ~20% vs. the case of specular reflectors; see Figure S2d). This is a direct consequence of increased losses through the top face of the device due to randomization of light propagation direction after the reflection from the diffuse back or edge surfaces.43 This effect is absent in the case of the metal-film-based reflectors that keep the reflected light within the original waveguided modes. Thus, in our further studies, we have used LSCs with the metal-film-terminated edges and back surface. In order to quantify the concentration factor as a function of geometric gain, we incorporate a small, square-shaped opening at the back of the device with the area varied from 42 to 0.8 mm2. Given the top surface area of 2,000 mm2, these values correspond to G from 47 to 2,500. An important element of a high-performance LSC is a selective top reflector, which is transparent for incoming light but strongly reflecting for the PL signal emitted by the LSC fluororphores.15,42-48 The challenge in designing such reflectors is that in addition to spectral selectivity they should exhibit performance that is insensitive (or only weakly sensitive) to the light propagation direction for both incident and reemitted radiation. Thin silver films are uniquely suited as selective reflectors in proof-of-principle studies of light concentration. For example, according to our tests, a 50-nm layer of silver has reflectivity greater than 95% independent of the angle of incidence across the entire sqw-QD PL spectrum, and at the same


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time, features a semi-transparent window around 325 nm, which can be used to access QDs with an external excitation source (Figure 2b). Based on our measurements, the overall transmittance of the 50-nm Ag film for the commercial 325-nm light emitting diode (LED; UF3VF-1X009, Marubeni) is 0.50. To evaluate the performance of the LSC with the Ag-film top reflector, we use integrating sphere measurements (Figure S3a,b), which we validate via direct PV measurements using a PV cell coupled to the exit aperture of the device with an index matching polymer (Norland optical adhesive 65, Norland Products Inc.) as shown in Figure S3c,d.49 The results of these measurements are displayed in Figure 2c as

int

vs. G (open red

circles) and compared to those for the plain quartz top reflector (black open squares). In the same plot, we also show the enhancement factor (open blue triangles) due to the use of the top Ag mirror calculated as the ratio of the !int values for the situations with and without the Ag film reflector. Based on these data, the device with the silver mirror shows a more than two-fold enhancement in performance for G =102, which further increases to more than three-fold for G = 2,500. These are direct indications of a considerably enhanced light trapping within the LSC waveguide due to the highly reflecting Ag window. In fact, by fitting experimental results with eq 4 (lines in Figure 2c), we obtain that !trap increases from 0.62 for the quartz slide as the top reflector to 0.86 for the Ag-film reflector. Based on the measured !int, we can calculate external (C =!absG!int) and internal (Cint =G!int) concentration factors for the Ag top reflector displayed in Figure 2d by red and blue symbols, respectively, and compare them to the plain-quartz case (black symbols); lines with the matching colors show modeling. Due to high !PL of the sqw-QDs, we obtain high values of C (external and internal) of >20 even with a standard quartz reflector. The use of the Ag mirror allows for improving C to 33.5 The increase in concentration is even higher (up to 14 ACS Paragon Plus Environment

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~66.9) if evaluated in terms of Cint (open red symbols), as this representation eliminates attenuation of incident light due to only partial transmittance of the Ag reflector. As a means to improve the transmittance of a top reflector while preserving strong confinement of waveguided light, we have explored multi-layered distributed Bragg reflectors (DBRs) fabricated by Optical Filter Source per our specifications. The transmittance and reflectance spectra of a Bragg mirror used in our experiments are displayed in Figure 3a. These measurements were conducted for normal incidence (# = 0), while the angle-resolved measurements are shown in Figure S4. For angles up to ~40°, the DBR provides excellent average reflectivity of over 95% across the sqw-QD PL spectrum and even for # = 75° it drops only by ~20%. At the same time, this mirror is strongly transmitting across the green-to-blue portion of the spectrum (360-510 nm) where T1 is ~90% for # up to 40° and drops to 69% for # = 75°. These properties make these DBRs well suited for applications as selective reflectors in devices targeting concentration of shorter-wavelength light with % < 500-600 nm. The measurements of LSCs with the DBR (455 nm excitation) indicate that their light trapping efficiency (!trap = 0.84 - 0.85) is similar to that of devices with the Ag reflector, which leads to comparable internal quantum efficiencies (compare Figures 3b and 2c). However, due to improved transmittance of the top layer, the external concentration factors of DBR-based LSCs are considerably higher than those of devices utilizing the Ag-film reflector (compare Figures 3c and 2d). Specifically, with G = 102, we able to reach C = 20.7, and then boost the concentration up to 58.8 for G = 2,500. Even higher concentration factors are revealed by the analysis of a spectrally resolved PL signal. Due to a change in the absorption coefficient across the emission profile, 15 ACS Paragon Plus Environment

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the waveguiding efficiency is a spectrally dependent quantity, i.e., !wg = !wg(%). In the case of the QDs used in the present study, "(%) rapidly decreases in the range % > 610 nm, which leads to the reduction in reabsorption losses, and hence, increasing !wg(%). Experimentally, this effect is manifested in the distortion of the PL spectrum (apparent narrowing and a red shift), which becomes especially pronounced for large geometric gain factors (compare spectra shown by magenta and purple lines in Fig. 3d). The increase in !wg(%) at longer wavelength can be interpreted in terms of a spectrally dependent concentration factor (C%), which increases with %. The C%-factor can be related to !wg(%) by C% = !abs!PL!trap!wg(%). The overall concentration factor derived from spectrally integrated PL measurements can be expressed via C% using ! ! !! !

!! !!" !!!!" . !!" ! !"

As indicated before, SPL(") is the emission

profile undistorted by reabsorption, while C%SPL(%) describes the PL spectrum at the LSC output. In order to experimentally determine the spectral shape of C%, we divide the spectrum of emission collected through the LSC aperture (Fig. 3d, purple line) by the spectrum measured for the dilute QD solution (Fig. 3d, magenta line) in the absence of reabsorption effects. We further adjust the amplitude of the derived spectrum so as the calculated value of

!!

becomes equal to the concentration factor observed in spectrally integrated

measurements. The spectrally resolved concentration factor obtained in this way is displayed in Fig. 3d by the red line. It can be closely reproduced by calculations (black line in Fig. 3d) using eq 4 wherein QLSC is replaced by the spectrally dependent LSC quality factor !! defined earlier in this work. This analysis indicates a gradual increase in C% with increasing wavelength. The concentration factor is approximately 30 on the blue side of the emission spectrum (~620 nm); it increases to ~70 at the center of the PL band (~635 nm), and further 16 ACS Paragon Plus Environment

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to ~120 on its red side (~670 nm). This increase is a direct consequence of a quick drop in the absorption coefficient past 610 nm. To test the applicability of the DBR-based devices for concentrating broadband light, we have studied their performance as a function of % using a series of LEDs operating at peak wavelengths ("exc) ranging from 325 to 505 nm (Figure S5a). Depending on the specific LED used in the measurements, we varied the concentration of QDs in solution such as to maintain the same optical density of 0.8 ("1d = 1.84) for all excitation wavelengths (Figure 4a). The results of these studies are summarized in Figure 4b, where we show C as a function of G, and Figure 4c, where the maximum realized values of C (external (solid blue squares) and internal (open red circles)) are plotted vs. "exc together with the concentration factors measured for a reference device with a quartz slide as a top reflector (solid black triangles). For excitation at 325 nm, the maximum measured external concentration factor is ~30.2 (G = 2,500); it increases to 55.2 – 62.2 within the 385 – 455 nm wavelength range and then drops to ~47.4 at 505 nm (Figure 4c, solid blue squares). The peak value of C realized with the Bragg mirror (62.2) is more than a factor of 3 higher than that measured for the reference device with the quartz window, which is a direct result of improved light recycling. In the cased of the DBR-based LSC, the observed variation in C can be explained by considering spectrally dependent changes in both the amount of absorbed light (i.e., !abs) and the . In addition to spectral dependence of transmittance of the top surface, !abs also varies due to %-dependent reflectivity of the metal film terminating the back side of the device (i.e., R2; see Figure S5a,b). The value of , on the other hand, changes primarily due to the %-dependent absorption coefficient (calculated by averaging " over the LED spectrum). If we account for all of these factors, we can accurately model the measurements 17 ACS Paragon Plus Environment

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using eq 4 (lines in Figure 4b,c). These results indicate the ability of our LSC devices to maintain high concentration factors (C of 30.2 to 62.2) over a wide range of wavelengths (325 – 505 nm); see Figure 4c (solid blue squares). Based on these results, we can also obtain the spectral dependence of internal concentration factors (Figure 4c; open red circles). Since Cint is linked to !int, its spectral dependence is mainly controlled by the %-dependent QLSC (see eq 4), and as QLSC drops in the case of longer excitation wavelengths (% > 400 nm), so does Cint (Figure 4c). At 325 nm, the calculated maximum value of Cint is 65.7 (G = 2,500), and it gradually decreases to 44.1 for 505 nm. Finally, we have evaluated the performance of our DBR-based LSCs as a function of the angle of incidence (!, Figure 5a). The results of these measurements are displayed in Figure 5b as the normalized output flux vs. ! for both the DBR- (red line) and quartz-window (blue line) based devices (!exc = 455 nm, G = 2,500). In the ideal case of a !-independent concentration factor, the output flux '2 would follow the cos(!) dependence (black line in Figure 5b) in accordance with the angular dependence of the incident flux (Figure 5a). The measured values of '2, however, deviate from the cos(!) dependence indicating a progressive reduction in the concentration with increasing ! (Figure 5c). In fact, the presence of the DBR leads to a faster drop in C compared to the no-DBR case. As a result, while for normal incidence, the DBR yields a ca. factor of 3 higher concentration than the plain quartz window, at ! = 75° both types of the devices are characterized by the same values of C, producing the same output flux. Overall, however, when averaged over all incident angles according to

!

!

!

! ! ! ! !"# !! ! ! ! !! ! !"# !

! !" !"

!

! ! ! ! !! ! !

! !"# ! !"!!!!!!!(6)

the use of the DBR results in for more than 2.6 fold enhancement in the C-factor (44.9) vs. a quartz window (17.4). The cos(#) weighting factor used in the averaging procedure accounts 18 ACS Paragon Plus Environment

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for the angular dependence of the incident flux which reproduces the situation of the average day-time exposure of an LSC device of a fixed orientation (no tracking) to natural sunlight. Thus, despite its stronger sensitivity to the angle of incidence compared to the plain top window, the DBR still provides a considerable gain in the overall amount of collected light when " varies from -90° to 90° throughout the day. This work demonstrates high-concentration LSC devices with unprecedented Cfactors of up to 62.2 for spectrally integrated PL and reach ~120 for the red portion of the emission spectrum. The key elements of this work are finely engineered sqw-QDs with high QLSCs of around 100 and nearly perfect emission efficiencies (

PL

> 95%), and a special

LSC cavity equipped with a top selective reflector (DBR or a thin silver film) which allows for improved trapping (

trap

up to 0.86) of reemitted light. The device measurements are in

excellent agreement with results of analytical modeling, which allows us to project that a further enhancement in concentration to more than 100 is feasible by boosting QLSC to 200 and higher. The presently studied CdS/CdSe/CdS sqw-QDs have been optimized for applications in the green-blue region of the optical spectrum. The next challenge is translating these advances obtained with II-VI materials into the range of longer wavelengths (red and near-IR) which would make these high-concentration devices better suited for harvesting sunlight. Such future studies might take advantage of the recently demonstrated, highperformance near-IR LSC fluorophores such as CuInSexS2-x QDs20,30 or indirect Si QDs.29 Synthesis of CdS/CdSe/CdS sqw-QDs. Cadmium oxide (CdO, 99.95%, metals basis), oleic acid (OA, 90%), 1-octadecene (ODE, 90%), Se (99.99%), S (99.998%) and 1-dodecanethiol (DDT, Ë98%) were purchased from Alfa Aesar. Tri-n-octylphosphine (TOP, technical grade, 90%) were obtained from Sigma Aldrich. All chemicals were used as purchased. We prepared 0.5 M Cadmium oleate (Cd(OA)2), 2M selenium in tri-n-octylphosphine (TOPSe), 19 ACS Paragon Plus Environment

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0.25 M of sulfur dissolved in ODE (S-ODE) and 0.5 M 1-dodecanethiol in 1-octadecene and stored them in a glovebox filled with Ar until use. All syntheses were performed using a standard Schlenk line technique under Ar atmosphere. Sqw-QDs were fabricated using synthetic procedures of ref39. To fabricated CdS seeds with radius r = 1.3 nm, 0.3 mmol of CdO, 0.9 mmol of OA, and 10 mL of ODE were loaded into a 3-neck flask and degassed under 110 °C for 1 hr. The reaction flask was heated to 270 °C under Ar atmosphere to form a clear solution of Cd(OA)2. 0.6 mL of 0.25 M SODE was swiftly injected into the flask to form CdS seeds. After 10 min of reaction, the flask was cooled to room temperature, and the fabricated particles were purified twice by the usual precipitation/redispersion method. To deposit the CdSe emissive layer onto the CdS seeds, 0.1 g of CdS particles and 10 mL of ODE were degassed at 110 oC for 1 hr and heated up to 300 °C under Ar atmosphere. The desired amount of a mixed precursor solution of 0.1 M Cd(OA)2 and 0.1 M of TOPSe diluted in ODE was injected at a rate of 5 mL/h into the reaction flask. After the injection was completed, the temperature was maintained for 10 min and then the mixture was cooled to room temperature to quench the reaction. The products were washed twice by a precipitation/redispersion method. For fabricating a thick CdS shell, 0.1 g of CdS(r = 1.3 nm)/CdSe (l = 0.9 nm) particles and 10 mL of ODE were mixed in a flask and degassed under 110 °C for 1hr. The reaction flask was heated to 300 °C. At this temperature, the desired amounts of 0.5 M Cd(OA)2 and 0.5 M of DDT in ODE were added to the flask at a rate of 2 mL/h. After the injection was completed, the temperature was maintained for 30 min and then the reaction mixture was cooled to room temperature. The resulting QDs were purified twice by the precipitation/redispersion method. Purified QDs were dispersed in a nonpolar solvent for use.


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Figure Captions Figure 1. (a) An LSC coupled to a PV at its right edge; other edges and the back side are terminated with fully reflecting mirrors. The top side is equipped with a selective reflector having high transmittance for incident light (blue arrows) and high reflectance for reemitted light (red arrows). The length and the height of the device are L and d, respectively; the corresponding geometric gain factor is G = L/d. From the standpoint of calculations of internal efficiencies (

int),

this device is equivalent to the 2L-long LSC wherein the mirror on

the left edge is replaced with the second PV (dashed lines). Angle 2!esc denotes the escape cone defined by the angle of total internal reflection at the glass-air interface when the top surface is not equipped with a selective reflector. #1 and #2 are the incident and the output photon fluxes, respectively. Red and black circles are emissive and nonemissive QDs, respectively. (b) A concentration factor of an LSC (d = 1 cm) as a function of geometric gain factor calculated using eq 4 for four different sets of parameters QLSC, %trap, %PL and $1d indicated in the table; the parameters in line 4 (dashed black line) approximately describe a high-concentration device (C = 30.3) from ref15. (c) Typical absorption (light blue) and emission (red) spectra of thick-shell QDs that allow for obtaining a high LSC quality factor (QLSC) due to a large difference between absorption cross-sections of a small emitting core (g-QDs) or a thin emitting layer (sqw-QDs) and a large absorbing shell. Figure 2. (a) A schematic depiction of a device based on sqw-QDs (inset) and employing a selective reflector as the top window. All other device sides are terminated with a highly reflective metal film. The back side has a small square-shaped opening with a varied area (0.8 to 42 mm2) used to control the geometric gain factor. The device dimensions are 5$4$1 cm3. The QDs are loaded inside the device as solution samples with the concentration adjusted such as to produce a desired optical density at the excitation wavelength (typically


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0.8). (b) Transmission (blue line) and reflection (red line) spectra of a top mirror fabricated by depositing a 50-nm Ag film onto a glass slide in comparison with absorption (cyan shading) and PL (magenta shading) spectra of sqw-QDs. The Ag film shows nearly perfect reflectivity at the QD emission wavelength (R = 0.95 at 636 nm), while it exhibits a sharp peak in the transmission spectrum (T = 0.58) around 325 nm which allows us to efficiently excited QDs using a narrow-band, 325-nm LED. (c) Internal quantum efficiency (%int) derived from integrating-sphere measurements as a function of geometric gain factor for devices with (red circles) and without (black squares) a 50-nm Ag front reflector. Blue open triangles show the enhancement in %int obtained as a result of improved light confinement within the LSC waveguide due to the top Ag reflector. Color-matched lines are the modeling using eq 4. (d) Concentration factors (external) of the devices with and without the top Ag reflector (blue triangles and black squares, respectively). Red circles show the internal concentration factor for the Ag-film-based LSC obtained by accounting for partial transmittance of the silver window. Lines are calculations using eq 4. Figure 3. (a) Transmission (blue line) and reflection (red line) spectra of a Bragg mirror for normal incidence in comparison to the absorption (cyan shading) and PL (magenta shading) spectra of sqw-QDs. (b) Internal quantum efficiency (%nt) of the LSC with a DBR mirror measured using the integrating sphere method (solid circles) and the PV response (open circles) as a function of G. Excitation wavelength is 455 nm. (c) Concentration factor vs. G for the LSCs with (red circles) and without (black squares) the DBR. Same excitation wavelength as in ‘b’. (d) The measured (red line) and calculated (black line) concentration factor as a function of PL wavelength in comparison to absorption (blue line) and emission (magenta line) spectra of the dilute sqw-QD solution in a plain quartz cuvette. The spectral shape of the C-factor was obtained from the ratio of the PL spectrum measured through the


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LSC exit aperture (purple line) and the PL spectrum of a dilute QD solution (magenta line); see text for details. Figure 4. (a) Absorption spectra of sqw-QD samples (lines) used in studies of spectral dependence of concentration using five narrow-band LEDs with emission wavelengths from 325 to 505 nm. The QD concentration in each sample is adjusted such as to produce the same optical density (OD) of 0.8 at the excitation wavelength. Optical density relates to the absorption coefficient " by OD = ("d)/ln(10), where d is the sample thickness (= 1 cm in our experiments). The PL spectrum of the QDs is shown by magenta shading. (b) Concentration factors (external) of LSCs with the DBR as a function of G for different excitation wavelength (symbols) in comparison to modeling using eq 4 (color-matched lines). (c) Maximum external (solid blue squares) and internal (open red circle) concentration factors (G = 2,500) of DBR-LSC derived from the measurements in ‘b’ as a function of excitation wavelength in comparison to modeling (color matched solid lines). Solid black triangles are measured concentration factors for a reference device with a quartz slide as a top window (black line is modeling using eq 4). Figure 5. (a) A schematic of measurements of the angular dependence of the LSC concentration factor. Incident photon flux #1 varies as cos(!) with changing the angle of incidence !. (b) Normalized output photon flux (#2) of the LSCs with (red line) and without (blue line) a top Bragg mirror (G = 2,500) as a function of ! along with the cos(!) dependence (black line); 455-nm LED excitation. (c) The angular dependence of the concentration factor for devices with (red circles) and without (black squares) DBR; obtained from data in ‘b’. (d) The angular dependence of the enhancement ratio of concentration factors with and without the DBR.


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ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. TEM images and PL quantum yield measurements of sqw-QDs, comparison of diffuse polytetrafluoroethylene (PTFE) and specular metal-film reflectors, evaluation of LSC performance using integrating-sphere and photovoltaic (PV) measurements, optical spectra of Bragg mirrors, optical characterization of the metal film used for fabricating back and edge reflectors (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Telephone: 505-665-8284. ACKNOWLEDGMENT This work was supported by the Center for Advanced Solar Photophysics (CASP), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. The authors declare no competing financial interest.


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Nano Letters

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