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SUPPLEMENTARY INFORMATION ARTICLE NUMBER: 16157 | DOI: 10.1038/NENERGY.2016.157 NATURE ENERGY | www.nature.com/natureenergy 1 Hongbo Li, Kaifeng Wu, Jaehoon Lim, Hyung-Jun Song, and Victor I. Klimov* Center for Advanced Solar Photophysics, Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Supplementary Figure 1. (a) A histogram of quantum dot (QD) sizes for a sample of thick- shell CdSe/Cd 1-x Zn x S “giant” QDs (g-QDs) with x = 0.5 and the CdSe mean core diameter of 4 nm (the same sample as in Figure 1 of the article). The average g-QD size is 12.2 ± 2.2 nm. (b) The histogram of particle sizes for the same sample after overcoating g-QDs with silica shells. The average size of a composite particle is 22.5 ± 2.3 nm. The corresponding average silica shell thickness is 5 nm. Doctor-blade deposition of quantum dots onto standard window glass for low-loss large-area luminescent solar concentrators

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Page 1: SUPPLEMENTARY INFORMATION - Nature Research€¦ · Supplementary Note 1. Effect of dielectric environment of photoluminescence lifetimes Time-resolved photoluminescence (PL) measurements

SUPPLEMENTARY INFORMATIONARTICLE NUMBER: 16157 | DOI: 10.1038/NENERGY.2016.157

NATURE ENERGY | www.nature.com/natureenergy 1

1

Supplementary Information Low-loss, large-area luminescent solar concentrators fabricated by doctor-blade deposition of quantum dots onto standard window glass Hongbo Li, Kaifeng Wu, Jaehoon Lim, Hyung-Jun Song, and Victor I. Klimov* Center for Advanced Solar Photophysics, Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Supplementary Figure 1. (a) A histogram of quantum dot (QD) sizes for a sample of thick-shell CdSe/Cd1-xZnxS “giant” QDs (g-QDs) with x = 0.5 and the CdSe mean core diameter of 4 nm (the same sample as in Figure 1 of the article). The average g-QD size is 12.2 ± 2.2 nm. (b) The histogram of particle sizes for the same sample after overcoating g-QDs with silica shells. The average size of a composite particle is 22.5 ± 2.3 nm. The corresponding average silica shell thickness is 5 nm.

Doctor-blade deposition of quantum dots onto standard window glass for low-loss large-area luminescent solar concentrators

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Supplementary Figure 2. Photoluminescence (PL) intensities of g-QDs as a function of reaction time during QD overcoating with silica. Normally, it takes 40 hours to complete the shell deposition. The reaction monitored in this plot produces the shell with the average thickness of 5 nm. The first, “time-zero” data point corresponds to a pristine g-QD sample before adding any tetraethyl orthosilicate (TEOS) or ammonium. The data show that there is no any observable PL intensity drop during silica-shell deposition. This is in sharp contrast to previous reports where the deposition of silica shells resulted in at least ~60% of the PL QY drop.

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Supplementary Figure 3. (a) PL spectra of uncoated (red; lower panel) and silica-coated (blue; upper panel; 5 nm shell thickness) g-QDs in solutions (dashed) and spin-cast films (solid); in solution samples, uncoated and silica-coated dots are dissolved, respectively, in toluene and ethanol. The ~3 nm redshift of the PL peak of the film vs. solution sample in the case of uncoated g-QDs is a signature of energy transfer (ET). This shift is absent in the case of silica-coated g-QDs indicating a nearly complete suppression of ET. (b) PL QYs of solution vs. film samples. Uncoated g-QDs show a significant PL quenching (by 38%) due to ET upon assembly into close-packed films. On the other hand, the PL QY of silica-coated g-QDs is not modified in films vs. solution samples, which is a direct result of suppressed ET. Error bars represent a standard deviation in PL quantum yields from several independent measurements.

600 625 650 675 700 7250.0

0.4

0.8

1.2

1.6

2.0 QD solution QD film QD/silica solution QD/silica film

Nor

mal

ized

PL

(a.u

.)

Wavelength (nm)

010203040506070

QD solution

QD/silicafilm

QD/silicasolution

QD film

PLQ

Y(%

)

a b

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Supplementary Figure 4. A photograph of a setup used to evaluate the performance of fabricated thin-film luminescent solar concentrators (LSCs). It consists of a fiber-coupled light emitting diode (LED) emitting at 405 nm, an integrating sphere, and a compact spectrometer (Ocean Optics). Square-shaped LSCs fabricated on substrates of different sizes (from 1 to 4 inch) with edges masked by a carbon tape.

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Supplementary Figure 5. (a) A typical difference spectrum obtained by subtracting the emission spectra collected at the output port of the integrating sphere with and without an LSC. The areas of the "positive" band at ~630 nm and the "negative" band at 405 nm are proportional to, respectively, the total number of the photons emitted by the LSC (SPL) and the number of pump photons absorbed by it (Sabs). The ratio of the two quantities yields the total PL quantum yield of the LSC (ηPL,LSC = SPL/Sabs). (b-e) Measurements of LSCs of different sizes (from 1 to 4 inches; indicated in the figure). The spectra of total, edge, and face emission are shown by black, green, and red colors, respectively. The same spectra are displayed in the inserts in the normalized form. The edge emission spectrum shows a redshift with regard to the spectrum of face emission, which is a result of reabsorption/reemission effects experienced by waveguided light. As expected, this shift increases with increasing the device dimensions.

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.u.)

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ηPL,LSC = SPL/Sabs

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Supplementary Figure 6. Symbols are literature values1-7 of internal quantum efficiencies (ηint) of QD-LSCs in comparison to values realized in the present studies (green circles; device areas from 6.5 to 412 cm2); the data are shown as a function of a light-collecting device area. Green line is ηint calculated using the model described in Supplementary Note 2 for the parameters of LSCs studied in the present work; the model does not account for "extrinsic" losses due to scattering at optical imperfections within the matrix and at the LSC surface. The fact that the experimentally measured internal quantum efficiencies of our LSCs are close to the theoretical curve indicates that these devices are virtually scattering-free; together with reduced losses to re-absorption, this results in the efficiencies that are on a par with or superior to the highest values reported in the literature. In fact, the internal efficiency of our 412 cm2 LSC is comparable to that of a considerably smaller literature device (purple triangle; ~150 cm2 area), which is one of the current record holders.

Inte

rnal

qua

ntum

effi

cien

cy

LSC area (cm2)

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Supplementary Table 1. Overview of literature results for QD-based LSCs.1-8 The internal concentration factor is defined as a product of the internal quantum efficiency and the geometric gain factor. Ordered by LSC

area QD Type QD

QY LSC Size

(L× W × T) cm×cm×cm

Light Source

Internal Quantum Efficiency

Internal Concen-tration Factor

Power Conversion Efficiency

Notes

Nano Lett., 2014, 14, 4097-4101.

Ref 5

CdSe/CdS core/shell

86% 2cm × 2cm × 0.2 cm

400 nm 59% 1.5 NA

Scientific Reports, 2015, 5,

17777. Ref 4

CuInS2/ZnS core/shell

81% 2.2 cm × 2.2 cm

× 0.3 cm

450 nm 26.5% 0.5 8.7

Advanced Energy Materials, 2016,

6, 1501913. Ref 7

PbS/CdS core/shell

40-50%

10 cm × 1.5 cm × 0.2 cm

solar simulator

4.5% 2.2 NA 1)

Sol. Energy Mater. Sol. Cells, 2011, 95, 2087-

2094. Ref 8

CdSe/CdS/CdZnS/ZnS

core/multi-shell

45% 4.95cm × 3.1 cm× 0.4 cm

solar simulator

NA NA 2.8% 2)

ACS Nano, 2014, 8, 3461-3467.

Ref 2

Mn2+

-doped ZnSe/ZnS

50% 2.5 cm × 7.5 cm

× 0.042 cm

400 nm 37% 8.1 NA

Optics Express, 2011, 19, 24308-

24313. Ref 6

PbS NA 2.54cm × 7.62 cm× 0.41 cm

solar simulator

~8% 0.2 NA

Nat Photon, 2014, 8, 392-399.

Ref 1

CdSe/CdS core/shell

45% 21.5 cm × 1.3 cm

× 0.5 cm

solar simulator

10.2% 4.4 NA 3)

Nat Nano, 2015, 10, 878-885.

Ref. 3

CuInSexS2In/ZnS core/shell

40% 12 cm × 12 cm × 0.3 cm

solar simulator

16.7% 1.7 NA

Present study Silica-coated CdSe/CdZnxS1-x

core/alloyed shell

70% 10.2 cm × 10.2 cm

× 0.16 cm

405 nm 24% 3.8 NA

Present study Silica-coated CdSe/CdZnxS1-x

core/alloyed shell

70% 20.3 cm × 20.3 cm

× 0.16 cm

405 nm 15% 4.8 NA

1) Three edges of the LSC slab were terminated with mirrors. 2) Three edges of the LSC slab were terminated with mirrors and a diffuse, white reflector was placed at the bottom of the LSC plate. 3) White diffuse reflectors were placed in the proximity to the long-face edges of the LSC.

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Supplementary Note 1. Effect of dielectric environment of photoluminescence lifetimes Time-resolved photoluminescence (PL) measurements (Figure 2e of the main text) indicate

that the 1/e PL decay time in the case of the silica-coated g-QDs is longer than that of the

uncoated g-QD sample (26.2 ns vs. 19.5 ns). Importantly, uncoated g-QDs used in this study

were dissolved in toluene, while silica-coated samples were prepared in ethanol.

The radiative decay rate, kr, of a QD with the high-frequency dielectric constant εQD placed in

a medium with the high-frequency dielectric constant ε can be determined from the

expression:

𝑘! =!!

!!!!!!!!𝜑 𝜀 𝑓!" !𝜔!, (S1)

where, φ is the oscillator strength of the QD optical transition, ω is the emission frequency,

and fLF is the local field factor. The local-field factor can be calculated from:

fLF =3ε

2ε + εQD .

The dielectric constant of silica shell is 2.18, which is very close to the dielectric

constant of toluene (𝜀toluene = 2.24). If we assume that in the case of silica-coated QDs, the

dielectric constant of the external medium is equal to that of silica, then the ratio of radiative

decay rates between coated and uncoated samples would be 0.95. This is, however,

inconsistent with our observations that indicate a stronger difference.

Since the silica shell is only a few-nanometer thick and is also porous, it is reasonable

to assume that the dielectric properties of the environment experienced by the g-QDs are

defined not by silica but rather ethanol. The effect of silica can, in principle, be accounted for

within the effective medium theory.9,10 However, considering that the volume fraction of

silica in the silica/ethanol medium is small, the effective dielectric constant should approach

that of ethanol. This leads to the conclusion that the observed difference in PL lifetimes

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9

between the silica-coated and uncoated g-QDs is primarily due the difference in dielectric

constants of the solvents used to prepare the studied samples.

For ethanol and toluene, 𝜀 is 1.76 and 2.24, respectively. For g-QDs, εQD is

approximately 7.69. Based on these values,

𝑘!,!"!!"#$𝑘!,!"#$%&%

=𝜀!"!!"#$𝜀!"#$%&%

×𝑓!",!"!!"#$𝑓!",!"#$%&%

!

= 0.71.

The calculated ratio is very close to the ratio of the measured PL decay rates (19.5/26.2 =

0.74), confirming our assessment that the observed difference in PL lifetimes is linked to the

difference in the dielectric constants of the solvents. This further indicates that encapsulation

of the g-QDs into thin silica shells does not appreciably modify the dielectric environment

“seen” by the QDs.

Supplementary Note 2. Analytic model of planar thin-film LSCs

Here we provide a brief description of the analytic model developed in ref 11 for calculating

optical efficiencies and concentration factors of planar LSCs. In this model, the internal

quantum efficiency (ηint) or the collection efficiency (ηcol) is defined as: 𝜂!"# = 𝜂!"# =

𝜂!"𝜂!"#$𝜂!", where 𝜂!"is the “true” PL quantum (QY) of QDs measured in dilute solutions,

𝜂!"#$ is the efficiency of light trapping into waveguide modes (75% for a waveguide with the

refractive index n =1.5) and 𝜂!" is the waveguiding efficiency defined as a fraction of the

first-generation, waveguide-trapped PL photons that eventually reach the LSC edges.

For the situation when every re-absorption event is followed by nonradiative

recombination, 𝜂!" can be described by 𝜂!"(!) = 1 (1+ 𝛽𝛼!𝐿), where 𝛼! is the absorption

coefficient of the LSC at the emission wavelength and L is its length. Based on numerical

calculations by Weber and Lambe,12 β can be approximated by a constant equal to 1.4, which

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10

provides ±15% accuracy in describing the exact solution for α2L up to 20. 11 The

corresponding collection efficiency, 𝜂!"#(!) = 𝜂!"𝜂!"#$𝜂!"

(!) , accounts only for the first-

generation PL photons produced following the absorption of the original incident light. In

reality, absorption of waveguided radiation is followed by reemission, which increases the

overall collection efficiency and can be accounted for by summing the contributions from the

second, third, etc. reemission events.

To account for the second-generation of reemitted photons (collection efficiency 𝜂!"#(!)),

we apply the first-generation collection efficiency 𝜂!"#(!) to the fraction of the photons (1-𝜂!"

(!))

removed from the propagating modes by the first reabsorption event. This leads to 𝜂!"#(!) =

𝜂!"𝜂!"#$(1− 𝜂!"! )𝜂!"#

(!). Similarly, 𝜂!"#(!) = 𝜂!"𝜂!"#$(1− 𝜂!"

! )!𝜂!"#(!), 𝜂!"#

(!) = 𝜂!"𝜂!"#$(1−

𝜂!"! )

!𝜂!"#(!), etc. The total collection efficiency is the sum of contributions due to all photon

generations, which yields: 𝜂!"# = 1− 𝜂!"𝜂!"#$(1− 𝜂!"! )

!!𝜂!"#(!). Using the expression for

𝜂!"! , we obtain:

𝜂!"# = 𝜂!"# = 𝜂!"𝜂!"#$ 1+ 𝛽𝛼!𝐿(1− 𝜂!"𝜂!"#$)!!

. (S2)

Using eq. S2, one can calculate the external quantum efficiency from ηext = ηcolηabs.

Here ηabs, is the LSC absorptance, which can be found from ηabs = (1 - R)[1 – exp(-α1d)],

where R is the reflection coefficient at the excitation wavelength (~4% in our case), 𝛼! is the

absorption coefficient of the LSC at the excitation wavelength, and d is the LSC thickness.

The final expression can be presented as

𝜂!"# =(!!!)(!!!!!!!)!!"!!"#$!!!!!!(!!!!"!!"#$)

. (S3)

In ref 11, eq. S3 was benchmarking against numerical Monte Carlo (MC) ray-tracing

simulations and also directly compared to experimental measurements on LSCs based on QD

solutions. It was found that the analytic model provided an excellent agreement with both MC

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11

results and experimental data over a wide range of LSC parameters. This suggests that it

should also be applicable to the LSCs studied in the present work.

We found, however, that when we use the parameters of our LSCs (ηPL,α1, α2) in eq.

S3, the model considerably underestimates the results of the measurements for ηext. This

discrepancy relates to the difference in geometries of devices considered in ref11 and studied

in the present paper. The original model of ref 11 was developed for a homogeneous

distribution of fluorophores across the LSC thickness. In our layered LSCs, however, the

fluorophores are concentrated in the top thin layer (thickness d) deposited onto a transparent

glass slab (thickness D), which apparently affects the overall LSC efficiency. As indicated by

our Monte-Carol modeling, this difference in geometries can be accounted for by introducing

an effective absorption coefficient for propagating light,

α2,eff = α2[d/(D + d)], (S4)

which reduces the problem of a bi-layer LSC to that of a single-layer device with the

uniformly distributed LSC fluorophores. Using eq. S4 in eq. S3, we find a very close

correspondence between the calculations and the measurements (see Figure 5d of the article),

which validates our use of the adjusted theory of ref11 for evaluating the expected

performance of the layered LSCs studied in this work for the situations of higher QD PL QY

and larger device sizes.

Supplementary Note 3. Power conversion efficiencies of a stand-alone PV and a coupled

LSC-PV system

A power conversion efficiency (PCE) of a conventional photovoltaic (PV) cell is expressed as

ηPV = VocJscFWs

, (S5)

where e is the elementary charge, Voc is an open circuit voltage, JSC is a short-circuit current

density, F is a fill factor, and Ws is a solar radiation power density. The short-circuit current

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12

density can be related to the spectrally resolved external quantum efficiency (EQE, Q) of a

PV device by

Jsc = e Φs (ν )0

∫ Q(ν )dν = ens Qs , (S6)

where v is the photon frequency and Φs(v) is the photon flux spectral density connected to Ws

by Ws = (hν )Φs (ν )0

∫ dν (h is the Planck constant). In eq. S6, we have introduced the

following quantities: ns = Φs (ν )0

∫ dν - the total solar photon flux density, and

Qs = ns−1 Q(ν )Φs (ν )0

∫ dν - the PV EQE averaged over the solar spectrum. Based on eqs. S5

and S6, we can present PCE as

ηPV = eVocFhν s

Qs , (S7)

where hν s = ns−1 (hν )Φs (ν )0

∫ dν is the average energy of a solar photon.

Next, we apply a similar formalism to derive the expression for the PCE of a

combined LSC-PV system. Specifically, using eq. S6, we can present the short-circuit current

density as

Jsc,LSC = e ΦPL (ν )0

∫ Q(ν )dν = e QPL nPL , (S8)

where ΦPL(v) is the spectral density of the PL photon flux at the output of the LSC, nPL is the

total (spectrally integrated) photon flux of the output LSC radiation, and QPL is the PV

EQE averaged over the emission spectrum of the LSC fluorophore.

The value of nPL is connected to ns by the LSC external quantum efficiency (ηs,ext) and

the geometric gain factor (G = ALSC/ APV; ALSC and APV are the LSC and PV areas,

respectively) as follows:

nPL = Gηs,extns . (S9)

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13

We would like point out that quantity ηs,ext used in eq. S9 is different from the single-

wavelength efficiency introduced in the main text; here it is not a single-wavelength

parameter but, instead, is determined by the LSC light harvesting performance across the

entire solar spectrum. On the other hand, the LSC internal quantum efficiency (ηint) is

independent on the wavelength of incident light, and hence, a single-wavelength quantity used

in the main text is also applicable in the case of eq. S9. The efficiencies ηs,ext and ηint are

connected by the total LSC absorptance (ηs,abs) across the solar spectrum:

ηs,ext =ηs,absηint , (S10)

where

ηs,abs = ns−1 [1− R(ν )]

0

∫ [1− e−α (ν )d ]Φs (ν )dν ; (S11)

in the last expression, R(v) and α(v) are spectrally dependent LSC reflection and absorption

coefficients, respectively. Combining eqs. S8-S11, we obtain

Jsc,LSC = eGηs,absηint QPL ns . (S12)

We will define the efficiency of the LSC-PV system (ηLSC-PV) as the total power of the

PV divided by the total solar flux incident onto the LSC, i.e.,

ηLSC−PV =VocJsc,LSCFAPV

WsALSC=eVocJsc,LSCF

WsG. (S13)

In eq. S13, we assume that the open circuit voltage of the LSC-PV system is unchanged

compared to the stand-alone PV, which is strictly true in the ideal radiative-recombination-

only limit,13,14 and also is a reasonable approximation in the realistic non-ideal case.

Expressing Ws via ns and vs, and using Jsc,LSC from eq. S12, we obtain:

ηLSC−PV == eVocFhν s

QPL ηs,absηint . (S14)

Finally, by comparing eqs S7 and S14, we can directly relate the efficiency of the stand-alone

PV device to that of the device coupled to the LSC:

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ηLSC−PV ==ηPV

QPL

Qs

ηext =ηPVqLSCηabsηint . (S15)

In eq. S15, we have introduced the LSC “spectral re-shaping” factor qLSC = QPL / Qs ; in a

correctly designed device, the LSC emission peaks near the spectral maximum of the PV EQE

and the value of qLSC is greater than unity. For a typical Si PV, Qs is ca. 0.45, while a

single-wavelength EQE above the absorption onset can be as high as 0.9-0.95; based on these

values qLSC is ca. 2.

Supplementary Note 4. Derivation of LSC efficiencies from the PV performance of a

coupled LSC-PV system

The formalism developed in the previous section can be used to quantify the performance of

LSC devices based on comparative PV measurements of a solar cell with and without an LSC

light collector. Below, we apply these measurements to validate the results of integrating

sphere studies of the 10.16×10.16 cm2 device and to evaluate the efficiency of the larger area

device (20.32×20.32 cm2) that could not be measured with the integrating sphere due its size

limitation.

In these experiments, we use inexpensive flexible amorphous silicon (a-Si) modules

purchased from Power film, USA. They consist of 5 single cells connected in parallel; the

module dimensions are 0.15 × 10 cm2 and the power conversion efficiency is 4 - 5% under

AM 1.5G illumination. The module is installed on one edge of an LSC using an index-

matching polymer adhesive (NoA 68, Norland Products, USA) for minimizing coupling

losses between the LSC and the PV. Electro-optical properties of the devices were analyzed

using a voltage source meter Kiethley 236.

We conduct our measurements under natural outdoor illumination with the solar flux,

which is close to that under standard AM 1.5G illumination (100 mW/cm2). The current

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density (J)-voltage (V) characteristics for the two LSC sizes are displayed in Supplementary

Figure 7. The open-circuit voltages and fill factors are almost identical for the PV-only and

the LSC-PV systems, as expected for a fairly small difference in the incident light

intensities.15 The short-circuit currents, however, are different as a result of the difference in

the photon flux incident onto the PV cell. We will use this difference to evaluate the

concentration factors and quantum efficiencies of the studied LSCs.

Using eqs. S6 and S12, we obtain that the ratio of the short-circuit currents measured

with and without the LSC is given by

Jsc,LSCJsc

=ηs,absGηintQPL

QS

=ηs,absCintQPL

QS

, (S16)

here we introduce the internal concentration factor defined as

Cint = Gηint . (S17)

Based on eqs. S16 and S17,

Cint =1

ηs,abs

Jsc,LSCJsc

⎛⎝⎜

⎞⎠⎟

Qs

QPL

. (S18)

Using factory supplied EQE data for solar cells used in our measurements, we calculate Qs

= 0.18 and QPL = 0.57. Further, by integrating the absorptance of our LSC samples over the

solar spectrum, we find ηs,abs = 0.056. Using the above values, we can re-write eq. S18 as

follows:

Cint = 5.7Jsc,LSCJsc

⎛⎝⎜

⎞⎠⎟

. (S19)

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Supplementary Figure 7. The J-V measurements for the PV-only and the LSC-PV system for two LSC sizes, L = 10.16 cm (a) and 20.32 cm (b). For the smaller device, the ratio of the short-circuit currents Jsc,LSC / Jsc( ) is 0.58, while for the larger 0.65. The latter quantity should be corrected (multiplied) by a factor 1.33 to account for a partial shielding of the LSC output by the solar-module contacts. This yields, the corrected current ratio of 0.87 (for L = 20.32 cm).

Now, we can use eq. S17 to derive the LSC concentration factors of devices analyzed in

Supplementary Figure 7. Based on the measured short-circuit currents we obtain Cint = 3.3

and 5.0 for the devices with L = 10.2 and 20.3 cm, respectively. Using geometric-gain factors

of these devices (16 and 32, respectively), we obtain ηint = 0.21 and 0.15. The value obtained

for the 10.2 cm device is very close to both the efficiency obtained from integrating sphere

measurements (ηint = 0.24) as well as ηint predicated by the theoretical model (ηint = 0.25). A

close correspondence between all three values indicates that both optical and electrical

methods allow for accurate evaluation of the LSC performance. This assessment is further

confirmed by the fact that ηint derived from the PV characterization of the larger device (ηint

= 0.15) is virtually identical to the value obtained from the model (ηint = 0.16). One more

conclusion of this analysis is that our theoretical model does allow for accurate projection of

the performance of larger devices based on the measurements conducted on LSCs of smaller

sizes.

0 1 2 3 4

01

2

3

4

5

6

78

9

1010.2 X 10.2 cm 80 mW/cm2

Cur

rent

den

sity

(m

A/c

m2 )

Voltage (V)

With LSC Without LSC

0 1 2 3 4

01

2

3

4

5

6

78

9

1020.3 X 20.3 cm 90 mW/cm2

Cur

rent

den

sity

(m

A/c

m2 )

Voltage (V)

With LSC Without LSC

a b

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17

Supplementary Note 5. Cost estimations for thin-film QD-LSCs

In our calculations, we consider two scenarios: (1) research-lab-scale production and (2) mass

production. In the first scenario, the cost of the chemicals is estimated based on prices of

chemicals from Sigma-Aldrich and Alfa-Aesar, while in the second scenario the prices are

based on quotations from on-line retailers such as Alibaba. The table below provides the

summary of these calculations.

Supplementary Table 2

Raw Materials Lab-scale 1Mass production2

(order size: ~1000 kg)

QD synthesis $5.9/g $1.1/g

Solvents $1.6/g $0.1/g

Silica coating $9.2/g $0.5/g

Total $16.7/g $1.7/g

1 Sigma-Aldrich and Alfa-Aesar

2 Alibaba

In our devices, 1.6 g of QDs and 30 g of PVP are needed for fabricating the 1 m2 LSC

coating. Considering the PVP cost of $0.015/g and using the QD cost in the case of bulk-scale

production, we obtain that the total per-m2 cost of the QD/polymer coating is $3.17/m2. We

assume that for the improved protection, the QD layer is sandwiched between two pieces of

glass; with $3 per-piece price (Alibaba), this yields $6/m2. Approximating the cost of other

materials required to assemble a complete device by $1/m2, we obtain that the total cost of the

QD-LSC is ~$10/m2, which is comparable to a literature estimate of $11/m2 for dye-based

LSCs.16

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18

Supplementary Note 6. Cost of solar electricity for a PV module vs. an LSC-PV system

Using the above derivations, we can compare the costs of electricity produced with and

without an LSC light collector. A traditional metric for the cost of solar electricity is the price

of 1 W of peak power, that is, the power generated under full solar flux Ws,0 = 1 kW/m2. This

quantity (kPV), usually expressed in unit of $/W, can be related to the device PCE and the per-

m2 cost of a solar module (mPV) by

kPV = mPV

ηPVWs,0

. (S20)

For a modern high efficiency silicon PV module fabricated, for example, by SolarCity, ηPV =

22.5% and kPV is $0.55/W. Based on eq. S20, this corresponds to the device cost mPV =

$124/m2.

In our calculations of the cost of solar electricity in the case of the LSC-PV system, we

assume that a 1 m2 LSC (mLSC per-m2 cost) is coupled to a PV cell with the area 1/G m2,

where G is the geometrical gain factor introduced earlier. The total cost of such a system is

mLSC-PV = mLSC + G-1mPV; this corresponds to the following cost of solar electricity produced

with the PV-LSC system:

kLSC−PV = mLSC−PV

ηLSC−PVWs,0

= mPV ( f +G−1)

ηPVηabsηintqLSCWs,0

, (S21)

where f = mLSC/mPV is the ratio of the LSC to the PV per-m2 costs. Based on the above

estimations of the QD-LSC cost (mLSC =$10/m2; Supplementary Note 5) and a typical Si PV-

system cost (mPV = $124/m2), f = 0.08.

To evaluate a potential cost advantage due to an LSC solar collector, we introduce a

“cost-ratio” factor defined as rLSC−PV = kLSC−PV / kPV . Based on eqs. S20 and S21,

rLSC−PV = ( f +G−1)ηabsηintqLSC

. (S22)

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19

Supplementary Figure 8. The experimentally measured dependence of a normalized short-circuit current on the incident angle (θ) of solar radiation for a stand-alone PV cell (black) and the same cell coupled to a QD LSC (red). These measurements were conducted under natural outdoor illumination on a sunny day; the light intensity for normal incidence was 90 mW/cm2. Both measurements deviate from the ideal cos2(θ) dependence (blue) which is a result of a contribution from diffuse light. The LSC-PV system is more efficient in harvesting diffuse radiation, therefore, its performance is affected by the angle of incidence to a lesser degree.

Finally, we incorporate in eq. S22 an “angular-correction" factor ( χθ), which accounts

for the fact that the LSC-system is less sensitive than the stand-alone PV to changes in the

incident angle of solar radiation (θ). Specifically, since the LSC can absorb light incident onto

both the front and the back side, it is more efficient in harvesting diffuse radiation than a

standard PV under conditions of normal outdoor illumination. As a result, the efficiency of a

PV averaged over all incident angles that occur during the daylight time ηPV ,θ is reduced to

a greater degree compared to its peak efficiency (ηPV ,0 ; normal incidence of sunlight)

compared to the LSC-PV system. Thus, the angular-correction factor, defined as

χθ = ηLSC−PV ,θ /ηLSC−PV ,0( ) ηPV ,θ /ηPV ,0( )−1 , (S23)

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20

is greater than unity. Based on our measurements of the angular dependence (natural outdoor

illumination) of the power output of a stand-alone PV and the same PV coupled to a QD-LSC

(Supplementary Figure 8), χθ ≈ 1.4. A final expression for rLSC−PV which accounts for χθ is:

rLSC−PV = ( f +G−1)χθqLSCηabsηint

. (S24)

or

rLSC−PV = γ (G−1 + f )

ηs,absηint, (S25)

where γ = χθqLSC( )−1 <1 .

Now, we can use eq. S25 to estimate the cost-ratio factor for devices studied in the

present work. According to our previous discussions, for our QD-LSCs f = 0.08 and χθ = 1.4.

Further, using a spectral-reshaping factor of a standard PV cell (qLSC = 2), we obtain γ = 0.36.

On the basis of the experimentally measured absorption spectrum of our QDs, we find that the

LSC absorptance across the solar spectrum, ηs,abs, is ~0.06; this value is considerably lower

than the single-wavelength absorptance at 405 nm (ηabs = 0.75) measured in this work, which

is a direct result of a high absorption onset of our QDs. As was pointed out earlier, the

internal LSC efficiency is independent on excitation wavelength; therefore, the single-

wavelength values obtained in the present study can be directly used in eq. S25.

The results reported in the main text indicate that ηint = 42%, 24%, and 15% for

devices with lengths L = 2.54, 10.16, and 20.32 cm, respectively. Using eq. S25, we obtain

that the cost-ratio factors, rLSC-PV, for these LSCs are 4.7, 3.6, and 4.5. A nonmonotonous

dependence of rLSC-PV on L suggests that there is an optimal device length, or an optimal

geometric gain factor (Gmin), which minimizes rLSC-PV. To find this value (rmin,LSC-PV), we

incorporate a theoretical dependence of ηint vs. G (see eqs. S2 and S4 of Supplementary Note

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21

2) into eq. S25. Now, we can produce continuous plots of rLSC-PV vs. G and use them to

determine Gmin and rmin,LSC-PV.

The plot of rLSC-PV vs. G for the experimental parameters of LSCs studied in the

present work is shown in Supplementary Figure 9a (dashed black line). It does exhibit a

minimum based on which Gmin = 13.5 and rmin,LSC-PV = 3.4. If we review the results of our

calculations for the experimentally studied devices, we can see that the 10.16-cm LSC has

near-optimal dimensions, and therefore its cost-ratio factor (3.6) is close to rmin,LSC-PV.

Based on the above analysis, we can conclude that our present proof-of-principle

devices would not allow for any cost savings compared to a stand-alone PV. This is mostly a

result of their very low absorptance (~6% across the solar spectrum) and an imperfect PL QY

of the QDs (ηPL = 70%). To evaluate a potential effect of the PL QY improvement on the

cost-ratio factor, we conduct the calculations of rLSC-PV for ηPL = 90% (dashed-and-dotted

blue line in Supplementary Figure 9a) and 100% (red solid line in Supplementary Figure 9a ).

Due to a strong (nearly quadratic) dependence of ηint on ηPL in the range of large PL QYs

(ηPL > 40%),11 rLSC-PV,min quickly drops with increasing ηPL and reaches the value of ~1.8 for

the 100% PL QY. This indicates that the improvement in the PL QY alone does not allow one

to break through the rLSC-PV = 1 limit.

Next, we evaluate the effect of absorptance on the cost-ratio factor, assuming that the

increase in ηs,abs occurs as a result of lowering the absorption onset without affecting the

absorption coefficient at the PL wavelength. If we treat ηs,abs as an adjustable parameter and

keep the PL QY at the experimental value of ηPL = 70%, we can reach a break-even condition

(rLSC-PV = 1) with ηs,abs = 20% (red solid line in Supplementary Figure 9b), i.e., in the situation

of a still fairly transparent device; previously, the devices with a comparable absorptance

were realized, for example, in ref. 3. If we further increase the absorptance to 30%, rmin,LSC-PV

becomes equal to 0.68, indicating a potential 32% cost saving due to the use of an LSC light

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22

collector (blue dashed-and-dotted line in Supplementary Figure 9b). Finally, if we consider a

device with the same absorptance but a higher QD PL QY (ηPL = 90%), a potential cost

saving increases to more than 55%, indicating a possibility of a two-fold reduction of the cost

of solar electricity due to the LSC technology (green solid line in Supplementary Figure 9b).

Supplementary Figure 9. A calculated cost-ratio factor, rLSC-PV, as a function of the LSC geometric gain factor (G) for several combinations of the QD PL QY and absorptance (A) indicated in the legends. The parameters used in the calculations: f = 0.08, χθ = 1.4, and qLSC = 2.

The parameters considered in the last example are feasible to obtain with, for example, QDs

of CuInSe2-xSx studied previously in the context of LSC applications in refs.3 Thanks to their

near-IR band-gap, these QDs provide a good coverage of the solar spectrum which allows one

to easily realize absorptance of 20% and higher for the solar spectrum. A current limitation of

these QDs is a fairly low PL QY, typically less than 50%. Recently, however, we have been

able to overcome this deficiency by growing an ultra-thick (>3 nm) ZnS shell. Our newly

developed CuInSe2/ZnS show ηPL > 70%. At present, these QYs have been realized in

solution samples, and now we are working on encapsulating them into silica shells, and then a

polymer matrix.

6.0

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Cost

ratio

12 3 4 5 6

102 3 4 5 6

1002

Geometric gain factor

QY = 70% 90% 100%

Gmin=13.5

rmin,LSC-PV=3.4

6.0

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Cost

ratio

12 3 4 5 6

102 3 4 5 6

1002

Geometric gain factor

QY=70%; A=6% QY=70%, A=20% QY=70%, A=30% QY=90%, A=30%

a b

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23

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