In triplet–triplet annihilation based photon upconversion, controlling triplet energy transfer (TET) through the system is key to unlocking higher efficiencies. In this work, we vary the size of colloidally synthesized CdSe nanocrystals (NCs) to examine the effects on TET during photon upconversion, using steady-state measurements and transient absorption spectroscopy. As the CdSe NC size increases, the photon upconversion quantum yield (QY) decreases due to the decrease in the rate of TET from CdSe to the surface bound anthracene transmitter ligand, as expected for the Marcus description of energy transfer from the transmitter to the NC. Long microsecond transmitter lifetimes are critical to high photon upconversion QYs.

Triplet–triplet annihilation (TTA) based upconversion systems show great promise for use in efficient photovoltaic and bioimaging technologies. While purely organic TTA upconversion systems rely on finding new sensitizers for every wavelength of interest, inorganic nanocrystals (NCs) are widely tunable sensitizing materials with robust absorption and emission properties. In addition to tunability, NCs can have low rates of nonradiative recombination in spectral areas of interest such as the near-infrared (NIR). By combining the strong absorption and small exchange splitting of inorganic nanocrystals with existing organic TTA materials, we can design robust and flexible upconversion systems if all the elementary steps in triplet energy transfer are understood.1 Ultimately, these systems will allow the size and composition of quantum dots (QDs) to be varied to select for the absorption of desired wavelengths of light, providing an optimum design path for efficient upconversion systems with diverse applications.1–4 

In the model system studied here, CdSe NC photosensitizers absorb 532 nm light from a continuous wave laser [Fig. 1(a)]. This energy then transfers to the spin-triplet excited state of a bound 9-anthracene carboxylic acid (9-ACA) transmitter ligand. A second triplet energy transfer (TET) step may occur to diphenylanthracene (DPA) emitter molecules, where two neighboring DPA molecules in their triplet excited states combine via spin allowed TTA (black dotted arrows) to produce one in the singlet excited state (S1) and one in the ground state (S0). The newly populated singlet state can then emit violet light centered at 430 nm in the solution. Because triplet–triplet annihilation and fluorescence are intrinsic properties of the emitter molecule, this work focuses on elucidating the bottlenecks hindering triplet energy transfer from the NC donor to the bound 9-ACA ligand and, subsequently, to the DPA emitter [TET1 and TET2 in Fig. 1(a)]. Our steady-state photon upconversion experiments and transient absorption (TA) spectroscopy reveal that TET1 is in the Marcus normal regime.5,6 The efficiency of the first TET step, ΦTET1, is as high as 85% for small QDs7 due to the large driving force but decreases for larger particles. In contrast, ΦTET2 is quantitative for small NCs but small for large CdSe QDs. TA measurements show that this is because smaller NCs support long 9-ACA transmitter lifetimes on the order of hundreds of μs, whereas 9-ACA has short (∼18 ns) lifetimes on large nanoparticles, decreasing ΦTET2.

FIG. 1.

(a) Energy diagram depicting photon upconversion, showing photoexcitation of CdSe nanocrystals, triplet energy transfer (TET) TET1 to the bound 9-anthracene carboxylic acid transmitter ligand (9-ACA), and TET2 to the diphenylanthracene (DPA) emitter. (b) Normalized absorption (solid lines) and photoluminescence (dashed lines) spectra of seven zb-CdSe nanocrystals dispersed in toluene. 505 nm CdSe is reprinted with permission from Huang et al., J. Am. Chem. Soc. 141(25), 9769–9772 (2019). Copyright 2019 American Chemical Society.

FIG. 1.

(a) Energy diagram depicting photon upconversion, showing photoexcitation of CdSe nanocrystals, triplet energy transfer (TET) TET1 to the bound 9-anthracene carboxylic acid transmitter ligand (9-ACA), and TET2 to the diphenylanthracene (DPA) emitter. (b) Normalized absorption (solid lines) and photoluminescence (dashed lines) spectra of seven zb-CdSe nanocrystals dispersed in toluene. 505 nm CdSe is reprinted with permission from Huang et al., J. Am. Chem. Soc. 141(25), 9769–9772 (2019). Copyright 2019 American Chemical Society.

Close modal

Several zinc-blnde (zb)-CdSe nanocrystals (NCs) were synthesized with diameters ranging from 2.4 to 5.3 nm. Figure 1(b) contains the absorption (solid lines) and emission (dashed lines) spectra of all seven CdSe explored in this work (A–G). This range of CdSe NCs was chosen for DPA triplet photosensitization. Considering that the DPA’s lowest excited triplet state is at 1.8 eV, and the CdSe NC bandgap here varies from 2.45 eV to 2.02 eV, the driving force for TET1 here ranges from 0.65 eV to 0.22 eV. Smaller CdSe NCs can be synthesized; however, these small particles exhibit lower stability (increased ripening) and begin to absorb in the same region as the DPA emitter, detracting from the goal of photon upconversion. The NCs were functionalized with the 9-ACA ligand and re-dispersed in 3 mM diphenylanthracene (DPA) for photon upconversion (see details in the supplementary material) with 532 nm cw light. In terms of photon upconversion, larger CdSe NCs required higher ligand surface densities than their smaller NC counterparts. Like has been shown previously,7,8 there is an optimal 9-ACA surface density that results in a maximum photon upconversion quantum yield (QY), where too few 9-ACA transmitter ligands limit TET and too many result in ligand stacking and excimer formation, providing loss pathways for TET (Fig. S1 shows this ligand optimization). Table I shows the NC size, absorption, and photoluminescence (PL) maxima (λABS and λPL, respectively); PL QY, ΦPL; average number of surface bound 9-ACA ligands, n; as well as the surface density of this transmitter molecule. Equation (S1) gives the upconversion QYs in Table I (out of a 100%). The small particles A and B have high photon upconversion QYs, ΦUP of about 12%–16%. ΦUP drops to ∼8% to 10% for mid-sized CdSe NCs that absorb strongly in the green, while larger CdSe NCs that absorb to the red of 600 nm suffer from low ΦUP of ∼0.4%–1.7%.

TABLE I.

Key parameters of CdSe NCs used in upconversion and TA experiments.

CdSe NC radius (nm)λABS (nm)λPL (nm)CdSe NC ΦPL (%)ΦUP (%)na (9-ACA/CdSe NC)9-ACA densitybkTET1c (ns−1)
Ad 1.20 505 520 2.1 12.7 7.4 0.409 59.8 
1.23 511 529 29.2 15.8 8.4 0.443 15.2 
1.27 523 536 18.7 10.0 5.2 0.257 8.89 × 10−3 
1.54 552 562 18.6 8.5 15.3 0.515 1.86 × 10−4 
2.11 591 602 14.9 1.7 36.6 0.657 1.22 × 10−4 
2.58 612 620 5.3 0.4 65.1 0.777 5.65 × 10−5 
2.66 615 620 6.6 1.0 22.5 0.253 6.74 × 10−5 
CdSe NC radius (nm)λABS (nm)λPL (nm)CdSe NC ΦPL (%)ΦUP (%)na (9-ACA/CdSe NC)9-ACA densitybkTET1c (ns−1)
Ad 1.20 505 520 2.1 12.7 7.4 0.409 59.8 
1.23 511 529 29.2 15.8 8.4 0.443 15.2 
1.27 523 536 18.7 10.0 5.2 0.257 8.89 × 10−3 
1.54 552 562 18.6 8.5 15.3 0.515 1.86 × 10−4 
2.11 591 602 14.9 1.7 36.6 0.657 1.22 × 10−4 
2.58 612 620 5.3 0.4 65.1 0.777 5.65 × 10−5 
2.66 615 620 6.6 1.0 22.5 0.253 6.74 × 10−5 
a

The average number of molecules per QD, obtained from UV–Vis absorption spectra in Fig. 1(b) and extinction coefficient in Table S1.

b

Units of (n/nm2).

c

Total rate of TET (not normalized by n).

d

Data reprinted with permission from Huang et al., J. Am. Chem. Soc. 141(25), 9769–9772 (2019). Copyright 2019 American Chemical Society.

In order to study the rates of triplet energy transfer, TA spectra were acquired for each NC with 9-ACA attached to the surface at the ligand loading where ΦUP was previously maximized, but without any DPA present. Ultrafast TA spectra were acquired with each CdSe NC excited at its band edge to obtain kTET1. As shown in Fig. 1(a), kTET1 describes the rate of TET from the CdSe NC to the bound 9-ACA transmitter ligand. Figure 2 shows the ultrafast TA spectra of a small sized CdSe C [Fig. 2(a)] and a large sized CdSe G [Fig. 2(b)] with the CdSe NC ground state bleach (GSB) at its absorption maxima and the triplet excited state absorption (ESA) of 9-ACA marked with vertical dotted lines. (Ultrafast TA spectra of the other CdSe/9-ACA samples B, C, D, E, F, and G are shown in Fig. S2.) Global fits of the TA data were used to extract the average rate of triplet energy transfer, kTET1, from these six CdSe NCs to the bound 9-ACA ligands. The recovery of the CdSe GSB was analyzed 30 nm blue of the excitation wavelength at the second GSB minima to avoid scattering contribution from the pump. The CdSe GSB was globally fit with the kinetics at 435 nm, which included contributions from the ESA of the 9-ACA T1–Tn transition and the CdSe NC donor. The trajectory of the CdSe GSB has been fit using Eq. (1), using two exponentials, and the ESA kinetics globally fit with an additional term to describe kTET1 (see supplementary material Sec. 2, Fig. S3),

It=Σi=12Ai exptt0τi.
(1)

Global fittings of the GSB and ESA are performed with the linked parameters of t0 and τi. The fitting results and parameters are shown in Table S2. The results are summarized in Table I, which shows that kTET1 decreases as the CdSe size increases, corresponding to a decrease in upconversion QY. As the driving force for TET1 decreases from 0.65 eV for the smallest CdSe to 0.22 eV for the largest CdSe NCs, kTET1 decreases from 59.8 ns−1 to 0.0674 µs−1. The data here suggest that TET1 is squarely in the Marcus normal regime.

FIG. 2.

Ultrafast transient absorption (TA) spectra of 523 nm (a) and 615 nm absorbing (b) CdSe zb nanocrystals C and G. Vertical dotted lines show the ground state bleach (GSB) of CdSe NCs and 435 nm excited state absorption (ESA) corresponding to the growth of the 9-anthracene carboxylic acid triplet. The absorption of CdSe C and G is plotted in broken black lines. Nanosecond TA gives the kinetics at selected wavelengths at (c) 520 nm for CdSe C and (d) 605 nm for CdSe G with native oleic acid ligands only (CdSeOA, red), transmitter ligands (CdSe/9-ACA, blue), 9-ACA triplet ESA (green, 10×), and their corresponding fits (black dotted lines).

FIG. 2.

Ultrafast transient absorption (TA) spectra of 523 nm (a) and 615 nm absorbing (b) CdSe zb nanocrystals C and G. Vertical dotted lines show the ground state bleach (GSB) of CdSe NCs and 435 nm excited state absorption (ESA) corresponding to the growth of the 9-anthracene carboxylic acid triplet. The absorption of CdSe C and G is plotted in broken black lines. Nanosecond TA gives the kinetics at selected wavelengths at (c) 520 nm for CdSe C and (d) 605 nm for CdSe G with native oleic acid ligands only (CdSeOA, red), transmitter ligands (CdSe/9-ACA, blue), 9-ACA triplet ESA (green, 10×), and their corresponding fits (black dotted lines).

Close modal

Nanosecond TA measurements were conducted to extract the transmitter triplet lifetime, i.e., the 9-ACA lifetime when bound to NCs. We had previously obtained these data for CdSe A, the smallest NC.7 To obtain these parameters for the mid-sized and large CdSe NCs, CdSe C, and G were excited with 532 nm nanosecond pulses, and the kinetics at 435 nm and the CdSe GSB were collected [Figs. 2(c) and 2(d)]. As shown in Fig. 2(c), the GSB of CdSe C completely recovers in <100 ns, but the triplet ESA at 435 nm shows a decay constant up to 500 µs. When bound on mid-sized CdSe C, the decay of this long-lived 9-ACA exciton absorbing at 435 nm can be fit monoexponentially to give a 260 ± 7.8 µs triplet lifetime [Fig. 2(c)]. This shows that spin–orbit coupling with the CdSe lattice does not strongly impact the anthracene’s triplet excited state, unlike tetracene’s markedly shortened triplet lifetime when bound on PbS NCs.9 In contrast, the ESA at 435 nm corresponding to the 9-ACA triplet was very short-lived for the large CdSe G NCs. This can be rationalized from the lowest excited triplet energy levels of 9-ACA and CdSe G absorption maxima (1.83 eV and 2.02 eV, respectively) being relatively close. This results in barrierless downhill forward energy transfer and thermally activated back energy transfer between large CdSe NCs and anthracene triplet excitons. Evidence for this hypothesis can be seen in the longer CdSe G exciton lifetime in the presence of 9-ACA. The intensity weighted lifetime of CdSe G NCs with and without 9-ACA, τG-AN and τG, respectively, decreases from 25.3 ns to 17.9 ns, as monitored by the recovery of the CdSe NC’s ground state bleach at 605 nm, excited at 532 nm, measured with ns-TA [Fig. 2(d)]. A similar trend is observed with the amplitude weighted lifetime (Table S3). Using τG, τG-AN, and the intrinsic lifetime of surface bound anthracene, τAN = 260 µs from CdSe–C, we can calculate the 9-ACA triplet lifetime when bound on CdSe G, τAN-G, using the set of coupled rate equations10,11 governing the equilibrium in this system,

kTET1=kGτGAN1+τANG1kGτGAN1τANG1kGkAN,
(2)
kbackTET1=kANτGAN1+τANG1kAN+τGAN1τANG1kGkAN.
(3)

Solving Eqs. (2) and (3) using ns-TA data gives kTET1 = 0.068 µs−1 (close to the value of 0.0674 µs−1 in Table I from ps-TA analysis), a backward TET rate from 9-ACA to CdSe G, kbackTET1, of 39.7 µs−1 and τAN-G, the 9-ACA lifetime on CdSe G of 17.8 ns. kbackTET1 can be expressed through a simple Boltzmann approximation, relating kbackTET1 to kbackTET10 expressed as

kbackTET1=kbackTET10 expΔEkbT,
(4)

where ΔE is the difference between CdSe G and 9-ACA triplet exciton energy levels. From Eq. (4), taking into the account the Stokes shift in the NC PL that would lower the driving force or ΔE (the energy gap between the CdSe donor and the 9-ACA acceptor), we can calculate kbackTET10 to be on the same order of magnitude as kbackTET1. The fact that Eqs. (2) and (3) give a value of kbackTET10 3 orders of magnitude higher than kTET1 might initially suggest that the principle of detailed balance does not hold here. However, this may be rationalized by the fact that the density of triplet acceptor states on CdSe NCs is larger than 9-ACA due to its rich band structure. In addition, NC trap states have been implicated in triplet energy transfer from 9-ACA,12–14 and in-gap trap states in CdSe G might serve as a thermodynamic sink for 9-ACA triplet excitons.

Unlike the case of pyrene functionalized NCs that exhibited thermal re-population of CdSe photoluminescence from pyrene,15 the presence of surface bound 9-ACA does not significantly lengthen the CdSe lifetime.16–18 All our 9-ACA functionalized CdSe NCs here showed NC exciton lifetimes on the order of tens of nanoseconds, in line with previous reports in the literature (Table S2).19–22 Considering that the 9-ACA ligand densities on the CdSe NCs’ surface here (0.25–0.66 9-ACA/nm2) and for the CdSe/pyrene work are about the same, and the propensity for pyrene to form excimers, perhaps, it is the pyrene excimer exciton and not the triplet exciton that equilibrates with the CdSe NC’s band edge exciton and, thus, increases the particle lifetime.15 

To conclude, we have looked deeper into the first triplet energy transfer step in TTA based upconversion systems to identify where further optimization is needed to increase transition efficiencies. Through static fluorescence upconversion experiments and TA spectroscopy, we have shown that the first TET step is strongly correlated with the NC size. Smaller NCs have a larger rate of TET, resulting from a larger driving force. It is demonstrated that for small NC systems, both TETs contribute efficiently to the upconversion quantum yield for CdSe/TTA hybrid systems. The variation in photon upconversion and PLQY with the CdSe NC size is illustrated in Fig. 3. Based on these results, we believe that the future of efficient energy transfer in quantum dot systems will revolve around finding ways to lengthen transmitter triplet state lifetimes23 to increase the probability of efficient energy transfer in this complex system.

FIG. 3.

The photoluminescence quantum yield (PLQY, red circles) and photon upconversion QY (black squares) of seven zb-CdSe nanocrystals (NCs) in toluene using R6G in ethanol as the fluorescence standard plotted vs wavelength of the first absorption maxima of each NC.

FIG. 3.

The photoluminescence quantum yield (PLQY, red circles) and photon upconversion QY (black squares) of seven zb-CdSe nanocrystals (NCs) in toluene using R6G in ethanol as the fluorescence standard plotted vs wavelength of the first absorption maxima of each NC.

Close modal

See the supplementary material for the complete description of experimental methods, synthesis, and data fitting procedures.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This work was supported by the National Science Foundation, Grant Nos. OISE-1827087 to M.L.T. and 1532125 to D.F. M.L.T. acknowledges the Air Force Office of Scientific Research (AFOSR) award (No. FA9550-19-1-0092) for equipment and the Alfred P. Sloan foundation grant (No. FG-2017-9559) for support.

1.
M.
Wu
,
D. N.
Congreve
,
M. W. B.
Wilson
,
J.
Jean
,
N.
Geva
,
M.
Welborn
,
T.
Van Voorhis
,
V.
Bulović
,
M. G.
Bawendi
, and
M. A.
Baldo
, “
Solid-state infrared-to-visible upconversion sensitized by colloidal nanocrystals
,”
Nat. Photonics
10
(
1
),
31
34
(
2016
).
2.
Z.
Huang
,
X.
Li
,
M.
Mahboub
,
K. M.
Hanson
,
V. M.
Nichols
,
H.
Le
,
M. L.
Tang
, and
C. J.
Bardeen
, “
Hybrid molecule-nanocrystal photon upconversion across the visible and near-infrared
,”
Nano Lett.
15
(
8
),
5552
5557
(
2015
).
3.
C.
Mongin
,
S.
Garakyaraghi
,
N.
Razgoniaeva
,
M.
Zamkov
, and
F. N.
Castellano
, “
Direct observation of triplet energy transfer from semiconductor nanocrystals
,”
Science
351
(
6271
),
369
372
(
2016
).
4.
R. S.
Khnayzer
,
J.
Blumhoff
,
J. A.
Harrington
,
A.
Haefele
,
F.
Deng
, and
F. N.
Castellano
, “
Upconversion of sub-band gap light in solar cell; powered photoelectrochemistry, WO3 nanostructured anode
,”
Chem. Commun.
48
(
2
),
209
211
(
2012
).
5.
R. A.
Marcus
, “
Theoretical relations among rate constants, barriers, and Broensted slopes of chemical reactions
,”
J. Phys. Chem.
72
(
3
),
891
899
(
1968
).
6.
R. A.
Marcus
and
P.
Siders
, “
Theory of highly exothermic electron transfer reactions
,”
J. Phys. Chem.
86
(
5
),
622
630
(
1982
).
7.
J.
De Roo
,
Z.
Huang
,
N. J.
Schuster
,
L. S.
Hamachi
,
D. N.
Congreve
,
Z.
Xu
,
P.
Xia
,
D. A.
Fishman
,
T.
Lian
,
J. S.
Owen
, and
M. L.
Tang
, “
Anthracene diphosphate ligands for CdSe quantum dots; molecular design for efficient upconversion
,”
Chem. Mater.
32
(
4
),
1461
1466
(
2020
).
8.
Z.
Huang
,
D. E.
Simpson
,
M.
Mahboub
,
X.
Li
, and
M. L.
Tang
, “
Ligand enhanced upconversion of near-infrared photons with nanocrystal light absorbers
,”
Chem. Sci.
7
(
7
),
4101
4104
(
2016
).
9.
Z.
Huang
,
Z.
Xu
,
M.
Mahboub
,
Z.
Liang
,
P.
Jaimes
,
P.
Xia
,
K. R.
Graham
,
M. L.
Tang
, and
T.
Lian
, “
Enhanced near-infrared-to-visible upconversion by synthetic control of PbS nanocrystal triplet photosensitizers
,”
J. Am. Chem. Soc.
141
(
25
),
9769
9772
(
2019
).
10.
V.
Gray
,
B.
Küçüköz
,
F.
Edhborg
,
M.
Abrahamsson
,
K.
Moth-Poulsen
, and
B.
Albinsson
, “
Singlet and triplet energy transfer dynamics in self-assembled axial porphyrin–anthracene complexes: Towards supra-molecular structures for photon upconversion
,”
Phys. Chem. Chem. Phys.
20
(
11
),
7549
7558
(
2018
).
11.
J.
Andraos
, “
A streamlined approach to solving simple and complex kinetic systems analytically
,”
J. Chem. Educ.
76
(
11
),
1578
(
1999
).
12.
M.
Mahboub
,
P.
Xia
,
J.
Van Baren
,
X.
Li
,
C. H.
Lui
, and
M. L.
Tang
, “
Midgap states in PbS quantum dots induced by Cd and Zn enhance photon upconversion
,”
ACS Energy Lett.
3
(
4
),
767
772
(
2018
).
13.
E. M.
Rigsby
,
K.
Lee
,
J.
Sun
,
D. A.
Fishman
, and
M. L.
Tang
, “
Primary amines enhance triplet energy transfer from both the band edge and trap state from CdSe nanocrystals
,”
J. Chem. Phys.
151
(
17
),
174701
(
2019
).
14.
Y.
Han
,
S.
He
,
X.
Luo
,
Y.
Li
,
Z.
Chen
,
W.
Kang
,
X.
Wang
, and
K.
Wu
, “
Triplet sensitization by “self-trapped” excitons of nontoxic CuInS2 nanocrystals for efficient photon upconversion
,”
J. Am. Chem. Soc.
141
(
33
),
13033
13037
(
2019
).
15.
C.
Mongin
,
P.
Moroz
,
M.
Zamkov
, and
F. N.
Castellano
, “
Thermally activated delayed photoluminescence from pyrenyl-functionalized CdSe quantum dots
,”
Nat. Chem.
10
(
2
),
225
230
(
2018
).
16.
M.
Nirmal
,
D. J.
Norris
,
M.
Kuno
,
M. G.
Bawendi
,
A. L.
Efros
, and
M.
Rosen
, “
Observation of the “dark exciton” in CdSe quantum dots
,”
Phys. Rev. Lett.
75
(
20
),
3728
3731
(
1995
).
17.
S. A.
Crooker
,
T.
Barrick
,
J. A.
Hollingsworth
, and
V. I.
Klimov
, “
Multiple temperature regimes of radiative decay in CdSe nanocrystal quantum dots: Intrinsic limits to the dark-exciton lifetime
,”
Appl. Phys. Lett.
82
(
17
),
2793
2795
(
2003
).
18.
P. C.
Sercel
,
A.
Shabaev
, and
A. L.
Efros
, “
Photoluminescence enhancement through symmetry breaking induced by defects in nanocrystals
,”
Nano Lett.
17
(
8
),
4820
4830
(
2017
).
19.
M.
Korkusinski
,
O.
Voznyy
, and
P.
Hawrylak
, “
Fine structure and size dependence of exciton and biexciton optical spectra in CdSe nanocrystals
,”
Phys. Rev. B: Condens. Matter Mater. Phys.
82
(
24
),
245304
(
2010
).
20.
M.
Califano
,
A.
Franceschetti
, and
A.
Zunger
, “
Lifetime and polarization of the radiative decay of excitons, biexcitons, and trions in CdSe nanocrystal quantum dots
,”
Phys. Rev. B: Condens. Matter Mater. Phys.
75
(
11
),
115401
(
2007
).
21.
A. L.
Efros
, “
Fine structure and polarization properties of the band edge excitons in semiconductor nanorystals
,” in
Semiconductor and Metal Nanocrystals: Synthesis and Electronic and Optical Properties
, edited by
V. I.
Klimov
(
Marcel Dekker
,
New York
,
2003
), p.
103
.
22.
A. L.
Efros
,
M.
Rosen
,
M.
Kuno
,
M.
Nirmal
,
D. J.
Norris
, and
M.
Bawendi
, “
Band-edge exciton in quantum dots of semiconductors with a degenerate valence band: Dark and bright exciton states
,”
Phys. Rev. B
54
(
7
),
4843
4856
(
1996
).
23.
Z.
Xu
,
Z.
Huang
,
C.
Li
,
T.
Huang
,
F. A.
Evangelista
,
M. L.
Tang
, and
T.
Lian
, “
Tuning the quantum dot (QD)/mediator interface for optimal efficiency of QD-sensitized near-infrared-to-visible photon upconversion systems
,”
ACS Appl. Mater. Interfaces
12
,
36558
(
2020
).

Supplementary Material