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# Understanding and tuning blue-to-near-infrared photon cutting by the Tm3+/Yb3+ couple

## Abstract

Lanthanide-based photon-cutting phosphors absorb high-energy photons and ‘cut’ them into multiple smaller excitation quanta. These quanta are subsequently emitted, resulting in photon-conversion efficiencies exceeding unity. The photon-cutting process relies on energy transfer between optically active lanthanide ions doped in the phosphor. However, it is not always easy to determine, let alone predict, which energy-transfer mechanisms are operative in a particular phosphor. This makes the identification and design of new promising photon-cutting phosphors difficult. Here we unravel the possibility of using the Tm3+/Yb3+ lanthanide couple for photon cutting. We compare the performance of this couple in four different host materials. Cooperative energy transfer from Tm3+ to Yb3+ would enable blue-to-near-infrared conversion with 200% efficiency. However, we identify phonon-assisted cross-relaxation as the dominant Tm3+-to-Yb3+ energy-transfer mechanism in YBO3, YAG, and Y2O3. In NaYF4, in contrast, the low maximum phonon energy renders phonon-assisted cross-relaxation impossible, making the desired cooperative mechanism the dominant energy-transfer pathway. Our work demonstrates that previous claims of high photon-cutting efficiencies obtained with the Tm3+/Yb3+ couple must be interpreted with care. Nevertheless, the Tm3+/Yb3+ couple is potentially promising, but the host material—more specifically, its maximum phonon energy—has a critical effect on the energy-transfer mechanisms and thereby on the photon-cutting performance.

## Introduction

Lanthanide-based phosphors offer wide possibilities for colour conversion, absorbing one colour of light and emitting another1. The conversion process often involves energy transfer between lanthanide dopants2,3. Consumer applications, such as lighting and displays, usually rely on colour conversion by conventional ‘downshifting’ luminescence: the material emits one redshifted (lower-energy) photon for each photon it absorbs. The energy level structures of the lanthanides, however, offer more colour-conversion possibilities. Unconventional energy-transfer pathways between lanthanide dopants can be designed, which lead to ‘upconversion’ luminescence4,5,6 or ‘photon cutting’7,8. Upconversion involves merging of the energy of multiple photons by the phosphor material, i.e., it absorbs two (or more) low-energy photons and emits one higher-energy photon. Photon cutting is the inverse process (therefore also known as ‘downconversion’), whereby one higher-energy photon is absorbed and two (or more) lower-energy photons are emitted.

This work explores new strategies to achieve photon cutting by lanthanide-doped phosphors. The process was first proposed as a concept that could drastically increase the efficiency of fluorescent lighting, offering the prospect of ultraviolet-to-visible conversion efficiencies of up to 200%7. However, with the advances in blue light-emitting diodes over the past two decades9, the societal need for new fluorescent-lighting technologies has decreased. Photon cutting has been identified as a potential method to break the Shockley–Queisser limit of 33.7% in photovoltaics10,11,12. This limit otherwise sets the maximum conversion efficiency of single-junction solar cells under standard solar irradiation, determined by the optimum balance between thermalization losses and transmission losses13. A photon-cutting phosphor should reshape the spectrum from the sun before it enters a solar cell by converting high-energy photons into multiple lower-energy photons. Using this concept, the maximum achievable solar-cell efficiency increases to ~40%14.

Photon-cutting phosphors exhibiting Yb3+ emission have been of particular interest, because the emission at ~10,000 cm−1 matches the bandgap (9000 cm−1) of crystalline silicon solar cells. Desirable phosphors are codoped with a sensitizer ion that absorbs in the visible spectral range and transfers its energy to two Yb3+ ions. Phosphors doped with Tb3+/Yb3+8,15, Ce3+/Yb3+16,17,18, Tm3+/Yb3+19,20,21,22,23, Pr3+/Yb3+24,25, and other ion couples have been proposed. However, not all types of energy-transfer process between ion couples yield two (or more) excited Yb3+ ions per absorption event. For example, the Ce3+-to-Yb3+ energy-transfer mechanism in codoped yttrium aluminium garnet (YAG; Y3Al5O12) yields only a single Yb3+ excitation, so YAG:Ce3+,Yb3+ is not a photon cutter despite a favourable energy-level structure16,17. Unfortunately, the energy-transfer mechanisms are unclear for many potential photon-cutting phosphors, resulting in contradictory19,20 or poorly supported interpretations in the literature12. This complicates the identification and optimization of promising photon-cutting materials. Photon correlation measurements are a direct way to prove photon cutting26. Unfortunately, these measurements are difficult for Yb3+ emission, because single-photon detectors with high efficiencies and low dark counts are not readily available for the near-infrared region.

Here we study the potential of photon cutting with the Tm3+/Yb3+ lanthanide couple. The existing literature makes contradictory claims about the mechanism of energy transfer from the Tm3+ 1G4 level to Yb3+12, with important implications for the photon-cutting potential of the Tm3+/Yb3+ couple. A cooperative mechanism would, but a phonon-assisted cross-relaxation mechanism would not, result in blue-to-near-infrared photon cutting with the potential to increase the current output of crystalline Si solar cells10,11,12. We measure and model the dynamics of Tm3+-to-Yb3+ energy transfer in four different host materials with systematically varied doping concentration. We identify phonon-assisted cross-relaxation as the dominant energy-transfer mechanism in Tm3+/Yb3+-codoped YBO3, YAG, or Y2O3. In contrast, cooperative energy transfer dominates in Tm3+/Yb3+-codoped NaYF4. Consequently, only NaYF4 is a promising host material to achieve photon cutting for silicon photovoltaics with the Tm3+/Yb3+ couple. We can rationalize our results by considering the maximum phonon energies of the four host materials:6,27 the more phonons required for phonon-assisted cross-relaxation, the lower the rate28. Our work highlights the possibility of tuning the energy-transfer pathways in lanthanide-based phosphors with the appropriate choice of host material and thereby achieving photon-conversion efficiencies above 100%.

## Results

To investigate the Tm3+-to-Yb3+ energy-transfer mechanism in Tm3+/Yb3+-codoped YBO3, YAG, Y2O3, and NaYF4, we recorded luminescence spectra (emission and excitation) and luminescence decay curves. As an example, Fig. 1a shows the emission spectrum of microcrystalline YBO3 doped with 0.1% Tm3+ and 2% Yb3+ upon excitation in the blue region (at 465 nm; 21,500 cm−1). This spectrum shows similar features to those previously measured on Tm3+/Yb3+-codoped borates and other host materials29,30,31. The emission line centred at 10,000 cm1 (shaded red) is due to the 2F5/2 → 2F7/2 transition of Yb3+, and that centred at 12,500 cm1 (shaded green) is due to the energetically overlapping 1G4 → 3H5 and 3H4 → 3H6 transitions of Tm3+. The appearance of Yb3+-based emission following excitation of the Tm3+ 1G4 level (see Fig. 1b for an excitation spectrum) evidences the occurrence of energy transfer from Tm3+ to Yb3+.

Many previous studies on Tm3+/Yb3+-codoped materials have concluded that Tm3+-to-Yb3+ energy transfer follows the cooperative mechanism (Fig. 1c)19,21,22,23: an excited Tm3+ dopant in the 1G4 level transfers its energy in a single step to two nearby Yb3+ dopants. This process brings the Tm3+ donor back to its 3H6 ground state and excites both Yb3+ acceptor ions to their 2F5/2 excited state. Subsequently, both Yb3+ ions can emit a photon with an energy of approximately 10,000 cm1. Effectively, this process cuts a single blue photon into two infrared photons with sufficient energy to be absorbed by crystalline Si (Fig. 1d)10,11,12.

Evidence for the cooperative mechanism has been scarce to absent12. The near match between the energy of the Tm3+ 1G4 level and double the energy of the Yb3+ 2F5/2 level suggests the possibility of cooperative energy transfer21,22,23, but this alone is not proof. In fact, the observation of strong Yb3+ emission in a sample with an Yb3+ doping concentration as low as a few percent21,22,23 is inconsistent with cooperative energy transfer. Indeed, efficient cooperative energy transfer occurs only if a Tm3+ ion is in nearest-neighbour proximity to two Yb3+ ions in the crystal, which is unlikely unless the Yb3+ doping concentration exceeds ~25%8.

An alternative Tm3+-to-Yb3+ energy-transfer mechanism could be cross-relaxation (Fig. 1e)12,32: Tm3+ in the excited 1G4 level transfers part of its energy to a nearby Yb3+ ion. Tm3+ thereby relaxes to the intermediate 3H5 level and Yb3+ is excited to the 2F5/2 level. Although Yb3+ can subsequently emit a photon that can be absorbed by crystalline Si, the energy of the 3H5 level (8500 cm1) is lower than the bandgap of Si. Hence, Tm3+-to-Yb3+ cross-relaxation yields at most one useful photon (Fig. 1f) for Si-based photovoltaics.

Tm3+-to-Yb3+ cross-relaxation may seem unlikely, as the energy mismatch between the Tm3+ 1G4 → 3H5 and Yb3+ 2F7/2 → 2F5/2 transitions is as large as 2000–3000 cm−1 (compare Fig. 1a, b)31. This energy mismatch could, however, be bridged by multiphonon emission. As multiphonon processes generally become less efficient as the number of phonons involved increases28, one may expect a strong effect of the host material on the occurrence of cross-relaxation. To test and exploit this, we investigated the Tm3+-to-Yb3+ energy transfer in a series of host materials with different phonon energies (Fig. 1g–j). Specifically, we prepared microcrystalline Tm3+/Yb3+-codoped YBO3 (Fig. 1a, b, g; highest phonon energy of 1050 cm−1)33,34, YAG (Fig. 1h; 860 cm−1)35,36, Y2O3 (Fig. 1i; 600 cm−1)37, and NaYF4 (Fig. 1j; 370 cm−1)38. In these materials, Tm3+-to-Yb3+ cross-relaxation would be a two-phonon-, three-phonon-, four-phonon-, or six-phonon-assisted process, respectively, considering a mismatch of ~2000 cm−1 between the closest crystal-field components of the transitions involved (see Fig. 1a). A series of samples was prepared for each material with systematically varied Yb3+ concentration. The Tm3+ concentrations were chosen to be low enough to minimize Tm3+-to-Tm3+ cross-relaxation39,40 but sufficiently high to obtain a sufficient luminescence signal. X-ray diffraction (XRD) analysis (Supplementary Fig. S1, Supplementary Information) confirmed the synthesis of phase-pure samples for all Yb3+ concentrations. The different crystallite sizes (Fig. 1g–j) in the range of 100 nm–1 μm have negligible influence on the energy-transfer interactions, because these occur mostly at distances of 1 nm and shorter. We have previously found only minor influences of the crystal size even for particles as small as 2 nm in radius41.

The emission spectra of the four Tm3+/Yb3+-codoped materials are qualitatively similar (Fig. 2a–d). All four materials show an emission feature centred at 12,500 cm−1 that is strongest at 0% Yb3+ (dark red) and becomes weaker for higher Yb3+ concentrations (from red to blue/purple). This emission originates from the 1G4 → 3H5 and 3H4 → 3H6 transitions of Tm3+ (compare Fig. 1a). The decreasing intensity is further confirmation of Tm3+-to-Yb3+ energy transfer, which becomes more efficient at higher Yb3+ concentrations. Indeed, the emission feature at ~10,000 cm−1, due to the Yb3+ 2F5/2 → 2F7/2 transition (compare Fig. 1a), increases in intensity with increasing Yb3+ concentration in all materials. However, for the highest Yb3+ concentrations (>10% in Fig. 2a–c or >25% in Fig. 2d), the emission at 10,000 cm−1 is partly quenched. We ascribe this to concentration quenching. The line shapes of Tm3+ 1G4 → 3H5, Tm3+ 3H4 → 3H6, and Yb3+ 2F5/2 → 2F7/2 are different for the four materials but consistent with previous literature reports42,43. The differences are due to the different crystal fields experienced by the optically active lanthanides, which split the spin–orbit levels and affect the transition energies and rates differently in each material.

Identifying the mechanism and quantifying the efficiency of Tm3+-to-Yb3+ energy transfer requires measurement of the emission decay dynamics. As expected, we observe that for all four materials, the excited-state lifetime of the Tm3+ 1G4 level decreases with increasing Yb3+ concentration (Fig. 2e–h). This confirms energy transfer from the Tm3+ 1G4 level to Yb3+. At higher Yb3+ concentrations, Tm3+ ions have (on average) more and closer Yb3+ neighbours, so the energy-transfer rates are higher. At the highest Yb3+ concentrations (50% in Fig. 2e, f), the Tm3+ emission intensity is strongly quenched, so the signal-to-background ratio in the photoluminescence decay measurement is poor. Comparing the measurements on the different materials, we note that the decay dynamics depend less strongly on the Yb3+ concentration in NaYF4 (Fig. 2h) than in the other materials (Fig. 2e–g). This is our first indication that the Tm3+-to-Yb3+ energy transfer depends on the maximum phonon energy of the host material.

As a first analysis of the energy-transfer mechanisms in the four materials, we use the data of Fig. 2e–h and evaluate the average lifetime of the Tm3+ 1G4 level, $$\langle \tau \rangle = \sum\nolimits_i {{I_i}{t_i}/} \sum\nolimits_i {{I_i}}$$, where Ii is the emission intensity at delay time ti and the summation runs over all data points i constituting the photoluminescence decay curve as a function of Yb3+ concentration. The inverse of the average lifetime (Fig. 3a–d) is approximately equal to the average decay rate of the 1G4 level,

$$\left\langle \tau \right\rangle ^{ - 1} \,\approx k_0 + \left\langle {k_{{\mathrm{ET}}}} \right\rangle$$
(1)

where the first term k0 is due to relaxation processes not involving Yb3+, e.g., radiative decay or multiphonon relaxation, and the second term kET is due to energy transfer to Yb3+. The kET of a Tm3+ ion depends on the number of Yb3+ neighbours and hence on the Yb3+ doping concentration x in the crystal. Indeed, for all four host materials, τ−1 shows a constant offset k0 and a second term kET that increases with Yb3+ concentration. The outlying data points for the highest Yb3+ concentration in YBO3 and YAG (Fig. 3a, b) are due to the low signal-to-background ratio for these measurements, which makes accurate calculation of τ difficult.

The results of Fig. 3a–d indicate a qualitative difference in the energy-transfer mechanism between the higher-phonon-energy hosts—YBO3, YAG, and Y2O3—and the lowest-phonon-energy host NaYF4. In the higher-phonon-energy hosts, kET scales linearly with Yb3+ concentration x (dotted lines in Fig. 3a–c). This indicates the occurrence of cross-relaxation (Fig. 1e, f), which is a first-order process that scales linearly with the acceptor concentration. In contrast, NaYF4 shows a quadratic trend (dashed line in Fig. 3d). More precisely, fitting the power of the $$k_{{\mathrm{ET}}} \propto x^p$$ relationship (not shown) yields p = 1.8, close to a value of 2. This is consistent with cooperative energy transfer (Fig. 1c, d), which is a second-order process.

For further confirmation and quantification of the energy-transfer process, we turn to Monte Carlo modelling of the 1G4 decay dynamics8,44. As the energy-transfer rates scale strongly with the distance between the donor and acceptor and Tm3+ and Yb3+ dopants randomly substitute Y3+ cation sites in the host crystal, we expect that different Tm3+ ions in the crystal exhibit different energy-transfer rates. For a particular donor–acceptor pair, the energy-transfer rate for cross-relaxation via dipole–dipole coupling is

$$k_{{\mathrm{ET}}} = \frac{{C_{{\mathrm{xr}}}}}{{r^6}}$$
(2)

where r is the donor–acceptor separation and Cxr is a prefactor describing the overall strength of cross-relaxation. Cooperative energy transfer requires one donor and two acceptors and scales as

$$k_{{\mathrm{ET}}} = \frac{{C_{{\mathrm{coop}}}}}{{r_1}^6{r_2}^6}$$
(3)

where r1 is the distance from the donor to acceptor 1, r2 is the distance from the donor to acceptor 2, and Ccoop is the strength of cooperative energy transfer8. To model the energy transfer dynamics in a Tm3+/Yb3+-codoped sample, we Monte Carlo simulate dopant configurations and calculate from these the distribution of energy-transfer rates following Eqs. (2) and (3). More details of the model can be found in the Experimental section.

Figure 4 shows the Tm3+-to-Yb3+ energy-transfer dynamics in our samples. We isolate the Tm3+-to-Yb3+ energy-transfer dynamics from the total photoluminescence decay curves (Fig. 2e–h) by following the procedure introduced in Ref. 41: we divide each decay curve of a sample with x% Yb3+ by the decay curve of the corresponding sample with 0% Yb3+. We thus use the sample with 0% Yb3+ as a reference to remove the dynamics due to radiative decay of Tm3+ and Tm3+-to-Tm3+ from our data. Solid lines are fits to the Monte Carlo model for cross-relaxation (Eq. 2; Fig. 4a–d) or to the model for cooperative energy transfer (Eq. (3) and Fig. 4e–h). For each host material, we first determine the optimal values of Cxr and Ccoop for one Yb3+ concentration, as underlined in Fig. 4. Then, keeping the values found fixed, we plot the calculated decay curves for the other concentrations. The cross-relaxation model well matches the data for YBO3, YAG, and Y2O3 (Fig. 4a–c), while the cooperative model predicts too slow a decay at low Yb3+ concentrations and too rapid a decay at high Yb3+ concentrations (Fig. 4e–g). In contrast, for NaYF4, the cooperative model works well (Fig. 4h), whereas the cross-relaxation model shows deviations from the experimental data (Fig. 4d).

The quantitative analysis of Fig. 4 confirms that the energy-transfer mechanisms are different between the higher-phonon-energy hosts (YBO3, YAG, and Y2O3) and NaYF4. Cross-relaxation occurs in the higher-phonon-energy hosts, with rates comparable to radiative decay at Yb3+ concentrations as low as a few percent. In contrast, in NaYF4, the Tm3+-to-Yb3+ energy transfer is weak until high Yb3+ concentrations of >25%, and cooperative energy transfer dominates over radiative decay only at higher concentrations. Hence, we must conclude that NaYF4 allows for cooperative Tm3+-to-Yb3+ energy transfer not because the rate of this process is particularly high but rather because cross-relaxation is strongly suppressed.

## Discussion

We can determine how weak the cross-relaxation is in NaYF4 compared to the other hosts by analysing the measurements at low Yb3+ concentrations (≤25%) using the cross-relaxation model. This yields values for the Tm3+-to-Yb3+ cross-relaxation strength in NaYF4 of Cxr = (7 ± 6) × 101 Å6 ms−1. Cross-relaxation in NaYF4 is thus two orders of magnitude slower than that in the higher-phonon-energy hosts (Fig. 5a). This is consistent with the large energy mismatch between the 1G4 → 3H5 and 2F7/2 → 2F5/2 transitions involved in cross-relaxation (compare Fig. 1a, b). Our experiments show that the 2000–3000 cm1 mismatch can be bridged by a two-, three-, or four-phonon process in YBO3, YAG, or Y2O3, respectively. In contrast, the six-phonon-assisted cross-relaxation in NaYF4 is too slow to compete with other decay pathways from the Tm3+ 1G4 level. Closer inspection of Fig. 5a reveals that four-phonon-assisted cross-relaxation in Y2O3 is already slower by a factor of 3 than the corresponding lower-order processes in YBO3 and YAG. Qualitatively, such a strong dependence of the cross-relaxation rates on the number of phonons involved is expected from the exponential energy-gap law for nonradiative relaxation28. Quantitatively, however, the relation between the number of phonons involved and the cross-relaxation strength (Cxr) is not straightforward, as Cxr depends on various other factors such as the transition dipole moments of the electronic and vibrational transitions involved28,45. In general, lanthanide f–f transition dipole moments are different for different host materials, as they are strongly dependent on the crystal-field symmetry and covalency of the host material45. This explains why the intrinsic 1G4 decay rates k0 are different for the different host materials (Fig. 5b) and why Cxr does not monotonically increase with phonon energy (Fig. 5a). Future work may reveal that temperature further affects the delicate competition between phonon-assisted cross-relaxation and cooperative energy transfer.

The energy-transfer mechanism, the corresponding energy-transfer strength (Cxr or Ccoop; Eqs. (2) and (3)), and the decay rate k0 of the 1G4 level at 0% Yb3+ (Fig. 5b) determine the maximum quantum efficiency of visible-to-near-infrared photon-conversion achievable with a particular host material. In our definition of quantum efficiency, we include only the emission of photons that can be absorbed by crystalline Si. Creating two of these photons from a single Tm3+ ion in the 1G4 level requires cooperative energy transfer rather than cross-relaxation. To calculate the maximum quantum efficiency, we first construct the theoretical normalised photoluminescence decay curve of the 1G4 level for each host material for any arbitrary Yb3+ concentration:

$$I\left( t \right) = {\mathrm{e}}^{ - k_0t}T\left( t \right)$$

where T(t) is the multiexponential decay function due to energy transfer (see the ‘Methods’ section for details). The theoretical quantum efficiency is then given by

$$\eta = \eta _{{\mathrm{Tm}}} + \eta _{{\mathrm{Yb}}}$$

Herein,

$$\eta _{{\mathrm{Tm}}} = k_0{\int \nolimits_0^\infty} I\left( t \right){\mathrm{d}}t$$

is the efficiency of Tm3+ 1G4 emission, and

$$\eta _{{\mathrm{Yb}}} = Q\left( {1 - \eta _{{\mathrm{Tm}}}} \right)$$

is the efficiency of Yb3+ emission. The factor Q depends on the dominant energy-transfer mechanism in the host material. Its value is Q = 1 for the cross-relaxation process in YBO3, YAG, and Y2O3 or Q = 2 for cooperative energy transfer in NaYF4.

In Fig. 5c–f, we plot the maximum quantum efficiency for the different host materials as a function of Yb3+ concentration, calculated with our Monte Carlo model. We neglect intrinsic losses in Tm3+ due to nonradiative decay or infrared emissions as well as concentration quenching effects of the Yb3+ emission (see Fig. 2a–d). The calculations of Fig. 5c–f thus show the highest possible quantum efficiency that could be achieved if the materials are optimized to suppress any loss channel. As expected, the Yb3+ emission rapidly increases with increasing Yb3+ concentration in the higher-phonon-energy hosts (Fig. 5c–e), but the overall quantum efficiency never exceeds unity. In contrast, in NaYF4, the Yb3+ emission increases more slowly but pushes the overall quantum efficiency up to 132% in NaYbF4:Tm3+.

Our findings highlight the possibility of qualitatively altering the energy-conversion pathways in lanthanide-doped crystals by choosing a host material with the appropriate phonon spectrum. This allows us to change the blue-to-near-infrared conversion by the Tm3+/Yb3+ couple from a simple downshifting process in the higher-phonon-energy host materials into a photon-cutting process in the lower-phonon-energy host NaYF4. Only photon cutting in the NaYF4 host holds promise for enhancement of the current output of crystalline Si solar cells because it can convert blue photons into near-infrared photons of ~1000 nm with a quantum efficiency exceeding unity. Similar qualitative differences between host materials may be expected in terms of the (often very complicated) pathways of photon upconversion46. While previous studies have claimed achievement of high photon-cutting efficiencies with the Tm3+/Yb3+ couple in a wide variety of host materials, our findings show that photon cutting is only possible in host lattices with phonon energies not exceeding ~400 cm−1.

## Materials and methods

### Chemicals and materials

All chemicals were used without further purification. Y2O3 (99.999%) was purchased from Alfa Aesar; Tm2O3 (99.999%) from Heraeus; Yb2O3 (99.99%), Y2O3 (99.99%), Al(NO3)3.9H2O (≥98%), urea (BioReagent), and nitric acid (HNO3; puriss. p.a., ≥65%) from Sigma-Aldrich; and boric acid (H3BO3; ≥99.5%) from Merck.

### Synthesis of β-NaYF4:Tm3+,Yb3+ microcrystalline phosphors

β-NaYF4:0.3%Tm3+,x%Yb3+ powder samples were synthesized following the approach developed by Krämer et al.4.

### Combustion synthesis of Y2O3-, YAG-, and YBO3-based polycrystalline phosphors

A urea–nitrate solution combustion process was used for the synthesis of a series of polycrystalline powder phosphors of Y2O3, YAG, and YBO3 codoped with Tm3+ and Yb3+. Y2O3, Tm2O3, and Yb2O3 were used as lanthanide (Ln) sources, Al(NO3)3.9H2O as the Al source for YAG, H3BO3 as the B source for YBO3, and urea as the organic fuel for the combustion reaction. Stoichiometric amounts of Y2O3, Tm2O3, and Yb2O3 were dissolved in nitric acid to obtain aqueous solutions of mixed Ln(NO3)3. For the synthesis of Y2O3:Tm3+,Yb3+, solid urea (molar ratio urea/Ln = 2:1) was added to the Ln(NO3)3 solution. For YAG:Tm3+,Yb3+, an Al(NO3)3 solution (molar ratio Al/Ln = 5:3) and urea (molar ratio urea/Ln = 5:1) were added to the Ln(NO3)3 solution. For YBO3:Tm3+,Yb3+, solid urea (molar ratio urea/Ln = 3:1) and H3BO3 (5% molar excess) were added to the Ln(NO3)3 solution. After vigorous stirring for 20 min at approximately 70 °C, the resulting homogeneous precursor solution was placed in a preheated furnace at 500 °C in air to initiate the combustion reaction. Amorphous solid precursors formed from the solutions within a few minutes. Finally, annealing in ambient atmosphere at 1000 °C for 4 h, 1500 °C for 10 h, and 900 °C for 4 h produced crystalline Tm3+/Yb3+-codoped Y2O3, YAG, and YBO3, respectively.

### Characterization

Phase identification of all the prepared products was performed on a Philips PW1700 X-ray powder diffractometer using Cu K-α (λ = 1.5418 Å) radiation. XRD patterns were collected over a 2θ range from 10° to 80° at an interval of 0.02°. The morphology of the samples was checked using high-resolution scanning electron microscopy (Phenom ProX Desktop SEM, 10 keV) and a thin layer of sample powder on conducting carbon tape. Steady-state emission and excitation spectra were recorded using an Edinburgh Instruments FLS920 spectrophotometer equipped with different excitation sources, including a 450 W xenon lamp and an optical parametric oscillator laser (OPO; Opolette HE 355II; 20 Hz; pulse width ~7 ns), TMS300 monochromators, a thermoelectrically cooled R928 photomultiplier tube (PMT) for visible wavelengths, and a liquid-nitrogen-cooled R5509-72 PMT for near-infrared wavelengths. Photoluminescence decay curves were measured using multichannel scaling on the Edinburgh Instruments FLS920 spectrophotometer under pulsed OPO laser excitation.

### Modelling the energy-transfer dynamics

We used the Monte Carlo procedure to model the dynamics of the cross-relaxation and cooperative energy transfer described in detail in Ref. 44. Briefly, for each host material, we randomly generated several thousand different environments of an excited Tm3+ ion, i.e., a number of nearest Yb3+ neighbours, next-nearest neighbours, etc., taking into account the overall Yb3+ doping concentration. NaYF4 and Y2O3 have two possible crystal sites for the central Tm3+ ion, which were weighted by the relative occurrence. We made the simplification that the energy-transfer strengths Cxr and Ccoop are the same for all sites in the crystal structures. Next, for each environment i, we calculated the total energy-transfer rate kET,i by summing over all (pairs of) acceptors (see Eqs. (2) and (3)) and obtained an expression $$T\left( t \right) = A\mathop {\sum}\nolimits_i {e^{ - k_{{\mathrm{ET}},i}t}}$$ for the multiexponential energy-transfer dynamics. We determined the best value for Cxr (Eq. (2)) or Ccoop (Eq. (3)) by fitting our model to the data for one of the Yb3+ concentrations, indicated in Fig. 4 by the underlined value for x. Finally, we fitted our model to the data for all other Yb3+ concentrations, only optimizing the amplitudes A while keeping Cxr or Ccoop fixed.

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## Acknowledgements

This work was supported by the National Science Foundation of China (U1601205, 51472088, and 51125005) and by The Netherlands Center for Multiscale Catalytic Energy Conversion (MCEC), an NWO Gravitation programme funded by the Ministry of Education, Culture, and Science of the government of The Netherlands. F.T.R. acknowledges financial support from The Netherlands Organisation for Scientific Research NWO (VENI grant number 722.017.002). We thank T. van Swieten for critical reading of the manuscript.

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Yu, D., Yu, T., van Bunningen, A.J. et al. Understanding and tuning blue-to-near-infrared photon cutting by the Tm3+/Yb3+ couple. Light Sci Appl 9, 107 (2020). https://doi.org/10.1038/s41377-020-00346-z

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• DOI: https://doi.org/10.1038/s41377-020-00346-z

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