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 dopants^2,3. 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’ luminescence^4,5,6 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 photovoltaics^10,11,12. 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⁺/Yb^3+8,15, Ce³⁺/Yb^3+16,17,18, Tm³⁺/Yb^{3+19,20,21,22,23}, Pr³⁺/Yb^3+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 structure^16,17. Unfortunately, the energy-transfer mechanisms are unclear for many potential photon-cutting phosphors, resulting in contradictory^19,20 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 Tm^{3+ 1}G₄ 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 cells^10,11,12. 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 materials^29,30,31. The emission line centred at 10,000 cm⁻¹ (shaded red) is due to the ²F_5/2 → ²F_7/2 transition of Yb³⁺, and that centred at 12,500 cm⁻¹ (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 Tm^{3+ 1}G₄ level (see Fig. 1b for an excitation spectrum) evidences the occurrence of energy transfer from Tm³⁺ to Yb³⁺.

Fig. 1: Basic properties of Tm³⁺/Yb³⁺ codoped phosphors.

a Emission spectrum of YBO₃ doped with 0.1% Tm³⁺ and 2% Yb³⁺ upon excitation of the Tm^{3+ 1}G₄ level at 465 nm. The red-shaded band is due to the ²F_5/2 → ²F_7/2 emission of Yb³⁺, and the green-shaded band is due to the overlapping ¹G₄ → ³H₅ and ³H₄ → ³H₆ emissions of Tm³⁺³¹. b Corresponding excitation spectrum, measured by scanning through the Tm^{3+ 3}H₆ → ¹G₄ absorption transition and recording the intensity of the ¹G₄ → ³F₄ emission at 653 nm (15,300 cm⁻¹). c Cooperative energy transfer involves the distribution of the excited-state energy in the Tm^{3+ 1}G₄ level over two nearby Yb³⁺ ions. d This can eventually yield two near-infrared photons of 1000 nm emitted by Yb³⁺ per blue photon absorption event. e A Tm³⁺ ion in the ¹G₄ level can alternatively transfer part of its energy to a single nearby Yb³⁺ ion through phonon-assisted cross-relaxation. f This produces at most one near-infrared photon of 1000 nm. g–j Scanning electron micrographs of the four host materials in order of decreasing highest phonon energy: g YBO₃, h YAG, i Y₂O₃, and j NaYF₄. The scale bars represent 5 μm

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 ²F_5/2 excited state. Subsequently, both Yb³⁺ ions can emit a photon with an energy of approximately 10,000 cm⁻¹. 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 Tm^{3+ 1}G₄ level and double the energy of the Yb^{3+ 2}F_5/2 level suggests the possibility of cooperative energy transfer^21,22,23, 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 percent^21,22,23 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 ²F_5/2 level. Although Yb³⁺ can subsequently emit a photon that can be absorbed by crystalline Si, the energy of the ³H₅ level (8500 cm⁻¹) 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 Tm^{3+ 1}G₄ → ³H₅ and Yb^{3+ 2}F_7/2 → ²F_5/2 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-relaxation^39,40 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 Yb^{3+ 2}F_5/2 → ²F_7/2 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 Tm^{3+ 1}G₄ → ³H₅, Tm^{3+ 3}H₄ → ³H₆, and Yb^{3+ 2}F_5/2 → ²F_7/2 are different for the four materials but consistent with previous literature reports^42,43. 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.

Fig. 2: Emission spectra and decay dynamics as a function of Yb³⁺ concentration.

a Emission spectra of YBO₃ doped with 0.1% Tm³⁺ and increasing Yb³⁺ concentration as indicated in the plot, excited in the Tm^{3+ 1}G₄ level. The emission bands at 10,000 cm⁻¹ and 12,000 cm⁻¹ are due to radiative relaxation of the Yb^{3+ 2}F_5/2 and Tm^{3+ 1}G₄ levels (with overlap of ³H₄ → ³H₆ emission), respectively. b Same as in a, but for YAG. The Tm³⁺ concentration is 0.03% in these samples. c Same as in a, but for Y₂O₃. The Tm³⁺ concentration is 0.1% in these samples. d Same as in a, but for NaYF₄. The Tm³⁺ concentration is 0.3% in these samples. e–h Photoluminescence decay curves of the ¹G₄ level measured for the ¹G₄ → ³F₄ emission (~650 nm) from the same samples studied in a–d, using the same colour coding. These results show accelerated decay due to energy transfer at increasing Yb³⁺ concentration. All experiments were performed by exciting Tm³⁺ to the ¹G₄ level (~465 nm)

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 Tm^{3+ 1}G₄ level decreases with increasing Yb³⁺ concentration (Fig. 2e–h). This confirms energy transfer from the Tm^{3+ 1}G₄ 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 Tm^{3+ 1}G₄ level, $\langle \tau \rangle = \sum\nolimits_i {{I_i}{t_i}/} \sum\nolimits_i {{I_i}}$, where I_i is the emission intensity at delay time t_i 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 k_ET is due to energy transfer to Yb³⁺. The k_ET 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 k_ET 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.

Fig. 3: The average Tm³⁺-to-Yb³⁺ energy transfer rate.

Inverse of the average lifetime of the Tm^{3+ 1}G₄ level in (a) YBO₃, (b) YAG, (c) Y₂O₃, and (d) NaYF₄ as a function of Yb³⁺ concentration. These values are extracted from the photoluminescence decay curves shown in Fig. 2e–h. The dotted lines are linear fits, and the dashed line in panel d is a quadratic fit

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, k_ET 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 dynamics^8,44. 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 C_xr 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 C_coop 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 C_xr and C_coop 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).

Fig. 4: Monte Carlo modelling of energy transfer.

Tm³⁺-to-Yb³⁺ energy-transfer dynamics for different Yb³⁺ concentrations in (a, e) YBO₃, (b, f) YAG, (c, g) Y₂O₃, and (d, h) NaYF₄. The energy-transfer dynamics are isolated from the full photoluminescence decay curves (Fig. 2e–h) by dividing the data obtained for x% Yb³⁺ by the data for 0% Yb³⁺. Panels a–d show the results of a fit to a model of phonon-assisted cross-relaxation (Eq. (2)), whereas e–h show those for a model of cooperative energy transfer (Eq. (3)). See the Experimental section for details of the modelling procedure. The phonon-assisted cross-relaxation model matches the dynamics of YBO₃, YAG, and Y₂O₃, while the cooperative model matches the dynamics of NaYF₄

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 C_xr = (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 ²F_7/2 → ²F_5/2 transitions involved in cross-relaxation (compare Fig. 1a, b). Our experiments show that the 2000–3000 cm⁻¹ 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 Tm^{3+ 1}G₄ 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 (C_xr) is not straightforward, as C_xr depends on various other factors such as the transition dipole moments of the electronic and vibrational transitions involved^28,45. 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 C_xr 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.

Fig. 5: Comparing the photon-cutting potential of different host materials.

a Fitted Tm³⁺-to-Yb³⁺ cross-relaxation strength C_xr (see Eq. (2)) for the different host materials, plotted as a function of the maximum phonon energy of the host. b Corresponding intrinsic decay rates of the ¹G₄ level. c Calculated maximum quantum efficiency of YBO₃:Tm³⁺,Yb³⁺ as a function of Yb³⁺ concentration based on our phonon-assisted cross-relaxation model. We count only emission that can be absorbed by crystalline Si, i.e., visible emission from the Tm^{3+ 1}G₄ level (blue-shaded area) and near-infrared emission from Yb³⁺ (red-shaded area), and assume zero nonradiative decay from the Yb^{3+ 2}F_5/2 level. d Same, but for YAG:Tm³⁺,Yb³⁺. e Same, but for Y₂O₃:Tm³⁺,Yb³⁺. f Same, but for NaYF₄:Tm³⁺,Yb³⁺ and using our model for cooperative energy transfer. Of the four materials studied, only NaYF₄:Tm³⁺,Yb³⁺ is a photon-cutting phosphor that can produce two near-infrared photons (useful for crystalline Si) from a single blue photon absorption event

The energy-transfer mechanism, the corresponding energy-transfer strength (C_xr or C_coop; 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 Tm^{3+ 1}G₄ 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 C_xr and C_coop are the same for all sites in the crystal structures. Next, for each environment i, we calculated the total energy-transfer rate k_ET,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 C_xr (Eq. (2)) or C_coop (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 C_xr or C_coop fixed.