An up-conversion luminophore with high quantum yield and brightness based on BaF₂:Yb³⁺,Er³⁺ single crystals

Abstract

Up-conversion (UC) of near-infrared radiation to visible light has received much attention because of its use in the conversion of solar radiation, luminescence thermometry, biosensing, and anti-counterfeiting applications. However, the main issue hindering the successful utilization of UC is the relatively low quantum efficiency of the process. In order to design new UC systems with high quantum yield (ϕ_UC) values, we synthesized two series of co-doped BaF₂ single crystals with nominal concentrations of Yb³⁺ (2–15 mol%)/Er³⁺ (2 mol%) as well as Yb³⁺ (3 mol%)/Er³⁺ (2–15 mol%). The highest ϕ_UC value of 10.0% was demonstrated for the BaF₂:Er³⁺ (2 mol%) and Yb³⁺ (3 mol%) sample under 490 W cm⁻² of 976 nm excitation. To study the natural limit of UC efficiency, quantum yield values upon direct excitation (ϕ_DS) of the ⁴S_3/2 (ϕ_DS ≤ 4%) and ⁴F_9/2 (ϕ_DS ≤ 26%) levels were measured. Comparison of experimental values of quantum yields to the ones obtained using Judd–Ofelt theory reveals strong quenching of the ⁴S_3/2 state for all investigated compositions. In addition, we observed an unusually strong contribution of the Er³⁺:⁴I_9/2 excited state to both UC and down-shifting luminescent processes. This contribution becomes possible due to the very low maximum phonon energy of BaF₂ crystals (240 cm⁻¹).

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Introduction

Luminescent materials based on lanthanide ions – ranging from molecular complexes to inorganic phosphors – remain not only interesting from a scientific point of view but also relevant for many new applications.^1,2 These applications include optical nanoprobes for medical usage,^3–7 colour conversion materials for light emitting diodes,^8,9 organic light emitting diodes,¹⁰ solar radiation converters,^11–13 luminescent thermometers^14–17 and inks used for anti-counterfeiting purposes.^18,19 In general, the luminescence of lanthanide-based materials can be divided into two main types: Stokes and anti-Stokes. The majority of known luminescence materials exhibit Stokes emission, also known as down-shifted (DS) emission, meaning that emitted photons have lower energy than absorbed ones. Fewer materials exhibit anti-Stokes emission, where emitted photons have higher energy than the absorbed ones.

Anti-Stokes emission, the so called the up-conversion (UC) process, based on trivalent lanthanide ions (Ln³⁺) can reach high photoluminescence quantum yields of 5–11% under relatively low excitation intensity (<40 W cm⁻²),^20–23 in contrast to high light intensity (>10⁶ W cm⁻²) required for other prominent anti-Stokes processes such as multi-photon absorption and multi-harmonic generation.²⁴ Thus, lower-power light emitting diodes²⁵ or even xenon lamp (for a special case of dye-synthesized UC)²⁶ can be used as excitation sources in lanthanide based UC. Four main UC mechanisms generally considered are ground state absorption with a subsequent excited state absorption (GSA/ESA), energy transfer UC (ETU), cooperative UC and photon avalanche UC.^27,28 The ETU is the most efficient mechanism among these four and occurs at high Ln³⁺ concentrations (>2 mol%) and moderate excitation intensity.^29,30 At lower doping concentrations or higher excitation intensities, GSA/ESA can occur simultaneously with the ETU process or even start playing a dominant role.³¹

In order to increase the efficiency of the UC, co-doping with a material (called sensitizer) that has a high absorption cross-section can be utilized. If the goal is to achieve UC from the near-infrared (NIR) to visible (Vis) region, then co-doping with Yb³⁺ ions is often applied. The ²F_7/2 → ²F_5/2 transition of the Yb³⁺ is resonant with the f–f transitions of Er³⁺, Tm³⁺, and Ho³⁺ ions, thus providing efficient energy transfer. Thereby, Er³⁺/Yb³⁺, Ho³⁺/Yb³⁺, and Tm³⁺/Yb³⁺ pairs are often used in the NIR-to-Vis UC systems.^32–37

Another important factor for the efficient UC process is the host matrix, as it affects the environment around the optical centres. The host matrix has to have low phonon energy in order to minimize the non-radiative losses and favour radiative transitions. In a wide range of UC materials, fluorides are optimal candidates for use as the host due to their relatively low phonon energies and good chemical stability.^38,39 Recently, we investigated SrF₂:Yb³⁺,Er³⁺ single crystals and reported a very high UC quantum yield of 6.5%.²³ Inspired by this work, we assumed that a BaF₂ single crystal with maximum phonon energy of 240 cm⁻¹, which is significantly lower than the phonon energy of other prominent fluoride hosts (β-NaYF₄ – 360 cm⁻¹,⁴⁰ LaF₃ – 350 cm⁻¹,⁴¹ CaF₂ – 320 cm^−1 42 and SrF₂ – 284 cm^−1 42), is a good candidate for further improving the UC efficiency.

It is known that the normally forbidden f–f transitions in rare-earth element (Ln³⁺) ions become partially allowed in materials with a low crystal symmetry and strong local distortion of the crystal field. Though, the BaF₂ crystal (as well as SrF₂ and CaF₂ hosts) exhibits a high cubic crystal symmetry with a fluorite structure which is usually not favourable for an efficient UC process.⁴³ However, co-doping with Yb³⁺ and Er³⁺ occurs via the substitution of the divalent cation and requires charge compensation via negative fluorine ions (F⁻) in interstitial positions. These interstitial anions reduce the symmetry of Ln³⁺ single ion centres giving rise to trigonal and tetragonal symmetry and, thus, increase the probability of radiative transitions.⁴⁴ Moreover, at higher dopant concentrations preferential clustering of lanthanide ions occurs, which can reduce inter-ionic distances and enhance both ETU and cross-relaxation processes.^45,46

There have been a number of studies dedicated to the optical properties of BaF₂ doped with Er³⁺ and Yb³⁺ ions. The majority of works have used glasses or glass ceramics.^47–50 Although these studies provide some insight into their UC behaviour, a more extensive study of the optical properties is required in order to get a more detailed picture of UC properties of BaF₂-based materials. Thus, the focus of this work is (i) to assess how efficient UC in the BaF₂ host can be via measurements of the absolute quantum yield in an integrating sphere (ϕ_UC) for different concentrations of doping ions and (ii) to provide a more detailed understanding of UC mechanism in the BaF₂ host (via the study of both UC and DS luminescent properties). In this context, single-crystals of BaF₂ are great study objects because of two reasons (i) lack of grain boundaries reduces light scattering and ensures efficient dissipation of heat produced within non-radiative relaxation of excited ions^51–55 and (ii) large volume to surface ratio allows neglecting the surface quenching effect and improves chemical stability of the samples.

Experimental

Synthesis and characterization

Barium fluoride, ytterbium fluoride and erbium fluoride were highly pure (99.99% LANHIT, Russia). The powders of the fluoride precursors were preliminarily melted under a CF₄ fluorinating atmosphere. Afterwards, the fluoride single crystals were grown by the Bridgman technique in a vacuum furnace under a CF₄ fluorinating atmosphere. Both the heater with a temperature gradient (60–80 K cm⁻¹) and the crucible were made up of graphite. The temperature (1360 °C) and crystallization velocity (6.5 mm per hour) were chosen based on the phase diagrams of BaF₂–Ln³⁺.^56,57 The grown crystals are 5 cm long rods with 10 mm diameter. The crystals were cut in the direction perpendicular to the long axis and resulting discs (thickness of 2 mm and diameter of 10 mm) were polished for optical measurements.

Two series of the single-crystal BaF₂ crystals doped with Er³⁺ and Yb³⁺ ions were grown by the Bridgman technique. The first series consisted of BaF₂ doped with nominal concentrations of 2 mol% of Er³⁺ ions and 2, 3, 5, 7, 10, 15 mol% of Yb³⁺ (hereafter the mol% represents the nominal concentration of the Ln³⁺ ions used in the synthesis of the crystals, whereas the exact compositions estimated via wavelength-dispersive X-ray fluorescence (WDXRF) spectroscopy are reported in Table S1, ESI†). The second series is doped with 3 mol% of Yb³⁺ ions as well as 3, 5, 10, 15 mol% of Er³⁺ ions. These concentration ranges were chosen because the previous research has revealed a strong concentration quenching and deteriorated UC luminescence at higher doping concentrations of both ions.⁵⁸

The crystalline structure of the samples was determined using the powder XRD patterns recorded with a Bruker D2 PHASER diffractometer (CuKα radiation). For this purpose, a small part of the single crystal was ground into powder. The patterns were recorded in the 2 theta range from 10 to 70 degrees.

The concentration of elements Ba²⁺, Er³⁺ and Yb³⁺ were determined by WDXRF spectroscopy (Pioneer S4, from Bruker AXS). For the measurement, three replicates of each sample were analyzed. 25 mg of the sample material (accuracy ± 0.05 mg) were dissolved with 6 g EQF-TML-5050-5 (49.75% Li₂B₄O₇ + 49.75% LiBO₂ + 0.5% LiBr) in a platinum crucible at 1373 K. After cooling in a platinum stencil the fusion tablet was analyzed. For the calibration, four fusion tablets with matrix-adapted standards (BaF₂, Er₂O₃, and Yb₂O₃) were melted. Two to three energy lines of the elements were used for the calculation. The standard deviation in the determination of the chemical composition did not exceed 0.6 wt% for barium, 0.07 wt% for erbium, and 0.05 wt% for ytterbium.

Optical methods

The Raman spectrum for the undoped BaF₂ sample was recorded with an i-Raman device by Polytec (785 nm excitation, 3.5 cm⁻¹ resolution).

The refractive indices of the samples were measured with a Metricon 2010/M prism coupler using 1550 nm laser radiation (Thorlabs, TLK-L1550R). The detailed description of the setup was reported earlier.⁵⁹

Absorption spectra were recorded at room temperature using a UV-Vis spectrometer PerkinElmer Lambda 950 in the absorbance mode. The absorption coefficient was calculated using the following expression in eqn (1):

where α is the absorption coefficient in cm⁻¹, A is the absorbance data obtained from the device, and d is sample thickness in centimetres. The excitation spectra were recorded using a calibrated spectrophotometer Varian Cary Eclipse.

The setup and the methodology for the estimation of ϕ_UC under 976 nm excitation have been described previously.^23,60 To record ϕ_DS of the ⁴S_3/2 → ⁴I_15/2 and ⁴F_9/2 → ⁴I_15/2 transitions of the Er³⁺ ions a tunable CW laser (SolsTis with EMM-Vis, M-Squared Lasers Ltd) pumped by a 532 nm laser (Verdi-V18, Coherent) was utilized. The system was tuned to 522 nm for the direct excitation of the ⁴S_3/2 level and to 652 nm for the direct excitation of the ⁴F_9/2 level. For the measurement of ϕ_DS of the ⁴I_13/2 → ⁴I_15/2 transition upon direct excitation, a tunable laser kit (Thorlabs, TLK-L1550M) operating at 1520 nm was used as the excitation source. The remaining setup was the same as described in our earlier publication.⁶⁰

Luminescence lifetimes of the emissive levels were measured with a home-built optical system described previously.⁶¹ Briefly, 525 nm, 976 nm, and 633 nm (Roithner) and 1550 nm (Thorlabs) laser diodes mounted in temperature stabilized mounts (TCLDM9, Thorlabs) and driven by a laser diode controller (ITC4001, Thorlabs) as well as 375 nm LED also driven by the controller (ITC4001, Thorlabs) were used as the excitation sources. The power of the laser beam was adjusted with a controlled rotatable neutral density filter (Thorlabs). The remaining setup was the same as described in our previous publication.⁵⁹

Results and discussion

Crystal structure characterization

The measured powder XRD patterns are presented in Fig. 1 together with JCPDS card 04-0452 (BaF₂). The unit cell parameters (a) calculated from the XRD data are given in Table S1 (ESI†). They are in a good agreement with the values of the BaF₂ unit cell parameter (a = 6.200 Å) available in the literature.⁶² It is observed that the unit cell parameter decreases with the increase of doping concentration of both Yb³⁺ and Er³⁺. This may be attributed to the fact that ionic radii of Er³⁺ and Yb³⁺ ions are smaller than that of Ba²⁺.⁶³ This discrepancy results in a lower volume of the unit cell and reduced distance between doping ions, which, in turn, allows for a higher local concentration of the doping ions.

Fig. 1 Powder XRD patterns of the BaF₂:Yb³⁺, Er³⁺ samples.

Raman spectroscopy was performed for the undoped BaF₂ crystalline sample. The spectrum has one distinct peak at 240 cm⁻¹ (Fig. S1, ESI†), which perfectly correlates to the value of ∼240 cm⁻¹ observed earlier in several other publications,^42,64 and reveals low phonon energy of the BaF₂ host.

In addition, the exact chemical composition of the samples was studied by WDXRF spectroscopy. The obtained weight% of the doping ions, via the WDXRF method, allowed the calculation of the mol% values that represent the fraction of the Ba cations substituted with rare-earth ions. The resulting values are given in Table S1 (ESI†). For the sake of clarity, we will use the nominal concentrations of Er³⁺ and Yb³⁺ (related to the sample names) in further discussion. The uncertainties for the concentrations were 0.30 wt%, 0.02 wt%, and 0.02 wt% for barium, erbium, and ytterbium, respectively.

Optical characterization

Absorption and luminescence spectra

The absorption spectra shown in Fig. 2 demonstrate absorption bands in ultraviolet (UV), Vis and near infrared (NIR) ranges, characteristic of Er³⁺ and Yb³⁺ ions. The narrow absorption bands arise from the f–f transitions of the Er³⁺ and Yb³⁺ ions. The positions of the lines are in accordance with the literature data.^23,32,33 The shape of the peaks remains the same in all samples. It demonstrates that the local environment of the doping ions is consistent and there are no strong local deformations of the crystal structure in the investigated range of doping concentrations.

Fig. 2 Absorption spectra of two series of co-doped BaF₂ single crystals (a) samples with fixed Er³⁺ concentration whereas Yb³⁺ concentration varied from 2 to 15 mol% and (b) samples with fixed Yb³⁺ concentration where Er³⁺ concentration varies from 2 to 15 mol%.

Table 1 displays the values of the peak absorption cross-sections of the most prominent absorption bands of Er³⁺ and Yb³⁺. For instance, the peak cross-section of the Yb³⁺:²F_7/2 → ²F_5/2 absorption band is 0.62–0.7 pm² in the concentration range of Yb³⁺ of 3–15 mol%. The absorption cross-section of the Yb³⁺:²F_7/2 → ²F_5/2 transition was calculated only for the samples with 2% of Er³⁺ because at higher doping concentrations the contribution of the Er³⁺ absorption becomes significant at this wavelength.

Table 1 Peak absorption cross-sections for optical transitions in Er³⁺ and Yb³⁺ ions, pm²

	378 nm	406 nm	450 nm	522 nm	650 nm	1506 nm	976^a nm
	Er^3+:^4I15/2 → ^4G11/2	Er^3+:^4I15/2 → ^2H9/2	Er^3+:^4I15/2 → ^4F5/2	Er^3+:^4I15/2 → ^2H11/2	Er^3+:^4I15/2 → ^4F9/2	Er^3+:^4I15/2 → ^4I13/2	Yb^3+:^2F7/2 → ^2F5/2
a The absorption cross-section of the Yb^3+:^2F7/2 → ^2F5/2 transition was calculated only for the samples with 2% of Er^3+, because at higher doping concentrations the contribution of the Er^3+ absorption results in the overestimation of the absorption cross-section.
Er2Yb2	0.91	0.09	0.12	0.64	0.40	0.37	0.52
Er2Yb3	0.98	0.11	0.13	0.68	0.42	0.40	0.62
Er2Yb5	1.25	0.13	0.16	0.87	0.54	0.52	0.69
Er2Yb7	1.23	0.14	0.18	0.89	0.55	0.56	0.70
Er2Yb10	1.31	0.16	0.20	0.97	0.61	0.62	0.69
Er2Yb15	1.28	0.15	0.19	0.94	0.58	0.62	0.66
Er3Yb3	1.01	0.11	0.14	0.73	0.46	0.44
Er5Yb3	0.99	0.13	0.16	0.76	0.51	0.49
Er10Yb3	0.99	0.16	0.21	0.86	0.64	0.68
Er15Yb3	0.81	0.15	0.19	0.73	0.57	0.67

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The values are in line with the absorption cross-section values of the Er³⁺ and Yb³⁺ ions in hosts with a comparable structure available in the literature.^{23,45,65–67} Overall, Yb³⁺ ions in the BaF₂ host demonstrate absorption cross-section comparable to values reported for CaF₂ (0.55 pm²)⁶⁶ and SrF₂ (0.89 pm2),⁶⁷ whereas absorption cross-section in oxide crystals is usually higher. For example, Yb³⁺ absorption cross-sections of 0.8 pm² in YAG,⁶⁸ 1.7 pm² in Gd₂O₃,⁶⁹ and 8 pm² in GdVO₄⁷⁰ were previously reported. Another noticeable trend in the data is the significant increase in the absorption cross-section of Er³⁺ bands with the increase of both Er³⁺ and Yb³⁺ doping concentrations.

This phenomenon has already been reported by Auzel et al.⁷¹ and may be attributed to the fact that trivalent Er³⁺ and Yb³⁺ ions substitute divalent Ba²⁺ ions in the crystal. Higher amounts of the doping ions create stronger local distortion of the crystal field that favours the radiative transitions in the Ln³⁺ions.⁴⁵

The emission spectra of co-doped BaF₂ crystals are presented in Fig. 3. The DS emission spectra obtained under 375 nm excitation (⁴G_11/2 level of the Er³⁺ ions) are given in Fig. 3a and b while the UC emission spectra obtained under 976 nm excitation (²F_5/2 level of the Yb³⁺ ion) are shown in Fig. 3c and d. All spectra have typical emission bands of the Er³⁺ and Yb³⁺ ions with the emission of Er³⁺ ions located around 405 nm (²H_9/2 → ⁴I_15/2), 521 nm (²H_11/2 → ⁴I_15/2), 540 nm (⁴S_3/2 → ⁴I_15/2), 650 nm (⁴F_9/2 → ⁴I_15/2), 810 nm (⁴I_9/2 → ⁴I_15/2) and 850 nm (⁴S_3/2 → ⁴I_13/2) and the emission of {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold at 1020 nm. The position of these transitions on the energy level diagram is additionally given in Fig. S2 (ESI†). Under 375 nm excitation, the relative intensities of the Er³⁺ emission bands do not exhibit a strong dependence on the doping concentrations of Yb³⁺ until it reaches 10 mol% (see Fig. 3a). At this point, the relative intensity at 668 nm strongly increases, indicating two possible effects: (i) a strong depopulation of the ⁴S_3/2 level and/or (ii) an extra population of the ⁴F_9/2 level. The ²H_9/2 → ⁴F_9/2 transition in Er³⁺ is resonant with the ²F_7/2 → ²F_5/2 transition in Yb^3+ 72 (as shown in Fig. S2, ESI,† transition ①). If existing, these transitions lead to both a lower population of the ⁴S_3/2 level and an increase of the ⁴F_9/2 level population in line with the results presented in the Fig. 3a. The increase in the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold relative intensity at high doping concentrations can also be explained in a similar manner.

Fig. 3 Emission spectra of the samples under (a and b) – 375 nm (intensities of all spectra in the range from 900 to 1100 nm decreased to one-third of their original intensity) and (c and d) – 976 nm excitation (I = 490 W cm⁻²). All spectra were normalized using the intensity of the ⁴S_3/2-⁴I_15/2 (549 nm) peak.

In addition, Fig. 3a displays a change of the shape of the blue edge of the 1020 nm emission bands. This observation suggests strong self-absorption of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold starting from low Yb³⁺ doping concentration of 3 mol%. This behaviour is expected of Yb³⁺-doped materials as it was observed in materials with Yb³⁺ doping concentration as low as 1 mol%.⁷³

The increase of the Er³⁺ concentration (Fig. 3b) results in a continuous increase of the relative intensity of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold. However, the increase of the relative intensity at 668 nm is observed only for the highest concentration (15 mol%) of Er³⁺. This behaviour can be explained by two energy transfer processes (Fig. S2, ESI†): (i) ⁴F_7/2 → ⁴I_11/2 which is resonant with the ⁴I_15/2 → ⁴I_11/2 transition (Fig. S2, ESI,† transition ②) and (ii) ⁴F_5/2 → ⁴F_9/2 which is resonant with the ⁴I_15/2 → ⁴I_13/2 transition (Fig. S2, ESI,† transition ③).⁷² The contribution of the first energy transfer process can give rise to the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold emission. In turn, the contribution of the second process can be responsible for increase of the relative intensity of the ⁴F_9/2 level. It is reasonable that the ground state of Er³⁺ is a weaker energy acceptor than the ground state of Yb³⁺ as quenching is observed at a significantly higher concentration of Er³⁺ (15 mol%) as compared to the Yb³⁺ concentration (10 mol%).

The relative ratio of UC emission peaks has a much weaker dependence on the concentrations of the doping ions (Fig. 3c and d). In contrast to UV excitation, the increase in the Yb³⁺ concentration results in a moderate decrease in the 668 nm relative emission. This is due to the fact that the upper level of Er³⁺ is less involved in the UC process. Thus, we assumed that the energy transfer processes from the upper levels of Er³⁺ are unlikely to occur for all investigated samples at excitation intensities up to 490 W cm⁻². The significant increase in the emission at around 800 nm at high Er³⁺ concentrations (Fig. 3d) can be explained by the increasing population of the ⁴I_9/2 level from the ⁴I_13/2 state due to the resonance of this transition to the ⁴S_3/2 → ⁴I_9/2 transition, as shown in Fig. S3 (ESI†) (transition ①). However, these cross-relaxation processes become significant only if the concentration of Er³⁺ is high (>5 mol%). The proposed pathways for the deactivation of upper Er³⁺ levels were also confirmed via measurements of excitation spectra for the Er³⁺: ⁴F_9/2 energy level monitored at 660 nm (Fig. S4, ESI†).

Luminescence decay

The luminescence decay kinetics of the ²H_9/2, ⁴S_3/2, ⁴F_9/2, ⁴I_13/2 levels of the Er³⁺ ions as well as the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold are recorded using two excitation sources: a 976 nm diode laser (excitation of the ²F_5/2 level of the Yb³⁺ ions) and a 375 nm LED (excitation of the ⁴G_11/2 level of the Er³⁺ ions). The obtained curves are given in Fig. S5–S8 (ESI†). All of the luminescence decay curves except those at 540 nm exhibit mono-exponential behaviour under 375 nm and 976 nm excitations. In the case of ⁴S_3/2 → ⁴I_15/2 (540 nm) transition, the decay demonstrates strong non-mono exponential behaviour (see Fig. S6a and b, ESI†) and therefore it was fitted with a double exponential function (eqn (2)) that gives a good level of conformity between the fit and the experimental data.

The mean decay times presented in Fig. 4 and Table S2 (ESI†) are calculated using eqn (3)⁷⁴

Fig. 4 Luminescence decay time of ⁴S_3/2 → ⁴I_15/2 (green symbols) and ⁴F_9/2 → ⁴I_15/2 (red symbols) transitions of the Er³⁺ ions as well as decay time of {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold (brown symbols) under 375 nm (empty symbols) and 976 nm (filled symbols) excitation as a function of Yb³⁺ (a) and Er³⁺(b) nominal concentrations. The dashed lines are a guide to the eye. The exact decay times are presented in Table S1 (ESI†).

Fig. 4 indicates that under 375 nm excitation the increase in Yb³⁺ and Er³⁺ concentration leads to a decrease in the decay times of both ⁴S_3/2 and ⁴F_9/2 energy levels. This decrease can be explained by the excitation energy migration within an excited state manifold. If an excitation migrates until it meets a quenching centre, the migration process reduces the decay time of the excited state.⁷⁵ The quenching process can be based on cross-relaxation or interaction with a ground state (for instance the cross-relaxation with the resonance between ⁴S_3/2 → ⁴I_9/2 and ⁴I_13/2 → ⁴I_9/2 transitions (Fig. S3, ESI,† transition ①)) or interaction of the ⁴H_11/2 level with the Er³⁺ground state: ⁴H_11/2 → ⁴I_13/2 is resonant with ⁴F_15/2 → ⁴I_9/2 (Fig. S3, ESI,† transition ②). In addition, the observed decay time can also decrease, if the increased Ln³⁺ ion concentration affects the crystal lattice and thereby the lifetimes of radiative transitions. For instance, previously we observed an increase in the absorption cross-section (absorption enhancement) with the increase of the dopant concentration (Table 1). We can assume that the radiative rate also increases with the increase of Yb³⁺ and Er³⁺ concentration that results in an additional drop in the decay time.

Under 976 nm excitation the decay times of the ⁴S_3/2 and ⁴F_9/2 energy levels are extended compared to the decay times obtained under 375 nm excitation. This proves that in the case of UC excitation, the population of the higher states of the Er³⁺ ions is governed by energy transfer from long-lived intermediate states with lower energy. For instance, the decay time of the ⁴S_3/2 level reflects the long decay time of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold. At higher Yb³⁺ concentrations the decay time of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold decreases due to ETU enhancement. This effect leads to the shortening of ⁴S_3/2 decay time at a high Yb³⁺ content. In contrast, at higher Er³⁺ concentrations the decay time of the ⁴S_3/2 level under 976 nm excitation becomes longer. This again reflects the increase of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold decay time with the increase of the Er³⁺ concentration.

This trend in the decay time behaviour for the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold – it decreases with the increase in the Yb³⁺ concentration, but increases with the increase in the Er³⁺ content for both excitation types – is quite an interesting observation, as both ions are from the same {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold.

Under certain conditions, the prolongation of the decay time can be attributed to the effect of reabsorption, when luminescence is reabsorbed and reemitted several times within the same crystal. However, the reabsorption of 1020 nm emission can have only a minor effect (Fig. 3b) and cannot explain the increase of {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold decay time with the increase in the Er³⁺ concentration. Alternatively, the increase of {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold decay time observed under 976 nm excitation can reflect the fact that the lifetime of Er³⁺:⁴I_11/2 is much longer than the lifetime of the Yb³⁺:²F_5/2 state. For instance, the lifetimes of 7.41 ms and 0.77 ms were measured for single Er³⁺doped (5 mol%) and single Yb³⁺ doped (5 mol%) BaF₂ crystals, respectively (Fig. S9, ESI†). Thus, an increase in the Er³⁺ concentration should increase the contribution of the long-lived Er³⁺:⁴I_11/2 state to the decay time of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold, and increase it.

The additional prolongation of the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2}) manifold decay time observed under 375 nm excitation at a high Er³⁺ concentration can be explained by the increasing role of the Er³⁺:⁴I_9/2 level in the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2}) manifold population. Fig. S3 (ESI†) demonstrates a number of possible ways (① and ②) by which the Er³⁺:⁴I_9/2 level can be populated by a further transition to the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2}) manifold. In the crystals with low maximum phonon energy (240 cm^-1 for BaF₂), the rate of multiphonon relaxation for the ⁴I_9/2 → ⁴I_11/2 transition (with the energy gap of ΔE = 2000 cm^{- 1}) is very slow and, thus, the decay time approaches the radiative lifetime of the ⁴I_9/2 state after 10 ms.⁷⁶ Thus, this weakly emissive, but long-lived state can be considered as an additional reservoir (in parallel with the {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} manifold and the Er³⁺:⁴I_13/2 state) of metastable excited states influencing the DS and UC processes. Under this circumstance, the moderate and high concentrations of Er³⁺ contribute to the population of the ⁴I_9/2 state increasing the lifetime of ⁴S_3/2, ⁴F_9/2, and {Er³⁺:⁴I_11/2 & Yb³⁺:²F_5/2} states.

Quantum yield

The UC quantum yield ϕ_UC is the main figure-of-merit parameter, which can help to understand the physical mechanism and practical value of the UC process. The ϕ_UC, as it was introduced previously, is the internal quantum yield. The internal quantum yield characterizes the conversion efficiency of absorbed photons into emitted photons. However, the parameter of brightness (B), which depends also on a number of absorbed photons, is more important for some applications.⁷⁷ It can be calculated as:where α is the absorption coefficient.

The highest ϕ_UC and brightness values for the UC emission integrated in the 400–900 nm range as well as the ϕ_UC values of certain emission bands are given in Table 2. Additionally, the ϕ_UC values of the ²H_11/2–⁴I_15/2, ⁴I_9/2–⁴I_15/2 and ⁴S_3/2–⁴I_13/2 are presented in Table S3 (ESI†) and ϕ_DS values under 375 nm excitation are noted in Table S4 (ESI†). The highest measured ϕ_UC values reach 9.9% and 10.0% under an excitation intensity of 490 W cm⁻² in the samples doped with 2% of Er³⁺ as well as 2 and 3% of Yb³⁺ ions, respectively. These results significantly exceed the ϕ_UC values of 6.5% observed in the SrF₂ single crystals²³ as well as 2.8% observed in SrF₂ nano- and micro- particles⁶¹ doped with Er³⁺ and Yb³⁺ ions.^22,23 At the same time the sample doped with 2% of Er³⁺ and 10% of Yb³⁺ demonstrates the highest brightness value.

Table 2 Maximum ϕ_UC (at an intensity of 490 W cm⁻²) for ⁴S_3/2 → ⁴I_15/2, and ⁴F_9/2 → ⁴I_15/2 transitions of Er³⁺ emission and total ϕ_UC in the 400–900 nm range under 976 nm excitation

	^4S3/2 → ^4I15/2	^4F9/2 → ^4I15/2	Total	Brightness, cm^−1
Er2Yb2	0.021	0.063	0.099	0.121
Er2Yb3	0.023	0.061	0.100	0.192
Er2Yb5	0.021	0.053	0.088	0.262
Er2Yb7	0.023	0.043	0.081	0.374
Er2Yb10	0.019	0.036	0.068	0.495
Er2Yb15	0.013	0.027	0.048	0.419
Er3Yb3	0.018	0.043	0.064	0.120
Er5Yb3	0.017	0.03	0.062	0.148
Er10Yb3	0.008	0.01	0.026	0.121
Er15Yb3	0.002	0.004	0.011	0.065

---

This composition should provide the largest number of emitted photons per volume and can be optimal for UC applications of luminescent BaF₂:Yb³⁺, Er³⁺ materials.

The power dependent ϕ_UC under 976 nm excitation is summarized in Fig. 5, where the following trends can be observed: (i) under lower excitation intensity (<100 W cm⁻²) the samples exhibit an increase of ϕ_UC with the increase of the Yb³⁺ concentration; (ii) in contrast, under high excitation intensity, a reduced concentration of Yb³⁺ is preferable for achieving higher ϕ_UC values; (iii) increase of Er³⁺ concentration results in increased ϕ_UC at intensity <10 W cm⁻², and lowered ϕ_UC in the broad intensity range (10–490 W cm⁻²). A similar effect was also observed in β-NaYF₄ doped with Er³⁺.⁷⁸

Fig. 5 Intensity dependence of the UC quantum yield (ϕ_UC) under 976 nm excitation.

Another UC figure-of-merit parameter, critical power density (CPD), is calculated for each sample using an earlier published method.⁶⁰ This parameter describes the saturation ϕ_UC and facilitates the comparison of different UC materials. Combined with the maximum ϕ_UC value, it can provide a full set of characteristics required for the analysis of application perspectives of UC materials.

The beneficial low CPD values of the ⁴S_3/2 → ⁴I_15/2 transition of the Er³⁺ ions were earlier reported for the most efficient UC materials as 0.7 W cm⁻² in β-NaYF₄, 1.0 W cm⁻² in YF₃ and 1.0 W cm⁻² in La₂O₃.⁶⁰ The smallest CPD value of the ⁴S_3/2 → ⁴I_15/2 transition in the BaF₂ crystal (with 2% of Er³⁺, 15% of Yb³⁺ ions) is 1.1 W cm⁻², which is just fractionally higher than the values calculated for the best UC materials. Table S5 (ESI†) shows the results for the samples that provided the best fit.

Possible heating of samples was considered during the intensity-dependent measurements. To monitor a possible change of the sample temperature an approach from the literature⁷⁹ was utilized. The ratio between ²H_11/2–⁴I_15/2 (521 nm) and ⁴S_3/2–⁴I_15/2 (545 nm) emission bands was calculated. The results are presented in Fig. S10 (ESI†). They show that noticeable heating is observable only at the highest power densities (>200 W cm⁻²) in the samples with high Yb³⁺ and Er³⁺ doping concentrations. We assume that the increase of sample temperature can be responsible for the drop of ϕ_UC observed at intensity >200 W cm⁻² for samples with high doping concentrations.

A more detailed study of the down-shifting emission of the ⁴S_3/2 and ⁴F_9/2 levels at direct excitation (522 nm for ⁴S_3/2 and 652 nm for ⁴F_9/2) should help to have a deeper insight into the UC process efficiency. We observed that the ϕ_DS of the 540 nm emission under 522 nm excitation is in the range of 1–4% and ϕ_DS of the 660 nm emission under 652 nm excitation is in the range of 15–26% (Table S6, ESI†). Additionally, the ϕ_DS values of ⁴F_9/2–⁴I_15/2, ⁴I_9/2–⁴I_15/2 and ⁴S_3/2–⁴I_13/2 emission bands under 522 nm excitation can be found in Table S7 (ESI†).

It is clear that the value of ϕ_DS gives an indication of the maximum achievable ϕ_UC for this particular level. It cannot exceed half of this value (ϕ_DS ≤ 4% for ⁴S_3/2 → ⁴I_15/2 transition and ϕ_DS ≤ 26% in case of ⁴F_9/2 → ⁴I_15/2 transition) due to the fact that the UC process involves at least two photons. The lack of any strong dependence on the Yb³⁺ concentration in both cases means that there are no transitions from ⁴S_3/2 and ⁴F_9/2 levels of Er³⁺ interacting with the ground state of Yb³⁺. However, in both cases, there is a strong drop in ϕ_DS values with the increase in the Er³⁺ concentration. This may prove that there is a strong energy migration and quenching within the Er³⁺:⁴S_3/2 state even at relatively low Er³⁺ concentrations like 5% as it was assumed in the Luminescence Decay section.

Judd–Ofelt analysis

The experimental lifetimes are compared with radiative lifetimes of some levels of the Er³⁺ ions, which is calculated using the Judd–Ofelt theory by the standard procedure.^80,81 The detailed description of transition probability calculation is presented in the corresponding section of the ESI.†

Knowing the transition probabilities, it is possible to calculate the radiative decay time (τ_r) of a level and the corresponding branching ratio (β). These results together with experimentally measured decay times (τ) upon the direct excitation of the corresponding level in Er³⁺ ions (Fig. S11, ESI†) can help to predict the quantum yield value for three transitions: ⁴S_3/2 → ⁴I_15/2, ⁴F_9/2 → ⁴I_15/2 and ⁴I_13/2 → ⁴I_15/2. The resulting values were calculated using eqn (8) and are summarized in Table S9 (ESI†) together with τ, τ_r, β.

These results provide an insight into the possible application of the Judd–Ofelt theory to study UC and DS processes in Ln³⁺ co-doped systems. Altogether, the obtained values of the radiative decay times are close to the results of other studies devoted to optical properties of Er³⁺ ions in fluoride single crystals and micropowders.^76,82–84

Although an acceptable level of conformity between theoretical prediction ( in Table S9, ESI†) and experimental results ( in Table S6, ESI†) for the ⁴F_9/2 → ⁴I_15/2 transition exists (the relative difference doesn’t exceed 20% in most cases), in the case of ⁴S_3/2 → ⁴I_15/2 and ⁴I_13/2 → ⁴I_15/2 transitions a discrepancy between quantum yields extracted from the Judd–Ofelt calculation and the experimental one is significant. The values of estimated via Judd–Ofelt analysis always exceed unity for the ⁴I_13/2 → ⁴I_15/2 transition, because the measured decay times (τ) are longer than predicted radiative lifetimes (τ_r). Unfortunately, it remains unclear whether Judd–Ofelt theory describes well the ⁴I_13/2 → ⁴I_15/2 transition with strong magnetic dipole contribution or there is another energy transfer process and/or strong emission reabsorption leading to the elongation of the decay time. For the ⁴S_3/2 → ⁴I_15/2 transition, the predicted values of also overestimate the quantum yield in all investigated samples. We observed again the elongation of the decay times combined with rather small values of measured experimentally. This discrepancy is observed along with the strong deviation of ⁴S_3/2 → ⁴I_15/2 decays from the single-exponential behaviour (Fig. S11, ESI†) and can indicate the existence of an energy transfer pathway (energy migration⁸⁵ thermal coupling between ⁴S_3/2 and ²H_11/2 states,⁸⁶ for instance) and/or strong emission reabsorption which cannot be described using our simplified model. However, we believe that in our future work including Yb³⁺ and Er³⁺ single-doped crystals with a concentration range starting from very low dopant concentrations (0.1 mol%) we will be able to explain this interesting behaviour.

Conclusions

Optical properties of co-doped BaF₂ single crystals were investigated for a broad range of Er³⁺ (2–15 mol%) and Yb³⁺ (2–15 mol%) doping concentrations. All samples demonstrate efficient UC emission under 976 nm excitation. A very high ϕ_UC value of 10.0% (at 490 W cm⁻²) was observed for the sample doped with 2% of Er³⁺ and 3% of Yb³⁺. This value exceeds previously reported ϕ_UC for SrF₂ single crystals (6.5%) and approaches the efficiency of the best UC material known to date (NaYF₄:Yb³⁺, Er³⁺ with a quantum yield of 11% ²¹). The investigation of UC and DS luminescent spectra, lifetimes and quantum yields under multiple excitation wavelengths of 375, 522, 653, 976 and 1520 nm, as well as a comparison of the experimental results with predictions of Judd–Ofelt theory highlights the complexity of the UC process. More specifically, our results demonstrate a significant reduction of luminescence quantum yield of the Er³⁺:⁴S_3/2 state in the DS regime, which in turn reduces the quantum yield of its emission in UC regimes. Due to the low maximum phonon energy of BaF₂ crystals (240 cm⁻¹), we observed an unusually strong contribution of the Er³⁺:⁴I_9/2 state in the temporal behaviour of both UC and DS processes.

Author contributions

The manuscript was written through the contribution from all authors. E. M. and D. B. conducted spectroscopy experiments and E. M. wrote the paper. V. A. K. and A. N. N. grew the BaF₂ single crystals. T. B. performed WDXRF analysis of the chemical composition. S. V. K., A. T. and C. W. developed the original concept of the paper. P. P. V., I. A. H. and B. S. R. contributed equally to scoping and structuring the paper and provided additional guidance on experimental methods. All authors have approved the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The reported study was funded by the RFBR (project number 21-53-12017 of S. V. K., V. A. K., and A. N. N.) and DFG (project number TU 487/8-1 of A. T. and B. S. R.). B. S. R. acknowledges the financial support provided by the Helmholtz Association: (i) a Recruitment Initiative Fellowship to B. S. R.; (ii) the funding of chemical synthesis equipment from the Helmholtz Materials Energy Foundry (HEMF); and (iii) the Science and Technology of Nanosystems research programme. E. I. M. acknowledges the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities No. 0671-2020-0051 and the scholarship of the President of the Russian Federation.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1tc00104c

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