Light Conversion upon Photoexcitation of NaBiF₄:Yb³⁺/Ho³⁺/Ce³⁺ Nanocrystalline Particles

Abstract

NaBiF₄ nanocrystalline particles were synthesized by means of a facile precipitation synthesis route to explore upconversion emission properties when doped with lanthanide ions. In particular, the incorporation of the Yb³⁺-Ho³⁺-Ce³⁺ triad with controlled ion concentration facilitates near-IR pumping conversion into visible light, with the possibility of color emission tuning depending on Ce³⁺ doping amount. We observed that introducing a Ce³⁺ content up to 20 at.% in NaBiF₄:Yb³⁺/Ho³⁺, the chromaticity progressively turns from green for the Ce³⁺ undoped system to red. This is due to cross-relaxation mechanisms between Ho³⁺ and Ce³⁺ ions that influence the relative efficiency of the overall upconversion pathways, as discussed on the basis of a theoretical rate equation model. Furthermore, experimental results suggest that the photoexcitation of intra-4f Ho³⁺ transitions with light near the UV-visible edge can promote downconverted Yb³⁺ near-IR emission through quantum cutting triggered by Ho³⁺-Yb³⁺ energy transfer mechanisms. The present study evidences the potentiality of the developed NaBiF₄ particles for applications that exploit lanthanide-based light frequency conversion and multicolor emission tuning.

1. Introduction

Light conversion includes a series of photon management procedures for modifying light energy and frequency in a selected spectral range, which find wide application in diverse technologies such as solar and photovoltaic, photosynthetic biomass production, bioimaging and lighting [1,2,3,4,5]. Trivalent lanthanide ions (Ln³⁺)-doped materials historically represent an interesting class of luminescent light converters since, under appropriate photoexcitation, they give rise to photophysical mechanisms which can lead to wavelength shift and multicolor emission, with careful control of the chromaticity output [6,7,8,9,10,11].

Upconversion (UC), where two or more absorbed low-energy photons are converted into a higher-energy one, and downconversion (DC) via quantum cutting (QC), where the absorption of a single high-energy photon originates two or more photons emitted at lower energies, are widely mentioned as nonlinear processes that bring to light frequency modification [12]. These mechanisms are highly fostered in lanthanide-doped phosphors due to the unique optical properties exhibited by lanthanide ions, deriving from a characteristic ladder-like arrangement of energy levels from ultraviolet to near-infrared and parity-forbidden intra-4f transitions with long-lived intermediate states. Among the most studied types of lanthanide-based UC systems, phosphors based on Yb³⁺-Ln³⁺ (Ln³⁺ = Er³⁺, Ho³⁺, Tm³⁺) pairs still receive great attention due to the incomparable near IR-to-visible UC emission efficiency [8,13,14,15]. This is due to an overall photophysical process based on a sequence of sensitizer–activator energy transfer mechanisms, which exploits the large absorption cross section of Yb³⁺, the sensitizer ion, under 980 nm photoexcitation, and the resonant level matching with the activator ion (Er³⁺, Ho³⁺, Tm³⁺), which is promptly promoted to high-energy states by the conversion of several absorbed near-infrared (NIR) photons and then relaxes radiatively, producing an emission spectrum characteristic of the Ln³⁺ energy levels scheme. In particular, both Yb³⁺-Er³⁺ and Yb³⁺-Ho³⁺ pairs show UC photoluminescence in the visible range dominated by a green and a red emission, both originating from two-photon UC processes. The relative intensity of the two bands determines the chromaticity output and can be controlled by concentration of the doping Ln³⁺ species.

Strategies for UC efficiency enhancement as well as for color output tuning include the incorporation of a further doping species for manipulating the Yb³⁺-Ln³⁺ UC pathways and then sensitize and/or foster specific emission outputs. Relevant results in Yb³⁺-Er³⁺ UC efficiency increase was achieved by embedding alkali or transition metal ions, such as Li⁺, Fe³⁺, Cd²⁺, into Ln³⁺-doped matrix, while pure single red band resulted by means of Mn²⁺ codoping of NaYF₄:Yb³⁺/Er³⁺ NPs [16,17,18,19,20]. Redshift tuning of UC emission is particularly appealing in the field of bioimaging and biolabeling, since it achieves emission in the first biological window and simultaneous suppression of visible light noise. In this regard, Ce³⁺ incorporation has been reported as a valid method for green-to-red conversion in Yb³⁺/Ho³⁺ codoped fluoride hosts [21,22,23,24,25]. Photophysical mechanisms underlying the sensitizer–activator process are influenced by the presence of Ce³⁺ since it can enhance the population of the activator intermediate states involved in the red band UC emission process by virtue of its peculiar 4f energy level structure.

To develop efficient lanthanide-based UC phosphors, the choice of the host matrix is crucial. It is well known that fluoride materials offer several advantages, such as the extremely low phonon energy. Mainly for this reason, they are widely considered for the preparation of both bulk and nanostructured lanthanide-doped UC systems used in several fields, such as theranostics, nanothermometry, color displays, optical encoding, to name a few [26,27,28,29,30,31]. Bismuth-based compounds are characterized by a high refractive index, which induces a reduction in multiphonon relaxation rates and enhancement of spontaneous emission probability; namely, they are a popular choice as a host for optical dopants suitable for the realization of UC phosphors and optical thermometers [32,33,34,35,36]. Recently, Yb³⁺/Ln³⁺ (Ln³⁺ = Er³⁺, Ho³⁺, Tm³⁺) codoped NaBiF₄ nanoparticles have been prepared by means of a room-temperature, one-pot synthesis procedure, representing a valuable alternative with respect to conventional methods based on high-temperature solvothermal and hydrothermal route employed for the preparation of fluoride-based particles [37]. Later, the issue of thermal and chemical stability of the bismuth based fluoride materials has been addressed to exploit their potential in possible photonic applications [38].

Within the scope of a research activity related to the development of a specific class of Bi-based fluoride compounds with tailored optical properties, this study was conceived to elucidate the properties of light conversion of Yb³⁺/Ho³⁺/Ce³⁺ tridoped NaBiF₄ nanocrystalline particles (NPs). The investigation of UC emission chromaticity control as a function of Ce³⁺ content is aimed at establishing the condition for green-to-red conversion tuning. A theoretical model based on a steady-state rate equations scheme for Ho³⁺ energy level population is adopted to account for the different photophysical mechanisms taking place in the Yb³⁺-Ho³⁺ UC pathways, and to define the role of Ce³⁺ in the emission chromaticity shift, finding a real agreement with the observed experimental trend. Furthermore, spectroscopic results show that UV-visible excitation promotes Yb³⁺ NIR emission, which is particularly efficient through photoexcitation of Ho³⁺ energy levels around the UV-visible edge. This may represent a possible fingerprint of a DC process triggered by a Ho³⁺-Yb³⁺ QC mechanism. The point is discussed on the basis of a proper photophysical scheme, considering that the observed visible-to-NIR QC-mediated DC expands the potentiality of the investigated NaBiF₄:Yb³⁺/Ho³⁺/Ce³⁺ NPs for applications as a spectral converter.

2. Materials and Methods

2.1. Chemicals

Bi(NO₃)₃·5H₂O (99.99%), NH₄F (99.9%), Yb(NO₃)₃·5H₂O (99.9%), Ho(NO₃)₃·5H₂O (99.9%), Ce(NO₃)₃·5H₂O (99.9%), NaNO₃ (99.9%), ethylene glycol (EG, 99.8%), ethanol (EtOH, 99.8%), Milli-Q water. All reagents were purchased from Sigma Aldrich, Italy.

2.2. Synthesis

The preparation route of the investigated Ln³⁺-doped NPs is a modification of the procedure reported by Lei et al. in [37]. In a typical synthesis, 1 mmol of Bi, 1 mmol of Ln³⁺ nitrates and 2 mmol of NaNO₃ were dissolved into 10 mL of EG. In another beaker, 6 mmol of NH₄F was dissolved in 25 mL of EG, and then added to the above solution under stirring; on the basis of the results of our previous work [38], the NH₄F amount was chosen to stabilize the hexagonal NaBiF₄ phase. The obtained solution was stirred, at room temperature, for one minute, and the product was collected by centrifugation and washed with anhydrous ethanol three times before natural drying. The synthesized NaBiF₄ NPs incorporate Yb³⁺ and Ho³⁺ ions with doping level set to 10 and 2 at.%, respectively, as optimal condition to maximize the UC emission, with different amounts of Ce³⁺ up to 20 at.% for controlled chromaticity output tuning.

2.3. Characterization

X-ray powder diffraction (XRPD) measurements were performed by means of a Philips diffractometer with a PW 1319 goniometer with Bragg–Brentano geometry, connected to a highly stabilized generator, a focusing graphite monochromator and a proportional counter with a pulse-height discriminator. Nickel-filtered Cu Ka radiation and a step-by-step technique were employed (steps of 0.05° in 2θ), with collection times of 30 s per step.

Size and morphology determination of the nanoparticles and EDX analysis were carried out with a Carl Zeiss Sigma VP Field Emission Scanning Electron Microscope (FE-SEM) equipped with a Bruker Quantax 200 microanalysis detector.

Room-temperature photoluminescence (PL) and PL excitation (PLE) measurements, as well as time-resolved PL analysis, were carried out by means of a FluoroLog 3–21 system (Horiba Jobin-Yvon) equipped with a 450 W xenon arc lamp as excitation source, whose wavelength was selected by a double Czerny–Turner monochromator and signal detection stage including an iHR300 single grating monochromator coupled to a Hamamtsu photomultiplier tube (model R928P for visible range; model R5509-73 N₂-cooled for NIR range). Alternatively, PL spectra were acquired by means of a QE65 Pro Ocean Optics spectrometer. Upconversion measurements were performed by using a CNI MDL-III-980 diode laser as 980 nm photon pumping source, with output power of 2 W over a spot of 5 × 8 mm² (power density of 5 W/cm²). For time-resolved PL investigation, the Fluorolog system operated in TCSPC/MCS mode, and the sample excitation was achieved through a pulsed laser source (Horiba SpectraLED) featuring 460 nm peak wavelength and 30 nm spectral FWHM.

3. Results and Discussion

The following results represent a comprehensive characterization of a Ce³⁺-free Yb³⁺/Ho³⁺ codoped sample (Ce_0) as compared to tridoped samples embedding a Ce³⁺ content of 2 (Ce_2), 5 (Ce_5), 10 (Ce_10) and 20 at.% (Ce_20).

3.1. Structural and Morphological Characterization

Figure 1a reports the XRD measurements of the investigated samples. All the diffractograms match well with the crystallographic pattern of the hexagonal NaBiF₄ phase (chart JCPDS#41-0796), regardless of Ln³⁺ doping content. At the highest Ce³⁺ amount it is noticed the appearance of some faint peaks, which could be attributed to the formation of secondary fluoride phases. From the XRD pattern fitting, we estimated the trend of the cell volume parameter as a function of the Ce³⁺ content. In this regard, Figure S1 shows that the cell volume progressively shrinks by increasing the Ce³⁺ doping level, tending to a plateau for large concentration, in agreement with the fact that Ce³⁺ has a smaller ionic radius with respect to Bi³⁺ (1.14 Å vs. 1.17 Å, respectively).

Morphological properties of the studied NPs can be characterized by the representative SEM image of the tridoped sample with 10 at.% of Ce³⁺ (Ce_10), which is shown in Figure 1b. The synthesized NaBiF₄ NPs appear as nm-sized spheroidal aggregates, resulting from the assembly of smaller primary nanocrystals [38]. Further SEM images relating to the other investigated samples are included in Figure S2. EDX spectrum together with related elemental maps for Ce_10 sample are reported in Figures S3 and S4, respectively.

3.2. UC Properties and Color Tuning Effect

The analysis of the fluorescence properties characterizing the investigated Ln³⁺-doped NPs firstly focuses on UC emission due to Yb³⁺-Ho³⁺ sensitizer–activator coupling and on the chromaticity tuning driven by Ce³⁺ incorporation.

Figure 2a presents upconversion photoluminescence (UCPL) spectra measured in the visible range under 980 nm light pumping and representative NPs with different Ce³⁺ content. The spectra are dominated by three main emission features with maximum at around 540 nm (named as GRN band, being peaked in the green range), 645 nm (named as RED band, being peaked in the red range) and 750 nm, attributed to Ho^{3+ 5}S₂/⁵F₄ → ⁵I₈, ⁵F₅ → ⁵I₈ and ⁵S₂/⁵F₄ → ⁵I₇ transitions, respectively. It can be observed that the progressive increase in Ce³⁺ content determines a decrease in intensity for the GRN band compared to the RED one. In addition, for Ce³⁺ content higher than 5%, the overall luminescence emission signal settles down at about 70% of the intensity of the Ce³⁺ undoped sample (Ce_0), as shown in the inset of Figure 2a. This evidence suggests that the impact of any detrimental effects, such as fluorescence quenching due to high lanthanide ions concentration, is rather limited for the system under investigation.

The CIE chromaticity diagram and the photographs of the observed luminescence spots are reported in Figure 2b,c, respectively. The Ce³⁺-induced color rendering index modification is clearly appreciable, going from a pale green emitted spot for the Ce³⁺ undoped sample to dark orange, reaching 20 at.% of Ce³⁺ doping.

In the context of the photophysical mechanisms underlying the UCPL activity observed for the Ln³⁺-doped NPs, the diagram of Figure 3 depicts the main relaxation and transition processes that involve 4f energy levels for the Yb³⁺-Ho³⁺-Ce³⁺ triad. The trigger of the overall mechanism is the intra-4f Yb^{3+ 2}F_7/2 → ²F_5/2 ground-to-excited-state transition under 980 nm light, whose absorption by Yb³⁺ ions is characterized by a very large cross-section. Due to the long Yb^{3+ 2}F_5/2 lifetime, the Ho³⁺ upper excited states can be populated through a very effective Yb³⁺-Ho³⁺ energy transfer (ET) interaction. The diagram highlights the three main mechanisms, labeled as ET1, ET2, and ET3, that lead to the excitation of the Ho^{3+ 5}I₆, ⁵F₅ and ⁵S₂/⁵F₄ levels, respectively, and thus activate the UC emission pathways for the generation of the observed emissions in the visible range.

As previously reported, the GNR band, as well as the emission peaked at 750 nm, is a consequence of the relaxation process from the Ho^{3+ 5}S₂/⁵F₄ excited state, which is populated through a sequence of ET1 and ET3 mechanisms involving Ho^{3+ 5}I₆ state as the intermediate level. On the other hand, the RED band originates from the relaxation of the Ho^{3+ 5}F₅ state, whose excitation can occur through two possible UC paths. One ends with the direct Ho^{3+ 5}F₅ population through non-radiative relaxation of Ho^{3+ 5}S₂/⁵F₄ level after a combined sequence of ET1 and ET3 mechanisms. The other is instead based on a sequence of ET1 and ET2 processes, interspersed by Ho^{3+ 5}I₆ non-radiative relaxation to the Ho^{3+ 5}I₇ level. Therefore, both paths include a multiphonon relaxation step which is supposed to strongly affect the overall efficiency for the RED band emission process. In fact, it is worth considering that both ⁵S₂/⁵F₄ → ⁵F₅ and ⁵I₆ → ⁵I₇ transitions span an energy gap of about 3000 cm⁻¹. Since the typical phonon energy for fluoride-based hosts is relatively low (i.e., in the order of 500 cm⁻¹), the upper excited level depopulation must involve a substantial number of phonons, limiting the occupancy of the lower excited level and then the resulting RED band intensity.

In this scenario, Ce³⁺ incorporation becomes effective. As shown in the diagram of Figure 3, Ce³⁺ ion admits a unique intra 4f transition involving the ²F_5/2 ground and the ²F_7/2 excited states. The separation between these energy levels matches the gap that characterizes both the Ho^{3+ 5}S₂/⁵F₄ → ⁵F₅ and ⁵I₆ → ⁵I₇ transitions. This implies that cross-relaxation (CR) mechanisms take place, involving the transitions Ho^{3+ 5}I₆ + Ce^{3+ 2}F_5/2 → Ho^{3+ 5}I₇ + Ce^{3+ 2}F_7/2 (labeled as CR1) and Ho^{3+ 5}S₂/⁵F₄ + Ce^{3+ 2}F_5/2 → Ho^{3+ 5}F₅ + Ce^{3+ 2}F_7/2 (labeled as CR2), which flank the multiphonon relaxation steps in the overall upconverting process that leads to the population of the Ho^{3+ 5}F₅ excited state. UCPL measurements reported in Figure 2a demonstrate that the efficiency of the CR1 and CR2 processes is such as to lead to a manifest RED band enhancement with respect to GRN one as the Ce³⁺ content increases.

3.3. Rate Equation Modeling of UC Mechanisms

In order to account for the impact of Yb³⁺-Ho³⁺ ET and Ce³⁺-mediated CR processes on the resulting UCPL activity, we have revisited the model proposed by Chen et al. in [21] to formalize a system of rate equations describing the time evolution of the population of Ho³⁺ excited energy levels involved in the observed emission processes:

$$\frac{d{N}_1^{Ho}}{dt}=w_{21}^{MP}{N}_2^{Ho}+c_2{N}_2^{Ho}{N}_0^{Ce}-w_1{N}_1^{Ho}-k_1{N}_1^{Yb}{N}_1^{Ho} ,$$

(1)

$$\frac{d{N}_2^{Ho}}{dt}=k_0{N}_1^{Yb}{N}_0^{Ho}-w_2{N}_2^{Ho}-k_2{N}_1^{Yb}{N}_2^{Ho}-c_2{N}_2^{Ho}{N}_0^{Ce} ,$$

(2)

$$\frac{d{N}_3^{Ho}}{dt}=w_{43}^{MP}{N}_4^{Ho}+k_1{N}_1^{Yb}{N}_1^{Ho}+c_4{N}_4^{Ho}{N}_0^{Ce}-w_3{N}_3^{Ho} ,$$

(3)

$$\frac{d{N}_4^{Ho}}{dt}=k_2{N}_1^{Yb}{N}_2^{Ho}-w_4{N}_4^{Ho}-c_4{N}_4^{Ho}{N}_0^{Ce} .$$

(4)

The symbols used in the equations have the following meaning: $N_i^{Ho}$ (with $i=0, 1, 2, 3, 4$) refers to the population density of Ho^{3+ 5}I₈ ground and ⁵I₇, ⁵I₆, ⁵F₅, ⁵S₂/⁵F₄ excited levels, respectively; $N_i^{Yb}$ (with $i=0, 1$) refers to the population density of Yb^{3+ 2}F_7/2 ground and ²F_5/2 excited levels, respectively; $N_i^{Ce}$ (with $i=0, 1$) refers to the population density of Ce^{3+ 2}F_5/2 ground and ²F_7/2 excited levels, respectively; $w_i$ (with $i=1, 2, 3, 4$) refers to the overall transition rate from Ho³⁺ $i$ level to the lower ones, while $w_{21}^{MP}$ and $w_{43}^{MP}$ are the multiphonon-assisted relaxation rates for Ho^{3+ 5}I₆ → ⁵I₇ and ⁵S₂/⁵F₄ → ⁵F₅ transitions, respectively; $k_i$ (with $i=0, 1, 2$) refers to the coupling constant for the Yb³⁺-mediated ET processes involving Ho^{3+ 5}I₈ → ⁵I₆, ⁵I₇ → ⁵F₅ and ⁵I₆ → ⁵S₂/⁵F₄ transitions, respectively;$c_i$ (with $i=2, 4$) refers to the coupling constant for the Ce³⁺-mediated CR processes involving Ho^{3+ 5}I₆ → ⁵I₇ and ⁵S₂/⁵F₄ → ⁵F₅ transitions, respectively.

In steady-state conditions under cw pumping excitation, from Equations (1)–(4) we obtain the following expressions for the Ho³⁺ excited levels:

$$N_1^{Ho}=\frac{\left(w_{21}^{MP}+c_2{N}_0^{Ce}\right)k_2{k}_0{N}_1^{Yb}{N}_0^{Ho}}{\left(w_1+k_1{N}_1^{Yb}\right)\left(w_2+k_2{N}_1^{Yb}+c_2{N}_0^{Ce}\right)} ,$$

(5)

$$N_2^{Ho}=\frac{k_0{N}_1^{Yb}{N}_0^{Ho}}{\left(w_2+k_2{N}_1^{Yb}+c_2{N}_0^{Ce}\right)} ,$$

(6)

$$N_3^{Ho}=\frac{\left[k_1\left(w_{21}^{MP}+c_2{N}_0^{Ce}\right)\left(w_4+c_4{N}_0^{Ce}\right)+k_2\left(w_{43}^{MP}+c_4{N}_0^{Ce}\right)\left(w_1+k_1{N}_1^{Yb}\right)\right]k_0{\left(N_1^{Yb}\right)}^2{N}_0^{Ho}}{w_3\left(w_2+k_2{N}_1^{Yb}+c_2{N}_0^{Ce}\right)\left(w_1+k_1{N}_1^{Yb}\right)\left(w_4+c_4{N}_0^{Ce}\right)} ,$$

(7)

$$N_4^{Ho}=\frac{k_2{k}_0{\left(N_1^{Yb}\right)}^2{N}_0^{Ho}}{\left(w_2+k_2{N}_1^{Yb}+c_2{N}_0^{Ce}\right)\left(w_4+c_4{N}_0^{Ce}\right)} .$$

(8)

Assuming that the transition rates for the Ho^{3+ 5}I₇ and ⁵I₆ levels are much larger than the corresponding upconversion rates, the latter terms can be relaxed in Equations (5)–(8), leading to the following reformulation of the previous expressions:

$$N_1^{Ho}=\frac{k_0{k}_2\left(w_{21}^{MP}+c_2{N}_0^{Ce}\right)N_0^{Ho}}{w_1\left(w_2+c_2{N}_0^{Ce}\right)}{N}_1^{Yb} ,$$

(9)

$$N_2^{Ho}=\frac{k_0{N}_0^{Ho}}{\left(w_2+c_2{N}_0^{Ce}\right)}{N}_1^{Yb} ,$$

(10)

$$N_3^{Ho}=\frac{k_0\left[k_1\left(w_{21}^{MP}+c_2{N}_0^{Ce}\right)\left(w_4+c_4{N}_0^{Ce}\right)+w_1{k}_2\left(w_{43}^{MP}+c_4{N}_0^{Ce}\right)\right]N_0^{Ho}}{w_1{w}_3\left(w_2+c_2{N}_0^{Ce}\right)\left(w_4+c_4{N}_0^{Ce}\right)}{\left[N_1^{Yb}\right]}^2 ,$$

(11)

$$N_4^{Ho}=\frac{k_0{k}_2{N}_0^{Ho}}{\left(w_2+c_2{N}_0^{Ce}\right)\left(w_4+c_4{N}_0^{Ce}\right)}{\left[N_1^{Yb}\right]}^2 .$$

(12)

Considering that Yb³⁺ light absorption occurs linearly in the adopted pump power regime, it can be stated that the parameter $N_1^{Yb}$ describing the population density of the Yb^{3+ 2}F_5/2 excited level is proportional to the intensity of the excitation source. Therefore, Equations (11) and (12) would imply a quadratic pump power dependence for the $N_3^{Ho}$ and $N_4^{Ho}$ population density parameters, and then for the emission intensitiy of GRN and RED bands, since they originate from Ho^{3+ 5}F₅ and ⁵S₂/⁵F₄ excited level relaxations, respectively. As a matter of fact, this behaviour finely agrees with the trends shown in the log–log plot of Figure 4a, where the linear fit of the experimental data related to the power density dependence of UCPL emission for Ce_10 sample resulted in a slope close to 2 for both GRN and RED emissions, thus confirming the occurrence of a two-photon UC process.

For a qualitative assessment of the observed chromaticity tuning effect, the bar graphs in Figure 4b evidence the Ce³⁺ content dependence for the intensity of the GRN and RED bands, as extracted from PL bands shown in the spectra of Figure 2a. Moreover, Figure 4b also reports the trend of the RED-to-GRN intensity ratio as a function of Ce³⁺ content, evidencing a progressive growth of this parameter up to 10 at.% of Ce³⁺, whereas with a Ce³⁺ content of 20 at.%, a sort of saturation effect takes place, leading to a less pronounced increase in the ratio.

From Equations (11) and (12), we can formalize an expression of the Ce³⁺ content dependence for the RED-to-GRN intensity ratio parameter:

$$\begin{array}{cc}\frac{I_{RED}}{I_{GRN}} \propto \frac{N_3^{Ho}}{N_4^{Ho}}& =\frac{\left[k_1\left(w_{21}^{MP}+c_2{N}_0^{Ce}\right)\left(w_4+c_4{N}_0^{Ce}\right)+w_1{k}_2\left(w_{43}^{MP}+c_4{N}_0^{Ce}\right)\right]}{w_1{w}_3{k}_2}\\ & =\frac{w_{43}^{MP}}{w_3}+\frac{w_{21}^{MP}{w}_4{k}_1}{w_1{w}_3{k}_2}+\left(\frac{c_4}{w_3}+\frac{w_{21}^{MP}{k}_1{c}_4}{w_1{w}_3{k}_2}+\frac{w_4{k}_1{c}_2}{w_1{w}_3{k}_2}\right)N_0^{Ce}+\frac{k_1{c}_2{c}_4}{w_1{w}_3{k}_2}{\left[N_0^{Ce}\right]}^2 .\end{array}$$

(13)

This equation accounts for the observed increase in the intensity ratio with the Ce³⁺ doping level. This behaviour is predictable by observing the structure of Equation (12), where the $N_4^{Ho}$ parameter, namely, the GRN emission intensity, is forced to decrease as the Ce³⁺ content rises.

Given the parabolic trend of the expressions in Equation (13), Figure 4b also includes a fit of the ratio values with a parabolic function, which results in a real agreement with the trend of the experimental values up to 10 at.% of Ce³⁺.

Furthermore, to generalize the proposed scenario and to validate the adequacy of the proposed rate-equation model, it is worth pointing out that similar experimental results are reported for Yb³⁺/Ho³⁺/Ce³⁺ tridoped fluoride systems investigated in the works of Gao et al. [22,39,40], Chen et al. [21], and Pilch-Wróbel et al. [41], where the trend of the resulting GRN intensity ratio recalls a parabolic dependence on Ce³⁺ doping level, in some cases reaching possible saturation effects at large Ce³⁺ content.

3.4. Efficiency of Ce³⁺-Mediated CR Processes

The observed color tuning effect is closely linked to the Ce³⁺ doping level adopted for the investigated samples. From the rate equations previously reported, it can be inferred that the CR processes impact on the occupancy of the Ho³⁺ levels involved in the overall UCPL mechanism. In particular, the CR1 and CR2 processes (identified by the coupling constants $c_2$ and $c_4$, respectively) constitute a depletion channel for the Ho^{3+ 5}I₆ and ⁵S₂/⁵F₄ levels, respectively, leading to the loss of efficiency of the GRN emission (and also of the PL signal at around 750 nm) and to the corresponding increase in the population of the levels involved in the photophysical mechanism responsible for the RED emission.

To account for the evolution of the Ho^{3+ 5}I₆ level occupancy, which is related to the $N_2^{Ho}$ parameter, Figure 5 shows the NIR emission deriving from Ho^{3+ 5}I₆ radiative relaxation to the ground state, as a function of the Ce³⁺ content. The fact that the luminescence signal promptly drops down as the Ce³⁺ content increases is a clear evidence of the Ho^{3+ 5}I₆ level depletion driven by the occurrence of the CR1 process.

For a quantitative assessment of the efficiency of the CR1 process, from Equation (10) we define the ratio of the NIR emission intensity due to Ho^{3+ 5}I₆ relaxation between a Ce³⁺-doped sample and the undoped reference as:

$$\frac{I_{NIR}\left[\mathrm{Ce}\text{\_}\mathrm{X}\right]}{I_{NIR}\left[\mathrm{Ce}\text{\_}0\right]}=\frac{w_2}{\left(w_2+c_2{N}_0^{Ce}\right)} .$$

(14)

The Ce³⁺ content dependence of this parameter can be evaluated from the trend of the experimental data shown in the inset of Figure 5.

The efficiency ${\eta }_{CR1}$ of the CR1 mechanism can be expressed as the ratio between the rate of the Ce³⁺-mediated process and the overall rate of the mechanisms that drive Ho^{3+ 5}I₆ depletion. Therefore, considering Equation (14), we obtain:

$${\eta }_{CR1}=\frac{c_2{N}_0^{Ce}}{\left(w_2+c_2{N}_0^{Ce}\right)}=1-\frac{I_{NIR}\left[\mathrm{Ce}\text{\_}\mathrm{X}\right]}{I_{NIR}\left[\mathrm{Ce}\text{\_}0\right]} .$$

(15)

The results of the calculation for the different Ce³⁺-doped samples are reported in

Table 1. Results of the intensity measurements of Ho³⁺ NIR emission, and of the calculations related to Ho³⁺ GRN emission lifetime and Ce³⁺-mediated CR efficiency for the investigated Ln³⁺-doped NaBiF₄ samples.

Sample	${\mathit{I}}_{\mathit{N}\mathit{I}\mathit{R}}$	${\mathit{\eta }}_{\mathit{C}\mathit{R}1}$	${\mathit{\tau }}_{\mathit{G}\mathit{R}\mathit{N}}$	${\mathit{\eta }}_{\mathit{C}\mathit{R}2}$
	normalized to Ce_0	[%]	[ms]	[%]
Ce_0	1.000	-	60.1	-
Ce_2	0.410	59.0	53.1	11.7
Ce_5	0.300	75.8	51.5	14.3
Ce_10	0.137	88.9	29.7	50.5
Ce_20	0.101	91.8	21.3	64.6

. It is worth noting that already with 2 at.% of Ce³⁺, the estimate is around 60% for ${\eta }_{CR1}$ parameter, which then grows to over 90% by increasing the Ce³⁺ content.

At this point, a comparison with the assessment of the efficiency for the CR2 process is proposed. In this case, the data for efficiency assessment have been extracted by considering the results of PL measurements by direct photoexcitation of Ho³⁺ ions under visible light exposure.

The spectra of Figure 6a show the typical Ho³⁺ emission signals in the visible range, together with a band at around 980 nm referable to the excited-to-ground-state relaxation originating from Yb^{3+ 2}F_5/2 level. This aspect is addressed in the next section. Figure 6b,c report the time-resolved PL decay curves for the Ho³⁺ GRN and RED emissions. As can be inferred from the trend of the lifetime estimates reported in the two insets, the GRN values progressively decrease as the Ce³⁺ content increases, while the RED one remains substantially unchanged. The different behaviour is strictly linked to the role played by the CR2 mechanism, through which the presence of Ce³⁺ ions involves the activation of a further non-radiative de-excitation channel of Ho^{3+ 5}S₂/⁵F₄, with consequent GRN emission weakening.

The CR2 conversion efficiency ${\eta }_{CR2}$ can be calculated according to the following equation, based on the lifetime ratio between a Ce³⁺-doped and the undoped sample:

$${\eta }_{CR2}=1-\frac{{\tau }_{GRN}\left[\mathrm{Ce}\text{\_}\mathrm{X}\right]}{{\tau }_{GRN}\left[\mathrm{Ce}\text{\_}0\right]} .$$

(16)

The values obtained for the investigated samples are reported in Table 1 for a final comparison among the efficiencies of the two Ce³⁺-mediated CR processes. What emerges is that the ${\eta }_{CR1}$ parameter is always greater than ${\eta }_{CR2}$ in the whole explored Ce³⁺ doping range, and therefore, it can be stated that CR1 process plays a primary role in the observed GRN-to-RED conversion effect induced by Ce³⁺ incorporation in the NaBiF₄:Yb³⁺/Ho³⁺ system.

3.5. Visible-to-NIR DC Effect

Here, we return to discuss the PL spectra in Figure 6a, obtained by direct Ho³⁺ excitation into ⁵F₁/⁵G₆ level through 448 nm pumping source. In addition to the typical visible emissions attributable to Ho³⁺ radiative transitions, a fluorescence band around 980 nm was also observed, which is linked to the Yb^{3+ 2}F_5/2 → ²F_7/2 relaxation. As these are the only Yb³⁺ intra-4f transitions, it is reasonable to hypothesize that the activation of the 980 nm band originates from a mechanism of indirect Yb³⁺ excitation mediated by Ho³⁺ ions. Several studies have already investigated the peculiarities of this phenomenology, highlighting its potentiality for the conversion of high-energy radiation into NIR photons in view of applications in the field of photovoltaics and solar cells technology [42,43,44,45].

Figure 7 reports a series of PLE spectra for the Yb³⁺/Ho³⁺ codoped sample (Ce_0), obtained by monitoring the intensity for the three main Ho³⁺ emissions in the visible range and the Yb³⁺ emission at 980 nm. To facilitate the comparison, the spectra were normalized with respect to the emission signal resulting under 483 nm excitation, corresponding to the Ho^{3+ 5}I₈ → ⁵F₃ ground-to-excited-state absorption. This gives the possibility to ascertain that, while the PLE spectra for Ho³⁺ emissions are characterized by almost the same intensity ratio between the different peaks in resonance with Ho³⁺ absorptions, for the Yb³⁺ emission the feature at 483 nm marks a sort of threshold beyond which the higher-energy peaks show enhanced relative intensity. This suggests a larger efficiency of the visible-to-NIR DC for the Yb³⁺/Ho³⁺ codoped system when operating with excitation light towards the UV-visible edge.

To get deeper inside the mechanism underlying the observed DC process, the scheme in Figure 8 depicts two of the major energy transfer processes proposed as responsible of the Ho³⁺-mediated Yb³⁺ ion photoexcitation [43]. On the one hand, upon Ho³⁺ excitation into high-energy 4f levels, which is followed by quick phonon-assisted relaxation to lower-lying ones responsible of Ho³⁺ visible emissions, resonant CR processes can take place, involving the transitions (i) Ho^{3+ 5}S₂/⁵F₄ + Yb^{3+ 2}F_7/2 → Ho^{3+ 5}I₆ + Yb^{3+ 2}F_5/2 and (ii) Ho^{3+ 5}F₅ + Yb^{3+ 2}F_7/2 → Ho^{3+ 5}I₇ + Yb^{3+ 2}F_5/2. The observation in the 980 nm PLE spectrum of Figure 7 of specific features at the wavelengths of Ho³⁺ direct pumping into ⁵S₂/⁵F₄ and ⁵I₆ levels could reflect the activation of these CR processes.

On the other hand, it has been proposed that, at high Yb³⁺ doping level, Ho³⁺-Yb³⁺ pairs can effectively interact through a cooperative energy transfer (CET) mechanism that originates from the Ho³⁺ levels involved in non-radiative relaxation processes, in particular, Ho^{3+ 5}F₃ with transition scheme Ho^{3+ 5}F₃ → 2Yb^{3+ 2}F_5/2, as it nearly falls at twice the energy for Yb³⁺ ground-state relaxation [43]. As this CET mechanism is configurable as a two-photon NIR QC and supposing an intrinsic larger efficiency with respect to the mentioned CR processes, this would explain the enhanced relative intensity of the PLE peaks in the 980 nm spectrum when pumping with photons in the UV-blue range.

A further aspect to note is linked to a possible role of Ce³⁺ in the observed visible-to-NIR DC process. The PL spectra of Figure 6a show that the increase in Ce³⁺ content determines an enhancement of the Yb³⁺ 980 nm band with respect to the different Ho³⁺ emissions in the visible range. This cannot be solely attributed to a Ce³⁺-induced loss in efficiency for the Ho³⁺ radiative processes, otherwise we would expect at least a lifetime decrease for the Ho³⁺ PL emission at 650 nm. Rather, the idea is that the presence of Ce³⁺ can foster the Ho³⁺-Yb³⁺ ET coupling. In this regard, in the literature, a role of the Ce³⁺ 5d states is invoked, suggesting a first ET process from Ho³⁺ high-energy 4f levels to Ce³⁺ 5d ones upon UV-blue light pumping, followed by a Ce³⁺-Yb³⁺ cooperative DC involving Ce³⁺ 5d non-radiative relaxation and ET to a pair of Yb³⁺ ions, with final 980 nm photon emission [46].

As a final suggestion, it is worth considering a peculiar aspect that emerges in the PL spectra of Figure 6a. These show that the Ho³⁺ emission bands in the visible range seem to float above a background luminescence signal. The inset of Figure 7 highlights that, under UV photoexcitation, this PL signal is strongly enhanced, resulting in a wide band with peak located at around 565 nm and characterized by a large Stoke shift with respect to the 300 nm absorption threshold which appears in the PLE spectrum. Luminescence emissions in the visible spectral range, also active at room temperature, have been observed for the NaBiF₄ system [38]. In general, RT luminescence activity observed for bismuth-based compounds is typically attributed to Bi³⁺ s-p transitions.

4. Conclusions

This work has focused on the investigation of the luminescence properties exhibited by NaBiF₄ NPs embedding specific amount of Yb³⁺, Ho³⁺ and Ce³⁺ ions. Operating in UC mode, which determines NIR-to-visible conversion through Yb³⁺-Ho³⁺ ET mechanisms, we observed that the variation of the Ce³⁺ content induces a modification of the PL chromaticity output as determined from the relative intensity of the two main visible Ho³⁺ emission features (GRN and RED bands). The effect is attributed to a pair of efficient CR mechanisms, by which a color tuning effect takes place with progressive green-to-red conversion with increasing Ce³⁺ content. On the basis of a rate equations model, we established a hierarchy between the two Ce³⁺-mediated CR processes from the experimental data, and a parabolic dependence on the Ce³⁺ content of the intensity ratio between the Ho³⁺ RED and GRN emissions in a specific Ce³⁺ doping range, beyond which a saturation effect is observed.

Furthermore, direct photoexcitation of Ho³⁺ ions into high-energy levels originates luminescence spectra featuring an intense 980 nm Yb³⁺ band as the result of a visible-to-NIR DC mechanism. The Yb³⁺ emission process is particularly efficient with UV-visible pumping above the energy threshold corresponding to the Ho^{3+ 5}I₈ → ⁵F₃ transition, then suggesting the occurrence of a QC process driven by Ho³⁺-Yb³⁺ CET that enhances the overall DC mechanism. Moreover, we observed that the presence of Ce³⁺ ions can contribute to this process by further fostering the visible-to-NIR DC effect.

All these evidences make Yb³⁺/Ho³⁺/Ce³⁺ doping of the developed NaBiF₄ NPs as a promising way to prepare phosphors with controlled UC and DC emission performance for possible applications in several fields such as photonics, bioimaging and anticounterfeiting.