1. Introduction

The field of upconversion (UC) has escalated over the past several years. By doping lanthanide ions into low phonon host lattice structures in the form of bulk phosphors, thin films and nanoparticles (NPs), UC materials have had growing viability in drug delivery mechanisms [1,2], sensing [3], theranostic treatments [4–6], photodynamic therapy (PDT) [7,8], nanothermometry [9,10], multifunctional nano-probes [11], photochemical catalysis [12], anti-counterfeit technology [13], and photovoltaic (PV) devices [14].

Since it is free from instrument settings, the photoluminescence quantum yield (PLQY), shown in Eq. (1), is crucial for comparing between UC materials and their viability in various applications [15]:

The greatest challenges still facing UC materials are the small absorption coefficients and low PLQYs associated with lanthanide dopants [17]. Current enhancement approaches include varying particle size and crystal structure [18], selecting better host materials and optimizing the crystal field [19], utilizing plasmonic structures [20,21], adjusting dopant concentrations and combinations [22,23], employing passivation layers [24], introducing organic antennas [25], and increasing excitation irradiance by spectral concentration [26,27]. Although generally overlooked in UC devices, the efficiency of various other optical devices has been enhanced due to exploiting light scattering. Scattering in organic PV cells (OPV’s) has been used to increase the optical path length inside the solar cell, allowing for power conversion efficiency (PCE) improvements of 19% [28]. Additionally, dye-sensitised solar cells are usually thin and low absorbing and for this reason, it is important to introduce some light scattering to obtain a higher absorption [29]. Although scattering magnitudes are reduced as objects approach the nanoscale, as described by the Rayleigh scattering equation [30], NPs have also been shown to induce scattering-based optical benefits. For example, gold (Au) and silicon dioxide NPs have been used as scattering centres to improve optical absorption, resulting in power conversion efficiencies up to 8.8% in PV cells [31]. Furthermore, Rodriguez et al. showed how barium titanate and lead titanate NPs (∼50 nm) were both able to increase the second harmonic scattered signal as their concentration in solution increased [32]. Since UC has a non-linear power dependency [33], UC materials are particularly susceptible to changes in excitation power density (PD), which can be introduced via scattering. The scattering magnitude depends on the average particle size (Aps) within the media [34], particle geometry [35], RI disparity (Δn) between the particles and their encapsulant [36], and the wavelength of incident electromagnetic radiation [37,38]. Rapaport et al. investigated the optimization of bulk KY₃F₁₀:15%Yb³⁺, 2%Er³⁺ UC phosphors for emissive display applications [39]. They highlighted scattering as a key issue to optimize UC displays and examined how phosphor-encapsulant Δn affected the UC raw efficiency (total visible emitted power divided by incident pump power on the sample). Three scattering effects were clarified: (a) excitation beam backscatter limiting the number of incident photons propagating through the sample and reducing the UC raw efficiency, (b) decreasing excitation beam penetration depth restraining the number of ions involved in the UC mechanisms, and (c) altering the irradiance patterns in the sample and therefore changing the UC efficiencies. Rapaport et al. concluded that when the phosphor-encapsulant Δn was minimised in a sample, the UC was less efficient due to lower irradiance and beam scattering, despite more pump light being absorbed, when compared to a sample with a Δn mismatch at equal pump power. However, simultaneously the penetration depth was longer, and a greater input power was required to saturate the efficiency of the sample with minimised Δn.

Further study is needed to show how scattering influences the PLQY in different Aps regimes. In regards to the scattering response of materials at the nanoscale, seminal work by Noguez showed that particles have negligible scattering properties when they are 10 nm or less in size (using silver NPs) [40]. In terms of UCNPs, Kraft et al. were able to compare iPLQYs of β-NaYF₄:20%Yb³⁺, 2%Er³⁺ for particle sizes ranging from 12 nm to 43 nm [41]. It was concluded that no effects of excitation light scattering were present in relation to particle size by comparing the smallest and largest sample absorption measurements. Another report using UCNP-Au NPs nanocomposites (total radius = 20 nm), supports this argument by suggesting that absorption effects dominate the optical response as opposed to scattering effects at this scale [42].

Emission self-absorption (SA) is another effect to consider for optical device optimisation. In terms of materials doped with Er³⁺, SA occurs due to the close overlap between absorption and emission bands present in the erbium ions [17]. If a photon emitted by an ion is absorbed by another ion of the same type, it would gain an additional possibility to decay non-radiatively, resulting in an overall loss in PLQY. SA in UC materials has been previously investigated by Boccolini et al. who presented a theoretical model that detailed how SA influences UC PLQY measurements [43]. Further work by this team, led to the development of a model that combines both the nonlinear UC power dependence and losses due to SA to predict the optimal UC layer thickness, to maximise the ePLQY (minimize SA effects) for a given dopant concentration and excitation power in a (Er³⁺)-doped β-NaYF₄ UC-PV device [44]. Ultimately, it was concluded that an ideal Er³⁺ concentration was needed in the excitation volume to achieve optimal results [44]. It is important to clarify that their models were ‘scatter-free’ and the experimental data diminished scattering effects by minimising the Δn between β-NaYF₄ and the polymeric encapsulant. Therefore, any changes to the media excitation PD or SA probability, influenced by light scattering, were not considered. The attention when choosing an UC phosphor encapsulant for device applications has been driven by looking for binders with low absorption at excitation wavelengths [45]. It has often been assumed that matching the phosphor and encapsulant RI would produce optimal emission properties, by maximizing light penetration depth and sample absorption. For instance, Trupke et al. investigated the possibility of enhancing solar cell performance by exploiting UC materials, using a model with RI matched components [46]. However, Badescu et al. expanded on this model and concluded that the solar energy conversion efficiency depends on the RI of the cell and UC material due to photon flux changes between them [47].

Overall, this prompted us to investigate the effects of scattering and SA on the absorbance, PLQY, and total emission in UC materials of various size regimes. Emission analysis of micron-sized NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor (Aps = 4.2 ± 2 µm), NaYF₄:20%Yb³⁺, 3%Er³⁺ sub-micron ball-milled phosphor (Aps = 406 ± 272 nm) and nanosized NaYF₄:18%Yb³⁺, 2%Er³⁺ UCNPs (Aps = 31.8 ± 9.0 nm) was carried out under different scattering environments with the addition of computational supporting data. This study reveals prevalent ePLQY and net UC emission benefits as well as limitations due to scattering and SA, and large differences between microscale and nanoscale particle size regimes.

2. Results and discussion

2.1 Light scattering simulations

The effect of scattering on the media excitation PD is first presented via Multiphysics simulations (COMSOL), which solves Maxwell’s equations computationally using finite element methods. The Poynting vector points along the wave propagation direction and represents the power per unit area. This was therefore calculated throughout the media to acquire PD data. Similarly, the net electric field (E-field) was found by calculating the E-field amplitude at points over the geometry of interest. All PD and net E-field data was calculated over Area 1, which consisted of RI media and particles that represented NaYF₄ (with particle RI (n_p) = 1.48) [48]. Area 2 represented only similar RI media. A propagating E-field was generated at Port 1 or via a dipole emitter. In port-based simulations, the transmission could be calculated using an S-parameter (S21), which defines the power transfer relationship from Port 1 to Port 2. The simulations shown in Fig. 1(a), represent incident near-infrared (NIR) radiation (expressed by a 980 nm E-field) propagating through Area 1 containing particles in the size range 1 µm to 10 µm. The simulation geometry is presented in Fig. 1(b). The media RI (n_m) of Area 1 varied for each iteration. As shown in Fig. 1(c), when Δn = 0, a transparent solution was established and provided the smallest PD within the media. The PD within Area 1 was observed to increase as the RI disparity became greater. However, the scattering simultaneously negatively affected the beam transmission [Fig. 1(d)], as more light is redirected away from the bulk of the media, which will represent less dopants exposed to the beam deeper in the sample.

 

Fig. 1. (a) PD simulations of 980 nm E-field travelling through particles (1 µm to 10 µm) and media of various RI, (b) simulation geometry, (c) Area 1 PD vs media RI and (d) S21 vs media RI. (e) PD simulations of a dipole (540 or 660 nm) emitting through particles (1 µm to 10 µm) and various RI media, (f) simulation geometry and (g) Area 1 PD vs media RI. (h) PD simulations of a dipole (540 or 660 nm) emitting from various positions through particles (1 µm to 10 µm) and media, (i) simulation geometry and (j) Area 1 PD vs media RI.

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The simulations shown in Fig. 1(e), use similar ideas but concentrate on the effect scattering has on the UC emission (540 or 660 nm). The geometry used is shown in Fig. 1(f). The emission originates from a dipole moment, which transmits through a RI media containing NaYF₄ (1 µm to 10 µm) particles of similar random geometry and position to the first simulation. Again, n_m changes upon every iteration. The PD [Fig. 1(g)] increases as Δn between the media and particles becomes greater. This correlates to a greater average photon path length between origin and escaping the media. A longer path length translates into a higher probability of the emission becoming self-absorbed, an effect which becomes more prominent in larger scattering environments. It is important to realize then, that not only is the number of dopants in the media important as Boccolini et al. demonstrated, but the amount of scattering in the media can also alter the SA probability [44].

Similarly, if the incoming excitation is absorbed in the inner areas of the sample, the emission will have a longer path to exit the sample, as shown by simulations in Fig. 1(h), which would result in a higher SA probability. The geometry of these simulations is labelled in Fig. 1(i). Increases in PD [Fig. 1(j)] are observed as the dipole emitter location approaches the centre of the sample (n_m = 1.60).

2.2 Scattering in NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor (Aps ∼4.2 µm)

The local field effects between surface dopants and surrounding media that are responsible for changes in radiation decay rate and PLQY in UCNPs [49,50], are negligible when discussing bulk materials due to the higher core-to-surface dopant ratio. In order to demonstrate whether the PLQY of bulk UC materials was susceptible to scattering effects, commercial phosphor samples of NaYF₄:20%Yb³⁺, 3%Er³⁺ (n_p = 1.48) were embedded in various liquids that each possess negligible NIR absorption, which represented different n_m [48].

The Aps (4.2 ± 2 µm) was determined using scanning electron microscopy (SEM) analysis [Figs. 2(a) and 2(b)]. The phosphor comes as a phosphor with grains of varying size and a white colour due to the scattering. As observed in Fig. 2(c), the phosphor appears more transparent when encapsulated by Toluene (Δn = 0.017), more whitish in Hexane (Δn = 0.105) and white when in air (Δn = 0.48). This has a direct consequence when upconverting the light under 980 nm laser exposure, as can be seen in Fig. 2(d). The first vial, phosphor in air (n_m = 1), presents the green upconverted light in only a small, but intense spot. A clear distinction can be seen in the second vial, phosphor in pyridine (n_m = 1.507), where the green upconverted light appears from a larger area due to the excitation light penetrating further into the sample in addition to a greater number of excited dopants. The absorption originates due to the Yb³⁺ absorption along this wavelength range. The intensities of both green and red UC emissions are presented in Fig. 2(e). Since the excitation power remains constant, so does the number of incident photons. However, the percentage of absorbed incident photons [Fig. 2(f)], which is needed for ePLQY calculations, is calculated by subtracting the intensity of excitation light not absorbed by the sample by the intensity of excitation light when no sample is in the integrating sphere. It therefore changes due to variations in photons coming into the sample, absorbed photons and reflected photons. The highest value, 74%, was observed with toluene (n_m = 1.497), which has the closest RI match with the phosphor (n_p = 1.48) and therefore the highest level of transparency. The smallest value, 24%, occurred when the Δn was greatest, indicating that fewer particles deeper in the sample were excited due to scattering. Importantly, neither the highest ePLQY nor net emission were produced when the Δn was minimised, as commonly presumed [44,46]. Net UC emission benefited from higher RI discrepancies (Δn = 0.1379), with increases of 70.5% and 70.2% for the 540 nm and 660 nm emissions, respectively [Fig. 2(g)]. However, the higher levels of scattering, n_m = 1, resulted in a clear decrease in the net UC emission. The ePLQY, depends on both the net UC emission and overall absorption. Therefore, the highest efficiency (0.0475% for the 540 nm UC emission) is found for n_m = 1 [Fig. 2(h)]. This emerges due to less light penetrating through the sample, in combination with the energy density becoming concentrated at the front region of the material. The ePLQY is minimal when the indices are matched. Increases in ePLQY of 380% and 485% were obtained for the 540 nm and 660 nm UC emissions respectively (Δn = 0.4969). Between UC emissions, the percentage increases in net UC emission were similar however, a discrepancy in ePLQY percentage enhancements exists. This likely originates since different energy transfer mechanisms are responsible for various UC emissions. There are examples in the literature where less efficient UC mechanisms are more susceptible to enhancement techniques than others due to these differences [19].

 

Fig. 2. (a) NaYF₄:20%Yb³⁺, 3%Er³⁺ (4.2 ± 2 µm) UC phosphor particle size histogram. (b) Phosphor SEM. (c) Images of phosphor in various RI media under ambient light. (d) Images of the phosphor in various RI media under 980 nm laser excitation. (e) #Events vs media RI (510 nm to 690 nm). (f) Absorbed incident photons vs media RI (960 nm to 1000 nm). (g) Net UC emission vs media RI (510 nm to 690 nm). (h) ePLQY vs media RI (510 nm to 690 nm).

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Various scattering and SA effects are claimed to be working in conjunction to produce these observed experimental results. Comparisons to computational simulations are used to justify these claims as well as provide data for RI media of which there are no common solvents with negligible NIR absorption (n_m = 1 to 1.3). PD benefits from 980 nm excitation scattering, as shown in simulations [Fig. 1(c)], aligned with experimental observations yielding increases in both net UC emission and ePLQY. The non-linear power dependence of UC makes this effect very prominent. The simulated decrease in beam transmission through the sample [(Fig. 1(d)] is likely to be a less outstanding effect in comparison but helps to explain why the rate of this increase decreases experimentally at higher scattering media, as fewer ions are excited deeper inside the sample [Figs. 2(g) and 2(h)]. The simulation data in Figs. 1(e) and 1(g) justifies that the UC emission has a higher chance of becoming reabsorbed in higher scattering media, which will also be contributing to the observed tapering of these benefits as scattering increases further. Higher scattering media results in a greater net UC emission occurring near the front of the sample compared to closer to the centre. As the simulation results in Figs. 1(h) and 1(j) show, this emission would have a lower chance of SA. Although this benefits the observed net UC emission and ePLQY as scattering increases, this effect appears to be dwarfed by the two previous combined detrimental effects in highly scattering media. It is important to highlight that these scattering benefits to UC occurred using low excitation power densities from a Xenon lamp. This was done because, as Rapaport et al. highlighted, the maximum efficiency of UC in high scattering media is reached at lower input powers [39]. Therefore, lower scattering media will eventually saturate at higher efficiencies and brightness as the power is increased since the excitation beam has access to a greater number of dopants. Using their experimental setup, they give an example of the excitation power magnitude where a high scattering media eventually stops producing higher raw efficiencies and emission power compared to an index-matched media using KY₃F₁₀:15%Yb, 2%Er phosphor.

As MacDougall et al. clarify, the AM1.5D spectrum, at an intensity of 0.09 W/cm², is commonly used to measure terrestrial concentrator and module efficiencies [51]. They therefore recommend using this spectrum to report UC-PV research, due to the intensity required for these devices. Overall, using the data provided, we propose that scattering has the potential to benefit device performances in these types of low intensity environments. This work also allows researchers to estimate the magnitude of ePLQY and net UC emission enhancement obtainable by similarly optimizing their devices.

2.3 Scattering in sub-micron NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor (Aps ∼406 nm)

Commercial NaYF₄:20%Yb³⁺, 3%Er³⁺ (analogous to the phosphor used in Section 2.2) was ground using a high energy ball mill to analyse scattering effects in an intermediate size region. The Aps (406 ± 272 nm) was determined using SEM analysis [Figs. 3(a), 3(b)]. Additional information on the ball-milling process can be found in the experimental section. Samples were made by encapsulating the phosphor in polydimethylsiloxane (PDMS) with various particle concentrations.

By looking at the samples under ambient light, one can see the visible scattering effects becoming greater as particle mass concentration (mg/mL) increases [Fig. 3(c), upper row]. The red laser transmission images are a good reference as to how the PD dispersion pattern from a visible laser light source changes under these different scattering conditions [Fig. 3(c), upper-middle row] and using a 800 nm long pass filter, the excitation beam scattering can also be observed [Fig. 3(c), lower-middle row]. When the concentration is low, the majority of UC is emitted from the centre of the sample (at the laser focal point), however, at high concentrations, this shifts towards the front of the sample as this is where the PD is greatest due to scattering [Fig. 3(c), bottom row]. Although the sample emission still appears green to the eye, the red emission appears more intense in spectrums, as shown in Fig. 3(d), and the UC emission ratio between the two UC peaks has changed significantly compared to its bulk phosphor counterpart in the previous experiment. Although previous literature demonstrates that in UC materials, moving from bulk to the nanoscale can increase the effects of non-radiative quenching, decrease total emission intensity (as the surface-volume ratio increases), and negatively impact the efficiencies of various individual UC peaks due to radiative-decay pathway changes resulting from the ions having a different electronic environment, these differences are due to the large excitation power discrepancy between the experiments [52–54]. Although 980 nm excitation would have been ideal, the large drop in UC efficiency meant a higher power excitation laser was needed to achieve a trend in the data, which was only available as a 960 nm source. Initially, it was expected that the net UC emission would increase with higher particle concentration, in addition to the ePLQY. This was originally observed at low particle concentrations [Figs. 3(e) and 3(f)]. The significant observation was that both these parameters peaked and then decreased at higher particle concentrations. Before declining, the total net UC emission had increased by 966.6% (from 8 mg/mL to 59 mg/mL) and the total ePLQY had increased by 378.9% (from 8 mg/mL to 40 mg/mL). Similarly, as shown in Fig. 3(g), there is a positive trend in the amount of absorbed excitation light incident on the encapsulated phosphor when the particle concentration increases. To interpret this, the ideal Beer-Lambert law (linear correlation between beam transmission and molar concentration of particles due to absorption effects instead of scattering effects) was plotted [Fig. 3(h)]. The power transmission of each sample (I) and a straight beam measurement without a sample (I₀) was acquired using the data shown in Fig. 3(g). Only samples with high particle concentrations (214 mg/mL and 272 mg/mL) appear to show clear deviation from this idealized fit (the absorption coefficient was calculated to be 0.27 M^-1cm^-1). This implies that the 960 nm excitation beam during both these sample measurements was experiencing significant scattering, however, the other values obtained showed a higher linear proportionality to the sample concentration and therefore, absorption effects (compared to scattering effects).

 

Fig. 3. NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor (406 ± 272 nm) (a) SEM image and (b) particle size histogram. (c) Images of various phosphor particle concentrations in PDMS acquired under: ambient light (upper row), red laser (∼660 nm) illumination (upper middle row), 960 nm excitation with an 800 nm long pass filter in front of the camera lens (lower middle row) and 960 nm excitation (bottom row). The following parameters were plotted against particle concentration: (d) #Events (UC emissions from 500 nm to 700 nm), (e) net UC emission, (f) ePLQY, (g) absorbed incident photons, (h) Ln (I/I₀) and (i) 960 nm laser beam transmission compared to a PDMS reference.

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Overall, this suggests that the limitation observed in ePLQY was primarily due to increased SA of the UC emission due to higher particle concentration. Scattering of the 960 nm beam was prominent at higher concentrations and appeared to later decrease the rate of the decline in ePLQY however, optimal results were obtained when the SA was minimized. The laser transmission through each sample was measured [Fig. 3(i)] and experimentally supports the theory that this decline is also linked to the diminishing light penetration depth through the sample and increased scattering away from the bulk, limiting the number of ions deep within the sample that can become excited. This data aligns with literature, where prominent peak shifts in UC materials with similar composition have not been reported when their size is varied [55–57].

2.4 Scattering in NaYF₄:18%Yb³⁺, 2%Er³⁺ NP dispersions (Aps ∼31.8 nm)

An investigation was carried out to observe whether similar scattering and SA effects, that influence the emission output of bulk UC phosphor, were significant at the nanoscale. NaYF₄:18%Yb³⁺, 2%Er³⁺ UCNPs, with an Aps of 31.8 ± 9.0 nm and undoped NaYF₄ reference NPs, with an Aps of 38.8 ± 8.4 nm [Figs. 4(a) and 4(b)], were dispersed in water at various particle concentrations. Additionally, X-ray powder diffraction (XRD) data confirmed the cubic crystalline phase of the NPs [ Fig. 4(c)]. These particles had a separate dopant concentration and synthesis compared to the particles used in the previous experiments, therefore a direct emission comparison is not appropriate. By comparing straight beam measurements between the doped UCNPs and the reference undoped NaYF₄ NPs, the absorption was calculated and shown to increase linearly with particle concentration [Fig. 4(d)], as more dopants became available. The emissions were obtained for each concentration over the range of 400 nm to 700 nm [Figs. 4(e) and 4(f)]. Additionally, both the integrated UC emission [Figs. 4(g) and 4(h)] and ePLQY [Figs. 4(i) and 4(j)] increase with greater particle concentration for all UC emissions, as shown using linear fits with high correlation. This is due to a gradual increase in emission whilst the excitation beam remained constant. Following methods from other UCNP analysis techniques [58], the iPLQY was calculated using undoped NaYF₄ that was similarly diluted corresponding to the doped sample. The iPLQY data shows no clear trend with increasing concentration, therefore scattering and SA effects do not influence the UC efficiency to a measurable extent over this concentration range [Figs. 4(k) and 4(l)], which agrees with other studies [40,41].

 

Fig. 4. (a) NaYF₄:18%Yb³⁺, 2%Er³⁺ UCNPs and undoped NaYF₄ NPs size histogram with inset image of UCNPs (16.5 mg/mL) under ambient light. (b) SEM of UCNPs (left) and undoped NPs (right). (c) XRD data of UCNPs and undoped NPs, relative intensity vs 2 Theta (°). The following parameters were plotted against particle concentration: (d) Absorption, #Events in the ranges (e) 400 nm to 425 nm and (f) 500 nm to 700 nm, net UC emission for the (g) 540 nm and 660 nm UC peaks and (h) 410 nm UC peak, ePLQY for the (i) 540 nm and 660 nm UC peaks and (j) 410 nm UC peak, and finally iPLQY for the; (k) 540 nm and 660 nm UC peaks and (l) 410 nm UC peak.

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3. Conclusion

This work provides evidence of the benefits and limitations available when exploiting scattering in microscale-to-nanoscale UC materials via PLQY analysis. By inducing a moderate amount of scattering in NaYF₄:20%Yb³⁺, 3%Er³⁺ (4.2 ± 2 µm), the maximum total 540 nm and 660 nm ePLQYs were observed to increase by 380.2% and 484.8% (over the range n = 1.4969 to 1.000). The overall net UC emission enhancement was 70.5% (over the range n = 1.4969 to 1.359). This was due to a combination of effects including: excitation beam scattering that created local 980 nm PD increases within the media that positively benefited UC’s non-linear power response as well as an increase in emission generated further away from the sample center; decreasing the amount of SA in the sample. The rate of these enhancements lessened as scattering increased further due to the reduction in beam penetration depth through the sample, increased light scattering away from the bulk media, and the increase in SA probability of emission generated at the center of the sample. Measurements of ePLQY were a priority for this work to show the opportunity for UC emission enhancement from an applications point of view. Future studies characterising the iPLQY of new lanthanide-doped materials should also take consideration of the described effects. NaYF₄:20%Yb³⁺, 3%Er³⁺ (406 ± 272 nm) ball-milled phosphor showed an initial trend of both increasing net UC emission and ePLQY with increasing particle concentration as expected since the excitation power remained constant whilst the number of incident photons that could be converted into UC emission increased. Interestingly, both parameters peaked and began declining at higher concentrations. Prior to this decline, increases of 966.6% (from 8 mg/mL to 59 mg/mL) in total net UC emission and 378.9% (from 8 mg/mL to 40 mg/mL) in total ePLQY were observed. Evidence showed that the limitation was primarily due to increases in SA effects rather than changes in excitation beam scattering. In addition to this, another similar experiment found that both increasing ePLQY and net UC emission had a linear relationship with increasing concentration in NaYF₄:18%Yb³⁺, 2%Er³⁺ (average size = 31.8 ± 9.0 nm) UCNPs. The strong correlations suggested that the enlargements were primarily due to the rise in the number of dopant ions. Additionally, the iPLQY remained stagnant against concentration, further suggesting that any scattering or SA effects were minimal at this scale and over this concentration range in comparison to absorption.

In conclusion, the particle size, concentration and Δn between UC particles and their encapsulant, are all key factors which influence the observed emission output of UC materials due to scattering and SA effects. For research involving the optimisation of UC devices that require relatively low excitation PD, such as PV cells, it is suggested that they introduce a moderate amount of excitation beam scattering into their materials by creating a RI difference of Δn > 0.4969 between the UC particles and the encapsulating media in order to enhance the UC PLQY. In terms of the most important factors to consider when characterising the UC PLQY, the size of the phosphor needs to be considered first. On the nanoscale, for our parameters, UCNP iPLQYs are not affected by particle concentration, due to minimal scattering and SA effects. Unrelated to these effects, the iPLQY of UC materials increases significantly with particle size due to decreases in surface quenching mechanisms [55]. At the bulk scale, scattering and SA effects now need to be considered. A study comparing the magnitude of both effects, using UC material of identical doping, size and volume, has yet to be carried out. In the absence of parasitic effects, the ePLQY is dependent on particle density within the excitation path. Therefore, for samples with identical concentration, the sample with smaller volume should have a higher ePLQY. However, particularly at high concentrations, changing the sample volume will affect the excitation beam path due to scattering effects. Scattering causes variations in PD, SA and limits the beam penetration depth which, will influence the ePLQY. Therefore, to continue progress towards accurate UC PLQY standards, we recommended that a uniform UC material optical cuvette volume should be used between research groups when characterising UC PLQY. Additionally, transparent samples have larger penetration depths and therefore the incident beam has access to more dopants. Since the UC emission saturation is related to the number of dopants that can be excited, future work should investigate ePLQY saturation as excitation power increases in samples of various scattering. The penetration depth is a significant factor therefore, ePLQY investigation of UC samples of various thickness, when scattering is taken into consideration, would also benefit the community.

4. Experimental section

4.1 Light scattering simulations

The scattering response of micro phosphor structures enveloped in media was analysed by COMSOL Multiphysics 5.2a in the 2D electromagnetic waves frequency domain (EWFD) module. All simulations used a random Gaussian function to generate parametric curves (with connected ends) that defined the irregular shapes of the distributed particles. A random distribution algorithm was used to define the particle position and size (to a range of a few microns). Scattering boundary conditions were used to minimize unwanted back-scattering effects from side boundaries. A free triangular mesh was generated over every domain, with a maximum element size of 0.1 µm, and a minimum of 0.01 µm. The imaginary part of the RI was constantly 0 for all material properties so that absorption was absent in the calculations. Additionally, inelastic scattering (i.e., Brillouin, Raman, etc.) was not considered and is beyond the scope of these simulations. The simulations shown in Fig. 1(a), consisted of two conjoined rectangular objects (Area 1 and Area 2). Port 1 generated a transverse electric (TE) wave mode and Port 2 had a PEC slit condition active to minimize reflection. For each iteration, n_m was altered. Figure 1(e) simulations were equivalently formed, with Area 1 representing a circular geometry with similar scattering boundary conditions. No ports were present and a dipole moment (540 or 660 nm) was placed at the centre of Area 1 instead. Again, n_m was varied. Finally, simulations presented in Fig. 1(h) had similar geometry to those in Fig. 1(e) however, the dipole moment location was moved linearly across the x-axis within Area 1. As the dipole was a point source, the mesh and results were comparable in each location. Here, n_m remained constant.

4.2 PLQY measurements

An Edinburgh Instruments spectrofluorometer (FLS920), equipped with an extended red-sensitive single-photon counting photon multiplier (Hamamatsu, R2658P) detector (ERD), and liquid nitrogen-cooled NIR photon multiplier (Hamamatsu, R-5587) detector (NIRD) was used for the PLQY measurements. Samples were placed in optical vials inside an integrating sphere (Yobin Yvon) to achieve absolute PLQY measurements [55]. Long pass filters and optical density filters were used to block second order effects and prevent detector over-saturation, respectively. Sample images throughout the paper were taken with an iPhone 6 rear camera (8 MP, f/2.2, standard). NIR scattering images were taken with the iPhone 6 front camera (1.2 MP, f/2.2, standard) with an 800 nm long pass filter (IR-80, square 50.8 mm, by Edmond Optics) in front of the lens.

PLQYs of NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphors (Aps = 4.2 ± 2 µm) were calculated using the ERD to measure sample emission and NIRD for sample absorption. A Xenon lamp was used for excitation (centred at 980 nm), with excitation and emission slits set to 22 nm, a 1200 excitation grating, an emission and straight beam measurement step of λ = 0.5 nm and a PD at the focal point of 1 W/cm².

PLQYs of high energy ball-milled NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphors (Aps = 406 ± 272 nm) were obtained using the ERD to measure both sample emission and absorption. A 960 nm laser (DS3-11322-112, BWT, Beijing) was used for excitation. The emission slits were 22 nm and a step size of λ = 2 nm was used for the emission and straight beam measurements. The laser provided an excitation PD of 939 W/cm². Each emission and absorption measurement was taken 3 times and the mean was calculated. The standard deviation of these values was used to define the error bars. For each PLQY measurement, the sample was removed and replaced, this allowed a different side of the sample to be exposed to the excitation beam in each occasion to include errors from possible non-uniform particle distribution. Transmission data was obtained by placing the samples at the laser beam’s focal point (integration sphere removed) and placing a power detector (S121C, 400 nm to 1100 nm, Thor Labs) connected to a power meter (PM100D, Thor Labs) directly behind them.

PLQYs of NaYF₄:18%Yb³⁺, 2%Er³⁺ UCNPs (Aps = 31.8 ± 9.0 nm) were determined using the ERD to measure sample emission and NIRD for sample absorption. The slits were 3.5 nm and the step size used was λ = 0.5 nm (emission) and λ = 0.2 nm (excitation). A 3W, 980 nm laser diode (LSR-PS-II, LSR980NL-3W, by Lasever Inc.) was used for excitation with a PD of 753.08 W/cm².

4.3 Sample synthesis and preparation

Commercial bulk NaYF₄:20%Yb³⁺, 3%Er³⁺ UC phosphor was obtained from Sigma Aldrich and information on the UC mechanisms in similar Yb³⁺/Er^3+-doped phosphors are available in the literature [59]. The Aps was analysed using SEM analysis (Raith, PIONEER). Optical glass cuvettes (8 mm outer diameter) were filled with the NaYF₄:20%Yb³⁺, 3%Er³⁺ UC phosphor. Then, 0.4 mL of solvent was added to each vial, which is enough to impregnate all the phosphor without resulting in excess. The selection of solvents was intended to target a wide RI spread, whilst maintaining a low or inexistent absorption at 980 nm. ePLQY measurements on each sample were then carried out. In addition to air, the various RI media were created using the following solvents: ethanol, hexane, tetrahydrofuran, cyclo-hexane, cyclopentanone, chloroform, carbon tetrachloride, toluene and pyridine. The RI of these solvents can be found in the literature [60].

Of the commercial NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor mentioned above, sub-micron particles were achieved after a long period of repetitive high energy wet ball-milling (Pulverisette 7, Fritsch GmbH). The mill rotates two chambers simultaneously. Each 12 mL Zirconia chamber contained 0.5 mm Zirconia beads (20 g), 2 g NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor and 6 mL of water. The chambers were rotated at 800 RPM for 15 min, allowing for 5 min pauses before a 15 min rotation in the opposite direction. This process was repeated for a total time of 26 h including breaks. PDMS (Sylgard 184, Dowsil) was used as the encapsulant polymer for ball-milled NaYF₄:20%Yb³⁺, 3%Er³⁺ phosphor as it is easy to prepare and has low absorption in the visible and NIR regions [61–63]. Proceeding the milling, the sample was washed from the container walls using water and separated from the Zirconia beads using a metal filter. The phosphor was then dried in an oven (120 °C). After the water had evaporated, the phosphor was weighed and then dispersed in ethanol to achieve a known concentration. Different volumes of ball-milled phosphor in ethanol were pipetted on top of 1 mL of silicone elastomer, which resultantly formed an immiscible layer. The ethanol, which has a boiling point of 78.37 °C [60], was evaporated by using a high energy sonication needle (CL-18, Fisher Scientific), which was measured to reach temperatures >90 °C when operated at maximum input power using a thermistor. Therefore, the sonication needle simultaneously satisfied the objectives of dispersing the phosphor throughout the sample, removed bubbles originating from the mixing process and evaporated off the unwanted ethanol. Afterwards, 0.1 mL of curing agent (Sylgard 184, Dowsil) was added to each sample to achieve a silicone elastomer and curing agent volume ratio of 10:1. The samples were then moved to a 40 °C bath to accelerate polymerization and minimize sedimentation before being left overnight (15 h).

The synthesis of the acetate-capped NaYF₄:18%Yb³⁺, 2%Er³⁺ UCNPs was carried out using a similar procedure reported by Panov et al. [64]. A polyacrylic acid (PAA) surface-healing procedure was also carried out, which will be later discussed. Synthesis of Yb³⁺(18%) and Er³⁺(2%) co-doped NaYF₄ NPs was accomplished via the following procedure. A total of 1.0 mmol of the respective RECl₃ (RE – rare-earth metal) precursor mixture (0.8 mmol YCl₃, 0.18 mmol YbCl₃, and 0.02 mmol ErCl₃) was prepared by dissolving a total of 0.5 mmol of the corresponding RE₂O₃ constituents (0.4 mmol Y₂O₃, 0.09 mmol Yb₂O₃, and 0.01 mmol Er₂O₃) in a 3:2 v/v (mL) mixture of concentrated HCl and H₂O at 90 °C. After complete dissolution of RE₂O₃, the HCl/H₂O was evaporated at 100 °C to obtain dry RECl₃. Subsequently, a separate mixture was prepared by combining and vortexing, in the specified order of reagents, 4.3 mmol (172.0 mg) of NaOH, 2 mL of deionized H₂O, 2 mL of AcOH, 8 mL of ethanol, and 4.0 mmol (148.2 mg) of NH₄F. The resulting opaque mixture was then added to the dry RECl₃ salts, and the new mixture was vigorously stirred at room temperature for approximately 10 min. 11 mL of this final reaction mixture was transferred to a 35 mL glass microwave reaction vessel and inserted into a CEM Discover SP microwave reactor. The nanoparticles were grown at 200 °C for 10 min after an initial temperature spike to 210 °C. Following reaction completion, the obtained particle dispersion was transferred to a centrifuge tube, diluted to 25 mL with ethanol and centrifuged (Allegra X-30R, Beckman Coulter) for 5 min at 3,000 rpm (average RCF = 625). The supernatant liquid was decanted and the remaining white particle pellet was washed twice by means of re-dispersion in a 35 mL 3:7 v/v H₂O: ethanol mixture and subsequent centrifugation. Lastly, the washed product was re-dispersed in 7 mL of ethanol for storage. Healing of the acetate-capped NaYF₄:18%Yb³⁺, 2%Er³⁺ NPs with PAA was carried out to increase the stability of the NP dispersion in water. After dispersing 70 mg of dry NaYF₄:18%Yb³⁺, 2%Er³⁺ nanoparticle powder in 5 mL of H₂O, 180 mg of PAA was added. The pH of the solution was adjusted to 7.5 by adding ca. 4 mL of 0.5M NaOH. The resulting solution was stirred for 48 h at room temperature. Afterward, the solution was briefly sonicated and passed through a micro-mesh filter (EZFlow Syringe Filter, d = 13 mm, pore size = 0.22 µm) to get rid of the large nanoparticle agglomerates. The filtered, stable nanoparticle dispersion was stored in water. To investigate scattering, 1 mL of UCNPs with a known concentration was pipetted into a glass optical vial (4 mL volume). The appropriate measurements and pictures were taken before both the doped and undoped samples were diluted. The volume was kept constant after dilution by removing 1 mL of each NP solution and placing each into a new optical vial. The process was then repeated for the full particle concentration range (16.5 to 9.57 mg/mL). The crystalline phase of the NP samples was determined by powder X-ray diffraction (XRD) with a Rigaku Ultima IV diffractometer (Cu Kα, λ = 1.5401 Å). The morphology and size distribution were investigated by transmission electron microscopy (TEM, FEI Tecnai Spirit). For TEM observations, samples were dispersed on a Formvar/carbon film supported on a 300 mesh copper grid. By analysing 248 particles with the ImageJ software, the UCNP size distribution was determined to be 31.9 ± 9.0 nm and by analysing 154 particles, the undoped NP size distribution was found to be 38.8 ± 8.4 nm.