1. Introduction

Photon upconversion (UC) in trivalent erbium (Er³⁺) ion-doped materials is a striking feature for a number of technological applications, such as solid state lasers [1], optical amplifiers [2], light-emitting displays [3], biolabels [4] and photovoltaics (PV) [5]. This wide range of applications originates from the UC property of absorbing two photons and emitting one higher energy photon due to energy transfer (ET) between the excited Er³⁺ ions [6, 7].

Shalav et al. first proposed the use of UC in order to overcome the so-called Shockley-Queisser limit, which defines an upper limit on the efficiency of a PV device [8]. Later, authors from the same group pioneered the research in harvesting the spectral conversion properties provided by a Er³⁺-based UC luminescent layer coupled to a bifacial silicon PV cell (UC-PV device)[9, 10]. In an Er³⁺-based UC-PV device an additional photocurrent is generated by using part of the near-infrared (NIR) solar spectrum, which would not otherwise be harvested in a standard silicon solar cell.

Figure 1 shows the typical design of a Er³⁺-based UC-PV device in which IR sub-bandgap photons with wavelength at around 1500 nm (∼0.8 eV) are absorbed and converted by an UC layer underneath a bifacial solar cell. The UC process populates the ⁴I_9/2 level, which relaxes to the lower ⁴I_11/2 level. Due to the transition ⁴I_11/2 → ⁴I_15/2, the resulting emission at around 980 nm (∼1.2 eV) is finally absorbed and converted into electricity by the silicon solar cell (bandgap energy ∼1.1 eV).

 

Fig. 1 Two sub-bandgap photons are converted into a higher energy photon by an UC layer placed underneath a bifacial solar cell. The pump energy scheme within Er³⁺ ions of the ⁴I_13/2 level shows how the UC process populates the ⁴I_9/2 level and consequently to the lower ⁴I_11/2 due to fast decay. The radiative decay to the ground state from this level leads to an emission characterized by two main peaks centered at 977 nm and 1005 nm, corresponding to photon energies just above the silicon bandgap E_g. The lifetimes values reported have been measured in our lab.

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Recent theoretical studies based on a detailed-balance approach have predicted that an ideal Er³⁺-based UC-PV device could reach up to 7% relative increase with respect to the efficiency of a silicon solar cell, which in terms of absolute efficiency corresponds to an increase from 25.95% to 27.88% under non concentrated sunlight and from 36.61 % to 39.43 % at the thermodynamic limit of concentration (46200 suns) [11]. The concept of ideal UC refers to a system which totally absorbs the exciting radiation and converts exactly two photons into one higher energy photon. Therefore an ideal UC corresponds to a system absorbing 100% of the incident radiation and having an internal photoluminescence quantum yield (iPLQY) of 50%, or equivalently to a system showing an external photoluminescence quantum yield (ePLQY) of 50%. Where ePLQY and iPLQY are defined as the ratio of incident (or absorbed) photons over the emitted ones, respectively.

Experimentally, the highest iPLQY of 12±1 % (ePLQY~5.5%) was reported by Martin-Rodriguez et al. in a gadolinium oxysulfide host (Gd₂O₂S:10%Er³⁺) under monochromatic excitation at 1500 nm with an irradiance of 0.07 Wcm⁻² [12]. Fischer et al. reached the highest ePLQY value of 9.5±0.7 (iPLQY= 10.1±1.6 %) for monochromatic excitation at 1520 nm with an irradiance of 0.47±0.25 Wcm⁻² employing a BaY₂F₈:30% Er³⁺ doped upconverter [13]. Under broadband excitation the highest iPLQY of 16.2±0.5 % (ePLQY = 3.4±0.1 %) was reported by MacDougall et al. in a sodium yttrium fluoride (β -NaYF₄: 10% Er³⁺) UC material centered at 1523 nm, 80 nm bandwidth and irradiance of 227±10 Wcm⁻² [14], even though it was later noted to be over-estimated [15]

Although recent progress has shown overall increase of both iPLQY and ePLQY, those values are still far from demonstrating a substantial benefit of UC when applied to silicon PV devices. The above mentioned results also show a significant difference between ePLQY and iPLQY values among Gd₂O₂S and β -NaYF₄. The two hosts are in fact affected by a considerable amount of scattering which reduces the absorption of the incoming light. Consequently, it is common to achieve high iPLQY values which corresponds to low ePLQY values, and the other way around [16]. However in the BaY₂F₈ sample scattering does not represent a limiting factor due to the possibility of synthesizing it in bulk crystalline form, as demonstrated by the small difference between ePLQY and iPLQY reported in [13].

The Er³⁺ concentration in the host plays a key role. A higher concentration decreases the average distance between the Er³⁺ ions which leads to higher probability of ET among these ions, but at the same time this enhances the probability of non-radiative cross-relaxation mechanisms [17]. Ways of limiting these losses have been extensively studied in literature and have been mainly focused on the search of low phonon energy hosts, synthesis of UC nanoparticles and optimization of the Er³⁺ ion doping level [16, 18, 19].

The aim of our experimental study is to analyze the UC luminescent properties of BaY₂F₈ samples under different monochromatic excitation wavelengths as a function of Er³⁺ concentrations and thicknesses. In particular we will show how the ePLQY and iPLQY can be optimized via minimization of self-absorption, a loss mechanism whose effect on a UC-PV device has been only theorized by the same author [21], and which is now experimentally demonstrated for the first time in a UC material.

2. Materials and method

2.1. Crystal synthesis

Er³⁺ doped BaY₂F₈ single crystal samples were grown by the Czochralski method in a concentration of 10at%, 20at% and 30at% using a self-made furnace developed by Physics Department Laboratories in Pisa. Growth powders with 99.999% purity level were used in order to avoid contamination affecting the optical quality of the crystals. Vacuum condition of 10⁻⁷ mBar and high-purity (99.999%) argon atmosphere were established before and during the growth process. A temperature of 972 °C, pulling rate 0.5 mm/h, rotation rate 5 rpm were used as growth parameters. After the growth, X-ray backscattering Laue diffractometry has been performed to check the crystallinity. Finally, the resulting crystals were cut and optically polished using a colloidal alumina (Al₂O₃) slurry consisting in 1 μm particles suspended in deionized water.

The samples prepared were: three samples of 10%Er:BaY₂F₈ with thickness (1.05±0.01) mm, (1.41±0.01) mm and (2.00±0.01) mm, three samples of 20%Er:BaY₂F₈ with thickness (0.49±0.01) mm, (1.25±0.01) mm and (2.05±0.01) mm and two samples of 30%Er:BaY₂F₈ with thickness (1.76±0.01) mm and (2.33±0.01) mm.

2.2. Characterization

All spectroscopic measurements were carried out at room temperature (296 K). Absorption spectra in the NIR range of 950–1650 nm were measured with a spectrophotometer (Perkin-Elmer, Lambda 950) using a resolution of 0.5 nm. Fluorescence spectra were obtained using a calibrated spectrofluorometer (Edinburgh Instruments, FLS920) equipped with a NIR tunable laser (HP-Agilent, 8168-F) and a liquid nitrogen cooled NIR photo-multiplier tube (Hamamatsu, R5509-72). The laser tunability covers the range 1450–1590 nm. The laser beam was coupled into a optical fiber, collimated and then focused to the sample through a 50 mm focal length lens.

As shown in Fig. 2, ePLQY and iPLQY measurements were performed with the upconverting samples placed in a holder at the center of an integrating sphere (Jobin-Yvon). The sample holder had one hole of 3 mm diameter to allow the incident pump to enter and another one on the opposite side to allow the luminescence to exit. The uncertainty for the calibrated data is ±3% and the measurement accuracy on the ePLQY and iPLQY measurements is 10% [15].

 

Fig. 2 Experimental setups used for photoluminescence measurements, with (a) and without (b) integrating sphere.

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3. Results and discussion

3.1. BaY₂F₈ crystal absorption

The absorption spectra of the Er³⁺ doped BaY₂F₈ crystal measured for three different Er³⁺ doping level (10%, 20% and 30%) are shown in Fig. 3. The spectra, corresponding to the excitation of the ⁴I_13/2 level from the ground state level ⁴I_15/2, extend over the range 1400–1650 nm. All three Er³⁺ doping levels present a similar distribution: the highest peak centered at 1493 nm, more peaks with a lower absorption coefficient distributed between 1520–1540 nm and an absorption tail extending up to 1650 nm.

 

Fig. 3 Absorption coefficient spectra in the range 1400–1650 nm of the investigated Er³⁺ doped BaY₂F₈ crystals for doping levels of 10%, 20% and 30%. The green dot-dashed curve represents the ⁴I_11/2 → 4I_15/2 excitation spectrum in the range 1450–1590 nm (λ_emission = 977 nm) relative to a BaY₂F8:20% Er³⁺ sample. All spectra have been measured at room temperature (296K).

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The Er³⁺ absorption in BaY₂F₈ host result much stronger comparing to β -NaYF₄ host. A 20% Er³⁺ doped β -NaYF₄ has its highest absorption peak at around 1523 nm with a value of 5.5 cm⁻¹ [20], whereas a BaY₂F₈ with the same doping level (20% Er³⁺) has an absorption coefficient of 14.5 cm⁻¹ at 1524 nm and it reaches 25 cm⁻¹ at 1493 nm. As discussed previously, this difference is attributed to the negligible scattering by BaY₂F₈ crystal. Even if there are no record in literature of absorption coefficients values relative to Gd₂O₂S host, we suppose that also in this case the amount of scattering due to its microcrystalline nature reduces the absorption to lower levels respect to BaY₂F₈. The absorption coefficient values for different Er³⁺ doping levels in BaY₂F₈ and at three different wavelengths (1493 nm, 1524 nm and 1556 nm) have been reported in Table 1. The selected wavelengths correspond to the excitations used in this work for the ePLQY and iPLQY determination presented in section 3.2 and we will refer to those values later in the discussion.

Table 1. Absorption coefficients relative to three different Er³⁺ concentration and at different wavelengths.

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Figure 3 also displays the excitation spectrum relative to a BaY₂F₈:20%Er³⁺ sample, which has been carried out tuning the laser excitation wavelength within the interval 1450–1590 nm (the maximum allowed by the tunable laser) and providing a constant power of 2.00±0.06 mW at each achievable wavelengths. Its value is proportional to the emission intensity at 977 nm associated with the transition ⁴I_11/2→⁴I_15/2.

The highest peak of the excitation spectrum coincides with the highest absorption peak centered at 1493nm, however in the excitation spectrum the peak results in a much wider profile. This effect can be ascribed to a saturation effects caused by the high absorbance of the sample. It is important to stress the fact that the UC is a non-linear process which strongly depends on the energy density of the exciting radiation. The radiation provided by the Sun in the NIR range would not be sufficient to enhance the UC process unless it is concentrated. This means that a UC-PV device would require to work in combination with a concentrating PV system. Thus, the available solar radiation for such a technology corresponds to the standard solar spectrum called air mass coefficient 1.5 direct (AM1.5D), which corresponds to the average direct component of the solar irradiance at mid-latitudes at a zenith angle of 48.2 degrees.

In Fig. 4 we compare the solar spectrum AM1.5D and the optical density of a 30% Er³⁺ doped BaY₂F₈ crystal extending in the wavelength interval of 1400–1650 nm.

 

Fig. 4 Comparison of solar spectrum AM1.5D (yellow area) and a 1.73 mm thickness BaY₂F₈:30%Er³⁺ optical density (blue patterned area) in the range 1400–1650 nm. The dotted black line represents the total solar photons absorbed by the sample.

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According to Fig. 4, although NIR photons are provided by the Sun through the whole absorption window of the UC material, their distribution over this region results non-uniform. The amount of solar flux at sea level is reasonably constant only in the region between 1500 and 1650 nm with a value around 2⋅10¹⁸ m⁻²s⁻¹nm⁻¹. However, below 1500 nm the solar flux drops distinctly towards zero due to water vapor absorption in the atmosphere [22]. As a consequence, the highest absorption peak around 1493 nm corresponds to an amount of solar flux which is 25% less respect to the average value at longer wavelengths.

Due to the non optimal matching between the UC material absorption and the solar spectrum an UC-PV device would require a thick UC layer (order of mm) to absorbs most of the NIR radiation. In the next section we will show instead that thinner samples considerably reduce losses due to self-absorption and provide higher PLQYs. The absorbed solar photons by the sample achieving the best performances in terms of ePLQY (BaY₂F₈:30%Er³⁺ 1.76 mm thick) has been calculate using the absorbance and the AM1.5D spectrum. The UC sample would absorb only 45% of the total solar flux when considering the wavelength interval 1400–1650 nm. The percentage of absorbed solar photons would increase up to 87 % if the integration is reduced to the interval 1470–1540 nm.

3.2. Photoluminescence measurements

The NIR photoluminescence of Er³⁺ doped BaY₂F₈ was measured according to the pumping scheme of Fig. 1. The emission spectra of all samples were recorded under two different experimental situations, namely with and without integrating sphere (see Fig. 2). The measurement without the integrating sphere was set up such that the excitation beam was focused near the edge of the sample and the emission was collected perpendicularly from the adjacent side. This was done by using a mask with an entrance hole for the pump and another one for the collection. The mask also avoided the collection of photons emitted from other parts of the sample. By doing so, the length covered inside the sample by the detected photons was reduced, and consequently the probability of incurring in a self-absorption loss was minimized. For this reason we assume that the photoluminescence spectra measured without using the integrating sphere are not affected by self-absorption.

The obtained photoluminescence spectrum without using the integrating sphere measured under 1493 nm excitation of BaY₂F₈:20%Er³⁺, relative to the transition ⁴I_11/2→⁴I_15/2, and the ground state absorption spectrum of the same material, corresponding to the opposite process (⁴I_15/2→⁴I_11/2), are compared in Fig. 5.

 

Fig. 5 Comparison of emission spectrum (measured without integrating sphere) relative to the transition ⁴I_11/2→⁴I_15/2 measured under 1493 nm excitation of BaY₂F₈:20%Er³⁺ (black solid line) and ground state absorption spectrum of the same material (blue patterned area) in the range 950–1050 nm.

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The photoluminescence presented Fig. 5 is characterized by an emission distributed over two separated region, one between 965–985 nm and the other in the interval 985–1020 nm. The region of shorter wavelengths originates from the radiative decay of electrons populating the lower levels of the ⁴I_11/2 manifold to the ground state, while the region of longer wavelengths is due to the radiative decay of electrons populating the highest levels of the same manifold, as represented in Fig. 1.

The ground state absorption spectra strongly overlap the emission spectrum in the interval 965–985 nm. At longer wavelengths there is still a weak absorption by Er³⁺ ions as the measurements were performed at room temperature. Hence, some of higher states at the top band of the manifold 4I_15/2 are populated by thermal excitation (kT ≃ 205 cm⁻¹ when T = 296K) increasing the probability of absorption not only from the exact ground state but from the whole manifold 4I_15/2.

Another key point emerging from Fig. 5 is that the emission at 977 nm reaches a peak intensity 1.5 times higher than the one centered around 1000 nm. In the following discussion we will show that, when the sample are measured using an integrating sphere, the emission peak intensities will change drastically due to the self-absorption affecting mainly the region around 977 nm.

3.3. ePLQY and iPLQY measurements

The ePLQY and iPLQY measurements were performed on Er³⁺ doped BaY₂F₈ crystals using the integrating sphere setup as described in section 2.2. All samples have been tested under the same excitation conditions. The focused beam size was measured using the 20/80 knife-edge scan technique [23, 24], resulting for each excitation wavelength in a spot diameter of (0.30±0.01) mm and a beam area of (7.1±0.5)⋅10⁻⁴ cm². A maximum power of 5.0±0.2 mW was achievable at each of the chosen wavelengths from the tunable laser, corresponding to a maximum irradiance of 7.0±0.7 Wcm⁻².

Figure 6 shows the NIR photoluminescence spectra measured for 3 different excitation wavelengths, 1556 nm, 1524 nm and 1493 nm, corresponding to increasing absorption coefficient (see Table 1 for their values). Each subplot (Figs. 6(a)–6(i)) corresponds to a particular excitation wavelength and a specific Er³⁺ doping level, and it contains the photoluminescence spectra measured for all different thicknesses available.

 

Fig. 6 NIR photoluminescence spectra measured for 3 different excitations wavelengths: 1556 nm, 1524 nm and 1493 nm. Each subplot corresponds to a particular excitation wavelength and Er³⁺ doping level, and each one contains the emission spectra measured for different thicknesses (green-dotted for the thinner sample, blue-solid for the thicker, and red-dashed for the middle thickness, when present). All spectra have been measured using the integrating sphere setup.

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The area underneath each spectrum represents the overall flux of emitted photons with wavelength between 900 nm and 1100 nm which is directly proportional to the ePLQY of the samples, whose values are reported in Table 2. As previously anticipated, a common feature to all spectra reported in Fig. 6 is the substantial difference in the peak distribution respect to the emission spectrum measured without integrating sphere presented in Fig. 5. For each spectrum the highest peak is now centered around 1005 nm, while the peak centered at 977 nm is affected by a drastic reduction in intensity, which is the peak where the overlap between absorption and emission spectra is stronger.

Table 2. ePLQY and iPLQY (in brackets) values measured for all investigated samples and corresponding to 3 different excitation wavelenghts: 1556 nm, 1524 nm and 1493 nm. All measures are affected by a relative error of 10%. The highest ePLQY and iPLQY values are highlighted in bold.

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From a closer look to Figs. 6(d)–6(f) (spectra relative to BaY₂F₈:20%Er³⁺ samples), an interesting effect is also observed. The ePLQY changes drastically within different thicknesses and different excitation wavelengths. It can be noticed that for 1556 nm excitation the thicker sample (2.05 mm) gives the highest ePLQY. Exciting at 1524 nm the same sample is now the second best, while at 1493 nm excitation is the lowest.

The existence of an optimal thickness depending on the excitation pump together with the drastic reduction of the emission around 977 nm suggest that self-absorption has a huge impact on the ePLQY of the UC material. The optimal thickness variation with different excitations is related to the fact that the absorption coefficient varies depending on the pump wavelength and Er³⁺ concentration. A higher absorption coefficient is equivalent to a high attenuation of the pump beam, meaning that most of the UC luminescence is originating from the ions present in the first hundreds of μm. In the case of 1493 nm excitation in a 20%Er³⁺ sample the absorption coefficient is 25 cm⁻¹, which means that at least 63% of the radiation is absorbed after 0.40 mm. Therefore, samples thicker than this value will increase the absorption but also the probability of incurring in self-absorption. In the case of 1556 nm excitation where the absorption coefficient results 3.9 cm⁻¹, the same amount of pump absorption is reached after 2.56 mm. This explain why the 20%Er³⁺ sample of thickness 2.05mm had the highest ePLQY at 1556 nm but the lowest at 1493 nm. An analytical model which describe more in detail how self-absorption and optimal thickness are related was presented in the case of a downconverter material in [25].

A similar behavior can be observed also for the 10%Er³⁺ samples (see Figs. 6(a)–6(c)), while for the 30%Er³⁺ samples (Figs. 6(g)–6(i)) the only appreciable effect is the increased emission at shorter wavelengths for the thinner sample, sugesting that probably we were too far from finding an optimal thickness in this case. However, the BaY₂F₈:30%Er³⁺ samples (1.76 mm thick) reached the highest ePLQY of 12.1±1.2 % for excitation at 1493 nm, corresponding to a iPLQY value of 12.4%, which instead is not the highest overall.

The absolute highest iPLQY value has been observed in the BaY₂F₈:20%Er³⁺ of thickness 0.49 mm reaching the value of 14.6±1.5 %, which correspond to a ePLQY of 10.1±1.0 %. We suppose that highest iPLQY values are achievable using thinner BaY₂F₈:30%Er³⁺ samples, but in our work it was not possible due to unavailability of material.

3.4. Estimation of self-absorption losses

An experimental method to quantitatively estimate the amount of losses due to self-absorption is presented in this section. In order to do so, each spectrum measured at a given excitation and given Er³⁺ concentration has been normalized such to equalize the emission value at 1020 nm. The choice of this specific wavelength has been done referring to Fig. 5. The wavelength 1020 nm correspond to a spectral region in which the absorption coefficient is nearly absent (less than 0.1 cm⁻¹ for each concentration) but a considerable amount of emission is still present. Therefore, all the emitted photons at 1020 nm and longer than this value are in a ”self-absorption free” spectral region and its shape will not be affected by this loss mechanism.

This method has been already used by Ahn et al. [26] and Wilson et al. [27] to correct luminescence emission spectra in organic dyes from self-absorption losses. Applying the normalization to all measured spectra of Fig. 6 we obtain a new set of plots, which are represented in Fig. 7.

 

Fig. 7 Normalized NIR photoluminescence spectra measured for 3 different excitations wavelengths: 1556 nm, 1524 nm and 1493 nm. Each subplot corresponds to a particular excitation wavelength and Er³⁺ doping level, and each one contains the normalized emission spectra measured for different thicknesses (green-dotted for the thinner sample, blue-solid for the thicker, and red-dashed for the middle thickness, when present).

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According to Fig. 7, without any exception, the emission at shorter wavelengths (around 977 nm) tends to increase his ratio respect to the longer wavelengths region (around 1005 nm) as the sample get thinner. As an example, in Figs. 7(d)–7(f) the emission around 1005 nm for the 2.05 mm sample is always much greater than the other, while in the 0.49 mm sample the two peaks intensity are almost equal. Hence, the ratio approaches the unity, which is still lower than the value of 1.5 calculated from Fig. 5, which represents a measurement not affected by self-absorption losses. Moreover, the total intensity, which is in this case related to the iPLQY, is also increasing in thinner samples. On the whole, the measured spectra displayed in Fig. 7 indicates that using thinner samples the losses due to self-absorption can be reduced, but not completely eliminated.

Using the same normalization method we compare the emission spectra of the thinner samples for each Er³⁺ doping level (measured in the integrating sphere) with the emission measured without the integrating sphere, for which the self-absorption losses can be neglected. The results are shown in Fig. 8, and the percentage of losses due to self-absorption has been estimated from the ratio of the total areas. Estimated losses of 47%, 30% and 51% have been calculated for 10%Er³⁺, 20%Er³⁺ and 30%Er³⁺ samples, respectively.

 

Fig. 8 Estimated losses due to self-absorption comparing the integrated emission spectra measured in the integrating sphere (black solid line and white area) and without integrating sphere (black dash line and red area). The losses and the iPLQY limit estimation refer to the highest iPLQY samples investigated: BaY₂F₈:10%Er (1.05 mm), BaY₂F₈:20%Er (0.49 mm) and BaY₂F₈:30%Er (1.76 mm).

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Finally, correcting the measured iPLQY of the thinner samples (see Table 2) for the estimated losses we can derive the iPLQY limit (self-absorption losses equal to zero) for each concentration. iPLQY limit values resulted from the correction are in the range of 13–19 %, 17–25 % and 20–30 %, for 10%Er³⁺, 20%Er³⁺ and 30%Er³⁺ doping level, respectively.

The normalisation has been tested also for wavelengths longer than 1020 nm up to 1050 nm to verify that our results are not affected by our particular selection. We found that the resulting normalization factors at each wavelength move away from the one calculated at 1020 nm with a relative error less than 5%. The 5% relative error due to the normalization has been taken into account when estimating the losses, resulting in a final relative error of 20%.

It results that in order to entirely remove self-absorption the sample as to be as thin as possible, but it is evident that this extreme case would reduce the pump absorption producing low ePLQY values. The finding of an optimal thickness provides the right balance between the absorption at the excitation wavelength and the minimization of self-absorption losses, but this is not enough to eliminate completely those losses.

4. Conclusions

In summary, we presented measurements of iPLQY and ePLQY of a Er³⁺ doped BaY₂F₈ crystal, in order to evaluate its potential for photovoltaics applications. The highest ePLQY measured in this study was 12.1±1.2 % for a BaY₂F₈:30at%Er³⁺ sample of thickness 1.75±0.01 mm, while the highest iPLQY corresponding to 14.6±1.5 % was measured in a BaY₂F₈:20at%Er³⁺ sample with a thickness of 0.49±0.01 mm. Both values were obtained under excitation at 1493 nm and an irradiance of 7.0±0.7 Wcm⁻². The reported iPLQY and ePLQY values are among the highest achieved in the case of a monochromatic excitation.

We also demonstrated that a optimal thickness exists for different cases depending on both the Er³⁺ concentration and the excitation wavelength in order to maximize the ePLQY, showing that losses due to self-absorption are substantially high. Those losses have been estimated through a normalization method in order to evaluate the maximum iPLQY achievable by the UC materials. The estimated iPLQY limit values were ∼16%, ∼21% and ∼25%, for 10%, 20% and 30% Er³⁺ doping level, respectively.

The outcome of this study suggests that thinner 30% Er³⁺ samples might produce iPLQY values up to 30%. Despite of this, achieving such a value requires the use of very thin samples with low absorbance resulting in ePLQY values more likely closer to 20%. However, as predicted by the same author in [21], the reflective layer present in a UC-PV device (see Fig. 1) could increase the pump absorption and reduce the self-absorption losses achieving higher ePLQYs respect to the one we can measure through photoluminescence measurements.

Another strategy that the authors suggest in order to increase the absorption would be to fabricate higher doped Er³⁺ samples, as from our study it is not clear what is the optimal Er³⁺ doping level to be used. Nevertheless, a higher Er³⁺ concentration will increase the probability for an emitted photon to be reabsorbed, or to incur into additional non-radiative losses like cross-relaxation.