Glass ceramics for frequency conversion

CHAPTER ELEVEN

Glass ceramics for frequency conversion Andrea Chiappini1, Lidia Zur1, Francesco Enrichi2, Brigitte Boulard3, Anna Lukowiak4, Giancarlo C. Righini5, Maurizio Ferrari1, 5 1

IFN-CNR CSMFO Lab. and FBK Photonics Unit, Povo-Trento, Italy Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Venice, Italy IMMM UMR CNRS 6283, Le Mans Université, Le Mans, France 4 Institute of Low Temperature and Structure Research, PAS, Wroclaw, Poland 5 Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Rome, Italy 2 3

11.1 Introduction Frequency conversion is an important mechanism driving the relaxation dynamics in rare earth doped materials with lots of applications in photonics. Among them, photovoltaics is one of the preeminent ones. The key is to control the absorption of the solar radiation, by shifting the unabsorbed wavelengths toward 980 nm, i.e., close to the band gap of crystalline silicon. It is recognized that glass ceramic systems are crucial for the tailoring of energy transfer mechanism [1e3]. In this chapter, we introduce the transparent glass ceramics and some highlights extracted from the current literature on frequency converters. The second section presents the fundamentals of the energy transfer process between rare earth ions. In the third section, an overview is presented on the use of rare eartheactivated luminescent materials in solar spectrum conversion, focusing the attention on the different couples of lanthanide ions, the host materials, and the quantum cutting mechanism that allow to properly choose the doping ions and therefore to improve the quantum efficiency. The specific role played by the host material is also discussed. Finally, the case study of Tb3þ/Yb3þ glass ceramic silica-hafnia is used to discuss linear and nonlinear energy transfer mechanisms as a function of the rare earth ions concentration.

11.1.1 Transparent glass ceramics Glass ceramics are nanocomposite materials exhibiting physical and chemical properties crucial in a broad spectrum of applications [4e6], especially in Solar Cells and Light Management ISBN: 978-0-08-102762-2 https://doi.org/10.1016/B978-0-08-102762-2.00011-2

© 2020 Elsevier Ltd. All rights reserved.

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Figure 11.1 High-resolution transmission electron microscopy image of a glass ceramic constituted by nanocrystals dispersed in the amorphous matrix.

photonics [2,3,7]. Glass ceramics are two-phase materials constituted by nanocrystals embedded in a glass matrix, and the volume fractions of crystalline and amorphous phases govern their properties. Fig. 11.1 shows a high-resolution transmission electron microscopy (HRTEM) image of a glass ceramic sample constituted by nanocrystals dispersed in an amorphous matrix. In the framework of the present discussion, where materialelight interaction and diffusion processes are crucial, transparency plays an important role [8,9]. The question presented by Tick [8,9] about the transparency in glass ceramic materials has now a positive answer, as demonstrated by a huge number of experimental results [10,11]. Concerning the physical reasons, the theoretical aspect of the low losses achieved in glass ceramics is not well described till now, although some general criteria for light propagation, related to nanocrystal size, interparticle spacing, spatial arrangement, particle size distribution, and clustering are commonly accepted. If we look at the photovoltaic application, the other crucial point consists in the energy transfer efficiency when nanocrystals are activated by rare earth ions or other chromophores. The local crystalline environment for the rare earth ion brings high absorption and emission cross sections, together with a decrease of the nonradiative relaxation when the nanocrystal exhibits low cut off phonon energy. Moreover, the crystalline environment allows the control of the rare earth ion partition and hence the tailoring of the ioneion interaction. These properties, as we will see in this chapter, are very useful in fabricating systems with a very efficient donoreacceptor energy transfer. In fact, it is well known that one of the methods to increase the solar cells

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efficiency is to exploit the maximum possible part of the solar spectrum using down- and up-conversion mechanisms [12]. A paper by Pablick et al. [13] summarizes well the principal aspects described in this section. It demonstrates how transparent, rare earth doped, fluorozirconate glass ceramics are effective up- and downconverters to increase solar cell efficiency. For downconversion applications, the efficiency of a silicon solar cell is expected to be significantly increased in the ultraviolet spectral region using europium-doped glass ceramics. In fact, a high-energy photon in the ultraviolet spectral range can be absorbed by the Eu2þ ion, followed by a subsequent emission of a photon in the blue spectral range, which can be more efficiently absorbed by a solar cell [13]. On the other side, Er3þ ions were employed for up-conversion process. An Er3þ-doped glass was placed on top of a monocrystalline silicon solar cell and excited with an infrared laser diode operating at 1540 nm. The solar cell does not absorb the 1540 nm excitation light, but does absorb the up-converted fluorescence from the Er3þ-doped glass. In fact, upon excitation at 1540 nm, Er3þ-doped glasses emit a strong up-converted fluorescence at several wavelengths and in particular at 980 nm, the most important frequency for photovoltaic applications [13]. In the next section we present the fundamentals of the energy transfer process.

11.2 Frequency conversion by energy transfer The possibility to tune the frequency conversion exploiting different mechanisms has a strong impact on a variety of technologies, including photovoltaics. One of the prominent research areas concerns the development of suitable glass ceramic materials doped with lanthanide ions to enhance the photovoltaics features, by employing different rare earth ions and materials and taking advantage from complementary mechanisms such as downshifting, downconversion, and up-conversion. Downconverters or down-shifters are designed to modify the spectrum such that UV and visible photons are generating a more red-rich spectrum that is converted at higher efficiency by the solar cell. Upconverters modify the spectrum of photons above band gap that are not absorbed by the solar cell, to effectively shift the IR part of the incident spectrum to the NIR or visible part. Rare earth ionedoped materials have been frequently investigated for solar cell applications to reduce the fundamental thermalization losses. In

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fact, they offer the opportunity to effectively use the high-energy and subband gap-energy photons that otherwise would be lost in direct-band gap absorbers. There are two primary loss mechanisms [14,15] in solar cells that arise from the intrinsic properties of the semiconductor material, which account for the fundamental energy conversion efficiency limitation of solar cells: (1) sub-band gap energy photon loss, where the photons’ energy is not enough to excite the semiconductor and generate electronehole pairs. For example, in the case of crystalline silicon solar cells, about 20% of the sun’s energy (AM1.5 solar spectrum) is lost owing to these losses [15]. (2) Thermalization of charge carriers, caused by the absorption of high-energy photons with energies larger than the band gap of the solar cell. A high-energy photon can only generate one electronehole pair, and its excess energy is transformed into heat. Besides these two primary losses linked to photon harvesting, there are many other loss mechanisms, which are, however, more related to the electronic properties of solar cells, including (3) contact voltage loss; (4) recombination loss as a result of poor interface or material quality; (5) junction loss; and (6) reflection loss from interfaces at the surface of a module. These fundamental losses directly lead to an efficiency limit of ca. 30% for all single-junction cells under nonconcentrated air mass AM1.5 illumination [16]. Moreover, the strongest portion of the solar spectrum lies in the 350e550 nm range, and this energy band (w2.3e3.5 eV) is twice the optical band gap of crystalline silicon (w1.12 eV). Therefore, about 30% of incident solar radiation is lost due to thermalization. One effective way to reduce energy loss by thermalization is the conversion of one high-energy photon into two near-infrared (NIR) photons, which is known as quantum cutting. Rare earth ions are ideal candidates for the quantum cutting process since the rich distribution of energy levels favors spectral absorption and sequential relaxation among the electronic states [17]. Among rare earth ions, Yb3þ has simple energy levels that allow NIR emission at w 980 nm exclusively, which can be efficiently absorbed by silicon solar cells. Therefore, much attention has been focused on RE-Yb3þ (RE ¼ Eu2þ [18], Pr3þ [19], Nd3þ [20], Er3þ [21], and Tb3þ [1]) co-doped powders, glasses, and glass ceramics. In the next section, an overview is presented of the results achieved by the use of rare eartheactivated luminescent materials for solar spectrum conversion.

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11.2.1 Downconversion and quantum cutting Quantum cutting is also called “downconversion” because it is an opposite photon conversion process to “up-conversion.” The concept is illustrated in Fig. 11.2 with two types of ions, I and II, with hypothetical energy-level schemes. Type I is an ion for which emission from a high-energy level can occur. Type II is an ion to which energy transfer takes place. For NIR quantum cutting applied for solar cells, the choice of the type II ion is always focused on Yb3þ ion, whereas the type I ion as a donor should be chosen to match with Yb3þ, that is, it should have an energy level with twice energy difference than the 2F5/2 / 2F7/2 transition of Yb3þ, centered at 980 nm (z10,000 cm1). In the first-order downconversion process, the presence of an intermediate electronic level around 980 nm in the donor allows the classical energy transfer process, where the emission

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Figure 11.2 Energy level diagrams for two (hypothetical) types of lanthanide ions (I and II), showing the concept of downconversion. Type I is an ion for which emission from a high energy level can occur. Type II is an ion to which energy transfer takes place. (A) Quantum cutting on a single ion I by the sequential emission of two visible photons. (B) The possibility of quantum cutting by a two-step energy transfer. In the first step (indicated by ①), a part of the excitation energy is transferred from ion I to ion II by cross relaxation. Ion II returns to the ground state by emitting one photon of visible light. Ion I is still in an excited state and can transfer the remaining energy to a second ion of type II (indicated by ②), which also emits a photon in the visible spectral region, giving a quantum efficiency of 200% (C and D). The remaining two possibilities involve only one energy transfer step from ion I to ion II. This is sufficient to obtain visible quantum cutting if one of the two visible photons can be emitted by the ion (I). Adapted from R.T. Wegh, H. Donker, E.V.D. van Loef, K.D. Oskam, A. Meijerink Quantum cutting through downconversion in rare-earth compounds, J. Lumin. 87e89 (2000) 1017e1019. http://doi.org/10.1016/S0022-2313(99)00514-1.

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spectrum of the donor intermediate-energy level resonantly overlaps with the absorption spectrum of the electronic energy level of the acceptor. When the intermediate is not present, we speak of second-order downconversion. A single emission of the donor at around 490 nm (z20,000 cm1) will excite two Yb3þ ions at the same time. Looking at the literature for NIR quantum cutting, there are numerous reports on a variety of lanthanide ion pairs, including (Tb3þ/Yb3þ) [22], (Pr3þ/Yb3þ) [23], (Tm3þ/Yb3þ) [24], (Er3þ/Yb3þ) [25], (Nd3þ/Yb3þ) [26], and (Ho3þ/Yb3þ) [27], among others. For the ions Er3þ, Nd3þ, and Ho3þ coupled with Yb3þ, a first-order resonant energy transfer has been well established to be the main mechanism for quantum cutting because each one of the donor ions has an intermediate energy level resonant with that of the acceptor Yb3þ ion [25e27]. For the Tb3þ/Yb3þ, Pr3þ/ Yb3þ, and Tm3þ/Yb3þ pairs, since the excited energy level of each donor ion is located at approximately twice the energy of that of Yb3þ, the quantum cutting mechanism was supposed to be a second-order cooperative energy transfer process [28,29]. The paper by Klampaftis et al. [30] summarizes the quantum cutting mechanisms of the donor Yb3þ pairs already studied in different papers. In this contest, it is worth mentioning the research of Meijerink and coworkers about the energy transfer mechanism for downconversion in the couple Pr3þ/Yb3þ in LiYF4 crystal [31]. In fact, the mechanism responsible for downconversion of one visible photon into two infrared photons is controversial in the case of the pair Pr3þ/Yb3þ. We can consider a twostep energy transfer process or a cooperative energy transfer from Pr3þ to two Yb3þ ions, i.e., a second-order process. Comparing the experimentally obtained decay curves of the donor as a function of the acceptor concentration with the Monte Carloesimulated decay curves, Meijerink et al. demonstrated that the first-order energy transfer by cross relaxation is the dominant energy transfer mechanism, not the cooperative energy transfer [31]. Their analysis is now largely used to evaluate the downconversion process also for other donors. It is evident from the literature that the main downconversion mechanism depends, in general, on the specific donor as well as from the donor/acceptor concentration. If, for instance, we look at the (Tm3þ/Yb3þ) pair, we can observe that, for oxyfluoride glasses and glass ceramics, the cooperative downconversion mechanism from Tm3þ to Yb3þ, upon 467 nm excitation wavelength, is strongly dependent on the Yb3þ content and on the structure of the system [29,32]. It is important to take into account the effect of the phonons that, in some cases, can play an

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important role in the phonon-assisted energy transfer process involving two Yb3þ ions [32]. The role of the matrix and of the devitrification process on the optical properties of the couple (Tm3þ/Yb3þ) are clearly described in Refs. [2,33]. Martin et al. highlighted the influence of the different rare earth dopants on the crystallization process, a corner stone in the fabrication of transparent glass ceramics [33]. They discussed the effect of the activation of KLaF4 glass ceramics by Tm3þ/Yb3þ ions on thermal and structural characterization results, as well as on the spectroscopic properties. Their paper contains a lot of interesting results regarding the role of the microstructure, but what is interesting here is the dynamics of relaxation upon 476 nm excitation and in particular the energy transfer process from Tm3þ to the Yb3þ, leading to different luminescence spectra in the case of the parent glass and the glass ceramics. This is a further confirmation that the spectroscopic properties are strongly related to the crystalline fraction, activated by rare earth ions, present in the glass ceramic. The next section discusses the energy converters for some classical and some very novel glass ceramic hosts.

11.3 Glass ceramic hosts Another important factor for efficient and applicable quantum cutting is the host material. The main reason is that the managing of the photons can be achieved playing with the composition of the glass ceramics and especially with the vibrational and structural properties of the nanocrystals containing the rare earth ions. Nonradiative multiphonon relaxation is reduced when the rare earth ion interacts with low-energy phonons, so that the efficiency of up- and downconversion processes is not reduced by competitive nonradiative relaxation mechanisms. Looking at the materials characterized by very low cutoff phonon energy, fluorides (w355 cm1), chlorides (w260 cm1), bromides (w170 cm1), and iodides (w140 cm1) appear as ideal luminescent hosts [34]. However, due to the high hygroscopicity of chloride, bromide, and iodide glasses, combined with other specific structural properties, we can see that among the most popular transparent glass ceramics one often finds fluorides [19], tellurides [35], and chalcogenides [36]. The most popular system seems to be the oxyfluoride glass ceramics [2,7,33], although innovative transparent glass ceramics for downconversion has also been obtained using HfO2 [37e39], SnO2 [11,40], and Nb2O5 [41] nanocrystals embedded in silica. For practical applications, the scattering of the light is an important

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drawback, so that the nanocrystals must be maintained with a size lower than about 20 nm in the most efficient applications [2,7,11,33,39,42]. In fact, particles with the size of hundreds of nanometers or more would cause severe sunlight scattering, which will reduce the downconverter efficiency. In conclusion, it is mandatory to use a transparent material in the front surface of a solar cell for the conversion of the sunlight. This is the reason of the enormous interest in the fabrication of novel glass ceramics, in order to get benefit from their specific thermal, mechanical, and spectroscopic properties without the drawbacks related to the turbidity. Low scattering losses can be obtained by reducing the refractive index and density fluctuations in the glass ceramics, or paying attention to the size of the nanocrystals, the second approach being the more widely used due to the reliability in the preparation and control of rare eartheactivated nanocrystals. Coming back to fluoride glass ceramics, Dieudonné et al. investigated downconversion mechanisms in Pr3þ/Yb3þ-activated fluoride glass ceramics waveguides [19]. This system is an example of smoothing of the density fluctuation. In fact, Pr3þ-Yb3þ transparent glass ceramics have been obtained from lanthanum fluorozirconate glasses through spinodal decomposition. The nanocrystals belong to the (La, RE)F3eZrF4 system (RE ¼ Yb, Pr), but the phase depends both on the glass composition and on the Yb3þ content. The crystalline environment of the rare earth ions in the glass ceramic is evidenced by the increase of absorption cross section and by the narrowing of the emission bands. Upon 476 nm excitation, authors observed an intense Yb3þ emission at 980 nm and a fast decay of the 3 P0 with the increase of the Yb3þ concentration. The energy transfer from Pr3þ to Yb3þ was demonstrated to be very effective in these fluoride glass ceramic waveguides, with an estimated efficiency of 92% for the composition 0.5 mol% Pr3þ/10 mol% Yb3þ [19]. The choice of working with planar waveguides is related to the possibility to use them as luminescent solar concentrators, with the aim to put small-sized cells in butt coupling configuration. Indeed, due to the low absorption cross section of rare earth ions, films are not able to absorb and convert enough light in transmission, while they work very well in waveguiding configuration [1,43] and could be easily integrated on special windows as a method for light harvesting [44]. The binary systems fabricated by solegel route are the most appealing for the realization of downconverters based on glass ceramics waveguides [1,3,11,19,42]. For instance, the system SiO2eNb2O5 exhibits controlled phase separation and homogeneous Nb2O5 nanocrystal growth under suitable fabrication process [41]. Cardoso et al. reported on the infrared emission

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and frequency conversion of Pr3þ/Yb3þ-activated SiO2eNb2O5 glass ceramic waveguides, prepared by the solegel process [41]. The conclusions of their research are attractive: for the 0.5 mol% Pr3þ and 1.0 mol% Yb3þ activated SiO2eNb2O5 glass ceramic waveguides, an energy transfer efficiency of 75% was obtained. In particular, they demonstrated that the SiO2eNb2O5 matrix efficiently acts in collecting UV light and plays an important role in the energy transfer processes to the Yb3þ ions, thus indicating a possible approach to integrate a downconverter into a Si solar cell [41]. Alombert et al. have demonstrated that silica-hafnia is a suitable matrix for the realization of rare earthedoped waveguide downconverters [1]. In this research, the pair Tb3þ/Yb3þ in 70SiO2e30HfO2 glass ceramic waveguides was investigated. The main results were the following: (1) glass ceramics increases the effective quantum efficiency compared to the parent glass; (2) the Tb to Yb energy transfer efficiency increases with the increase of the molar ratio Yb/Tb; (3) the TbeYb energy transfer efficiency increases with the increase of the total Yb þ Tb concentration; (4) a transfer efficiency of 38% was achieved for 1 mol% Tb3þ and 4 mol% of Yb3þ [1]. However, what the optimum concentration should be remained an open question, which has been recently successfully closed by Zur et al. [39]. In their paper, using the 70SiO2e30HfO2 matrix, as employed in Ref. [1], the authors performed a complete study, increasing the total molar concentrations of donors and acceptors up to 21%. Fig. 11.3 reports the effective quantum efficiency as a function of the total Tb þ Yb molar concentration. The graph is obtained on the basis of the data reported in Ref. [39]. The results obtained by Zur et al. [39] confirm what was remarked in the preliminary work of Alombert et al. [1] about the impressive efficiency of the Tb3þ to Yb3þ energy transfer in silicahafnia glass ceramic waveguides. The highest effective quantum efficiency of 194% has been obtained in the 70SiO2e30HfO2 glass ceramic waveguides containing 19 mol% of rare earths. At higher content of rare earth ions, the competitive luminescence quenching process becomes effective [45]. The obtained value, very close to the theoretical one, makes possible the application of these films as downconverting filters and efficient light concentrators [39]. As discussed in the case of Pr3þ-activated SiO2eNb2O5 waveguides [41], the interest to have a system absorbing in UV and transferring energy to another rare earth ion is very appealing for downconverters. Ion pairs RE/Yb3þ (RE ¼ Pr3þ, Nd3þ, Ho3þ, Er3þ, Tb3þ, Tm3þ) in various hosts were demonstrated to enhance the efficiency of photovoltaic cells by

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[Tb+Yb] mol% Figure 11.3 Transfer efficiency as a function of total Tb3þþYb3þ molar concentration in 70SiO2-30HfO2 glass and glass ceramic thin films. Adapted from L. Zur, C. Armellini, S. Belmokhtar, A. Bouajaj, E. Cattaruzza, A. Chiappini, F. Coccetti, M. Ferrari, F. Gonella, G.C. Righini, E. Trave, A. Vomiero, F. Enrichi Comparison between glass and glass-ceramic silicahafnia matrices on the down-conversion efficiency of Tb3þ/Yb3þ rare earth ions, Opt. Mater. 87 (2019) 102e106. http://doi.org/10.1016/j.optmat.2018.05.008.

quantum cutting process. However, these materials are still far from practical application because the absorption of the donor ion arises from the parityforbidden 4fe4f transitions, which are naturally weak in intensity and narrow in bandwidth. A sensitizer is therefore needed, which absorbs strongly in the region 300e500 nm and transfers efficiently to the acceptor. Ce3þ has been proven to be an excellent candidate because it allows the 4fe5d transition and can absorb broadband solar radiation in the UV-Vis region. Moreover, the absorption spectrum of Ce3þ can also be adjusted by changing the crystal field of the doped substrate. Therefore, a Ce3þ/Yb3þ co-doped system has attracted much attention in recent years [25,46e48]. Wang et al. [49] firstly reported Ce3þeYb3þ coupled quantum cutting in borate glasses, converting one absorbed UV photon at 330 nm into two NIR photons at 976 nm by the cooperative energy transfer process. However, the excitation spectrum of Ce3þ in borate glasses lies in the 200e400 nm region and cannot absorb the strongest solar radiation band. Borate glass also has disadvantages of poor chemical stability, poor mechanical stability, and high phonon energy, limiting the application in silicon solar cell. A Ce3þ/Yb3þ co-doped system has been realized in yttrium aluminum garnet (YAG) powders [50] and transparent ceramics [51,52]. The excitation spectrum of Ce3þ in YAG lies in the 300e500 nm region

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and better matches the strongest solar radiation band. Transparent YAG glass ceramics are excellent hosts for quantum cutting, due to their low phonon energies and high chemical and mechanical stability [53,54]. As an alternative to Ce3þ, co-doping with semiconductor or metal molecular-like nanostructures is a very promising approach for providing a broadband and efficient sensitization of trivalent rare earth ions. The most detailed studies are certainly related to Er3þ ions sensitized by silicon [55e57] or silver aggregates [58e63]. Recently, Ag ions, multimers, and nanoaggregates were investigated in many glassy materials for the sensitization of various RE3þ ions, such as Tb3þ [64,65], Eu3þ [66], Yb3þ [67]. Noteworthy, Enrichi et al. demonstrated that this process is very efficient also in glass ceramic materials doped by Tb3þ [67,68], Yb3þ [69], and Tb3þ/Yb3þ [70,71], with interesting prospects in the field of PV solar cells. A more appealing approach is based on wide band gap semiconductor nanocrystals embedded in amorphous matrix doped with rare earth ions. In this context, Tran et al. demonstrated that SiO2eSnO2 glass ceramic is a fantastic host for rare earth ions, presenting a huge absorption cross section in the UV range and the capability to embed, rightly in the SnO2 nanocrystals, up to 75% of the Er3þ ions [72]. In fact, SnO2 is a wide band gap semiconductor (Eg ¼ 3.6 eV) and exhibits a maximum phonon energy of about 630 cm1. Moreover, SnO2 nanocrystals present an intense absorption band at around 320 nm, so that they can act as efficient sensitizers of the rare earth ions [40,72e74]. The rare earth ions can be incorporated in the SnO2 nanocrystal and, in the case of the Er3þ doped SiO2eSnO2 system, Er3þ ions are going to substitute for the Sn4þ ions in the cassiterite structure. What is important here is that the excitation spectra of the SiO2e SnO2 planar waveguides activated by Er3þ ions show an intense emission from the Er3þ metastable state 4I13/2 when the excitation is in the SnO2 band gap, around 300 nm. This excitation wavelength, in fact, corresponds to the interband electronic transition of the SnO2 nanocrystals. The Er3þ luminescence spectra show a narrowing of the emission peaks, associated to the Stark multiplets, evidencing that the rare earth ions are effectively embedded in the SnO2 nanocrystals. Also, the emission intensity rises with the SnO2 content, indicating an increase of the number of the Er3þ ions embedded in the SnO2 nanocrystals as the SnO2 content increases. With a higher content of SnO2, the density as well as the size of nanocrystals increases, which makes easier the process of incorporation of the rare earth ions in the nanocrystals. It was shown that when the concentration of SnO2 increased from 10% up to 30%, the luminescence intensity of 1550 nm

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region was enhanced about 10 times. These very recent results confirm the important role of SnO2 as an efficient Er3þ luminescence sensitizer [40,75]. In the next section, we give more detailed information concerning the spectroscopic experiments for the assessment of the downconversion efficiency.

11.4 Energy transfer mechanism: the case of Tb3D/ Yb3D silica-hafnia Focusing the attention on the silica-hafnia matrix, several papers have been published for different applications, ranging from telecommunications to efficient frequency converters with the aim to enhance the efficiency of the solar cell. Briefly, it is worth mentioning that Zampedri et al. [76] demonstrated that SiO2-HfO2 is a suitable host to obtain low loss planar waveguides. Based on these results, Peled et al. exploited these features to realize a monolithic laser operating at 1.06 mm [77]. Moreover, Alombert et al. as mentioned in the previous section, demonstrated that glass ceramic silica-hafnia waveguides are excellent candidates for the realization of efficient downconverters [1]. However, although numerous papers have addressed the topic of Tb3þ/ Yb3þ co-doped systems for downconversion application, the study of the energy transfer process and the understanding of its mechanisms has led to different solutions and interpretations, also according to the different materials taken into consideration [20,37,78e80]. A deeper knowledge of the quantum cutting mechanism would allow an appropriate choice of the rare earth ions to increase the quantum efficiency. To date, the comparison of the lifetime of the 5D4 excited state of Tb3þ, with and without Yb3þ codoping ions, has been widely applied to estimate the transfer efficiency, assuming the lack of nonradiative processes. Based on these assumptions, the assessment of the energy transfer efficiency h, as a function of the acceptor’s concentration, can be obtained experimentally by the ratio of the integrated intensity of the Tb3þ/Yb3þ decay curves to the integrated intensity of the Tb3þ curve [37,39]: R ITbYb (11.1) hTbYb ¼ 1  R ITb dt Since the effective quantum efficiency is described as the ratio of the emitted to the absorbed number of photons, considering the systems discussed here, an optimal downconversion would give a quantum efficiency

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of 200%, i.e., two NIR emitted photons for each visible photon absorbed. Clearly, the linear relationship between the transfer efficiency and the effective quantum efficiency can be defined by: hEQE ¼ hTbr ð1  hTbYb Þ þ 2hTbYb z1 þ hTbYb

(11.2)

where the quantum efficiency for the Tb3þ hTbr is set to 1 [81]. Some criticisms about this approach, that gives an overestimation of the efficiency value, have been raised by authors studying oxyfluoride glasses, who found a lower total efficiency than that estimated by the lifetime analysis. The study of the transfer process can also be performed by investigating the power law dependence of the down-emission as a function of the excitation intensity. Even in this case, looking at papers in the literature, there is no a general consensus because some authors found a linear dependence [82e84] whereas others claimed a nonlinear downconversion process, responsible for the quantum cutting. Chen et al. reported a sublinear dependence with a slope of 0.5 of the Yb3þ emission intensity on the 485 nm excitation power [22]. The slopes of Yb3þ luminescence intensity versus excitation power were fitted to be between 0.5 and 1 in Tb3þ/Yb3þ codoped NaYF4 powders [85]. Moreover, an interesting paper of Strek et al. [80], based on the study of the slope as a function of the temperature, reported a value of n ¼ 0.5 at room temperature and n ¼ 1 at 77 K, pointing out a nonresonant quantum cutting energy transfer process. The comprehensive energy level scheme for the two ions and the possible decay paths is described in Fig. 11.4. Here we can observe that the excited Tb3þ ion in the 5D4 energy level, by absorption of a 488 nm blue photon, can transfer its energy to two Yb3þ ions in the ground state: this leads to the emission of two 980 nm photons. The mechanism of the energy transfer between the involved ions can be described by (1) a direct process or (2) the involvement of an intermediate virtual state (v). Considering only the Tb3þ system, according to Ref. [85], the following rate equations can be written as follows: dN1 ¼ sfN0  ATb N1  W1 N1 N0 þ W2 Nv2 dt dNv ¼ 2W1 N1 N0  2W2 Nv2 dt

(11.3) (11.4)

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Figure 11.4 Schematic energy level diagram in a Tb3þ/Yb3þ codoped host showing the energy transfer mechanism of the near-infrared quantum cutting under the excitation of the 7F6 / 5D4 (Tb3þ) transition.

Here N0, N1, Nv correspond to the populations of the Tb3þ ground state, excited state, and virtual state, respectively, and s indicates the absorption cross section of the Tb3þ ground state. ATb is the spontaneous radiative emission rate of Tb3þ, f is the pumping photon flux. W1 and W2 represent the coupling coefficients for the population and depopulation of the virtual state, respectively. The population of the 5D4 (Tb3þ) excited level (N1) and of the virtual state (Nv) can be obtained looking at the steady state solution of the previous equations. As to N1, taking in mind the fixed number of Tb3þ ions (NTb ¼ N0 þ N1), we have: N1 ¼

sf NTb ff sf þ ATb

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where the last passage holds because, for the small absorption cross section of rare earth ions and under standard pumping conditions, sf <
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If we consider the complete interacting system and neglect different processes, like the excited state absorption within Tb3þ ions or the energy back transfer from Yb3þ to Tb3þ, the rate equations for the excited states can be expressed as: dN1 2 ¼ sfN0  ATb N1  W1 N1 N0  kD NYb0 dt

(11.7)

where kD represents the parameter for the cooperative energy transfer from Tb3þ to Yb3þ. The calculation of the population of the 2F5/2 (Yb3þ) excited state, responsible for the 980 nm emission, can be obtained by the steady state solution: 2 2KD NYb0 2KD NYb0 N1 þ Nv fAf þ Bf1=2 (11.8) AYb AYb According to the proposed model, and assuming it is correct, there are two different contributions to the 980 nm photoluminescence coming from the population of the Yb3þ excited state: one comes from the direct population transfer and the other one comes from the virtual state mediated transfer. In the former case the proportionality is with the pump power, in the latter one with the square root of the pump power. Referring to the previous considerations, the nonlinear quantum cutting mechanism has been evaluated considering the case of confined systems based on 70% SiO2e30% HfO2 glass ceramic waveguides co-doped with Tb3þ/Yb3þ at different molar concentrations of rare earths, namely [Tb þ Yb]/[Si þ Hf] ¼ 9%, 12%, 15% [38]. Initially, Enrichi et al. evidenced that the incorporation of Yb3þ, respect to the samples doped only with Tb3þ, causes a strong reduction of the lifetime (see Fig. 11.5). This shortening in the luminescence decay is due to the energy transfer from Tb3þ to Yb3þ, with a very high efficiency, up to 179% for the sample doped with 15% of rare earth ions. Moreover, following the approach applied by Duan et al. [85], a further investigation of the energy transfer mechanism has been carried out by considering the power dependence behavior of the Yb3þ NIR emission @ 980 nm. The emission intensity at 980 nm was recorded as a function of the 488 nm excitation power; Enrichi et al. [38] have shown that the slope of the linear fit is very similar for the samples (see Fig. 11.6), varying from 1.11 to 1.15. A predominant direct transfer mechanism is therefore suggested by the values obtained. Furthermore, the same slope obtained by the investigation at low-pump-power conditions, between 4 and

NYb1 ¼

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Figure 11.5 Decay curves of the luminescence from the 5D4 metastable state of Tb3þ ions upon excitation at 355 nm for silica-hafnia glass ceramics waveguides for samples containing different concentration of rare earth ions. Adapted from F. Enrichi, C. Armellini, S. Belmokhtar, A. Bouajaj, A. Chiappini, M. Ferrari, A. Quandt, G.C. Righini, A. Vomiero, L. Zur Visible to NIR downconversion process in Tb3þ-Yb3þ codoped silica-hafnia glass and glass-ceramic sol-gel waveguides for solar cells, J. Lumin. 193 (2018) 44e50. http://doi.org/10.1016/j.jlumin.2017.08.027.

Figure 11.6 Power dependence, in the range of 70e400 mW, of the Yb3þ 980 nm emission under 488 nm excitation in the silica-hafnia glass ceramic waveguides with 9% of total rare earth concentration. The linear fit line is evident.

100 mW (see Fig. 11.7), allowed to exclude the role of excited state absorption processes, typical of high photon fluxes. As a final consideration, it is important to highlight that glass ceramic materials, and in particular the silica-hafnia matrix, can be considered suitable

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Figure 11.7 Power dependence, in the range of 5e130 mW, of the Yb3þ 980 nm emission under 488 nm excitation in the silica-hafnia glass ceramic waveguides with 9% of total rare earth concentration. The linear fit line is evident.

hosts for the realization of down-converting filters for the solar applications. Moreover, the possibility to fabricate low loss glass ceramic waveguides represents a valid alternative to the converting-only layers, giving the opportunity to realize solar concentrators in the NIR spectral region. A better understanding of the quantum cutting mechanism, made possible by the model reported in this section, allows a proper choice of the doping ions for an improvement of the quantum efficiency.

11.5 Conclusions This chapter has highlighted some photon management results and the properties of rare eartheactivated glass ceramics when employed as downconverters. The important role of nanocrystals in the enhancement of the energy transfer mechanism, as well as in the reduction of nonradiative relaxation process, is evidenced. SnO2 nanocrystals, in particular, appear to be efficient rare earth donors. An important issue concerns the analysis of linear and nonlinear mechanisms in the Tb3þ / Yb3þ energy transfer. Its dynamics can be investigated by looking at (1) the dependence of the decay curves on the donor/concentration and (2) the dependence of the emission intensity of the acceptor on the excitation power of the donor. Looking at the literature in this field, we can conclude that, although solegel technology allows to fabricate efficient glass ceramics, there is still

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much room for the optimization of the fabrication protocols, in particular for a controlled embedding of the rare earth ions in the oxide nanocrystals. The choice of the most efficient host matrix is another critical issue; nonoxide glasses and glass ceramics may offer other chances for the development of highly efficient downconverters. Finally, another important point is the feasibility of easy and low-cost integration of the downconverters on the silicon solar cells. The waveguiding configuration appears to be an appropriate solution.

Acknowledgments The research activity is performed in the framework of the Enrico Fermi Center’s MiFo (2017e20) project. This review contains several information that would have been impossible to obtain without the contribution of several colleagues who have been collaborating with us since many years: C. Armellini, A. Chiasera. A. Carpentiero, S. Varas, D. Massella, L.T.N. Tran (IFN-CNR, Trento), D. Zonta, V. Piccolo (University of Trento), S. Normani (University of Pardubice), M. Meneghetti (Université de Rennes), S. Berneschi, G. Nunzi Conti, S. Pelli (IFAC CNR, Firenze), R.R. Gonçalves (Universidade de S~ao Paulo), A. Bouajaj, S. Belmokhtar (Université Abdelmalek Ess^aadi, Tanger), A. Quandt (University of the Witwatersrand, Johannesburg), C. Duverger (Université du Maine, Le Mans), A. Vomiero (Luleå University of Technology), F. Gonella, E. Cattaruzza, E. Trave, P. Riello, A. Benedetti (Ca’ Foscari University of Venice), G. Alombert-Goget (Université Claude Bernard, Lyon), J.J. Velazquez (Alexander Dubcek University of Trencín), D.N. Rao (University of Hyderabad).

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