1. INTRODUCTION

Nowadays, the search for efficient upconversion (UC) materials is driven by numerous potential applications such as biological labeling [1], UC lasers [2, 3, 4, 5], imaging [6], and, recently, enhanced-efficiency solar cells [7, 8, 9, 10]. Among factors limiting the efficiency of conventional solar cells, one can mention fundamental losses provoked by (i) a loss of solar energy contained in the IR part of solar spectra, or sub-bandgap light transmission, and (ii) internal relaxation of hot carriers created after absorption of photons with energy much higher than the gap of the material. In the case of crystalline silicon solar cells, $\sim 20\%$ of solar energy contained in the AM1.5 solar spectrum is lost due to the transmission [8]. A promising approach to overcome the fundamental problem of sub-bandgap losses consists in optical conversion of the IR photons to the shorter wavelengths (upconversion) in solid-state materials doped with rare-earth (RE) ions [9, 10]. Theoretically, the Shockley–Queisser efficiency limit [11] can be pushed from close to 30% up to 40.2% for a silicon solar cell with an upconverter illuminated by nonconcentrated light [9].

One of the most popular and high-performing materials for solar cells today is crystalline silicon, with the energy gap $1.12\mathrm{eV}$ at $300\mathrm{K}$ corresponding to the shortwave transmission edge of about $1.1\mu \mathrm{m}$. Due to the specific energy-levels scheme, the ${\mathrm{Er}}^{3+}$ ion can be considered as a very promising candidate among REs for UC of photons with wavelengths longer than $1.1\mu \mathrm{m}$ to the shorter range. Encouraging results were published by Richards and Shalav, who reported an external quantum efficiency of about 0.6% for a silicon solar cell with a low-phonon energy $\mathrm{Na}\mathrm{Y}{\mathrm{F}}_4:\mathrm{Er}$ phosphor used as an upconverter at an illumination intensity of $\sim 0.2\mathrm{W}∕{\mathrm{cm}}^2$ at $1550\mathrm{nm}$ [9].

Two important issues govern the choice of the host to obtain a material with high UC efficiency. A host with a narrow phonon spectrum permits to prevent multiphonon relaxation from the excited Er levels. Multiphonon relaxation from the ${}^4\mathrm{I}_{11∕2}$ level, emitting at $\sim 1\mu \mathrm{m}$, dominates in most of the oxide hosts with phonon spectrum cut-off frequency about $\sim 1000{\mathrm{cm}}^{-1}$, and is partly suppressed in fluoride, chloride, chalcogenide, and bromide hosts with maximal phonon energy less than $600{\mathrm{cm}}^{-1}$. Another important issue is clustering of Er ions within the host. Nonradiative energy transfers with, in particular, cross-relaxations between Er ions are favored in materials containing groups of closely spaced Er ions or Er clusters. In the case of Er ions, due to the specific energy-levels diagram, energy transfer processes leading both to self-quenching of the luminescence and to UC are possible, whether being beneficial or detrimental for the whole UC efficiency. Finally, glassy or disordered hosts are preferred for the specific application as active layers for highly efficient solar cells: inhomogeneous broadening in absorption spectra of RE ions due to disorder of the host allows absorbing a larger part of the solar spectrum.

In this paper, we report on the results of a study of $1.5\mu \mathrm{m}$ to NIR UC and absolute UC efficiency measurements in Er-doped fluorozirconate glasses. The goal of this study is to quantitatively evaluate the potential of the Er-doped modified ZBLAN glasses for use as an upconverter material in crystalline-silicon–based solar cells. Fluoro-zirconate glass was chosen as a host due to its low maximal phonon energy, broad bands in RE ions spectra doped in the glass, relatively easy synthesis and high chemical stability compared to chlorides or bromides, which demonstrate lower maximal phonon energy but usually are highly hygroscopic. We have studied glasses prepared following two distinct synthesis procedures affecting the dopant local environment and favoring or suppressing formation of groups of closely spaced Er ions or clusters. Although ${\mathrm{Er}}^{3+}$ spectroscopic properties in ZBLAN-type glasses have been extensively investigated, we have studied absorption spectra and calculated the intensity parameters, radiative transition probabilities, and branching ratios for the reason of probable change in spectroscopic parameters due to the modified ${\mathrm{Er}}^{3+}$ local environment. The intensity parameters of ${\mathrm{Er}}^{3+}$-doped ZBLAN-type glasses were obtained in [12, 13, 14, 15], radiative transition probabilities were calculated in [16]. The UC luminescence spectra of ${\mathrm{Er}}^{3+}$-doped ZBLAN-type glass under IR excitation at $1520\mathrm{nm}$ are reported in [17] along with the discussion of mechanisms leading to the population of the ${\mathrm{Er}}^{3+}$ radiative levels. In the present study we have measured the absolute efficiency of UC of radiation at $\sim 1.53\mu \mathrm{m}$ to the NIR, visible (VIS), and UV spectral ranges in the Er-doped modified ZBLAN glasses. The results of the tests of photocurrent generation in a crystalline-silicon–based solar cell with the studied Er-doped ZBLAN glasses used as an upconverter at an illumination at $1.53\mu \mathrm{m}$ will be published in a forthcoming paper.

The UC processes are intensively studied since the 1960s, when Bloembergen’s idea of the IR quantum counter was proposed [18], and demonstrations of anti-Stokes emission in RE-doped solid-state inorganic materials were independently interpreted by F. Auzel [19, ] and by Ovsyankin and Feofilov [20]. However, only a few publications reporting on absolute UC efficiency measurements have appeared up to date [21, 22, 23, 24, 25, 26]. These data are of extreme importance for estimation of real feasibility of approaches suggested for applications. To the best of our knowledge, this is the first report on the measurements of absolute efficiency of $1.5\mu \mathrm{m}$ to NIR UC.

2. EXPERIMENTAL DETAILS

2A. Synthesis

In order to obtain glasses with different distribution of impurity ions, fluorozirconate glasses of two different types of composition were prepared: (i) diluted Er-doped glass Z17Er2% with composition 55.6% $\mathrm{Zr}{\mathrm{F}}_4,27.3\%$ $\mathrm{Ba}{\mathrm{F}}_2,2.9\%$ $\mathrm{La}{\mathrm{F}}_3,4.9\%$ $\mathrm{Al}{\mathrm{F}}_3,6.8\%$ NaF, 0.5%$\mathrm{In}{\mathrm{F}}_3$ (Er concentration $3.15\cdot {10}^{20}{\mathrm{cm}}^{-3}$); and (ii) concentrated Er-doped glass Z18Er5% with composition 54.0% $\mathrm{Zr}{\mathrm{F}}_4,26.6\%$ $\mathrm{Ba}{\mathrm{F}}_2,2.8\%$ $\mathrm{La}{\mathrm{F}}_3,4.8\%$ $\mathrm{Al}{\mathrm{F}}_3,6.6\%$ NaF, 0.5%$\mathrm{In}{\mathrm{F}}_3$ (Er concentration $8.07\cdot {10}^{20}{\mathrm{cm}}^{-3}$); according to the procedure proposed by F. Auzel [27]. Applying this procedure, different precursors were used for introducing the dopant ion into the host, which affected the spatial distribution of the impurity ions in the resulting glass and led to rather uniform distribution for the Z17Er2% sample and formation of groups of closely spaced Er ions or Er clusters for the Z18Er5% sample.

The constituent chemicals of 4N purity were melted in a Pt crucible at $850°\mathrm{C}$ in inert argon atmosphere then poured into a copper plate preheated at $260°\mathrm{C}$ and left for slow cooling inside the furnace. As a result, transparent glasses of light rose color were obtained.

For spectroscopic measurements, the samples were cut and polished in order to obtain thin plates with parallel faces. Concentration of Er ions per cubic centimeter in the obtained glasses was calculated on the basis of the results of the density measurements.

2B. Spectroscopic and Absolute Upconversion Efficiency Measurements

Absorption spectra were measured using the Varian CARY-5 spectrometer. Kinetics of luminescence from the ${}^4\mathrm{I}_{13∕2}$ and ${}^4\mathrm{I}_{11∕2}$ Er levels was measured at selective pulsed laser excitation (${\lambda }_{\mathrm{exc}}=980$ and $1530\mathrm{nm}$, respectively; emission of an optical parametric oscillator pumped by the 3rd harmonics of Thales Q-switched Nd:YAG laser; pulse duration $\sim 10\mathrm{ns}$, energy $\sim 3\mathrm{mJ}$ per pulse). Luminescence in the IR was analyzed with a HR 250 Jobin–Yvon monochromator and detected with a PbS (at $2.7\mu \mathrm{m}$) or InGaAs (at $1.55\mu \mathrm{m}$) detector. Luminescence decays were recorded with a Tektronix TDS 350 oscilloscope.

Refractive index was measured with Abbe refractometer at $589.3\mathrm{nm}$.

Upconversion luminescence was excited with a cw pig-tailed Er fiber laser (ELT-100 IRE Polus Group) delivering power up to $100\mathrm{mW}$ via a single-mode fiber with $8\mu \mathrm{m}$ core diameter. A splitter and a photodiode integrated into the device permitted to control the excitation power. The IR luminescence in the range of $900–1700\mathrm{nm}$ was analyzed by a monochromator (SpectraPro 750, dispersion $1.2\mathrm{mm}∕\mathrm{nm}$), detected by a liquid nitrogen cooled PbS detector, and corrected for spectral response of the system. Glass plates under study were brought as close as possible to the pumping laser fiber termination [Fig. 1a ], and the ensemble was introduced inside an integrating sphere covered with Spectralon™. An UC luminescence signal was delivered to a spectrometer (AVASpec-1024TEC) by an optical fiber. The whole setup (integrating $\text{sphere}+\text{spectrometer}$) is calibrated with the use of a halogen tungsten lamp ($10\mathrm{W}$ tungsten halogen fan-cooled Avalight-HAL). The scheme of setup for absolute UC efficiency measurements is shown in Fig. 1b. For both setups (with a monochromator and with an integrating sphere), the same sample holder [Fig. 1a] was used.

The Spectralon™ reflectance is still high $(\sim 98\%)$ at the pump wavelength; however, the pump radiation transmitted through the sample and reflected from the sphere inner surface does not constitute an additional source of excitation. When illuminating the sample with the pump beam diffused from the sphere surface, no UC signal was detected due to low pump-power density. This permits us to take into account only a single pass of the pump radiation through the sample. Furthermore, since the detection system does not respond at wavelengths longer than $1.1\mu \mathrm{m}$, the pump radiation arriving occasionally into the detection system does not introduce parasitic signals.

3. RESULTS AND DISCUSSION

3A. Absorption Spectra and Judd–Ofelt Calculations

Room temperature absorption cross-section spectra of Er:ZBLAN glasses recorded in the IR-VIS-UV are shown in Fig. 2 . At room temperature, the line shapes in the absorption cross-section spectra of both concentrated and diluted glass are very similar. The absorption cross-section at pump wavelength for the Z17Er2% and the Z18Er5% samples were ${\sigma }_{\mathrm{abs}}\left(1532\mathrm{nm}\right)=0.42\times {10}^{-20}{\mathrm{cm}}^2$ and ${\sigma }_{\mathrm{abs}}\left(1532\mathrm{nm}\right)=0.49\times {10}^{-20}{\mathrm{cm}}^2$, respectively. Weak absorption band around $820\mathrm{nm}$ corresponding to the ${}^4\mathrm{I}_{15∕2}\to {}^4\mathrm{I}_{9∕2}$ transition is not shown in Fig. 2 due to poor signal-to-noise ratio. The broad absorption band near $\sim 1.5\mu \mathrm{m}$, corresponding to the ${}^4\mathrm{I}_{15∕2}\to {}^4\mathrm{I}_{13∕2}$ transition, is located below the absorption edge of crystalline silicon $(\sim 1.1\mu \mathrm{m})$. The large FWHM $(\sim 70\mathrm{nm})$ of this band and the high integrated absorption cross-section $\int {\sigma }_{\mathrm{abs}}\left(\nu \right)\mathrm{d}\nu$ ($1.29\times {10}^{-18}\mathrm{cm}$ for the Z17Er 2% sample and $1.41\times {10}^{-18}\mathrm{cm}$ for the Z18Er 5% sample) are convenient for pumping with a source characterized by a broadband spectrum such as the AM1.5 solar radiation spectrum.

From the absorption spectra, the Judd–Ofelt intensity parameters [28, 29], spontaneous radiative transition probabilities, and branching ratios for Er in the glasses under study were calculated following common procedure described, for instance, by A. Kermaoui and F. Pellé [30]. The details will be published in a forthcoming paper. Reasonable values of the intensity parameters were obtained for both samples, they are represented in the Table 1 . Slight deviations from the intensity parameters obtained in [12, 13, 14, 15] are explained by different composition of the glass host, and, particularly, by a slightly different ${\mathrm{Er}}^{3+}$ local environment due to the special doping procedure. Using the obtained intensity parameters (summarized in Table 1 together with corresponding root mean square errors on electric–dipole oscillator strengths), the radiative transition probabilities, branching ratios, and radiative lifetimes for nine excited Er levels were calculated similarly to how it was done in [30]. The results obtained for the samples Z17Er2% and Z18Er5% are represented in Table 1, together with central wavelengths of radiative transitions and the energy gaps separating the excited Er levels in ZBLAN glasses determined by Y. D. Huang et al. [31].

The lifetimes of the ${}^4\mathrm{I}_{13∕2}$ and ${}^4\mathrm{I}_{11∕2}$ Er levels were measured experimentally using selective pulsed laser excitation; the obtained results are summarized in Table 1. The luminescence decays were purely exponential for both levels in both samples. For the ${}^4\mathrm{I}_{13∕2}$ level, the measured lifetimes are slightly longer than calculated. This may be attributed to the influence of reabsorption. The lumin escence from the ${}^4\mathrm{I}_{11∕2}$ level was detected at $\sim 2.7\mu \mathrm{m}$ (the ${}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{13∕2}$ transition) in order to avoid reabsorption.

Radiative quantum yield of the ${}^4\mathrm{I}_{13∕2}$ and ${}^4\mathrm{I}_{11∕2}$ levels can be estimated as

3B. Luminescence Spectra

The luminescence spectra of Er-doped fluorozirconate glasses excited by a cw laser-diode (LD) pumped Er fiber laser $(\lambda =1532\mathrm{nm})$, are shown in Fig. 3 . The spectra in the UV–VIS–NIR spectral domain $(380–1100\mathrm{nm})$ were recorded using the setup with an integrating sphere, which permits absolute measurements of the power of the luminescence emitted by the sample. The spectra in the IR spectral domain $(900–1700\mathrm{nm})$ were corrected for the spectral response of the registration system and scaled in order to obtain the same luminescence power of the band at $\sim 0.98\mu \mathrm{m}$ as that in spectra recorded using the setup with the integrating sphere. Both setups allow one to record spectra in energy per wavelength units. The as-obtained luminescence power spectra of Er-doped ZBLAN samples are shown in Fig. 3 in energy per wavelength units [Figs. 3a, 3b] and in photon flux per constant energy interval units [Figs. 3c, 3d]. The obtained UC luminescence spectra are in qualitative agreement with the results reported in [17].

For both samples, the most intensive emission bands are observed near $1.5\mu \mathrm{m}$ (transition ${}^4\mathrm{I}_{13∕2}\to {}^4\mathrm{I}_{15∕2}$, resonant with excitation) and near $0.98\mu \mathrm{m}$ (transition ${}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{15∕2}$). Several weaker luminescence bands are observed in the NIR (overlapped bands at $\sim 820\mathrm{nm}$, transition ${}^4\mathrm{I}_{9∕2}\to {}^4\mathrm{I}_{15∕2}$ and at $\sim 850\mathrm{nm}$, transition ${}^4\mathrm{S}_{3∕2}\to {}^4\mathrm{I}_{13∕2}$), red ($\sim 660\mathrm{nm}$, transition ${}^4\mathrm{F}_{9∕2}\to {}^4\mathrm{I}_{15∕2}$), green ($\sim 550\mathrm{nm}$, transition ${}^4\mathrm{S}_{3∕2}\to {}^4\mathrm{I}_{15∕2}$), and blue-UV ($410\mathrm{nm}$, transition ${}^2\mathrm{G}_{9∕2}\to {}^4\mathrm{I}_{15∕2}$) spectral domains. Note that, for population of the initial levels of these transitions, absorption of at least two (${}^4\mathrm{I}_{9∕2}$ level), three (${}^4\mathrm{F}_{9∕2}$ and ${}^4\mathrm{S}_{3∕2}$ levels), or four (${}^2\mathrm{G}_{9∕2}$ level) excitation photons are needed. The energy-levels scheme of Er permits various paths for population of these levels; the most probable processes are summarized in Fig. 4a .

A detailed study of energy transfer in fluorozirconate glasses is needed in order to identify the most efficient mechanisms of population of excited levels ${}^4\mathrm{I}_{11∕2}$, ${}^4\mathrm{I}_{9∕2}$, ${}^4\mathrm{F}_{9∕2}$, ${}^4\mathrm{S}_{3∕2}$, and ${}^2\mathrm{G}_{9∕2}$ upon excitation at ${\lambda }_{\mathrm{exc}}=1532\mathrm{nm}$; here we have only identified possible processes of population, relying on the consideration of the Er energy-levels scheme. Since in this paper we are especially interested in the absolute measurements of $1.5\mu \mathrm{m}$ NIR and VIS conversion efficiency, the detailed study of energy transfer in fluorozirconate glasses will be published in a forthcoming paper.

For clarity, in Fig. 4a, only the radiative transitions terminating at the ground state ${}^4\mathrm{I}_{15∕2}$ are shown. Experimentally, it was possible to detect a weak luminescence corresponding to transitions originating from the excited levels ${}^4\mathrm{I}_{11∕2}$, ${}^4\mathrm{F}_{9∕2}$, ${}^4\mathrm{S}_{3∕2}$, and ${}^2\mathrm{G}_{9∕2}$ and terminating at excited states; this will be addressed more thoroughly in the next sections of the paper.

3C. Upconversion Yield

In order to estimate the fraction of absorbed excitation photons that are subsequently reemitted in the anti-Stokes region, we have followed the procedure proposed by J. F. Suyver et al. [33].

The fraction of all photons emitted in the band i is calculated as

Next, we make an important assumption that each absorbed photon contributes to the emission of a photon, i.e., the depopulation of all the radiative excited levels is only possible via radiative transition to the ground state or UC via excited-state absorption (ESA) or energy transfer upconversion (ETU). Relying on this assumption, the fraction $R_i$ of absorbed excitation photons emitted in the band i can be calculated as follows:

(i) For the ${}^4\mathrm{I}_{13∕2}$ level, the experimentally measured lifetimes are slightly longer than calculated (possibly due to reabsorption), and we estimate the quantum yield of this level as close to 100%. The quantum yield of the ${}^4\mathrm{I}_{11∕2}$ level is $\eta =69.7\%$ and $\eta =76.4\%$ for the Z17Er2% and Z18Er5% samples, respectively. In a case of intense luminescence from the ${}^4\mathrm{I}_{11∕2}$ level, the reduced quantum yield of this level results in underestimation of the fractions of absorbed excitation photons used for UC luminescence. The higher energy radiative levels ${}^4\mathrm{F}_{9∕2}$, ${}^4\mathrm{S}_{3∕2}$, and ${}^2\mathrm{G}_{9∕2}$ are probably partly quenched by multiphonon nonradiative relaxations (MPNR), since they are separated from next lower levels by the energy gaps $\Delta \mathrm{E}\sim 2650{\mathrm{cm}}^{-1}$, $\sim 2980{\mathrm{cm}}^{-1}$, $\sim 1880{\mathrm{cm}}^{-1}$, respectively [24], and approximately five or fewer phonons are needed to span these energy gaps. Nevertheless, weak luminescence from these levels compared to the luminescence from the ${}^4\mathrm{I}_{13∕2}$ and ${}^4\mathrm{I}_{11∕2}$ levels permits us to suggest that no significant error will result from obeying the requirement of weak MPNR.

(ii) The requirement on the branching ratios of radiative transitions is not fully satisfied for the ${}^4\mathrm{I}_{11∕2}$ and the ${}^4\mathrm{S}_{3∕2}$ levels. However, the weak intensity of luminescence of the transitions originating from the ${}^4\mathrm{S}_{3∕2}$ level with respect to that originating from the ${}^4\mathrm{I}_{11∕2}$ and ${}^4\mathrm{I}_{13∕2}$ levels permits us to assume that the large branching ratio $\beta ({}^4\mathrm{S}_{3∕2}\to {}^4\mathrm{I}_{13∕2})\sim 0.28$ (Table 1) will not introduce significant error. The relatively high branching ratio obtained for the ${}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{13∕2}$ transition $\beta ({}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{13∕2})=0.18$ (Table 1) implies that $\sim 18\%$ of radiative transitions originating from the ${}^4\mathrm{I}_{11∕2}$ level, populated essentially by UC via ETU or ESA at $1.53\mu \mathrm{m}$ pumping, provoke luminescence in the Stokes region $(\sim 2.7\mu \mathrm{m})$ and are not taken into account in the luminescence spectra presented in Fig. 3. Consequently, the total fraction of absorbed excitation photons used for UC luminescence calculated using the Eq. (3) may be slightly underestimated. For other excited levels the branching ratios for transitions terminating at excited levels do not exceed 5% (Table 1) and should not introduce any significant error.

(iii) The energy-levels scheme of Er does not offer any cross-relaxation scheme leading to self-quenching of luminescence for the ${}^4\mathrm{I}_{11∕2}$ and ${}^4\mathrm{I}_{13∕2}$ levels, and the requirement of domination of radiative relaxation over cross-relaxation leading to self-quenching is satisfied for both levels. This is also supported by the fact that the decays of luminescence from these levels are purely exponential. Concerning higher energy excited levels, concentration self-quenching is usually observed in fluoride hosts for the luminescence originating from the ${}^4\mathrm{S}_{3∕2}$ and ${}^2\mathrm{G}_{9∕2}$ levels for Er concentrations above $\sim 1\%$. Again, we suppose that weak luminescence from these levels compared to the luminescence from the ${}^4\mathrm{I}_{13∕2}$ and ${}^4\mathrm{I}_{11∕2}$ levels permits us to suggest that self-quenching of luminescence from the ${}^4\mathrm{S}_{3∕2}$ and ${}^2\mathrm{G}_{9∕2}$ levels does not introduce significant error. The role of energy transfer processes in $1.53\mu \mathrm{m}$ to 0.98 and VIS upconversion will be discussed in a forthcoming paper.

The fractions $R_i$ of absorbed excitation photons emitted in the band i, calculated using Eq. (3), are presented in the Tables 2, 3 . The large fraction of absorbed photons reemitted in the NIR and VIS with the Z18Er5% sample (44.5% on total, in the $1.1–0.38\mu \mathrm{m}$ region) proves that this glass is very promising for use in the UC devices.

For real applications, the fraction of energy emitted in a specific spectral domain ${\eta }_i^{\exp }$ seems to be a more convenient parameter to characterize an UC material:

3D. Discussion

Slight discrepancy between the values of fractions $R_i$ of absorbed excitation photons emitted in the band i and the fractions ${\eta }_i^{\exp }$ of power emitted in a specific spectral domain is explained by the losses related to the thermalization of the emitting levels: the power reemitted in a specific luminescence band “i” ${\int }_{{\lambda }_0}^{{\lambda }_1}{P}_{\mathrm{meas}}^{\mathrm{UC}}\left(\lambda \right)\mathrm{d}\lambda$ is unavoidably less than the power of absorbed excitation photons needed to excite this luminescence $(p_i{\Phi }_i^{\mathrm{int}}\cdot h{\nu }_{\mathrm{\text{pump}}})$, as illustrated in Fig. 4b.

The relevant correction coefficients may be calculated as

Total luminescence energy yield can be calculated as the ratio of luminescence power emitted in the whole spectral range $P_{\mathrm{lum}}^{\mathrm{int}}={\int }_{380\mathrm{nm}}^{1100\mathrm{nm}}{P}_{\mathrm{meas}}^{\mathrm{UC}}\left(\lambda \right)\mathrm{d}\lambda$ to the absorbed pump power ${\eta }_{\mathrm{tot}}^{\exp }=P_{\mathrm{lum}}^{\mathrm{int}}∕P_{\mathrm{abs}}^{\mathrm{\text{pump}}}$. The total luminescence energy yields of 38% and 33% were obtained for the samples Z17Er2% and Z18Er5%, respectively. Then, the absolute energy yields of $1.5\mu \mathrm{m}\to 0.98\mu \mathrm{m}$ UC can be obtained: ${\eta }_2^{\exp }\cdot {\eta }_{\mathrm{tot}}^{\exp }=7.4\%$ and ${\eta }_2^{\exp }\cdot {\eta }_{\mathrm{tot}}^{\exp }=11.5\%$ for the samples Z17Er2% and Z18Er5%, respectively. Similarly the absolute energy yields of $1.5\mu \mathrm{m}\to$NIR–VIS UC were obtained as ${\sum }_{i=2}^6{\eta }_i^{\exp }\cdot {\eta }_{\mathrm{tot}}^{\exp }=8.1\%$ and ${\sum }_{i=2}^6{\eta }_i^{\exp }\cdot {\eta }_{\mathrm{tot}}^{\exp }=12.7\%$ for the samples Z17Er2% and Z18Er5%, respectively.

The experimentally measured total luminescence yields ${\eta }_{\mathrm{tot}}^{\exp }$ are lower than 100% in both samples under study. This may be partly explained as being due to possible losses in UC signal measured with the help of the integrating sphere. These losses are due to the fact that the reflectance of the metallic sample holder is generally lower than that of Spectralon™. However, we do not believe that more than 50% of luminescence could be lost because of low sample holder reflectance. A similar experimental setup with the same integrating sphere and detection system was used for the measurements of absolute efficiency of UC of $0.98\mu \mathrm{m}$ radiation to the VIS [34, 35, 36, 37, 38]; no significant loss of luminescence signal was detected.

Probable channels of relaxation of the excitation energy absorbed by the samples except luminescence in the $1.7–0.38\mu \mathrm{m}$ domain are considered below.

First, as was discussed above, the reduced quantum yield of luminescence from the ${}^4\mathrm{I}_{11∕2}$ level ($\eta =66.5\%$ and $\eta =76\%$ for the Z17Er2% and Z18Er5% samples, respectively) may be attributed to multiphonon relaxation or quenching on uncontrolled impurities. This can partly explain the reduction of the total luminescence yield.

As was discussed in the previous section, a part of radiative transitions, originating from the levels populated essentially by UC via ETU or ESA at $1.53\mu \mathrm{m}$ pumping, provokes luminescence in the Stokes region and thus is absent in the luminescence spectra in the $1.7–0.38\mu \mathrm{m}$ domain. Possible losses may be identified as being due to the transition ${}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{13∕2}$ at $\sim 2.7\mu \mathrm{m}$ (branching ratio $\beta ({}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{13∕2})∕({}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{15∕2})=\mathrm{18:\; 82}$). However, rough estimations relying on this branching ratio, fraction of photons emitted in the band corresponding to ${}^4\mathrm{I}_{11∕2}\to {}^4\mathrm{I}_{15∕2}$ transition ($f_2$ in Tables 2, 3), and approximate energy of photons at $\sim 2.78\mu \mathrm{m}$ show that the energy contained in this luminescence band may constitute no more than $\sim 2\%$ of absorbed pump energy for both samples Z17 Er2% and Z18 Er5%.

Another source of losses may originate from efficient nonradiative relaxation of excitation energy due to thermalization of the emitting levels and MPNR between closely spaced levels [e.g., ${}^4\mathrm{I}_{9∕2}⇝{}^4\mathrm{I}_{11∕2}$, process MPNR1 in Fig. 4a, or ${}^4\mathrm{F}_{7∕2}⇝{}^2\mathrm{H}_{11∕2}⇝{}^4\mathrm{S}_{3∕2}$, process MPNR2 in Fig. 4a] in a case when radiative relaxation from Er excited levels is preceded by multiple energy transfers. This hypothesis needs further investigation on the basis of a study of energy transfer processes in the considered Er-doped glasses.

Finally, the quenching of luminescence due to energy migration to eventual traps via highly populated ${}^4\mathrm{I}_{13∕2}$ level characterized by milliseconds-range lifetime, quantum yields close to 100% and typically very high migration rate in fluoride hosts, cannot be completely excluded.

The obtained results provide some evidence that the reliability of the results of estimations of UC efficiencies based on the analysis of luminescence spectra is limited if absolute measurements of UC luminescence intensity have not been performed. In addition to the analysis of luminescence spectrum, the absolute measurements of UC efficiency as it has been described [39, 40, 41] or using a setup with integrating sphere can be proposed as a mean to accomplish the characterization of UC material.

4. CONCLUSIONS

In this paper we report on the results of absolute upconversion (UC) efficiency (i.e., the ratio of UC luminescence power to the absorbed pump power) measurements in Er-doped fluorozirconate glasses in the limiting case of high-excitation pump power.

Absolute UC efficiency of $1.532\mu \mathrm{m}$ to NIR and VIS of 8.1% and 12.7% was obtained in Er-doped ZBLAN glasses Z17Er2% and Z18Er5%, respectively, under excitation with $75\mathrm{mW}$ cw pig-tailed Er fiber laser. The most part of UC emission energy is contained in the NIR part of the spectrum (at $\sim 1\mu \mathrm{m}$), absolute $1.5\mu \mathrm{m}\text{to}0.98\mu \mathrm{m}$ UC efficiency is 7.4% (Z17Er2%) and 11.5% (Z18Er5%). The studied glasses are promising for application as an active layer of UC solar cells with enhanced efficiency, since the $0.98\mu \mathrm{m}$ light has an absorption depth of only $\sim 100\mu \mathrm{m}$ and is thus strongly absorbed in a wafer-based silicon solar cell. For crystalline-silicon–based solar cells, approximately a half of the energy contained in the VIS part of the UC spectrum will be released as heat during thermalization of hot carriers created after absorption of VIS photons. To the best of our knowledge, this is the first report on the measurements of absolute efficiency of $1.5\mu \mathrm{m}$ to NIR UC.

The results of this study also reveal the problem of dual effect of energy transfer processes on efficiency of UC. The energy transfer processes represent, at the same time, efficient channels of high-excited-levels population via ETU and sources of losses via luminescence self-quenching accompanied by dissipation of energy due to phonon-assisted nonradiative relaxation. Choosing the correct dopant concentration, which governs the efficiency of energy transfer, is of great importance especially in cases when ESA is slightly off-resonant and, consequently, has poor efficiency. In the studied Er-doped ZBLAN glasses the higher absolute UC efficiency was demonstrated with the Z18Er5 sample, where dopant concentration is higher, and the synthesis favors formation of Er clusters or groups of closely spaced dopant ions. The obtained absolute UC efficiency is among the highest values published for $0.98\mu \mathrm{m}$ to VIS upconversion. This permits us to make a conclusion about the positive role of energy transfer in the hosts under study, in spite of relatively low overall luminescence yield achieved, which is attributed mostly to the dissipation of excitation energy via phonon-assisted nonradiative relaxation accompanying multiple energy transfers.

In conclusion, the results of our study of the UC processes under $1.53\mu \mathrm{m}$ excitation in the Er-doped modified ZBLAN glasses permit us to conclude about the potential of these glasses for application as an upconverter material in crystalline-silicon–based solar cells, the latter representing today the most popular and low-cost type of the existing solar cells. The use of the efficient conversion of the IR radiation near $1.53\mu \mathrm{m}$ to the wavelengths above the c-Si absorption edge demonstrated in this material will definitely improve the solar cells efficiency thanks to reducing the sub-bandgap losses. It is worth mentioning that the Er absorption band at $\sim 1.5\mu \mathrm{m}$ corresponds to the high atmospheric transmission band, and thus the studied materials are perfectly suitable for on-earth applications. To the best of our knowledge, the results of the measurements of absolute efficiency of $1.5\mu \mathrm{m}$ to NIR UC are reported for the first time. The results of the tests of photocurrent generation in the crystalline-silicon solar cells with the studied Er-doped ZBLAN glasses used as an upconverter at an illumination at $\sim 1532\mathrm{nm}$ along with the modelling of the complete setup (solar $\text{cell}+\text{upconverter}$) will be published in a forthcoming paper.

ACKNOWLEDGMENTS

This work is supported by the French National Agency for Research (ANR), program “Solar Photovoltaics,” project “Very high efficiency and photovoltaic innovation” (THRI-PV). The authors acknowledge partial support from the Russian Foundation for Basic Research (RFBR), grant 07-02-01063.

Table 1. Calculated Spectroscopic Parameters of Radiative Transitions and Judd–Ofelt Intensity Parameters $\left({\Omega }_n\right)$ of the ${\mathrm{Er}}^{3+}$ Ion in the Z17Er2% and Z18Er5% Glasses^a

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Table 2. Details for Emission Bands “i” $(i=1–5)$ Resulting from the Z17Er2% Sample^a

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Table 3. Details For Emission Bands “i” $(i=1–5)$ Resulting from the Z18Er5% Sample^a

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Fig. 1 Experimental setup for absolute UC efficiency measurements. (a) Sample is brought as close as possible to the fiber termination and attached to a metallic sample holder. (b) Schematic of experimental setup. Luminescence excitation source: cw pig-tailed Er fiber laser, ${\lambda }_{\mathrm{exc}}=1.532\mu \mathrm{m}$, pump $\text{power}=75\mathrm{mW}$ (stabilized, real-time control provided by integrated splitter and photodiode); a single-mode fiber with a core diameter $8\mu \mathrm{m}$. Integrating sphere: Avasphere; sphere diameter $5\mathrm{cm}$, sample port diameter $1\mathrm{cm}$, knife-edge sphere covered with Spectralon™. IR-UV-VIS spectrometer: AVASpec-1024TEC thermo-electric-cooled CCD fiber-optic spectrometer ($75\mathrm{mm}$ focal length). UC luminescence signal arrives on the end-face of an optical fiber in such a way that only diffused reflected luminescence is collected.

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Fig. 2 Room-temperature absorption spectra of Er-doped ZBLAN glass (sample Z18Er5%) in the (a) IR and (b) UV-VIS spectral domains. Absorption bands correspond to transition from the ground state ${}^4\mathrm{I}_{15∕2}$ to the excited states listed in the figures.

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Fig. 3 Luminescence spectra of Er-doped ZBLAN glasses, (a, c) sample Z17Er2% and (b, d) sample Z18Er5%. Note that in (c, d) the photon flux of the UC luminescence bands in the interval of $11000–27000{\mathrm{cm}}^{-1}$ (3- and 4-photon processes) is multiplied by a factor of 20, and the photon flux of the luminescence band at $\sim 6500{\mathrm{cm}}^{-1}$ (1 photon process) is multiplied by (c) a factor of 0.2 and (d) 0.5. Excitation: wavelength is shown by an arrow. Excitation power is $75\mathrm{mW}$. Identification of transitions corresponding to the luminescence bands is shown in the figures.

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Fig. 4 Energy-levels scheme of ${\mathrm{Er}}^{3+}$ ion. (a) Mechanisms of population of excited Er levels. Absorption of pump radiation (${\lambda }_{\mathrm{exc}}=1532\mathrm{nm}$): ground-state absorption (GSA) and excited-state absorptions (ESA1–ESA3) indicated by upward arrows; multiphonon nonradiative relaxations ($\mathit{MPNR}\mathit{1}$ and $\mathit{MPNR}\mathit{2}$) indicated by waved arrows; energy transfers ($\mathit{UC}\mathit{1}–\mathit{UC}\mathit{4}$); and radiative transitions indicated by downward arrows. Numbers near arrows denoting radiative transitions are wavelengths of luminescence in nanometers. (b) Losses of absorbed pump energy. Upward arrows, GSA and ESA; waved arrows, nonradiative relaxation providing thermalization of Stark sublevels of each multiplet and introducing losses; downward arrow, luminescence $\left(\mathit{LUM}\right)$.

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