Experimental and numerical analysis of Tm2+ excited-states dynamics and luminescence in CaX 2 (X = Cl, Br, I)

The prospect of using Tm2+-doped halides for luminescence solar concentrators (LSCs) requires a thorough understanding of the temperature dependent Tm2+ excited states dynamics that determines the internal quantum efficiency (QE) and thereby the efficiency of the LSC. In this study we investigated the dynamics in CaX 2:Tm2+ (X = Cl, Br, I) by temperature- and time-resolved measurements. At 20 K up to four distinct Tm2+ emissions can be observed. Most of these emissions undergo quenching via multi-phonon relaxation below 100 K. At higher temperatures, only the lowest energy 5d–4f emission and the 4f–4f emission remain. Fitting a numerical rate equation model to the data shows that the subsequent quenching of the 5d–4f emission is likely to occur initially via multi-phonon relaxation, whereas at higher temperatures additional quenching via interband crossing becomes thermally activated. At room temperature only the 4f–4f emission remains and the related QE becomes close to 30%. Possible reasons for the quantum efficiency not reaching 100% are provided.


Introduction
LSCs can become one of many building-integrated photovoltaic (BIPV) solutions that contribute to more sustainable buildings. LSCs make use of a special luminescent coating that absorbs sunlight and emits light of different energy towards solar cells mounted in the edges of a window. The window glass serves as a waveguide for the emitted light. * Author to whom any correspondence should be addressed.
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Key material challenges for the LSC coating involve: a large sunlight absorption fraction that includes ultraviolet and visible light, a high internal luminescence QE and the absence of self-absorption losses caused by a direct re-absorption of the emitted light by the coating [1,2]. Tm 2+ -doped halides have been identified as potential LSC coating material. The broad 4f-5d absorption bands allow it to absorb up to 63% of the solar spectrum (AM 1.5) while no self-absorption losses can occur due to the energy difference between the 4f-5d absorption and the 4f-4f emission. Besides, the energy of this emission corresponds well with the bandgap of copper indium selenide (CIS) solar cells. Furthermore, an optimised coating based on Tm 2+ -doped halides can appear colourless  [3]. However, not much is known about the QE of the 4f-4f emission after 4f-5d excitation. This parameter is directly proportional to the overall LSC efficiency and is mainly determined by the Tm 2+ excited-states dynamics [1,2]. Such dynamics has been studied intensely for CsCaX 3 :Tm 2+ (X = Cl, Br, I) tri-halide systems [4][5][6], but only once for some di-halides [7]. No QE values were reported in these works. In our previous study on NaX:Tm 2+ (X = Cl, Br, I) mono-halides [8] we investigated the excited-states dynamics and measured the QE, but we were unable to provide a full quantitative description of important processes such as: the quenching mechanism related to the lowest energy 5d-4f emission, the presence of the 4f-4f emission at 20 K, and the efficient non-radiative 5d-4f ground state route. We have therefore decided to extend our Tm 2+ excited-states dynamics study to CaX 2 :Tm 2+ (X = Cl, Br, I), where the substitution of Tm 2+ on Ca 2+ -sites required no charge compensation, making use of temperature-and time-resolved experiments; and a more quantitative approach using a numerical rate equation analysis. First, the excitation bands and emissions are classified. Subsequently, a qualitative description of the excited-states dynamics is provided for all three materials, followed by a quantitative modelling on CaBr 2 :Tm 2+ of time-and temperature-dependent 5d-4f and 4f-4f intensities and finally an overall discussion is provided focusing on the recorded QE-values.

Powder synthesis and preparation
The CaCl 2 :Tm 2+ , CaBr 2 :Tm 2+ and CaI 2 :Tm 2+ powder samples were respectively prepared by mixing CaCl 2 , CaBr 2 and CaI 2 (Alfa Aeser, 99.99%) with 1.0-2.0 mol % TmI 2 . The mixtures were ground into a homogeneous powder and inserted into quartz ampoules, which were then attached to a vacuum/inert gas system. After evacuation to 10 −1 mbar and three succeeding purges with dry nitrogen, the ampoules were evacuated further to 10 −3 mbar. Subsequently, the powders were heated using four Tecla burners. After 0.5-1 min the powders had completely molten and the heating was stopped. The solidified samples were removed from the ampoules and ground into a fine powder sample. All handlings were performed under strictly inert and dry conditions in a glovebox (MBraun, Garching, Germany).

Analytical characterisations
The Tm concentration in the samples was determined by means of inductively coupled plasma-optically enhanced spectroscopy (ICP-OES) measurements, using a Perkin Elmer Optima 4300DV spectrometer (Perkin Elmer, Waltham Massachusetts, USA). Diluted standards of Ca and Tm were used to constitute an intensity-concentration calibration line. The obtained values are reported in table 1. Differences with the nominal TmI 2 doping can largely be attributed to the accuracy of the used balance.
Diffuse reflectance spectra were recorded with a Bruker Vertex V80 spectrometer (Bruker, Karlsruhe, Germany), where the determined Kubelka-Munk (K-M) absorption was used to estimate the Tm 2+ /Tm 3+ ratio present in the samples. This ratio is derived from the integrated absorption bands of the Tm 2+ 2 F 7/2 → 2 F 5/2 and the Tm 3+ 3 H 6 → 3 H 5 transitions, in combination with their relative absorption strengths in NaI, that respectively amount to 1 and 3.4. These latter values were determined from the integrated absorption band values of purely doped Tm 2+ and Tm 3+ NaI samples combined with their ICP-OES Tm concentrations. The K-M spectra of the samples are provided in figure 1 in the supplementary information (https://stacks.iop.org/JPCM/33/255701/mmedia) (SI) and the retrieved Tm 2+ /Tm 3+ ratios are listed in table 1.
The x-ray diffraction patterns of the powders were obtained with a Philips X'pert-Pro diffractometer (Philips, Eindhoven, The Netherlands) in Bragg-Bretano geometry using CuK α radiation. The measurements took place at room temperature from 8 • to 80 • 2-theta with a 0.008 • resolution. Figure 2 in the SI shows the diffractograms. The crystallographic structures imply that the Tm 2+ dopant ions that occupy Ca 2+ sites have a (distorted) octahedral coordination leading to a lower 5dtriplet t-state and upper 5d-doublet e-state that are further split due to the octahedral distortion. Throughout this work we will use the short hand notation ( 2s+1 L J ,t 2g )s to assign the excited 4f 12 5d 1 levels, where 2s+1 L J represents the state of 4f 12 , t 2g denotes that the 5d-electron is in a level and stemming from the t-triplet, and s denotes the total electron spin of the excited state.
Fluorescence quantum yield measurements were performed using an Edinburgh FLS980 spectrometer (Edinburgh Instruments, Livingston, UK) with an integrating sphere, a 450 W Xenon arc lamp and a Hamamatsu C9940-02 near infrared (NIR) photomultiplier tube (PMT) (Hamamatsu Photonics, Hamamatsu, Japan). The CaX 2 :Tm 2+ (X = Cl, Br, I) samples were excited into the Tm 2+ ( 3 H 6 ,t 2g ) S=1/2 level at room temperature and the reflectance was measured and compared to that of highly reflecting BaSO 4 and their undoped hosts. The absorption contributions of the CaX 2 (X = Cl, Br, I) hosts were respectively estimated at 4%, 2% and 4%.
From the amount of emitted and host-corrected absorbed photons, QE values were calculated and also added to table 1.

Temperature-dependent measurements
The temperature dependent emission and excitation spectra were obtained by using a xenon lamp coupled to a double monochromator with three gratings and a Hamamatsu C9100-13 EM-CCD or H1033A-75 NIR-PMT that was attached to a single monochromator with three gratings to record the luminescence emerging from the samples. A calibrated EPLAB NBS 1000W quartz iodine lamp was used to acquire the wavelength dependent sensitivity of the detectors. The detection ranges of 400:1150 nm and 950:1600 nm for CCD and NIR-PMT, respectively, share an overlap that allows it to couple the output of both detectors and hence accurately determine the 5d-4f and 4f-4f emission ratio's over temperature Since the Tm 2+ 2 F 7/2 → 2 F 5/2 emission lies too close to the detection limit of the CCD detector, a small spatula amount of Ca 2 Si 5 N 8 :Yb 3+ was added to the samples. After exciting the Yb 3+ at 360 nm, the 2 F 5/2 → 2 F 7/2 emission at 985 nm was observed and used for the detector coupling. With the applied Tm 2+ excitation wavelengths (( 3 H 6 ,t 2g ) S=1/2level), there is no overlap with any of the Ca 2 Si 5 N 8 :Yb 3+ excitation levels and hence only Tm 2+ luminescence is observed [12].
The samples were heated and cooled with an APD Cryogenic Helium cooler (APD Cryogenics, Allentown Pennsylvania, USA) and Lakeshore temperature controller (Lakeshore Cryotronics, Westerville Ohio, USA).
Special hygroscopic sample holders protected the samples, during all measurements, against moisture and oxidation reactions. Similar sample holders were described by Rogers et al [13]. Figure 1 shows the excitation spectra of CaX 2 :Tm 2+ (X = Cl, Br, I) monitoring the Tm 2+ 2 F 5/2 → 2 F 7/2 4f-4f emission, at different temperatures. For CaCl 2 :Tm 2+ the spectra show much resemblance in shape to the earlier reported low temperature absorption spectra by Grimm et al [7] and Karbowiak et al [9]. Similarly, those of CaI 2 :Tm 2+ are akin to the room temperature absorption spectrum of Ten Kate et al [3]. The therein reported 5d-level classifications are appended to the spectra in figure 1.

Assignment of excitation bands
The spectra display a clear separation of around 5700 cm −1 between the ( 3 H 6 ,t 2g ) and ( 3 F 4 ,t 2g ) levels, which follows from the 4f 12 -level splitting into 2S+1 L J terms that are analogous to the Tm 3+ multiplets of the Dieke diagram [14]. In case of CaI 2 :Tm 2+ , an additional weak excitation band is observed close to 860 nm. Upon applying a redshift of 12 480 cm −1 , based on the works of Dorenbos [15], it follows that it represents a spin-forbidden (SF) transition to the ( 3 H 6 ,t 2g ) S=3/2 high-spin (HS) levels. For CaBr 2 :Yb 2+ , Larsen et al [16] observed the lowest energy low-spin (LS) and HS 5d-levels at respectively 25 133 and 23 696 cm −1 . Using retrieved redshifts of 10 797 and 10 304 cm −1 , respectively, these levels should then lie near 673 and 740 nm for CaBr 2 :Tm 2+ . The spectra in figure 1(b) indeed show a broad excitation band located at around 675 nm, thus representing the spinallowed (SA) transition to the ( 3 H 6 ,t 2g ) S=1/2 LS levels. No band is observed near 740 nm in the excitation spectra of the 4f-4f emission. Instead the expected ( 3 H 6 t 2g ) HS band is well observed at low temperatures in the excitation spectra monitoring the HS 5d-emission itself, see figure 3 in the SI. As the excitation spectra of the 4f-4f transition only become intense at elevated temperatures, the HS band is likely hidden due to the broadening of the LS bands. This clearly seems to happen for CaI 2 :Tm 2+ and might also be the case for CaCl 2 :Tm 2+ .

Classification of emissions
In figure 2 the temperature dependent emission spectra of the three samples are displayed upon exciting into their ( 3 F 4 ,t 2g ) levels. Up to four distinct Tm 2+ emissions can be distinguished. These emissions are labelled R 10 to R 40 and their decay times and relative intensities are provided at 20 K or 300 K in table 2. For CaCl 2 :Tm 2+ , Grimm et al [7] already identified the emissions in accordance to their transition. Since the energy of the Stokes' shift is in first approximation the same for all lanthanides in a specific host, reported literature values from for instance CaBr 2 :Eu 2+ and CaI 2 :Eu 2+ can be added to our observed emissions in CaBr 2 :Tm 2+ and CaI 2 :Tm 2+ to establish a direct connection with the excitation bands in figure 1 and hence retrieve the transitions related to the emissions. Figure 3 serves as a schematic overview of all excitation bands and emissions.

Qualitative description of temperature-dependent luminescence behaviour
The temperature dependent emission spectra of the materials reveal that, upon exciting into the ( 3 F 4 ,t 2g ) band at 20 K,  1 Assuming a small configurational offset between the two 4f 12 5d 1 (t 2g )-levels [19], the quenching W 43 as illustrated in figure 3 most likely occurs via multi-phonon relaxation. The fast quenching of emission R 40 leads to a feeding of the ( 3 H 6 ,t 2g ) LS levels and in case of CaI 2 :Tm 2+ the presence of emission R 30 . With an energy gap of 1100 cm −1 (around 10 vibrational quanta) between the LS and HS levels, the emission will quench rapidly via multiphonon relaxation W 32 , as witnessed in the emission spectra at 100 K. For CaCl 2 :Tm 2+ and CaBr 2 :Tm 2+ no emission R 30 is detected. This could be explained by a very rapid quenching via multi-phonon relaxation [18] or an LS → HS resonance energy transfer exciting a neighbouring Tm 2+ ion to its ( 3 H 6 ,t 2g ) HS levels [20], as described further in section 3.5. When subtracting the Stokes' shift energies for CaBr 2 :Eu 2+ from the lowest energy LS excitation bands of CaBr 2 :Tm 2+ it follows that the energy of the ( 3 H 6 ,t 2g ) LS emission is close to the ( 3 H 6 ,t 2g ) HS absorption. The same is true for CaCl 2 :Tm 2+ . Both scenarios lead to a feeding of the ( 3 H 6 ,t 2g ) HS levels from which emission R 20 occurs. For CaCl 2 :Tm 2+ and CaBr 2 :Tm 2+ this 5d-4f emission already has a strong presence at 20 K. It gradually becomes weaker as the temperature increases. The opposite behaviour is observed for 4f-4f emission R 10 because of a non-radiative feeding process W 21 .
For both materials the 5d-4f emission has fully quenched at respectively 270 K and 260 K and only 4f-4f emission R 10 remains. For CaI 2 :Tm 2+ , emission R 20 quenches at a significantly lower temperature of 110 K. It implies that within the temperature range of 110-190 K, only 5d-4f emission R 40 is present; the others already feeding the 2 F 5/2 level and leading to 4f-4f emission R 10 . This behaviour for CaI 2 :Tm 2+ is especially noticeable upon comparing with the excitation spectra of CaCl 2 :Tm 2+ and CaBr 2 :Tm 2+ in figure 1. For these latter materials the relative intensity of the 5d-excitation bands when monitoring the 2 F5/2 → 2 F7/2 emission, is the same for all temperatures. For CaI 2 :Tm 2+ the higher energy 5dbands have a much lower intensity (because these result in emission R 40 ) compared to the lower energy 5d-bands that do result in 2 F 5/2 → 2 F 7/2 emission. From 190 K onwards all 5d-4f emissions in CaI 2 :Tm 2+ have quenched so that excitation into the different 5d-bands all result in 4f-4f emission. The 5d-bands are now dictated by the oscillator strength of the 4f-5d transitions, as is also observed in case of CaCl 2 :Tm 2+ and CaBr 2 :Tm 2+ . As the energy gap between the ( 3 H 6 ,t 2g ) S=3/2 and 2 F 5/2 levels for CaCl 2 :Tm 2+ , CaBr 2 :Tm 2+ and CaI 2 :Tm 2+ respectively amounts to 3700, 3500 and 1460 cm −1 or 14, 22 and 13 vibrational quanta, the quenching mechanism related to emission R 20 can well be multi-phonon relaxation (MPR). However, since it involves a 5d-4f relaxation there is a large configurational offset and the optical phonon coupling strength, as defined by the Huang-Rhys factor, will be strong.  The configurational offset could enable quenching via interband crossing (IC) or inter-configurational relaxation [3,21]. This quenching mechanism involves the configurational crossover-point between the ( 3 H 6 ,t 2g ) S=3/2 and 2 F 5/2 levels, that can be breached at certain temperatures when enough energy becomes available. In case of a large Stokes' shift, the crossing point is likely to be breached at a lower temperature [22]. In the next subsection, the two proposed quenching mechanisms of MPR and IC for emission R 20 will be examined into more detail.

Quantitative description of temperature-dependent luminescence behaviour
Since the quenching mechanism of 5d-4f emission R 20 remains unclear, we have decided to evaluate it by performing a luminescence rate equations analysis on CaBr 2 :Tm 2+ involving all radiative and temperature-dependent non-radiative transitions after excitation into the ( 3 H 6 ,t 2g ) LS band. With LS emission R 30 not observed in CaBr 2 :Tm 2+ , we initially neglect its influence and assume the excitation will automatically end up in the lowest energy ( 3 H 6 ,t 2g ) HS levels. The scheme portrayed in figure 3 then allows us to describe the excited state population N i (i = 1, 2) of the 2 F 5/2 and ( 3 H 6 ,t 2g ) S=3/2 levels, respectively, via the rate equations below.
In this coupled set of equations, R 20 and R 10 represent the radiative transition rates in s −1 , W 21 the non-radiative transition or quenching rate of emission R 20 in s −1 , P portrays the laser power in cm −1 s −1 , σ the absorption cross section per wavelength of excitation energy in cm and N 0 the electron groundstate population, which is in good approximation considered to be unaffected by the excitation.
Following the scenario that emission R 20 quenches via multi-phonon relaxation, the non-radiative rate W 21 can be described according to the Reisfeld model [24][25][26] that is provided below.
In this relation: ω max represents the maximum optical phonon energy in cm −1 , k the Boltzmann constant in cm −1 . K −1 and T the temperature in K. Furthermore, p embodies the number of phonons consumed during the relaxation: p ∼ = ΔE/ ω max where ΔE is the energy gap in cm −1 . W p (0) is the multi-phonon decay rate at 0 K and is defined further via the following relation: Here, W 0 (0) is the decay rate at ΔE = 0 cm −1 and T = 0 K, and g the dimensionless electron-phonon coupling strength (Huang Rhys factor).
By considering the option of interband crossing, the nonradiative rate W 21 follows the relation below [27,28], where s represents the frequency factor in s −1 , ε the activation energy of the quenching process in cm −1 , k the Boltzmann constant in cm −1 . K −1 and T the temperature in K.
Especially at low temperatures the two expressions for the non-radiative rate W 21 predict a different temperature dependence, which should allow us to draw conclusions on their contribution to the observed non-radiative relaxation.

Model setting.
The fitting of our rate equation model and related quenching mechanisms to the temperature-and time-dependent intensity data, requires a set of starting values for the different parameters. The pump rate constant σPN 0 can be chosen arbitrary and is set at 1, where upon exciting into level |3 we assume a rapid quenching towards level |2 from which we monitor emission R 20 . The radiative rates R 10 and R 20 were estimated based on the luminescence lifetime of the emissions at respectively 20 and 30 K, assuming no quenching takes place at these temperatures.
For CaX 2 :Tm (X = Cl, Br, I) no direct values for the phonon energies ω max coupling to Tm 2+ are reported in literature. We have therefore decided to estimate these values based on known studies that involve such hosts, see table 1 [9][10][11]. The values are close to those reported for LaY 3 (Y = Cl, Br) [24]. The energy gap ΔE between levels |2 and |1 was determined on 3500 cm −1 and the required amount of vibrational quanta p to bridge it is around 22. A reasonable starting value for the W 0 (0) parameter was estimated from literature to be 1 . 10 14 s −1 [24,25]. Since not much is known on the electron-phonon coupling strength g between 5d-and 4f-states, the rough starting value of 2 was used from the numerical modelling work of Grimm et al [6]. The parameters constitute an overall W p (0) parameter of 18.7 s −1 . As an overall fitting strategy ω max and W p (0) are fitted, while ΔE was kept fixed.
In the case of IC, the thermal activation energy ε was approximated at 1694 cm −1 and retrieved from an Arrhenius plot of the integrated luminescence intensity of R 20 , see

Non-steady state rate equation analysis.
The derived rate-equations can be solved in a non-steady-state manner, assuming a time-dependent depopulation of the levels, with solutions provided in section 7.5 of the SI. The solution for level |2 was fitted onto the measured luminescence lifetime curves of 5d-4f emission R 20 . The related fits are displayed in figure 4, where from 300 K onwards the now weak emission is only faintly recorded. From each of the fit a value for W 21 was obtained, allowing us to establish a W 21 (T ) point series onto which the two quenching models can be tested. Figure 5 shows this series as represented in black, where small error bars of 0.1%-5%, based on the fitting, are attached. The MPR model, shown in solid dark red, is able to reproduce the low-temperature trend among the W 21 points. Yet, at high temperatures it is unable to mimic this and overall no accurate fit could be obtained. For IC, illustrated in solid orange, it is the other way around: an inaccurate representation at low temperature and a good depiction at high temperatures. Once more, the fit proved to be inaccurate. Based on these findings, the combined quenching via both MPR and IC was investigated. This option, as portrayed in blue, was able to provide a reasonable fit for both the low and high temperature range. The herewith obtained fitting parameters are added to table 3 and are close to our initial starting values; all within the same order of magnitude. For the combined quenching, the overall temperature development of MPR and IC are respectively portrayed in dashed red and dashed orange. The curves reveal that the low temperature regime is governed by MPR, whereas IC is dominant within the high temperature range. Furthermore, at around 170 K the non-radiative rate W 21 becomes stronger than the radiative rate R 20 , shown in dotted black, indicating that the quenching takes the upper hand.

Steady state rate equation analysis.
The previously outlined set of coupled rate equations can also be solved in a steady state fashion, where a steady depopulation of the levels assumed. As elaborated in section 7.6 of the SI, the solutions combined with the radiative rates can be used for fitting luminescence intensity curves. Figure 6 shows such curves for emissions R 20 and R 10 in CaX 2 :Tm 2+ (X = Cl, Br, I) as a function of temperature, where the luminescence intensities of both emissions were corrected for the sensitivity of detection and coupled via the method described in section 2.3. The data was normalised on the measured QE values of emission R 10 at room temperature, see table 1. For CaBr 2 :Tm 2+ , provided in panel b, the observed trends among the solid measured intensity data points are supported by those of the integrated luminescence lifetime curves from figure 4, displayed as open symbols. The light blue line shows a good fit for our combined quenching model (MPR + IC) onto the data points of emission R 20 . The retrieved fitting parameters are appended to table 3 and are very close to both our original starting values and those obtained from the non-steady state fitting. When inserting these fitted parameter values in the rate equation solution for level N 1 (note that the fits were done on level N 2 ), the dotted red line is acquired which follows the overall data trend, but is shifted by 10 K towards lower temperature. Our fitted model predicts a lower temperature and intensity for the intersection point between the R 20 and R 10 curves. Furthermore, at 250 K the fitted model reaches an intensity plateau while for the experimental data it is reached at a higher temperature.
The similarity between the luminescence intensity curves of CaBr 2 :Tm 2+ and CaCl 2 :Tm 2+ has incited us to extend the  It clearly follows the trends among the  data points and the obtained fitting parameters, appended to  table 8 in the SI, are reasonably close to their starting values. The dashed dark red line, as based on inserting the obtained fitting parameters into the rate equation solution for N 1 , is not able to perfectly mirror the measured intensity trends in emission R 10 . Especially at temperatures below 100 K, where 4f-4f emission R 10 is measured but not simulated by our model, and above 200 K, where the measured intensity is much lower than predicted.
From figure 6(c), it follows that for CaI 2 :Tm 2+ the quenching of emission R 20 is too strong for performing a fitting analysis with our model. Panel d shows that this is due to a large value of W 21 compared to W 32 as explained at the end of section 3.3.
The obtained steady-state fitting parameters for CaBr 2 :Tm 2+ and CaCl 2 :Tm 2+ , allow it to plot the non-radiative rate W 21 over temperature and inspect the development of the MPR and IC processes. Figure 7 shows these plots with colour coding in analogy to figure 5. For both materials the low temperature region is governed by MPR, while at high temperatures IC is dominant in CaCl 2 :Tm 2+ (panel a). In case of CaBr 2 :Tm 2+ (panel b), the MPR process stays strongest at even high temperatures; which differs from figure 7. Nevertheless both processes seems clearly involved in the quenching. For CaBr 2 :Tm 2+ , the non-radiative rate W 21 outmatches the radiative rate R 20 at around 160 K and the quenching prevails. For CaCl 2 :Tm 2+ this seems to happen at a slightly higher temperature.

Model limitations
The quenching of 5d-4f emission R 20 and intensification of 4f-4f emission R 10 predicts the presence of a risetime phenomena in the luminescence lifetime curves of the latter. Such a phenomena has been observed several times before in similar materials [8,22]. The solid curves in figure 8 reveal that also for CaBr 2 :Tm 2+ a risetime is measured, even at 20 K. The curves predicted by our three-level combined quenching model (MPR + IC), using fitting parameters from table 3 column 3, are provided by the dashed curves. For temperatures above 200 K, the curves overlap well with the experimental data. At lower temperatures however, where the 4f-4f emission intensity is very weak, the risetime predicted by the model is longer than experimentally measured. This discrepancy arises from a limitation of our model that is discussed in the next subsection.
3.5.1. HS → LS Interaction and 4-level model. So far we have assumed that the population of the 5d ( 3 H 6 ,t 2g ) LS state, immediately after excitation, is lost to the lower lying 5d (3H 6 ,t 2g ) HS state at all temperatures. It has allowed us to describe the feeding of 4f-4f luminescence by the 5d manifold and assign a combination of multi-phonon relaxation and interband cross- ing to such a temperature quenching process. However, it has been observed in various halides [5,29] that at low temperatures the LS-state population is significant and actually also the required time and/or temperature for LS → HS depopulation cannot be neglected. Here we present some evidence for LS → HS states interaction and discuss its influence on our model.
In figure 9 the lifetimes of the 5d-4f (3H 6 ,t 2g ) HS emission (blue dots) are compared to the risetimes of the 4f-4f emission (red dots) for CaX 2 :Tm 2+ (X = Cl, Br, I). Both emissions are monitored after excitation into the 5d (3H 6 ,t 2g ) LS levels. The (3H 6 ,t 2g ) HS lifetimes were obtained via a single exponential fitting of the 5d-4f decay curves, whereas a similar fitting strategy on 0-1 ms timescale was used for retrieving the 4f-4f risetimes. As is observed the lifetime of the (3H 6 ,t 2g ) HS emission behaves in a simple manner: at 20 K the lifetime τ d amounts to ∼300 μs (∼30 μs for CaI 2 :Tm 2+ ) and as the temperature increases it becomes shorter due to thermal quenching. This is well in-line with the measurements and modelling of its emission behaviour, see for instance figure 6. As discussed in previous sections, the quenching is due to a non-radiative feeding of 4f 2 F 5/2 level. As such, it is expected that the time scale related to the decay of the 5d-4f HS emission is reflected in the risetime components of the 4f-4f 2 F 5/2 → 2 F 7/2 emission. In case of CaI 2 :Tm 2+ this is observed at all temperatures. For CaCl 2 :Tm 2+ and CaBr 2 :Tm 2+ the risetime τ r components of the 4f-4f emission (red) are in good agreement with the 5d-4f HS lifetimes τ d (blue) only above ∼150 K. Below 150 K the 4f-4f risetimes deviate strongly from the 5d-4f HS lifetimes. While the 5d-4f HS lifetimes are around ∼300 μs, the τ r rise-times behave in a non-monotonic manner: for example in CaBr 2 :Tm 2+ at 20-50 K τ r is relatively short, in the order of a few microseconds; whereas between 50-150 K it increases up to ∼100 μs. This behaviour of the 4f-4f emission risetimes has been reported for CsCaX 3 :Tm 2+ [30] and is connected to the nonradiative relaxation from an LS to HS 5d-state during the feeding of a 4f excited state. Applied to our case, the short risetimes at 10-50 K could then be due to an LS 5d → 4f nonradiative relaxation with strong electron-phonon coupling. The 50-150 K increase in τ r is due to LS → HS thermally activated relaxation: partially populated HS and LS 5d-states both feed the 2 F 5/2 state.
The existence of 4f-4f emission after excitation into 5d manifold already at 10 K points to multi-phonon channel as the only relaxation process not disabled at He-temperatures [24,28]. In various compounds, the onset of LS → HS nonradiative relaxation is related to the energy difference between LS and HS states, the optical phonon mode to which the relaxation couples and the phonon coupling strength [24,26,28]. For the former two parameters (host phonon modes, hω LO , and LS-HS energy separation, E HS-LS ) the values can be obtained from literature. We have decided to check the relation between LS-HS populations with risetime behaviour for various compounds known from literature. Figure 6 in the SI reveals that there is a trend between the energy difference between the LS and HS states, in number of required phonons, and the T 50 temperature quenching onset related to the 5d LS-depopulation. The dependence has a huge uncertainty and deviation due to unknown phonon coupling strengths, but still we can expect that in our CaCl 2 :Tm 2+ and CaBr 2 :Tm 2+ compounds the LS 5d-state actively loses population at around 100-150 K, which is consistent with the observations in risetime kinetics in figure 9.
In the new assumption that below 150 K the electrons in the 5d ( 3 H 6 ,t 2g ) LS state do not immediately thermally relax to the HS state, we need to consider a 4-level system for our modelling.

Possible mechanisms for confined QE.
Direct QE measurements with an integrating sphere have resulted in QEvalues that are considerably lower than the 100% predicted by our model. Our data does not hint at any process explaining the lower-than-expected QE values. Below we suggest four possibilities that still need to be confirmed experimentally in future work. It may be that the QE-measurements are inaccurate. The special sample holder in the integrating sphere, that protects the powder sample from hygroscopicity and oxidation, may absorb part of the Tm 2+ NIR luminescence despite the fact it is made from Teflon and quartz parts. Alternatively, our samples may partly absorb excitation light by impurities or defects other than the Tm 2+ ions, this despite our approach to measure the absorption relative to undoped samples when calculating QE-values. In terms of luminescence quenching mechanisms, the lower QE-values may be caused by a thermally stimulated electron delocalisation to the conduction band as was explained our work on NaX:Tm 2+ mono-halides [8]. Our unpublished low temperature excitation and emission measurements on Tm 3+ -doped CaX 2 (X = Cl, Br, I) has revealed clear features related to bandgaps and CT bands. It does however not allow us to determine the energy of the lowest 5d-state with respect to the conduction band bottom with high enough certainty to decide on the possibility of this process. Finally, concentration quenching from the excited 4f-or 5d-states can result in a lower QE. In SrI 2 :Tm 2+ [23] concentration quenching only starts above 3 mol % Tm 2+ -doping. In other hosts like NaI [39] the quenching starts at a somewhat lower doping percentage of 0.5 mol %. With a Tm 2+ concentration of about 1 mol % in our samples, there may be some quenching but from the observed decay times of the 4f-4f emission of 3.6-5.3 ms it is likely not a strong process.
Although the quantitative fitting approach describes the overall temperature-and time-dependent well, two interesting deviations were observed and discussed. Firstly, at low temperature, we observe a risetime for the 2 F 5/2 → 2 F 7/2 emission, 15 times shorter than predicted by the model; which can likely be explained by an LS → HS resonance energy transfer interaction between neighboring Tm 2+ ions. Secondly, we observe a 2 F 5/2 → 2 F 7/2 quantum efficiency of 20-30% after 2 F 7/2 → ( 3 H 6 ,t 2g ) S=1/2 excitation for all three dihalides. Our model predicts a QE of 100% as it does not contain a non-radiative process to the ground state. Different explanations for this were provided and discussed, such as: absorption of 2 F 5/2 → 2 F 7/2 emission light by the hygroscopic sampleholder, partial excitation light absorption by impurities and defects, a thermally stimulated electron delocalization route to the conduction band, and concentration quenching effects.
This study allow us to gain a better understanding of the quenching processes of the Tm 2+ excited 5d-manifold and related feeding of the 2 F 5/2 → 2 F 7/2 emission. Based on the variety in phonon energies, 5d-level positions and Stokes' shifts of CaX 2 :Tm 2+ (X = Cl, Br, I), we were able to significantly shift the temperature onset of these processes. It provides design criteria for stable Tm 2+ 2 F 5/2 → 2 F 7/2 luminescence to be used for photovoltaic energy conversion in LSCs.