Critical Power Density: A Metric to Compare the Excitation Power

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A: New Tools and Methods in Experiment and Theory

Critical Power Density: A Metric to Compare the Excitation Power Density Dependence of Photon Upconversion in Different Inorganic Host Materials Reetu Elza Joseph, Carlos Jiménez, Damien Hudry, Guojun Gao, Dmitry Busko, Daniel Biner, Andrey Turshatov, Karl W. Krämer, Bryce Sydney Richards, and Ian A. Howard J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b03851 • Publication Date (Web): 09 Jul 2019 Downloaded from pubs.acs.org on July 17, 2019

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The Journal of Physical Chemistry

Critical Power Density: A Metric to Compare the Excitation Power Density Dependence of Photon Upconversion in Different Inorganic Host Materials

Reetu E. Joseph, † Carlos Jiménez, † Damien Hudry, † Guojun Gao, † Dmitry Busko, † Daniel Biner, § Andrey Turshatov, † Karl Krämer, § Bryce S. Richards, † ‡ * and Ian A. Howard† ‡ *

† Institute

of Microstructure Technology (IMT), Karlsruhe Institute of Technology, Hermann-von-

Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany § Department

of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, 3012 Bern,

Switzerland ‡Light

Technology Institute, Karlsruhe Institute of Technology, Engesserstrasse 13, 76131 Karlsruhe,

Germany * [email protected] * [email protected]

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Abstract In photon upconversion (UC) based on triplet-triplet annihilation, the upconversion photo luminescent quantum yield (UC-PLQY) depends on the excitation power density in a way that can be described by a single figure of merit. This figure of merit, the threshold value, allows the excitation power density required for efficient UC-PLQY to be compared between different triplet-triplet annihilation systems. Here, we investigate the excitation power density dependence of two-photon UC processes in a series of four lanthanide-doped inorganic host materials (oxides, fluorides, and chlorides) all doped with 18 mol.% of Yb3+ sensitizer ions and 2 mol.% of Er3+ activator ions. We demonstrate that an analogous figure of merit, which we call the critical power-density (CPD), accurately describes the UC power dependence of these samples. Better CPD values are obtained when the lifetime of the intermediate states is long. The UC-PLQY at the CPD is linked to the saturation UC-PLQY. Thus, a measurement of the UC-PLQY at this low power density can be used to estimate the theoretical saturation UC-PLQY in the absence of deleterious effects such as laser-induced heating. This is compared to another method to estimate the saturation based on the CPD model, namely taking half of the level’s PLQY under direct excitation. Our careful analysis of the upconversion spectra as a function of excitation power density gives several insights into the differing upconversion pathway in the hosts, and proves to be a useful tool for their comparison.


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INTRODUCTION Photon upconversion (UC) utilizing lanthanide ions was first proposed by Bloembergen in 19591 and experimentally demonstrated by Auzel in 1966.2 Via the UC process, two (or more) photons of longer wavelength absorbed in a material lead to the emission of a shorter wavelength photon. Research in this field accelerated when it was demonstrated that the efficiency of UC could be increased multiple times by co-doping with another material with a larger absorption cross-section.3-7 Common applications of UC materials include luminescence thermometry,8-9 and photonic marking used for example in bio-imaging.10 Ultimately, applications that require efficient performance at much lower power-densities of excitation-photons, such as photovoltaics or photocatalysis could also be realized. For this, the efficiency of the UC process – measured as the UC photoluminescent quantum yield (UCPLQY) as a function of the excitation power density – is an important characteristic of the UC material system. It is desirable to know what excitation power density is necessary for UC to become efficient for a given material system, in order to compare upconversion materials for a given application. In this contribution, we introduce a single-parameter figure of merit – the critical power-density (CPD) – for two-photon UC processes that: 1) allows the excitation power density dependence of the UC emission intensity to be readily compared between materials; 2) reveals physical insights into upconversion mechanisms; and 3) when combined with maximum UC-PLQY, provides a full description the twophoton UC performance. This will help to categorize and identify suitable material systems based on the excitation power density required for any desired application. Anderson-Engels et al. introduced a concept of balancing power-density (BPD) to compare the excitation power density dependence of different inorganic nano-materials exhibiting two-photon UC emission sensitized by trivalent ytterbium (Yb3+) ions.11 At the BPD, the intermediate energy state is driven into a state in which its depopulation by linear decay and energy-transfer to the higher-energy UC emitting state become equal. The BPD was found by searching for the point at which the slope of a log-log representation of UC intensity vs. excitation power density becomes equal to 1.5 (the slope changes from 2 to 1 as the excitation power density increases, for a two-photon UC process). Based on the BPD, reasonable predictions of the whole excitation power density-dependence of the UC could be made. However, we note that the BPD model overestimated the experimental UC-PLQY for nanoparticles (core and core-shell) at moderate power densities (2-11 W/cm2) and underestimates the UC-PLQY at higher power densities (>11 W/cm2). More recently, Christiansen et al. devised an



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analytical model for the intensity dependence of singly-doped Er3+ materials, modelling the two-photon 980 nm UC after 1500 nm excitation.12 This model included a parameter referred to as the saturation intensity (Isat), a single parameter that describes the intensity dependence of the UC process in this singly-doped system. We note that the equations derived by Christiansen et al. are directly analogous to those describing the excitation power density dependence of triplet-triplet annihilation upconversion (TTA-UC), with the saturation intensity being analogous to what is referred to as the “threshold intensity” in the TTA-UC community.13 Christiansen et al. studied nanoparticles – synthesized both with and without a NaLuF4 shell – that were spin-coated in monolayers on fused quartz substrates. At high excitation power densities, the model did not fit with the excitation power density-dependence data and several data points had to be excluded. We hypothesize that this is because of thermal effects at higher excitation power densities, with laser-induced heating substantially changing the steady-state temperature of the sample. Our recent publication points out the relevance of this correction and offers a method for this correction at high excitation power densities.14 Such a phenomenon is similar to the concern raised by Kaiser et al. that the BPD model does not take into account saturation effects for micropowder hosts.15 However, given that we are interested in describing the turn-on of the UC process –how well the UC system performs at lower power densities –we simply restrict our examination of the excitation power density to the regime before temperature or thermal effects become appreciable. We agree that additional characterization of excitation-laserinduced heating and other processes causing roll-off is important for applications that require high excitation power densities (>10 W/cm2). However, understanding the simpler dynamics of UC turn-on is still important in its own right, and should provide a basis upon which higher order corrections can be built to describe the behavior at high excitation power densities. In this contribution, we use a simplified rate equation model to consider a system with both sensitizer and activator and hence relevant to any energy transfer upconversion (ETU) system exhibiting twophoton UC. Our simplifications lead to rate equations equivalent to those used by Christiansen et al. to model activator-only systems. Although the model does not rigorously describe the internal photophysics of the ions, we find that it does a very good job of parameterizing the excitation power density of two-photon UC emissions for a wide range of inorganic host materials. It allows a useful figure of merit to be extracted, which we call the critical power-density (CPD). We conclude that determination of the CPD (or the BPD introduced by Anderson-Engels et al.) provides a good way of


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allowing upconversion hosts to be compared. Combined with the saturation UC-PLQY, a fairly complete characterization of the quality of the UC system can be given by just two numbers. Furthermore, we find an experimental correlation between these two figures-of-merit, as discussed further below. METHODS Derivation of CPD model: Monguzzi et al. defined a steady-state threshold intensity for TTA-UC.13 The similarity of two-photon inorganic UC with this organic case motivated us to look for the existence of such a similar threshold that could be used for characterization of different inorganic host materials. A highly-simplified version of the Er3+/Yb3+ sensitizer/activator system undergoing ETU is given in Figure 1. We assume that the intermediate state on the emitter and the excited-state of the activator are in resonance, and therefore can be described by a single excited-state population labelled A1. The generation rate - G for A1 (expressed as the number of ions excited per unit volume per second), can be determined from the excitation power density (converted into photon flux) and material absorption. We make the simplifying assumption that there is no depletion of the ground state A0 (i.e. that there is no absorption saturation in the range of excitation power densities considered). The UC emission level reached after a twophoton ETU process is labelled A2. The population of the two energy levels, A1 and A2 can then be expressed according to Equations (1) and (2): 𝑑𝐴1 𝑑𝑡 𝑑𝐴2 𝑑𝑡

= 𝐺 ― 2𝐴12𝑘𝐸𝑇12 ― 𝐴1𝑘1

(1)

= ― 𝐴2𝑘2 + 𝐴12𝑘𝐸𝑇12

(2)

where 𝐴12𝑘𝐸𝑇12 is the rate at which two ions in state A1 transfer their energies such that one ion moves to state A2 and the other ion relaxes to the ground state, 𝐴1𝑘1 the total single ion decay rate from A1 to the ground state A0, and 𝐴2𝑘2 the single ion decay rate from A2 to the ground state A0.

Considering only the steady-state behavior of the system, Equations (1) and (2) can be rewritten as: 𝐺 = 2𝐴12𝑘𝐸𝑇12 + 𝐴1𝑘1

(3)

𝑘𝐸𝑇12

𝐴2 = 𝐴12

(4)

𝑘2



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From Equation (3), an expression for 𝐴1 can be obtained from the positive root of the solution of the quadratic function: 2𝐴12𝑘𝐸𝑇12 + 𝐴1𝑘1 ― 𝐺 = 0 ⇒A1 = ⇒𝐴1 =

(5)

―𝑘1 ± (𝑘1)2 + 8𝐺k𝐸𝑇12

(6)

4𝑘𝐸𝑇12 𝑘1 4k𝐸𝑇12

( 1+

8𝐺k𝐸𝑇12 𝑘12

)

(7)

―1

Figure 1 Simplified energy level diagram for twophoton UC based on the ETU process. G is the rate at which energy carriers are generated in the first excited state A1, A0 is the ground state and A2 is the second excited state, kET12 represents the energy transfer UC rate from level A1 to level A2 and to the ground state A0, and k2 and k1 the single ion decay constants from A2 and A1, respectively. By substituting Equation (7) into Equation (4), we find a new expression for UC luminescence from the level A2.

𝑘2𝑟𝑎𝑑𝑘12

(

𝑈𝐶 = 𝐴2𝑘2𝑟𝑎𝑑 = 16𝑘2kET12 ―1 +

1+

𝐺

2

)

𝑘12 8kET12

(8)

where A2k2rad is the radiative decay rate from level A2 and 𝑘2 = 𝑘2𝑟𝑎𝑑 + 𝑘2𝑛𝑜𝑛 ― 𝑟𝑎𝑑. The generation rate can be calculated from the photon flux and absorption coefficient:

G =

𝐼𝛼 ℎ𝜈

(9)


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where α is the absorption coefficient (units: cm-1), I is the excitation power density (units: W cm-2) and

hν is the energy of a photon. By substituting G, Equation (8) can be written as: 𝑘2𝑟𝑎𝑑𝑘12

𝑈𝐶 = 16𝑘2k

( ―1 +

ET12

1+

(

⇒𝑈𝐶 = 𝐶 ―1 + 1 +

𝐼 2 𝐶𝑃𝐷

)

(10)

𝐼 2 𝐶𝑃𝐷

)

(11)

where C is a scaling constant and CPD is defined as the critical power-density (units: W cm-2). 𝑘12ℎ𝜈

(12)

𝐶𝑃𝐷 = 8kET12𝛼

The lower the CPD, the smaller the excitation power density at which UC becomes efficient, and the more suitable is the material for low-power applications. We see that CPD is proportional to the square of the rate constant k1, i.e., the inverse lifetime of the intermediate state A1. Therefore, to achieve a low CPD, longer intermediate state lifetimes are highly favored. Also a stronger absorption and faster rate of energy transfer UC to the second excited state are favorable as it leads to a decrease in CPD. For comparison, we also will fit our data to the BPD model,11 which describes the excitation power density dependence of the UC-PLQY as: 𝜂s

𝜂=

𝐼 𝐼b

(13)

𝐼

1+𝐼

b

where, η is the PLQY, ηs the saturation PLQY, I the excitation power density, and Ib the balancing power density. From this, we can easily express the intensity of UC emission as:

𝑈𝐶 ∝

𝐴𝐼2 𝐼b + 𝐼

(14)

where 𝐴 is a constant. Experimental Methods: We now investigate how accurately the experimentally-measured excitation power density dependencies of the UC luminescence are described by the CPD model derived from the simple



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approximations above. We also compare this to the BPD model in the literature.11 We do this by fitting the excitation power density dependence of two-photon UC from different inorganic host materials to Equations (11) and (14). Four microcrystalline hosts exhibiting UC upon near-infrared (NIR) excitation of 980 nm wavelength, namely β-NaYF4, YF3, La2O3, and YCl3 are selected for this purpose to span through a range of lattices with varying phonon energies. All the four hosts are doped with the same concentration of Yb3+ and Er3+, namely 18 mol.% and 2 mol.%, respectively. All materials are synthesized according to established procedures.16-18 All the samples are encapsulated with epoxy resin inside a N2-filled glovebox in 1 mm x 1 mm square capillaries made of borosilicate glass to prevent any environmental degradation. The UC vs excitation power density dependences of the different UC bands are obtained after integrating the spectra (total photon counts) for these bands at different excitation power densities. These spectra are captured using a spectrometer (Avantes, AvaSpec-ULS2048×64TEC), which is calibrated for intensity along with an integrating sphere (Labsphere, 6″ Ø, 3 P-LPM-060-SL) using a calibration lamp (Ocean Optics, HL-3plus-INT-CAL-EXT). The sample is placed in the middle of the integrating sphere and illuminated using 980 nm laser light focused with a 75 cm lens. The beam is found to be elliptical, with a minor-to-major axis ratio of 0.5. Applying the ISO standard secondmoment method on the beam spot measured by a beam profiler (Thorlabs, BP209-IR/M) and 2σ definition for the semi-minor and semi-major axes, the area of the ellipse defined by these is calculated as 4.6 x 10-3 cm2. This spot is impingent on a microcrystalline sample held in a thin borosilicate glass capillary (square 1×1 mm cross-section). A schematic of the excitation spot and sample is provided in the supplementary information Figure S1. The matching of the excitation spot diameter with the capillary width minimizes the amount of upconversion excited via light scattered outside the excitation spot. For the current modelling the excitation power density is taken to be the measured excitation power divided by the spot area as determined above. A 980 nm continuous-wave (CW) laser diode (Thorlabs, L980P200) mounted on a temperature controlled mount (Thorlabs, TCLDM9), and driven using a laser diode controller (Thorlabs, ITC4001) is used as the laser source. The excitation power density is varied by using a motorized variable filter wheel (Thorlabs, NDC-100C2) and the power is measured inline using a powermeter (Thorlabs, PM320E) by measuring the part of the beam reflected off a glass slide placed in the beam path. This power measured by the powermeter is calibrated to be 8% of the actual power reaching the sample. A 950 nm short-pass filter (Semrock,


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FF01-950/SP-25) is used to filter out the laser beam for detecting only the UC emission with the spectrometer. The system is automated by using a finite-state machine code written in LabVIEW (National Instruments, LabVIEW-Software). The UC spectra were acquired for back-to-back sweeps of excitation power density in both forward and reverse directions and no hysteresis effects were observed, proving the absence of laser-induced heating. This is because the range of excitation power densities we use is not high enough to cause laser induced heating, so further correction for laser induced heating is not required for our data. The same setup is used for measuring the UC-PLQY using the 3M method.19-20 For the measurements of the laser signal, the 950 nm short-pass filter is removed and another spectrometer (Thorlabs, CCS200/M) is employed. The spectra are acquired continuously at high excitation power densities to obtain the kinetics and thereafter the UC-PLQY values are corrected for thermal effects as per our previous publication.14 In case of direct excitation of the green level a 525 nm laser (Roithner, LD-51510MG) is used for excitation. Lifetimes of the samples are measured using a multi-channel-scaling (MCS) card (Picoquant, Timeharp 260). The sample is excited using a 980 nm CW laser diode (Thorlabs, L980P200) modulated at 25 Hz frequency with 33.33% duty cycle using the built-in functionality of the laser diode controller (Thorlabs, ITC4001). The trigger signal is fed to the MCS card after being delayed by 20 µs using a custom-built Arduino-based delay generator and the emission from the sample is detected at 990 nm and 1530 nm using a double monochromator (Bentham, DTMS300) coupled to an infrared single-photon detector (ID Quantique, ID220), whose signal was coupled to the MCS card after using appropriate electronics to scale down the signal to the level of the MCS card. The laser power is set at the lowest possible, such that the UC emission signal can be detected from the weakest emitting sample. In our case, this was at an excitation power density of 4 mW cm-2. We do this in an attempt to avoid repopulation of the Yb3+ 2F5/2 state at 980 nm via UC from the 4I13/2 state of Er3+ at 1550 nm.

RESULTS AND DISCUSSION Determination of the two-photon UC processes:



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Since our CPD model is only applicable to two-photon UC processes, it is important to analyze the UC emission spectra and select only regions whose emission is dominated by a two-photon process. In this section we carefully examine the excitation power density-dependence of the UC spectra for each of the four hosts (-NaYF4, YF3, YCl3, and La2O3) in order to rigorously determine which spectral regions are dominated by two-photon upconversion processes (and the energetic transitions these correspond to). We identify regions of green and NIR emission that are purely attributable to twophoton processes in -NaYF4, YF3, and YCl3. For La2O3, the red emission is also a two-photon process (Figure S1 of supporting information). In the following, we examine materials sequentially, developing an understanding of the processes in each material based on the changes in their UC emission spectra with excitation power density.

a) -NaYF4: 18% Yb3+, 2% Er3+ As the excitation power density increases, the amount of UC coming from three-photon processes will grow faster than that coming from two-photon processes. Therefore, if we normalize the UC spectra for each excitation power density to the total number of emitted photons emitted at that excitation power density (the integral under each curve), then the emission coming from two-photon processes should make a smaller relative contribution to the overall emission as the excitation power density is increased (whereas the relative contribution of the emission from three-photon processes increases). In other words, the UC spectrum (normalized to the total number of emitted UC photons) at each excitation power density can be seen as the weighted sum of two spectra, one corresponding to twophoton processes and another to three-photon processes. At each excitation power density, the twoand three-photon spectra each have a weight. The sum of the two-photon spectrum multiplied by its weight plus the three-photon spectrum multiplied by its weight gives the total spectrum at that excitation power density. The weight of the two-photon process should decrease with fluence, while that of the three-photon process should increase. We are now faced with the problem of factoring the known total UC emission spectrum as a function of fluence into the sum of two independent spectra and their associated weights. This is a problem often faced in chemometrics (the factorization of an evolving spectrum, into multiple independent spectra and their evolving weights), and we chose the MCR-ALS algorithm to solve this problem.21-22 This


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algorithm calculates the constituent spectra and their relative concentrations as another variable, like time or, in our case, the excitation power density increases. We use the MCR-ALS algorithm implemented in MATLAB to analyze the normalized UC-emission-spectra of -NaYF4: 18% Yb3+, 2% Er3+.23-24 We obtain two individual spectra as shown in Figure 2(a). The contribution (weight) of one of the spectra increases as excitation power density increases (indicated in blue). This is the spectrum of processes affected by 3-photon channels. The peaks are labeled in Figure 2(a) and their excitation by three-photon pathways is in agreement with current literature.25-26 The contribution of the other spectrum (shown in green), decreases as the excitation power density increases. We will show that these emissions are dominated by two-photon processes, and can be analyzed by our CPD method. These two-photon emissions stem from the 4S3/2 and 2H11/2 states.

Figure 2(a) Deconvoluted spectra from the total UC spectra of -NaYF4: 18% Yb3+, 2% Er3+ by the MCR-ALS algorithm with the corresponding radiative transitions assigned to the peaks. The green and blue colors are ascribed to two- and three-photon processes, respectively. (b) Relative



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contributions of the two components as the excitation power density increases. We assign the peak at 840 nm to the radiative relaxation of the 4S3/2 state to the 4I13/2 state as is also known from literature.27-29 To again confirm this, we normalize the entire spectra from 380 nm to 880 nm measured at different excitation power densities to the area under the green peak in the range 510-542 nm. Figure 3 gives these normalized spectra at different excitation power densities. The spectra are colorcoded so that the color changes from green to red as the excitation power density increases from 0.4 W cm-2 to 6.7 W cm-2. We see that the peaks from green band (510-542 nm) and NIR band (820870 nm) always have the same contribution confirming that they have the same origin. The peaks at 660 nm, 700 nm and the minute shoulder at 557 nm (shown in the inset of Fig. 3) behave in a different fashion, exhibiting a relative growth with respect to the green and NIR peaks as the excitation power density increases. This clearly indicates a three-photon UC process, as resolved by the MCR-ALS algorithm as indicated in Figures 2(a) and (b).

Figure 3 Overlaid UC spectra normalized to the area under the green peak (510-542 nm) in -NaYF4: 18% Yb3+, 2% Er3+. The color changes from green to red as excitation power density increases from 0.4 W cm-2 to 6.7 W cm-2. The minute shoulder at 557 nm is magnified in the inset. The shaded areas are selected for integration for evaluating UC dependence from two photon processes.


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As only the two-photon UC processes can be described by the CPD model, we select the peaks which result from two photon processes only and then exclusively integrate the wavelength regions which have peaks from two-photon processes. We therefore integrate the green peaks from 510-542 nm and the NIR peaks from 820-870 nm for analyzing the UC emission vs excitation power density dependence in the following section with the CPD model. These peaks are indicated by shaded areas in light blue in Figure 3.

b) YF3: 18% Yb3+, 2% Er3+ Armed with the information regarding the different emission peaks gained using the MCR-ALS algorithm, we normalize the UC emission spectra of YF3: 18% Yb3+, 2% Er3+ excited at 980 nm to the area under the two-photon green peak from 510-541 nm. Figure 4 gives the overlaid UC spectra in YF3: 18% Yb3+, 2% Er3+ for excitation power densities ranging from 0.3 W cm-2 to 4.5 W cm-2 colorcoded from green to red as excitation power density increases. The peaks at 557 nm, 660 nm, and 700 nm show a relative growth with respect to the two-photon processes with increase in excitation power density, indicating a three-photon process, similar to the case of -NaYF4. For YF3, we select the regions for integration as 510-541 nm and 820-870 nm as indicated by light blue shaded areas in Figure 4 for analysis with the CPD model, as they originate exclusively from two-photon UC processes.



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Figure 4 Overlaid UC spectra normalized to area under the green peak (510-541 nm) in YF3: 18% Yb3+, 2% Er3+. The color changes from green to red as excitation power density increases from 0.3 W cm-2 to 4.5 W cm-2. The minute shoulder at 557 nm is magnified in the inset. The shaded areas are selected for integration for evaluating UC dependence from two-photon processes.

c) YCl3: 18% Yb3+, 2% Er3+ YCl3 is a low-phonon-energy host with a maximum phonon energy of 260 cm-1, which enhances radiative relaxations as compared to multi-phonon relaxation pathways.30-31 In the early days of lanthanide ion research, Dieke studied the fluorescence spectra of YCl3 and most of the transitions have been measured and assigned.32 As in the case of the fluorides, we try to isolate the two-photon processes in the YCl3 lattice. Likewise, we normalize the UC-spectra to the area under the two-photon green peak from 510-550 nm as excitation power density increases from 0.4 W cm-2 to 3.2 W cm-2. The spectra are color coded from green to red and shown in Figure 5.


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Figure 5 Overlaid UC spectra normalized to the area under the green peak (510-550 nm) in YCl3: 18% Yb3+, 2% Er3+. The color changes from green to red as excitation power density increases from 0.4 W cm-2 to 3.2 W cm-2. The minute shoulder at 560 nm is magnified in the inset. The shaded areas in blue and red are selected for integration for evaluating UC dependence from two-photon processes.

As for the previous two host materials, the green (510-550 nm) and NIR (840-880 nm) peaks behave similarly and are of the same two-photon origin. Their areas are shaded in light blue in Fig. 5. Several additional emissions are observed in YCl3. The emissions of the 4F5/2 and 4G11/2 states at 456 nm and 510 nm, respectively, result from three photon excitations. The 4F7/2→4I15/2 transition at 490 nm is due to two-photon-excitation. The main difference of the chloride host lattice compared to the fluorides is the significant 4I9/2→4I15/2 peak at 810 nm. In fluorides it is depopulated by multi phonon relaxation to the 4I11/2 state. The emission from the 4I9/2 state (810 nm) diminishes with respect to the green emission when the excitation power density is increased. This behavior excludes a three-photon excitation and points towards a two-photon excitation of the 4I9/2 state via cross relaxation. Its peak area is shaded in pink in Figure 5 and is used as additional input for the CPD model. d) La2O3: 18% Yb3+, 2% Er3+ As opposed to the case of YCl3, La2O3 is a host lattice with a higher phonon energy with measured values ranging from 410 cm-1 to 935 cm-1,17, 33-34 resulting in stronger depopulation of excited states by



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multi-phonon relaxations. Two-photon UC processes are less affected by the reduction of the radiative emissions as compared to three-photon UC processes. We follow the same procedure as in the previous cases and normalize the whole spectra to the area under the green peak (515-550 nm) for different excitation power densities for isolating the two-photon UC processes for analysis with our CPD model. The resultant normalized spectra are plotted in Figure 6 and color-coded from green to red as excitation power density increases from 0.5 W cm-2 to 4.8 W cm-2. The green, red, and NIR peaks have the same relative contribution for all excitation power densities. Though the red emission is significantly more intense than the green emission in previous host lattices, it shows a subtle decrease in magnitude as compared to the green and NIR peaks as observable in the inset graph zoomed between 669 nm and 675 nm. The region between 557 nm and 559 nm is also zoomed in another inset graph. We observe a relative growth of the shoulder at 558 nm with respect to the green peak as opposed to red emission as the excitation power density increases. Accordingly, the red UCemission peak is of purely two-photon origin as opposed to the minute shoulder at 558 nm which is of three-photon origin. We mark the region of the green (515-550 nm) and the red peaks (640-680 nm) in Figure 6 as originating from two-photon UC processes with light-blue and pink shaded areas, respectively, for later analysis with the CPD model. The NIR peak (840-870 nm) is not considered for analysis as it is very weak for La2O3 and hence its signal-to-noise ratio is too low for analytical purposes.

Figure 6 Overlaid UC spectra normalized to the area under the green peak (510-550 nm) in La2O3: 18% Yb3+, 2% Er3+. The color changes from green to red as excitation power density increases from 0.5 W cm-2 to 4.8 W cm-2. The minute shoulder at 558 nm and the red peak at 671 nm are magnified in


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the inset graphs. The shaded areas in light-blue and pink are selected for integration for evaluating UC dependence from two-photon processes.

Fitting two-photon UC with the CPD model In the previous section, we isolated all the two-photon UC processes for analysis with the CPD model. We use the CPD and BPD models as given by Equations (11) and (14), respectively, to fit the excitation power density dependence of these UC emissions (shaded areas in Figures 3-6). We find that both the models work well to describe the dependence of the UC vs excitation power density for the four host materials. The top panels of Figure 7 show the fit of the experimental two-photon upconversion data to the CPD model for each of the hosts. The fits according to the BPD model are plotted in the top panels of Figure S2 of the supporting information. We plot the percentage residuals for the two models underneath the data plots (bottom panels of Figure 7 and Figure S2) and observe that they are well distributed on both sides of the zero axes for both models in all the four cases, indicating that both the CPD and BPD models can accurately describe the excitation power density dependence of the two-photon UC emissions. We provide the CPD parameters extracted for each case in Table 1. The BPD parameters are given in Table S1. We note that the ratio of BPD to CPD values remains more or less fixed around 3, testifying to the fact that, while not mathematically identical, these two approaches appear to provide equivalently valid methods of extracting a figure of merit to describe the excitation power densitydependence of UC. We employ the following conventions to denote these figures-of-merit in the rest of the manuscript: CPDgreen denotes the values calculated for the two-photon green emissions from 2H11/2 and 4S3/2 to the ground state 4I15/2; CPDred denotes the values calculated for the two-photon red emission from 4F9/2 to the ground state 4I15/2; CPDNIR1 denotes the values calculated for the two-photon NIR emissions from 4S3/2 to the 4I13/2 state; and CPDNIR2 denotes the values calculated for the twophoton NIR emissions from 4I9/2 to the ground state 4I15/2 in YCl3. In order to compare if these CPD values are consistent with literature reports, we can use the fixed factor determined above that the BPD is roughly a factor of three larger than the CPD. The most direct comparison is to the recent work of Kaiser et al.,15 who determined a BPD of 1.2 W/cm2 for the green UC emission of a commercial microcrystalline powder of β-NaYF4:21.4% Yb3+, 2.2% Er3+. This



Page 18 of 34

suggests a CPD for their material of around 0.4 W/cm2, which is in good agreement with our extraction of a 0.7 W/cm2 CPD for the similar material we synthesized (β-NaYF4:18% Yb3+, 2% Er3+). We also note that the saturation PLQY from the total UC emission of our material and that in the literature is equivalent, and very high (in both cases slightly over 10%). Furthermore, in their original work introducing the BPD concept, Liu et al. determined a BPD of 1.3 W/cm2 for NaYF4:Yb3+,Tm3+@NaYF4 nanoparticles, which would also correspond to a CPD around 0.4 W/cm2. In Figure S3 of the supporting information we show a fit to recently published data for the two-photon upconversion NIR emission of LiYF4:Yb3+,Tm3+ nanoparticles;35 for these data we determine a CPD of 0.1 W/cm2. As an aside, this low CPD for the Tm3+ emitter is interesting, and warrants further investigation. However, returning to the central point: these comparisons illustrate consistency of our data and CPD analysis with the literature.

Figure 7 Top panes: UC vs excitation power density for four microcrystalline inorganic host materials doped with 18% Yb3+ and 2% Er3+ along with the fits according to the Critical Power Density (CPD) model (a) -NaYF4 (b) YF3 (c) YCl3 and (d) La2O3. Bottom panes: percentage residuals obtained after fitting the data on top with the CPD model. Table 1 List of CPD values (W cm-2) observed in four microcrystalline inorganic host materials doped with 18% Yb3+ and 2% Er3+ Host

CPDgreen

CPDNIR1

CPDred

CPDNIR2


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-NaYF4

0.7±0.1

0.7±0.1

―

―

YF3

1.0±0.2

1.0±0.2

―

―

YCl3

0.8±0.1

0.8±0.1

―

0.3±0.05

La2O3

1.1±0.2

―

0.9±0.2

―

CPD and UC-mechanisms The CPD value for a given emission is clearly related to the mechanism via which that emission occurs. Emissions that have the same source states have the same CPD; for example, the CPDgreen and CPDNIR1 values (see Table 1) are equal in each of the host materials. As discussed in the previous section, this is because of their common source-state, 4S3/2. Therefore, an analysis of the CPD of different emission wavelengths establishes correlations between pathways through which the emission occurs. In YCl3, the CPDNIR2 is very different from that of the CPDgreen and CPDNIR1, which indicates a separate mechanism. The lower value of the CPD suggests that this emission comes from an intermediate state with a longer lifetime. In YCl3, the 4I13/2 state exhibits a significantly longer lifetime, as discussed in the next section. This suggests that the ~800 nm NIR2 emission is due to two-photon UC from the 4I13/2 state. Even in the absence of significant multi-phonon relaxation in this host material, the 4I13/2 state can be populated due to the Judd-Ofelt splitting of radiative transitions. The branching ratio from the 4I 11/2

state (980 nm) to the 4I13/2 state (1550 nm) is around 20%.36-38 Figures S5 and S6 of the

supporting information give more details about this mechanism. In the case of La2O3, we see that the CPD value for red emission is slightly lower than that of the green emission. This is because the dominant mechanism that feeds the 4F9/2 state (red 640-680 nm) in this host is two-photon-UC from the 4I13/2 state (1550 nm) plus the 4F5/2 state of Yb3+. However, there is also a minor contribution from multi-phonon relaxation from the 4S3/2 state that also feeds the 4F9/2 state, which increases at higher excitation power densities as the 4S3/2 state gets populated. The CPD values for red emission and green emission would have been the same if the source of the red emission was exclusively 4S3/2 state. We note that our conclusion that the red emission does not



Page 20 of 34

primarily come from multiphonon relaxation from the 4S3/2 is supported by the different emission spectra under direct excitation of the 4S3/2 level. Under direct excitation, the green to red ratio is far higher than under upconversion excitation, indicating that a significant portion of the red emission under upconversion excitation does not come through a 4S3/2 intermediate state (see SI).

Figure S7

in the supporting information contains details about these two mechanisms with an energy-leveldiagram. These examples show how careful examination of the power dependence of two-photon upconversion processes (for example by analysis through the CPD model) can help to understand upconversion mechanisms.

CPD and intermediate-state-lifetimes According to Equation (12), the CPD depends quadratically on the inverse lifetime of the first intermediate state k1. In other words, the larger the lifetime of the intermediate state, the lower the CPD value should be (provided that absorption coefficient and rate of energy transfer between the first and second excited energy states remain constant). In this section, we investigate experimentally whether there is a correlation between the CPD values obtained and the intermediate state lifetimes. The relevant intermediate state is the 2F5/2 of Yb3+ in case of green and NIR1 emissions and the 4I13/2 state of Er3+ for the NIR2 emission. We excite the materials at 980 nm and detect the fluorescence at 990 nm and 1530 nm to measure the lifetimes. Figure S6(a) of the supporting information shows the lifetime measurements at 990 nm for the four host lattices doped with 18% Yb3+ and 2% Er3+, and Figure S6(b) shows the lifetime of the 4I13/2 state of Er3+ detected at 1530 nm in the same four hosts. We list the single-exponentially fitted lifetimes in Table 2 along with the corresponding CPD values.

Table 2 Intermediate-state lifetimes and CPD values Host material

Lifetime of 990 nm emission (ms)

CPDred

Lifetime of 1530 nm emission (ms)

CPDgreen

CPDNIR1

CPDNIR2

-NaYF4

2.5

0.7±0.1

0.7±0.1

―

12±0.5*

―

YF3

1.6

1.0±0.2

1.0±0.2

―

10±0.5*

―

La2O3

0.6

1.1±0.2

―

0.9±0.2

9±0.5#

―


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YCl3

1.6

0.8±0.1

0.8±0.1

―

15±1#

0.3±0.05

* Single-exponentially fitted and not used in manuscript # bi-exponentially fitted and average lifetime calculated

We see that the CPD values decrease as the first intermediate-state lifetime increases. Figure 8 illustrates this by plotting the calculated CPD values vs the respective relevant intermediate-state lifetime. The relevant lifetime is that of the 2F5/2 state of Yb3+ in all cases except for the NIR2 in which case the relevant lifetime is that of the 4I13/2 state of Er3+. As seen in Figure 8, the general trend holds that the longer the intermediate-state lifetime, the lower the CPD value. Therefore, maximizing intermediate-state lifetimes is clearly critical for achieving good CPD values. This is consistent with literature results, for example the results of Hossan et al. demonstrate that the UC-PLQY in nanocrystals of β-NaYF4:Yb3+,Er3+ (and the rate with which the UC-PLQY turns on), significantly increase when the intermediate-state lifetime in increased.39 Similar observations are made for NaGdF4: 20% Yb3+, 2% Er3+ by Würth et al.40

Figure 8 Plot of Critical power density (CPD) vs single-exponential lifetime for intermediate-states at 990 nm in the hosts -NaYF4 , YCl3, YF3, and La2O3 doped with 18% Yb3+, 2% Er3+ and at 1530 nm in YCl3: 18% Yb3+, 2% Er3+ when excited at 980 nm.



Page 22 of 34

CPD and saturation PLQY UC-PLQY is the ratio of the number of upconverted photons emitted to the number of photons absorbed. Equation (10) gives an expression for the rate of UC. As the generation rate gives the number of photons generated due to absorption by the sensitizer, dividing Equation (10) by the generation rate gives the UC-PLQY.

𝑈𝐶𝑃𝐿𝑄𝑌 =

𝑈𝐶 𝐺

𝑘2𝑟𝑎𝑑𝑘12

= 16𝑘2k

=> 𝑈𝐶𝑃𝐿𝑄𝑌 =

( ―1 +

ET12𝐺

( ―1 +

𝐶𝑃𝐷𝑘2𝑟𝑎𝑑 2𝐼𝑘2

1+

1+

𝐼 2 𝐶𝑃𝐷

)

(15)

𝐼 2 𝐶𝑃𝐷

)

(16)

When the excitation power density equals the CPD, the expression for UC-PLQY becomes:

𝑈𝐶𝑃𝐿𝑄𝑌𝐶𝑃𝐷 =

𝑘2𝑟𝑎𝑑 2𝑘2

( ―1 + 2)2

(17)

The saturation UC-PLQY is the PLQY at very high excitation power densities, when UC is the dominant depopulation mechanism for the intermediate levels. The UC-PLQY is then no longer dependent on the excitation-power, once this saturation UC-PLQY is reached. The expression for saturation UC-PLQY can be found by evaluating the limit of Equation (16) at an excitation power density equal to infinity.

𝑈𝐶𝑃𝐿𝑄𝑌𝑠𝑎𝑡 = 𝑙𝑖𝑚 𝐶𝑃𝐷 𝐼→∞

𝑈𝐶𝑃𝐿𝑄𝑌𝑠𝑎𝑡 =

1𝑘2𝑟𝑎𝑑 2 𝑘2

=

(+

𝑘2𝑟𝑎𝑑 1 𝑘2 𝐼

𝑃𝐿𝑄𝑌𝐶𝑃𝐷 2 ( ― 1 + 2)

1 2𝐶𝑃𝐷

+

1 𝐼2

+

)

1 𝐶𝑃𝐷 × 𝐼

≈ 5.8 × 𝑃𝐿𝑄𝑌𝐶𝑃𝐷

(18) (19)

Interestingly, the saturation UC-PLQY for a particular level is 5.8 times the PLQY from this level at the excitation power density equal to the CPD. In the following, we consider whether this may provide an easier method of accurately establishing the saturation UC-PLQY, overcoming obstacles in standard measurements due to, for example, sample heating at the high power densities required to reach saturation. Figure 9 illustrates the problem that can be encountered in attempting to determine the saturation UCPLQY in the standard fashion.

The total UC-PLQY as a function of excitation power density,


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measured using the 3M technique inside an integrating sphere,20 is shown for all the four hosts. In case of La2O3, instead of the PLQY plateauing to a constant value (the saturation UC-PLQY) at high excitation power densities, as theoretically predicted, we observe that the UC-PLQY rises and then decreases dramatically. This is due to a combination of factors at high intensity, but dominated by laser-induced heating. In such cases, it is possible to estimate the saturation UC-PLQY by correcting this experimental curve for the losses due to laser induced heating.14 The procedure for correction of the measured PLQY is explained in detail in the supporting information. The corrected saturation UCPLQY values of the green states (2H11/2, 4S3/2), i.e., two-photon UC emissions in the green and NIR, are plotted in Figure 10. Measuring the saturation UC-PLQY in this way is very time consuming and much prone to errors. As an alternative we suggest two different methods to estimate the actual saturation UC-PLQY of two photon processes, based on the CPD model we developed.

Figure 9 Total UC-PLQYs (500-880 nm) as a function of excitation power density in the four hosts. Because the efficiency decreases at higher excitation power due to processes such as laserinduced heating, it is not trivial to extract a value for the saturation PLQY as is evident in the case of La2O3. The lines are just a guide to the eyes.

Looking at Equation (19), the saturation-PLQY for a level populated by a two-photon process should be 50% of the PLQY of that same level under direct excitation or 5.8 times the UC-PLQY at the CPD. These equations provide two alternative methods for estimating the saturation UC-PLQY. In order to measure the UC-PLQY of the 2H11/2 and 4S3/2 levels at the CPD, the excitation power density for each



Page 24 of 34

host was adjusted to the respective CPD and the PLQY measured, integrating all photons coming from emission associated with the 2H11/2 and 4S3/2 levels (green and NIR1 bands for all hosts). The saturation UC-PLQY for each of the host materials is calculated by multiplying the UC-PLQY at CPD with 5.8. These values are plotted in Figure 10, and agree well with the corrected experimentally determined saturation UC-PLQYs. More details are included in the supporting information. In order to measure the PLQY under direct excitation, we use a 525 nm laser diode (Roithner, LD-51510MG) at a very low excitation power density of 0.01 W cm-2 to directly excite the 2H11/2, 4S3/2 states of Er3+. Then we measure the number of photons emitted in the NIR1 band (for all hosts other than La2O3), or in the red band (for La2O3). We note that we cannot directly measure the green emission, as this is masked under the excitation laser. However, the ratio of the green to NIR1 (or red) peak intensity is fixed for a given host, and can be calculated from an upconversion spectrum. Therefore, knowing the PLQY of the emission from the NIR1 band (or red in case of La2O3) under direct excitation, the total PLQY for all emission from the 2H11/2 and 4S3/2 states under direct excitation can be easily calculated. These values are shown in Figure 10, and are in agreement with corrected experimentally determined saturation UC-PLQYs and the estimated saturation UC-PLQYs with the CPD method in all cases except for YCl3.

Figure 10 Saturation PLQYs estimated with three different methods for the four hosts doped with Yb3+, Er3+ (18/2%) In order to consider why the PLQY after direct excitation of the 4S3/2 of the YCl3 is so much higher than that after upconversion excitation we make the following hypotheses. Given the YCl3 is a low-phonon


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energy host, the lifetime of the 4S3/2 after direct excitation is significantly longer than in other hosts (see Figure S13). This means that three photon UC processes, in which the 4S3/2 state is an intermediate state, can play a larger role at lower power densities in reducing the 4S3/2 lifetime in the YCl3 host. This three-photon channel feeds the 2G7/2, 2K15/2, 2G9/2 levels from the 4S3/2 state. The energy gap between these three states and 4G11/2 state can be easily bridged with multi phonon relaxations, meaning the three-photon process leads to the depopulation of 4S3/2 state and the population of 4G11/2 state. From 4G 11/2

state, through another back energy transfer (BET) to the Yb3+ ion, the 4F9/2 state (red emitting) of

Er3+ can be populated.41 The ratio of red to green peaks in YCl3 in Figure S10, S11 and S12 of the supporting information is consistent with this mechanism. We see that the red to green ratio is small in case of direct excitation with 525 nm (Figure S12) compared to the other two figures where excitation is with 980 nm. The relative growth of the red peak at 659 nm as compared to the green peak at high excitation power densities (Figure S8 and Figure S9) also highlights the three-photon origin of the red emission (as also previously explained in the section on determining the two-photon UC processes). Therefore, we hypothesize that the discrepancy between the PLQY of the 4S3/2 state of the YCl3 between direct excitation and upconversion may be associated with depopulation of the 4S3/2 state due to a three-photon or cross-relaxation in the case of upconversion excitation. Both such processes would be aided compared to other material systems due to the long intermediate state lifetimes in YCl3.

To put these results in context, one can compare the saturation UC-PLQYs that we obtain to examples from the literature; NaYF4 is the ideal host to compare due to the richness of the literature examining it. For core-shell β-NaYF4: 2%Er, 18%Yb@NaYF4 nanocrystals, state-of-the-art determination of the UC-PLQYs for the green and red emission are approximately 2.5% and 3.0% at 70 W/cm2 (where both values are still increasing but approaching saturation).42 Combined, these lead to the reported maximum UC-PLQY of 5.5%. However, the NIR photon emission between 840-870 nm is not considered in this case. Based on our data shown in Figures 1 and 2, we estimate that more than half of the number of the green photons are emitted in this NIR band. We hypothesize that the inclusion of these photons may increase the saturation UC-PLQY for the nanoparticles in the literature to around 6.7 %. As mentioned previously, the state-of-the-art saturation UC-PLQY for β-NaYF4:Yb,Er micropowders is 10.5 % at 30 W/cm2.15 These results agree reasonably well with the maximum UCPLQY that we measure of 11% at 400 W/cm2 (as shown in Figure 9).



Page 26 of 34

Beyond the broad agreement, there are certain discrepancies that highlight open challenges in the characterization and comparison of UC materials. Firstly, there is significant variance in literature reports of the excitation power density at which the UC-PLQY starts to decrease (for a given emission level and for the total UC-PLQY). We find that the quantum efficiency of the green level continues increasing until at least 100 W/cm2 (see Figure S14), whereas in the literature it is not uncommon for the green UC- PLQY to begin to decrease much earlier (around 20-30 W/cm2).15, 41 We have observed that excitation-laser-induced heating affects the decrease of the total UC-PLQY at excitation power densities in this range, and hypothesize that laser-induced heating affecting the rate of multi phonon relaxation between the 4S3/2 state and the 4F9/2 state may play a role in explaining this discrepancy. Nonetheless, determining and rectifying the sources of such discrepancies is a topic of current interest in the community, and there is continued scope in the non-trivial task of developing simple and robust experimental methods to help alleviate discrepancies and better allow material comparison.

In summary the saturation UC-PLQY can be estimated, in cases where the upper state is not significantly emptied by additional three-photon or cross-relaxation processes, from the UC-PLQY at the CPD, or by half the PLQY under direct excitation. These two methods of estimation have the advantage of using low excitation power densities, and therefore avoiding effects such as laserinduced heating that need to be corrected for in standard saturation UC-PLQY measurements. Interestingly, our results suggest that these methods for estimation of the UC-PLQY work for standard host material β-NaYF4, despite the significance of a three-photon red channel. However, the data from Kaiser et al. suggest that these methods overestimate the maximum UC-PLQY of the green emission, due to it saturating much earlier (see Figure S14).15 This is an interesting discrepancy, and highlights that care should still be exercised in the application of this method for determining the saturation UCPLQY, as overestimation is possible. Further close examination of the discrepancy of when the UCPLQY of the green saturates and whether this is due to material- or measurement-related effects is an important component of the open challenge for accelerating the development of upconversion materials by providing better methods to accurately compare materials. This further work may reveal that certain two-photon processes might need to be modelled with rate equations including a population-dependent rate in the upper state that accounts for higher order depopulation rates in this state (such as a three photon channels in which this state is a precursor). Nonetheless, our


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investigation of four host materials suggests that the simple and tractable CPD model has merit for easily and accurately comparing the excitation power dependence of the upconversion emission between different hosts. Furthermore, in the measurements we made, the determining of the UCPLQY at the CPD provided an easy alternate route to determining the saturation UC-PLQY.

CONCLUSIONS To conclude, we compared the dependence of the UC intensity on the excitation power density for two-photon UC processes in a variety of host materials (microcrystalline powders). We have shown these can be described by the CPD model. The CPD, the single parameter extracted from the model, is a useful tool for comparing the performance of different upconversion host materials. The lower the CPD of a host, the quicker the UC process becomes efficient in the host. This is especially relevant for finding and comparing good hosts for UC under low excitation power densities. One of the major factors affecting the CPD is the intermediate excited state involved in UC. The longer the lifetimes of the intermediate state, the lower the CPD value. Thus, screening hosts for long intermediate state lifetimes would be a good way of identifying hosts that should have a low CPD. Also, with the help of the CPD model, we suggest two methods for accurately calculating the saturation UC-PLQY of an energy level. We find that multiplying the UC-PLQY at the CPD by a factor of 5.8 correlates well with half of the PLQY of the level when it is excited directly. Both of these agree well with the experimentally determined saturation UC-PLQY for a given state populated by two-photon processes. The ability to provide an estimate of the saturation PLQY using a low excitation power density measurement removes effects such as laser-induced heating that affect standard saturation PLQY measurements. In addition, by studying the UC spectra as a function of excitation power density, we show that detailed information can be obtained for the UC mechanisms in the four host materials. The mechanisms present in La2O3 show uniquely different features than those in YCl3, which in turn are different than those in -NaYF4, and YF3. In -NaYF4 and YF3, two photon upconversion to the 4S3/2 state is responsible for the dominant green and NIR emission. In the YCl3 emission from the 4I9/2 state is visible. This stems from two photon upconversion from the 4I13/2 state, and the fact that the 4I9/2 does not completely relax to the 4I11/2 (as in all other hosts) is a testament to the low phonon energy of the



Page 28 of 34

YCl3. Finally, the primary pathway for the red emission in the La2O3 is a two-photon process with the 4I 4 13/2 and I11/2

states. This is supported by a minor contribution of multi phonon relaxation from the 4S3/2

state after two photon upconversion from the 4I11/2 state. SUPPORTING INFORMATION Figure S1(a) Schematic diagram of sample placed inside the integrating sphere and (b) zoomed in view of the excitation spot inside the glass capillary (1 mm x 1 mm square cross-section). Figure S2- UC vs excitation power density of the red emission (4F9/2,4I15/2, 630-690 nm) of Er3+ (2%) sensitized with Yb3+ (18%) doped in microcrystalline hosts of (a) La2O3, (b) -NaYF4, (c) YCl3 and (d) YF3. Figure S3 UC vs excitation power density for four microcrystalline host materials doped with 18% Yb3+ and 2% Er3+ along with the fits according to the Balancing Power Density (BPD) model in (a) -NaYF4, (b) YF3, (c) YCl3, and (d) La2O3 and percentage residuals. Table S1 List of calculated CPD and BPD values (W cm-2) Figure S4- CPD fit to NIR upconversion emission of LiYF4:Yb3+, Tm3+ nanoparticles Figure S5 Lifetimes of different UC emissions from YCl3: 18% Yb3+, 2% Er3+ excited at 980 nm Figure S6 Mechanisms of UC in YCl3: 18% Yb3+, 2% Er3+ excited at 980 nm Figure S7 Mechanisms of UC in La2O3: 18% Yb3+, 2% Er3+ excited at 980 nm Figure S8 Time resolved luminescence at (a) 990 nm and (b) 1530 nm in 18% Yb3+, 2% Er3+ doped NaYF4, YF3, La2O3, and YCl3 excited at 980 nm. Figure S9 Integrated UC intensity of the green peak as a function of time at high excitation power densities. Figure S10 UC-emission spectra in the four host materials at high excitation power densities Table S2 Calculation of actual PLQY due to green states Figure S11 UC spectra measured at CPD for the hosts (a) -NaYF4, (b) YF3, (c) YCl3, and (d) La2O3.


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Table S3 Calculation of saturation UC-PLQY of green state from PLQY at CPD Figure S12 Emission spectra for 525 nm excitation at 0.01 W cm-2 of the Er3+ ions in 18% Yb3+, 2% Er3+ doped host lattices (a) -NaYF4, (b) YF3, (c) YCl3, and (d) La2O3. Table S4 Calculation of saturation UC-PLQY from direct excitation Figure S13 Lifetimes of 4S3/2 state of Er3+ in the four hosts

Figure S14: Excitation power density dependence of the efficiency of green UC emission with data set from Kaiser et. al and our data. ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support provided by the Helmholtz Association: i) a Recruitment Initiative Fellowship for BSR; ii) the Science and Technology of Nanosystems (STN) program; and iii) the Helmholtz Energy Materials Foundry (HEMF) project. REJ acknowledges the Deutscher Akademischer Austausch Dienst (DAAD) for her Ph.D. scholarship and the Karlsruhe School of Optics and Photonics (KSOP) for their support. REFERENCES

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Critical Power Density: A Metric to Compare the Excitation Power

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