# Boltzmann- and Non-Boltzmann-Based Thermometers in the First, Second and Third Biological Windows for the SrF2:Yb3+, Ho3+ Nanocrystals Under 980, 940 and 915 nm Excitations – Nanoscale Research Letters

Aug 30, 2022

### Structure Characterization

Figure 1a–e shows the TEM images of SrF2:Yb3+/Ho3+(12/x mol%) doped with different Ho3+ concentrations. The morphology of these NCs exhibits an ellipse or rectangle shape. Figure 1f demonstrates the average size of these synthesized NCs is about 50 nm. As shown in Fig. 1g, XRD patterns further prove that the diffraction peaks of the samples match the standard card of the SrF2 phase (JCPDS No. 06-0262) well. Both the TEM and XRD characterizations reveal that the doping of small amounts of Yb3+ and Ho3+ ions has almost no effect on the lattice structure and morphology of the SrF2 NCs.

### DCL and UCL Properties

In our preliminary experiment as shown in Additional file 1: Fig. S1, when the doping concentration of Ho3+ was fixed at 0.1 mol%, the intensity of UCL firstly increased and then decreased with the increase in Yb3+ concentration. The luminescence intensity reached its maximum when the concentration of Yb3+ was 12 mol%. Therefore, the Yb3+ concentration was fixed at 12 mol% and further investigated the dependence of the luminescence intensity on Ho3+ doping concentration of SrF2:Yb3+/Ho3+ (12/x mol%) NCs. Figure 2 shows the visible UCL and NIR DCL spectra of SrF2:Yb3+/Ho3+ (12/x mol%) NCs doped with different Ho3+ concentrations under the excitation of 980 nm laser. There are eight typical emission bands centered at 485, 541, 648, 750, 1012, 1186, 1950, and 2020 nm, which are ascribed to the transitions of 5F3 → 5I8, 5F4(5S2) → 5I8, 5F5 → 5I8, 5F4 → 5I7, 5S2 → 5I6, 5I6 → 5I8, 5F3 → 5F5 and 5I7 → 5I8 from Ho3+ ions, respectively. Obviously, the visible UCL and NIR DCL of SrF2:Yb3+/Ho3+ (12/x mol%) NCs exhibit different varying trends when doped with different Ho3+ concentration. The visible UCL increases with the increase in Ho3+ concentrations within a low concentration range and reaches the maximum at 0.4 mol% Ho3+ and then decreases sharply with the increase in Ho3+ ions again. Analysis of this phenomenon proves that concentration quenching plays an important role [27]. The increase in Ho3+ concentration promotes an increase in rare-earth-ion pair formation in the SrF2 lattice which correspondingly reduces the distance between Ho3+ ions compared the Yb3+–Ho3+ ions, thus facilitating the occurrence of cross-relaxation (CR) between the adjacent Ho3+ ions [28, 29]. For the NIR DCL part, the 1012 and 2020 nm emission intensities gradually decrease with the increase in Ho3+ concentration, whereas the 1186 and 1950 nm emission intensities are opposite. We speculate that this is mainly due to the CR process of Ho3+ ions (CR1 and CR2 in Fig. 3). The CR1 process of 5I7 + 5F5 → 5I8 + 5F3 can promote the population of 5F3 state and inhibit the population of 5I7 state, which will enhance the 1950 nm emission and decrease the 2020 nm emission, respectively. Similarly, the CR2 process of 5I7 + 5S2 → 5I6 + 5F5 enhances the population of 5I6 state and simultaneously reduces the population of 5S2 state, thus strengthening the 1186 nm emission and weakening the 1012 nm emission. Notably, the complex excited-state absorption (ESA) and energy transfer (ET) processes can also contribute to the above observed phenomenon.

Figure 3 illustrates the energy level diagram for Yb3+ and Ho3+ ions under 980 nm excitation, which also contains the ET, ESA, CR and non-radiative transition (NRT). Generally, Yb3+ ions can be populated through the 2F7/2 → 2F5/2 transition by directly absorbing 980 nm photon and then transferring the energy to adjacent Ho3+ ions through successive ET processes to populate the 5I6, 5F5 and 5F4 states of Ho3+ [30, 31]. Moreover, the 5F3 state is populated by the CR (5I7 + 5F5 → 5I8 + 5F3) process, followed generating the 485 nm (5F3 → 5I8) and 1950 nm (5F3 → 5F5) emissions. Subsequently, the electrons in the 5F4 state will transition to the 5I8 and 5I7 states, thereby emitting the 541 nm green light and 750 nm red emission, respectively [32, 33]. Simultaneously, partial electrons in the 5F4 state will populate to the 5S2 state by the NRT process, subsequently transitioning to the 5I6 generating NIR emission at 1012 nm. Similarly, the electrons in the 5F5 state will transition to the 5I8 state, thereby emitting the 648 nm emission. Additionally, the transitions from the 5I6 and 5I7 states to 5I8 state produce the 1186 nm and 2020 nm NIR emissions, respectively.

Notably, except excited by the 980 nm, the Yb3+ ions can also be excited at 940 and 915 nm lasers and then transfer energy to Ho3+ ions by ET process [34, 35]. To further explore the influence of different excitation sources on the emission spectra for the SrF2:Yb3+/Ho3+ NCs, we further investigate the photoluminescence properties of SrF2:Yb3+/Ho3+ (12/0.1 mol%) NCs under the 980, 940 and 915 nm excitations with the same pumping power density (11 W cm−2), as shown in Fig. 4. The results show that emission efficiency under 980 nm excitation is the highest compared with the 915 and 940 nm excitations, indicating that the largest absorption cross section at 980 nm and lowest absorption cross section at 940 and 915 nm. Under the same pumping power density, the intensity of visible emissions under 980 nm excitation is almost 40 times than that under 940 nm excitation and 80 times than 915 nm excitation, while the NIR light is almost 4.5 times than that under 940 nm excitation and nine times than that 915 nm excitation. The quantum yields of SrF2: Yb3+/Ho3+ (12/0.1 mol%) NCs were measured under 980 nm excitation which is ~ 0.51%. Unfortunately, we cannot measure the quantum yield of the SrF2:Yb3+/Ho3+ (12/0.1 mol%) NCs under 940 and 915 nm excitations, which is due to the relatively small absorption cross section and much weak luminescence intensity at these two wavelength excitations than that under 980 nm excitation [36,37,38]. In addition, the size of synthesized SrF2:Yb3+/Ho3+ NCs is about 50 nm, resulting in a large specific surface area which places the dopant lanthanide ions closer to the surface. This leads to an increase in non-radiative relaxations of the emitting and intermediate levels by solvent molecules.

Figure 5a displays the thermal images of SrF2:Yb3+/Ho3+ (12/0.1 mol%) NCs dispersed in ethanol solutions under the 980, 940 and 915 nm laser illustration with a step of 240 s. The excitation power density is 110 W cm−1. Over the 1440 s of the testing process, the temperature gradually rises while manifesting different magnitudes for different excitation wavelengths. Figure 5b further depicts the plot of temperature changes as a function of the heating times. During the heating time, the maximum temperature increases up to 38.5 °C and 41.8 °C under 915 and 980 nm excitations, respectively. In contrast, the temperature merely elevates from an initial 23.6 °C to the final 27.4 °C under 940 nm excitation. Obviously, the 940 nm laser-induced heating effect is unconspicuous compared to the 915 and 980 nm lasers. Therefore, the design of a higher sensitivity thermometer which can minimize thermal effects on organisms has more significant significance in the biological and medical fields.

### Ratiometric Temperature Sensing

Having obtained the efficient visible UCL and NIR DCL simultaneously under the excitation of 980, 940 and 915 nm lasers, here, we continue to investigate the ratiometric temperature sensing performances. Figure 6 displays the temperature-dependent spectra of SrF2:Yb3+/Ho3+ (12/0.1 mol%) NCs under the excitation of 980, 940 nm and 915 nm in the range of 303–573 K. Both the visible and NIR emissions are decreasing with the increase in temperature. However, the visible UCL thermally quenches more obviously than the NIR DCL. Under the 980 nm excitation, the intensity of visible 541 nm UCL at room temperature (303 K) is about 95 times than that at the highest temperature of 573 K, while red UCL (648 nm) decreases about 16 times from the 303 to 573 K, as shown in Fig. 6a. On the contrary, the NIR DCL has slight changes when the temperature varies from room temperature to 573 K, which possesses a relative highly thermal stability compared with the visible UCL. Particularly, the NIR DCL remains almost unchanged under the 915 nm excitation.

The temperature-dependent spectra ranging from the BW-I, BW-II and BW-III significantly demonstrate that they can be used for detecting the temperature in a wide range. Considering the actual energy levels of Ho3+ ions, especially both TCLs and NTCLs emissions, we choose different methods to analyze and calculate the performances of the Boltzmann-based and non-Boltzmann-based thermometers based on the TCLs or NTCLs. Traditional FIR technology measures the thermal dependence of FIR based on TCLs, which can be defined as follows:

$${text{FIR}}_{B} = frac{{N_{1} }}{{N_{2} }} = frac{{I_{1} }}{{I_{2} }} = Aexp left( { – frac{Delta E}{{KT}}} right)$$

(1)

where N and I represent the populations of the corresponding energy levels and fluorescence intensity, respectively. A is the constant that depends on the experimental system, T is the absolute temperature and K is the Boltzmann constant.

Arrhenius equation is undoubtedly a good method to analyze the mechanism of temperature sensing behavior when using the NTCLs method, which can be expressed as follows [39]:

$$I(T) = I_{0} /left( {1 + B{text{e}}^{{( – E_{a} /KT)}} } right)$$

(2)

where I0 is the UCL intensity of the measured NCs at room temperature (T0), I(T) is the UCL intensity at temperature T, B is the constant and Ea is the quenching activation energy. The definition of T and K is the same to Eq. (1).

Although there have been many related studies reported using Arrhenius equation to solve temperature dependence of luminescence intensity due to temperature quenching, in order to further verify the rationality of this equation in dealing with the relationship between Ho3+ fluorescence intensity and temperature, we randomly selected the emission intensity centered at 1012 and 2020 nm under 980 nm excitation and obtained the following results through normalization [37, 38]. Additional file 1: Fig. S3a and c shows the dependence of luminescence intensity on the temperature at 1012 nm and 2020 nm, and Additional file 1: Fig. S3b and d displays the fitted results by using Arrhenius equation, respectively. Both the fitting R2 values, well-fitted Eq. (2), are greater than 99%. The results indicate that the activation energy is deduced to be 0.27 for 1012 nm and 0.23 eV for 2020 nm, respectively.

Therefore, the FIR based on NTCLs can be modified as follows [40, 41]:

begin{aligned}hbox{FIR}_{N – B} &= frac{{I_{1} (T)}}{{I_{2} (T)}} = frac{{I_{0,1} }}{{I_{0,2} }}frac{{1 + B_{2} exp ( – E_{2} /hbox{KT})}}{{1 + B_{1} exp ( – E_{1} /hbox{KT})}} \ & approx alpha + beta exp left( – frac{{Delta E_{a} }}{hbox{KT}}right)end{aligned}

(3)

where I1(T) and I2(T) represent the UCL intensity of the two corresponding UCL emissions at temperature T, respectively. α and β are constants that are dependent on I0 and I(T). E1 and E2 are the corresponding quenching activation energy. (Delta E_{{text{a}}}) is a parameter associated with E1 and E2.

Figure 7 shows the FIR ratios of I648/I541, I1186/I1012 and I1950/I2020 as a function of the external temperature under tri-wavelength excitations. To ensure the accuracy of experimental data, we fitted the FIR ratios using the Gaussian fitting based on the integrated areas of each UCL peak. As a result, the values of FIR increase with the increase in temperature. Among them, the FIR of I648/I541 is fitted with Eq. (1), and the FIR of I1186/I1012 and I1950/I2020 is fitted with Eq. (3). All the fitting R2 values of curves are greater than 99.0%, indicating that the rationality of the FIR model is based on the TCLs and NTCLs.

To better evaluate the capability of a thermometer, the ({text{S}}_{text{R}}) is used to represent the relative sensitivity of the thermometer, which is defined as follows [42, 43]:

$$S_{R,B} = frac{1}{{{text{FIR}}}}left| {frac{{partial {text{FIR}}}}{partial T}} right| = frac{Delta E}{{{text{KT}}^{2} }}$$

(4)

begin{aligned}S_{R,N – B} &= frac{1}{{{text{FIR}}}}left| {frac{{partial {text{FIR}}}}{partial T}} right| \ &= frac{{Delta E_{{text{a}}} }}{{{text{KT}}^{2} }}frac{{beta exp ( – Delta E_{a} /{text{KT}})}}{{alpha + beta exp ( – Delta E_{a} /{text{KT}})}}end{aligned}

(5)

Equations (4) and (5) are the expressions (S_{R}) based on TCLs and NTCLs, respectively.

Figure 8 displays the relative sensitivity of different FIRs based on TCLs and NTCLs dependent on the temperature. In general, for all the UCL emission ratios, the (S_{R}) under 980 nm excitation is the highest, and the (S_{R}) under 940 nm excitation is the lowest. Particularly, the maximum (S_{R}) of I648/I541 based on TCLs reaches 0.94% K−1, 0.57% K−1 and 0.85% K−1 at the room temperature of 303 K under tri-wavelength excitations, and the value (S_{R}) decreases gradually with the increase in temperature which is consistent with that described in Eq. (4). It is interesting to note that the maximum (S_{R}) of I1186/I1012 and I1950/I2020 based on NTCLs under 980 nm excitation reaches 0.45% K−1 and 0.40% K−1 at the same temperature of 523 K. And the maximum (S_{R}) of I1186/I1012 attains 0.23% K−1 at 303 K, whereas the maximum (S_{R}) of I1950/I2020 reaches 0.17% K−1 at 398 K under 940 nm excitation. This is because the amplitude of fluorescence intensity varies with temperature under different excitation sources discrepantly, as shown in Fig. 6. In particular, the variation in NIR fluorescence intensity under excitation of 940 and 915 nm is significantly smaller than that under excitation of 980 nm, which leads to a higher relative sensitivity under 980 nm excitation.

For comparison, Table 1 summarizes the performances of our determined thermometers and compared them to the previously reported thermometers related to Ho3+ ions. The relatively higher performance can be achieved in the range of 303–573 K for FIRs of I648/I541, I1186/I1012 and I1950/I2020 in our experiment compared to the previous Ho3+-doped thermometers.

In addition to (S_{R}), the temperature uncertainty of (delta T) is a very significant parameter used to evaluate the performance of a thermometer, which is defined as [46]:

$$delta T = frac{1}{{S_{R} }}frac{delta Delta }{Delta } times 100%$$

(6)

where (Delta) is the average of measured FIR values in the experiment and (delta Delta) is the uncertainty of the calculated FIR.

Based on Eq. (6), we have calculated the temperature uncertainty of (delta T) for the I1950/I2020. We have obtained the (delta T<) 1.25 K under 980 nm excitation while (delta T<) 0.96 K under 915 nm excitation in the temperature range of 303–573 K. In addition, Fig. 9 shows the good repeatability of the temperature-dependent FIR for the NIR bands measured in several heating and colling circles. The results indicate that the thermometer based on NTCLs of Ho3+ has relatively high sensitivity and low temperature uncertainty.