Up-Conversion Luminescence and Optical Temperature Sensing Behaviour of Y₂O₃:Ho³⁺, Yb³⁺ Phosphors

Abstract

The up-conversion (UC) and temperature sensing behaviours of Y₂O₃:Ho³⁺, Yb³⁺ phosphors were investigated. A series of Y₂O₃:Ho³⁺, Yb³⁺ phosphors were synthesized using a solution combustion method. The cubic structure of the Y₂O₃ with an Ia$\overline{3}$ space group was analysed by using X-ray powder diffraction. Scanning electron microscopy was conducted to study the surface morphologies of the UC phosphors. Under 980 nm excitation, the UC emissions of Ho³⁺ from the ⁵S₂ → ⁵I₈, ⁵F₅ → ⁵I₈ and ⁵S₂ → ⁵I₇ transitions were observed, which occurred through UC energy transfer (ET) processes. The Yb³⁺ ion concentration severely affected the UC emission. The sensing behaviour of the phosphor was investigated through the green (⁵F₄, ⁵S₂ → ⁵I₈) to red (⁵F₅ → ⁵I₈) fluorescence intensity ratio (FIR). The maximum absolute and relative sensitivity values of S_A = 0.08 K⁻¹ and S_R = 0.64% K⁻¹ were obtained. The results revealed that the prepared Y₂O₃:Ho³⁺, Yb³⁺ phosphor is suitable for optical sensing at high temperatures.

1. Introduction

Lately, up-conversion (UC) materials based on lanthanide ions have been investigated extensively because of their potential application in colour displays, solar cells, optical communication, optical temperature sensors, and the lamp industry [1,2,3,4,5,6]. For efficient UC emission, Yb³⁺ has been extensively utilized as a sensitizer for trivalent lanthanide ions (Ln³⁺) doped into various hosts [7,8,9,10]. Yb³⁺ is an interesting ion that possesses only a ²F_7/2 ground state and a ²F_5/2 excited state that is set apart by approximately 10,000 cm⁻¹. Yb³⁺ is usually excited with near-infrared (NIR) and transfers energy to an activator resulting in visible emission through the energy transfer up-conversion (ETU) process. The energy level matching between Ho³⁺ and Yb³⁺ ions makes the couple to be a great choice for UC investigations [11]. Dwivedi et al. [7] investigated the UC luminescence of Gd₂O₃:Ho³⁺, Yb³⁺ phosphor and obtained a strong green UC emission. The visible UC luminescence of Y₂O₂S:Er³⁺, Yb³⁺ phosphor has been reported to be 2.2 times less bright than that of Y₂O₂S:Ho³⁺, Yb³⁺ phosphor [8]. The Ho³⁺, Yb³⁺ co-doping has also been proven to be a highly efficient UC system by other researchers [12].

The host material is of great importance in UC emission intensity. For efficient UC output, the host should have low energy phonons to minimize the probability of multiphonon relaxations of the lanthanide ions. The cubic phase of Y₂O₃ host possesses low phonon energy (~550 cm⁻¹), a wide bandgap, high melting point, and thermal stability that make it suitable for various phosphor applications [13,14]. Therefore, due to the matching ionic radii of Y³⁺ (0.900 Å), Ho³⁺ (0.901 Å), and Yb³⁺ (0.868 Å), Y₂O₃ may be considered as an ideal host for Ho³⁺-Yb³⁺ couple [15]. Pandey et al. [16] reported that the Yb³⁺ co-doping in Y₂O₃:Ho³⁺ enhanced the green emission intensity by nearly ~290 times. Wei et al. [17] investigated the UC luminescence strong dependence on concentration doping in Ho³⁺, Yb³⁺ co-doped Y₂O₃ and obtained a strong green emission that is applicable in biomedical fluorescent labels.

Research interest in optical temperature sensing with UC phosphors based on lanthanide ions is increasing in recent years. The fluorescence intensity ratio (FIR) between two emission bands, which calls for either thermally coupled or non-thermally coupled energy levels of the luminescent ions, is used in this. [18,19]. In the literature, it is reported that the FIR of green to red emission of Ho³⁺ ion can be identified as an optical temperature sensing indicator [20]. The FIR technique offered a high detection resolution and good sensitivity as it is typically independent of excitation-power fluctuation and spectrum loss. The FIR of thermally coupled energy levels (TCLs) (Ho³⁺:⁵F₃/³K₈) can be explained by a Boltzmann distribution of electrons [21,22]. According to the Boltzmann distribution, the temperature sensing sensitivity proportional to ΔE, can barely be improved further to a higher level since the energy separation ΔE of such levels is typically limited to 200–2000 cm⁻¹ to avoid an intense overlap between the two emission bands [23]. For this reason, using non-thermally coupled energy levels (non-TCLs) (Ho³⁺:⁵F₅/⁵F₄, ⁵S₂) is regarded as a useful addition to improve FIR sensitivity [19,21,23]. However, studies on the temperature sensing performance with the non-TCLs for Ho³⁺/Yb³⁺:Y₂O₃ phosphor are currently few. Wang et al. [24] investigated the performance of the optical temperature sensing based on non-TCLs of Ho³⁺ ion ((⁵F₄/⁵S₂ → ⁵I₈)/(⁵F₅ → ⁵I₈)) and found a maximum absolute sensitivity of 0.1603 K⁻¹. More deep investigations on the optical temperature sensing with non-TCLs of Ho³⁺ ion for Ho³⁺/Yb³⁺:Y₂O₃ phosphor are required.

In this work, Ho³⁺, Yb³⁺:Y₂O₃ up-conversion phosphors with various concentrations of Yb³⁺ were synthesized by the solution combustion method. The structural and optical properties were studied by X-ray powder diffraction (XRPD), scanning electron microscopy (SEM), and UV-vis-NIR spectra measurements. The UC emission and temperature sensing behaviour of the Ho³⁺, Yb³⁺:Y₂O₃ were investigated. Power dependence measurements and an energy level diagram confirmed the phenomenon involved in the UC process. The green (⁵F₄, ⁵S₂ → ⁵I₈) to red (⁵F₅ → ⁵I₈) FIR was used to analyse the behaviour of temperature sensing of the developed phosphor.

2. Experimental

2.1. Synthesis

The phosphor powder samples of Y_2−x−yO₃: Ho_x=0.005, Yb_y (y = 0, 0.002, 0.006, 0.01, 0.05, 0.1, 0.2) were prepared by a solution combustion method. Y(NO₃)₃·4H₂O (Sigma Aldrich, Darmstadt, Germany, 99.99%), Ho(NO₃)₃·5H₂O (Sigma Aldrich, 99.99%), Yb(NO₃)₃·5H₂O (Sigma Aldrich, 99.99%), and CH₄N₂O (Sigma Aldrich, 99.5%) were starting materials. As an example, for y = 0.05, 1.6026 g of Y(NO₃)₃·4H₂O, 0.0098 g of Ho(NO₃)₃·5H₂O, 0.0994 g of Yb(NO₃)₃·5H₂O, and 0.6690 g of CH₄N₂O were dissolved in 50 mL distilled water. The mixture was stirred using a magnetic stirrer in a 100 mL beaker for 30 min until a homogeneous solution was obtained. The solution was then heated at 500 ± 10 °C in a muffle furnace. The foam-like product was crushed using a pestle and mortar and was then annealed at 1100 °C in air for 2 h.

2.2. Characterization

The crystallinity and structure of the prepared samples were analysed by X-ray powder diffraction (XRPD) (Bruker AXS GmbH, Karlsruhe, Germany) using a Bruker D8 Advance diffractometer (40 mA, 40 kV) with Cu Kα radiation (0.154 nm). The morphology of the samples was analysed by a scanning electron microscope (JEOL JSM-7800F) equipped with an energy dispersed X-ray spectroscopy (EDS) device (JEOL, Tokyo, Japan). The diffuse reflectance measurements were acquired using a Lambda 950 UV-vis-NIR spectrophotometer (PerkinElmer Ltd, Beaconsfield, United Kingdom) in the range of 200–1200 nm. The UC emissions and decay curves were recorded using an FLS980 fluorescence spectrometer with 980 nm emitting diode lasers as the excitation source and power of 96 mW.

3. Results and Discussion

3.1. Structural and Surface Morphology Analysis

XRPD patterns of the Y_2−x−yO₃:Ho_x=0.005, Yb_y phosphors are shown in Figure 1. The XRPD patterns agree with the standard reflection peaks reported in JCPDS# 71-0099 [25], and indicate the cubic structure with an Ia$\overline{3}$ space group of the Y₂O₃ crystal. The XRPD patterns of the Y_2−x−yO₃:Ho_x=0.005, Y_by phosphors are shown in Figure 1. The introduction of Ho³⁺ and Yb³⁺ ions as co-dopants into Y₂O₃ did not change the structure type, but a small shift towards high angles in the diffraction reflection peaks was observed with increasing Yb concentration (Figure 1b). The shift is attributed to the ionic radius difference between the Yb³⁺ (0.868 Å) and Y³⁺ (0.900 Å) ions. Also, the peak shift verifies that Yb³⁺ are effectively incorporated into the Y³⁺ site [15].

The morphologies and elemental analyses of the prepared samples were studied using SEM and EDS, respectively. Figure 2 displays the SEM images of the prepared phosphors. All the images exhibited agglomerated spherical nanoparticles. The addition of Ho³⁺, Yb³⁺ did not change the morphology of the Y₂O₃ host. The EDS spectra of the Y_2−x−yO₃:Ho_x=0.005, Yb_y=0.2 are displayed in Figure 3. All the Y, O, Yb, and Ho elements expected in the sample were observed, which confirms the successful incorporation of Ho³⁺ and Yb³⁺ into the Y₂O₃ host. In addition, carbon was also detected in the spectrum, which could be from the carbon tape used when mounting the samples. The extra peak detected around 0.03 keV is due to electronic noise within the system. No impurities were detected in the spectra, which agrees with the XRD results.

3.2. Optical Properties

The reflectance spectra for the UC phosphors are presented in Figure 4. The absorption peak around 220 nm is associated with band-to-band transitions in the Y₂O₃ material [26]. The Ho³⁺ single doped Y₂O₃ exhibited sharp peaks centred at 361, 448, and 1008 nm due to ⁵I₈ → ³H₆, ³D₂, ⁵I₈ → ⁵G₆ and ³S_2, ⁵F₄ → ⁵I₆ transitions of the Ho³⁺ ion, respectively [27,28]. The Ho³⁺ 4f-4f absorptions in the UV-vis region remained unchanged when Yb³⁺ was added, which confirms that the Ho³⁺ ion concentration remained uniform. An additional absorption peak observed at 976 nm was observed with Yb³⁺ ion, which is associated with the ²F_5/2 → ²F_7/2 transition of the Yb³⁺ ion [28].

The optical bandgap of the Y₂O₃ was estimated from the Tauc plot [29], which is given by:

$${\left(F\left(R\right)hv\right)}^{\frac{1}{n}}=A(hv-E_g)$$

(1)

where A is a constant, $hv$ is the photon energy, $E_g$ is the energy bandgap and $n=\frac{1}{2}$ for the allowed direct bandgap of Y₂O₃. The diffuse reflectance, $R,$ of the sample was used to calculate the Kubelka–Munk function F(R) [29]

$$F\left(R\right)=\frac{(1-R{)}^2}{2R}$$

(2)

Figure 5 shows the Tauc plot and estimated optical bandgap of pure Y₂O₃. The linear fit extrapolation of the curve to zero absorption gives the optical bandgap [30,31,32]. The bandgap of the Y₂O₃ was estimated to be 5.74 eV, which agrees with the reported value of 5.8 eV reported by Jones et al. [33]. The optical bandgaps of the Y₂O₃ singly and co-doped with Ho³⁺ and Yb³⁺ ions were calculated using the same procedure and are tabulated in

Table 1. Optical bandgap of Y_2−x−yO₃:Ho_x=0.005, Yb_y UC phosphors.

Sample	Bandgap (eV)
Y2O3	5.74
Y2−x−yO3:Hox=0.005	5.72
Y2−x−yO3:Hox=0.005, Yby=0.006	5.68
Y2−x−yO3:Hox=0.005, Yby=0.2	5.61

. An alteration in the optical bandgap of the doped Y₂O₃ material was observed. It is known that introducing dopants into the Y₂O₃ lattice creates energy levels in the energy gap between the valence and conduction bands, which would decrease the optical band gap [34]. It is also known that the defects of the material, which are introduced during synthesis, can influence the bandgap value [35].

3.3. UC Luminescence Studies

Figure 6a presents UC emission spectra of the Y_2−x−yO₃: Ho_x=0.005, Yb_y nanophosphors excited using 980 nm excitation wavelength. The emission spectra are composed of four bands; the intense green, red, and near-infrared emission bands centred at 536, 550, 668, and 756 nm ascribed to the ⁵F₄ → ⁵I₈, ⁵S₂ → ⁵I₈, ⁵F₅ → ⁵I₈, and ⁵S₂ → ⁵I₇ transitions of the Ho³⁺ ions, respectively [36,37,38]. The increase in the Yb³⁺ concentration strongly enhanced the green emission. The maximal enhancement of green (⁵F₄ → ⁵I₈ and ⁵S₂ → ⁵I₈) emission was reached at y = 0.05 Yb³⁺ concentration, while, for higher concentrations, the emission intensity was then quenched, whereas the maximal enhancement of the red (⁵F₅ → ⁵I₈) and NIR emission (⁵S₂ → ⁵I₇) occurred at y = 0.1 Yb³⁺ concentration, as shown in Figure 6b. The reduction in UC intensity is attributed to a self-quenching effect [39,40]. It is known that the Yb³⁺ ion serves as a sensitizer of the Ho³⁺ ion in the UC emission, and thus, the Yb³⁺ ion efficiently transfers its energy to the Ho³⁺ ion [33]. According to the up-conversion process, the optimal concentrations of green (⁵S₂ → ⁵I₈) and NIR (⁵S₂ → ⁵I₇) luminescence should be the same as these two transitions have the same initial level ⁵S₂. The reason behind the different optimal concentrations between these transitions is still unclear, therefore, further analysis is needed to obtain reliable conclusions. Pandey et al. [16] reported that Yb³⁺ co-doping enhances the intensity of UC emission. It was reported that green emission was enhanced by nearly ~290 times and red by approximately ~150 times. The Gd₂O₃:Ho³⁺, Yb³⁺ phosphor exhibited a strong green emission alongside additional UC emission bands [7].

The UC emission normally occurs through UC ET from the Yb³⁺ to the Ho³⁺ ones. The decay curves were acquired to further confirm the UC between the Yb³⁺–Ho³⁺ pair. Figure 7 displays the luminescence decay curves of the ⁵S₂ → ⁵I₈ transition (situated at 550 nm) recorded under the 980 nm excitation, where the intensity is plotted versus time. All the luminescence decay curves were fitted with a double exponential function [28]:

$$I=A_1\exp \left(-\frac{t}{{\tau }_1}\right)+A_2\exp (-\frac{t}{{\tau }_2})$$

(3)

where $I$ is the intensity at time $t$, $A_1$ and $A_2$ are fitting constants, and ${\tau }_1$ and ${\tau }_2$ are the lifetimes. The average lifetimes (${\tau }_{ave})$ were determined using ${\tau }_{ave}=(A_1{{\tau }_1}^2+A_2{{\tau }_2}^2)/(A_1{\tau }_1+A_2{\tau }_2$). The ⁵S₂ level’s lifetime decreased as the Yb³⁺ concentration increased up to y = 0.05, but did not decrease further for higher doping concentrations, as presented in Figure 7b and

Table 2. The lifetime of the ⁵S₂ → ⁵I₈ transition of the Ho³⁺ ion of the Y_2−x−yO₃:Ho_x=0.005, Yb_y at different Yb³⁺ concentration.

Sample	Average Lifetime (µs)
Y2−xO3:Hox=0.005	254
Y2−x−yO3:Hox=0.005, Yby=0.002	241
Y2−x−yO3:Hox=0.005, Yby=0.006	226
Y2−x−yO3:Hox=0.005, Yby=0.01	223
Y2−x−yO3:Hox=0.005, Yby=0.05	92
Y2−x−yO3:Hox=0.005, Yby=0.1	99
Y2−x−yO3:Hox=0.005, Yby=0.2	121

. The decrease in the lifetime corresponds to the UC luminescence intensity improvement, which appears to indicate that it might be related to an efficient ET from Yb³⁺ to Ho³⁺. The trend in the lifetime for concentrations above y = 0.05 may be related to a self-quenching effect, as shown in Figure 6b.

The relation of UC emission intensity to the laser power for the co-doped phosphor was investigated to determine the number of excitation photons needed for each emission photon. Figure 8a represents the emission spectra of Y_2−x−yO₃:Ho_x=0.005, Yb_y=0.05 as a function of the laser power. The UC intensity continuously increased with laser power. The increase in laser power did not affect the peak position but enhanced the UC emission intensity for each of the observed bands (Figure 8b). The UC emission intensity relationship to laser power is modelled using the I α Pⁿ [41] relation, where I, P, and n are the UC emission intensity, pump power, and the number of pump photons involved in the UC emission process, respectively. Figure 8c represents the ln(power) versus ln(intensity). These plots give straight lines with slopes (n values) of 1.69, 1.88, and 1.92 for green (536 and 550 nm) and red (668 nm) emissions, respectively. According to the energy level diagram (see Figure 9), 536 and 550 nm peaks (⁵F₄, ⁵S₂ → ⁵I₈) and 756 nm peak (⁵S₂ → ⁵I₇) result from the same populated levels (⁵F₄, ⁵S₂) of Ho³⁺, and therefore, they have nearly same slopes. Pandey et al., [16] found n values of 2.28 and 1.91 for the green (550 nm) and red (668 nm) emissions. All the slope values are close to two, indicating the involvement of two NIR photons in all of the emission bands.

The energy transfer (ET) mechanism of the UC in the Ho³⁺, Yb³⁺:Y₂O₃ powders is illustrated in Figure 9. The Yb³⁺ ion is excited from the ground state ²F_7/2 to the excited state ²F_5/2 through the 980 nm excitation. The absorbed energy is then transferred via a non-radiative resonance ET to the nearby Ho³⁺ ion, exciting an electron from the ⁵I₈ ground state to the ⁵I₆ excited level. The excited ions in the ⁵I₆ level are further excited to the ⁵S₂, ⁵F₄ level of the Ho³⁺ ion through energy transfer up-conversion (ETU). The populated ⁵S₂, ⁵F₄ levels relax to the ⁵I₈ and ⁵I₇ states radiatively and result in green emissions at 536 and 550 nm through the ⁵F₄ → ⁵I₈, ⁵S₂ → ⁵I₈ transitions, and NIR emission at 756 nm through the ⁵S₂ → ⁵I₇ transitions. Moreover, the relaxation process from the ⁵S₂, ⁵F₄ level may populate the ⁵F₅ level via non-radiative multiphonon relaxation and result in a red emission at 668 nm through the radiative ⁵F₅ → ⁵I₈ transition [42,43]. The UC emission can also take place through cooperative energy transfer (CET) between two Yb³⁺ ions and one Ho³⁺ ion. The ⁵F₄, ⁵S₂ excited states of Ho³⁺ ions are situated twice of that Yb³⁺:²F_5/2 excited state. In this case, two Yb³⁺ ions can transfer their energy cooperatively to one Ho³⁺ ion in the ground state in which the Ho³⁺ ion is promoted to the ⁵F₄ and ⁵S₂ excited states. All these emissions are two-photon processes.

3.4. Optical Temperature Sensing

To study the properties of optical temperature sensing of the sample, the temperature-dependent UC was analysed using the FIR technique. Figure 10a shows the temperature-dependent UC spectra of the Y_2−x−yO₃: Ho_x=0.005, Yb_y=0.05 phosphor, with the most intense green emission centred at 550 nm associated with the ⁵S₂ → ⁵I₈ transition of the Ho³⁺ ion. For all the UC emission bands, no significant shift in wavelength position was observed from room temperature up to 623 K. It is also evident that as the temperature rises, thermal quenching causes all the bands to progressively lose their intensity (Figure 10b).

Figure 11 presents the temperature dependence of the I₅₃₆/I₆₆₈, I₅₅₀/I₆₆₈ and (I₅₃₆+I₅₅₀)/I₆₆₈ FIRs. Non-TCLs are often fitted by empirical functions due to the absence of quality physical models classifying temperature-dependences of the FIR parameters [44]. Therefore, FIR of the bands at 536, 550, and 668 nm can be fitted using the function:

$$FIR=\frac{I_2}{I_1}=B_0+B_{1}T+B_2{T}^2+B_3{T}^3$$

(4)

where $I_1$ and $I_2$ are the integrated emission intensities, $B_0, B_1,B_2, B_3$ are fitting constants, and T is the absolute temperature, respectively. The fitting data are included in Figure 11.

For temperature sensing, the relative sensitivity (S_R) and the absolute sensitivity (S_A) are two indispensable parameters which were calculated using the equations [45]

$${\mathrm{S}}_{\mathrm{A}}=\frac{dFIR}{dT}$$

(5)

$${\mathrm{S}}_{\mathrm{R}}=\frac{1}{FIR}\left(\frac{dFIR}{dT}\right)\times 100\%$$

(6)

Figure 12a,b shows the absolute and relative sensitivities versus temperature. As the temperature increased, both the absolute sensitivity and the relative sensitivity decreased. All the values reached maxima at 303 K. The maximum S_R values were determined to be 0.47 (I₅₃₆/I₆₆₈), 0.64 (I₅₅₀/I₆₆₈), and 0.59%K⁻¹ ((I₅₃₆ + I₅₅₀)/I₆₆₈), respectively, while the S_A values were found to be 0.02 (I₅₃₆/I₆₆₈), 0.06 ((I₅₃₆ + I₅₅₀)/I₆₆₈), and 0.08 K⁻¹ ((I₅₅₀/I₆₆₈), respectively. The (I₅₃₆ + I₅₅₀)/I₆₆₈ FIR had the largest S_A, while I₅₅₀/I₆₆₈ had the highest S_R values. The ⁵F₅/⁵F₄, ⁵S₂ levels are non-thermally coupled energy levels, and thus, the temperature sensor sensitivity is substantially higher [21].

Table 3. Maximal S_A and S_R values of different Ho³⁺, Yb³⁺ co-doped UC hosts.

Sample	Transitions	Temp Range (K)	Max SA (K−1)	Max SR (%K−1)	Ref.
Ho, Yb: Y2O3	5F4, 5S2 → 5I8, 5F5 → 5I8 5S2 → 5I8, 5F5 → 5I8	303–623	0.08 -	- 0.64	This work
Ho, Yb: LuYO3	5F4, 5S2 → 5I8, 5F5 → 5I8	298–578	0.1603	0.0102	[24]
Ho, Yb: NaLuF4	5F2,3,5K8 → 5I8, 5G6, 5F1 → 5I8	390–780	0.0008	0.83	[46]
Ho, Yb: CaWO4	5F2,3,5K8 → 5I8, 5G6, 5F1 → 5I8	303–923	0.0050	0.28	[47]
Ho, Yb: NaYF4	5F4, 5S2 → 5I8	313–393	0.0038	0.7230	[48]
Ho, Yb: Y2O3	5F4, 5S2 → 5I8	293–563	0.0071	-	[49]
Ho, Yb: Y2O3	5F4, 5S2 → 5I8	348–598	0.013	0.622	[50]
Ho, Yb: Y2O3	5F4, 5S2 → 5I8, 5S2, 5F4 → 5I7	0–300	0.0097	1.90	[51]

compares the optical temperature sensing performance data of Ho, Yb co-doped various UC hosts. From Table 3, in this work Ho, Yb:Y₂O₃ noticeably show better sensitivity results than other UC host materials. These results differ because other reported ones were acquired at different measuring temperature ranges and the hosts show a temperature-dependent nature. Different host materials could also make a difference in sensitivity due to the different properties of the hosts. Moreover, some studies report on temperature sensors that are based on ratiometric measurements of the sensing of the ³K₈ → ⁵I₈ and ⁵F₃ → ⁵I₈ transitions (blue band emissions), which are due to three photon UC processes, and they typically need much higher power of excitation [46,47]. Additionally, other studies focus on TCLs that use the ⁵F₄ → ⁵I₈ and ⁵S₂ → ⁵I₈ transitions in the two green bands, which may not be the best method for temperature monitoring since the bands are spectrally overlapped [48,49,50]. The difference in sensitivity results could also result due to the different experimental conditions of the Ho³⁺, Yb³⁺ co-doped UC host materials. Therefore, the Ho, Yb:Y₂O₃ phosphor used in this study represents a better optical temperature sensing option.

To further study the efficiency of the optical high temperature sensor, the temperature resolution or uncertainty (δT) associated with FIRs used was calculated as described in [52]:

$$\delta T=\frac{1}{S_R}\frac{\delta FIR}{FIR}$$

(7)

$\delta FIR$ represents the resolution/uncertainty of the FIR value. The temperature uncertainty ($\delta T)$ depends on the signal-to-noise ratio of the emission spectra and relative sensitivity (S_R) [53]. The best temperature uncertainty determined at 303 K was for I₅₃₆/I₆₆₈ FIR, i.e., $\delta T$ = 0.71 K. For other FIRs, temperature uncertainty values were determined to be 0.51 K for I₅₅₀/I₆₆₈ and 0.57 K for (I₅₃₆ + I₅₅₀)/I₆₆₈ at the same temperature, Figure 13. The temperature uncertainty at this temperature can be used for biological research [54]. As the temperature increased to 623 K, the temperature uncertainty reached maximum values at 7.61, 0.70, and 1.08 K for I₅₃₆/I₆₆₈, I₅₅₀/I₆₆₈ and (I₅₃₆ + I₅₅₀)/I₆₆₈, respectively. The temperature uncertainty at 623 K results in sufficient optical temperature sensing. Moreover, such temperature uncertainty at high temperature could be potentially used in industrial applications, especially for processes which require high temperature conditions as well as other fields, i.e., submicron-scale resolution [44]. Moreover, stability and repeatability for optical temperature sensing are also important factors. Therefore, several heating-cooling cycling experiments were performed on the Y_2−x−yO₃:Ho_x=0.005, Yb_y=0.05 phosphor to verify the repeatability of the synthesized material, Figure 14a–c. This was achieved by studying the FIR changes in the I₅₃₆/I₆₆₈, I₅₅₀/I₆₆₈, and (I₅₃₆ + I₅₅₀)/I₆₆₈ at 303 and 623 K, respectively. The deviation percentage of the FIR in the repeatability experiment was found to be 1.19%, 3.49%, and 3.25% for I₅₃₆/I₆₆₈, I₅₅₀/I₆₆₈, and (I₅₃₆ + I₅₅₀)/I₆₆₈, respectively. After 10 heating-cooling repeated cycles, the FIR values showed no obvious difference and could be reversed and repeated. These results indicate that the FIR based on non-TCLs own good stability, indicating that Y_2−x−yO₃:Ho_x=0.005, Yb_y=0.05 phosphor has good signal reproducibility and is a capable candidate for optical temperature sensing.

4. Conclusions

The UC intensity and optical thermometry characteristics of Y₂O₃:Ho³⁺, Yb³⁺ were investigated. The XRPD results confirmed the cubic structure of Y₂O₃ in space group Ia$\overline{3}$. The Yb³⁺ concentration did not change the agglomerated spherical nanoparticles morphology of the samples. From the diffuse reflectance spectra, the band gap decreased with increasing Yb³⁺ concentration. Under the 980 nm excitation wavelength, the UC luminescence showed four emission bands at 536, 550, 668, and 756 nm, assigned to the ⁵F₄ → ⁵I₈, ⁵S₂ → ⁵I₈, ⁵F₅ → ⁵I₈, and ⁵S₂ → ⁵I₇ transitions of the Ho³⁺ ions, respectively. The UC intensity had increased to a maximum value at y = 0.05 Yb³⁺ concentration. The UC process is ruled by a two-photon absorption process. The UC lifetime of the green emission (⁵S₂ → ⁵I₈) confirmed that the ET between the Yb³⁺ and Ho³⁺ plays a major role in the UC process. The optical temperature sensing behaviour was studied at a temperatures range of 303 K–623 K. The maximum absolute and relative sensitivity values were S_A = 0.08 K⁻¹ and S_R = 0.64% K⁻¹, respectively. The results reveal that Y_2−x−yO₃:Ho_x=0.005, Yb_y=0.05 is useful for optical high temperature sensors.