Tailoring of upconversion luminescence of Al³⁺ engineered titanate phosphor for non-invasive thermometry

The Er³⁺, Yb³⁺ and Al³⁺ co-doped Bi₄Ti₃O₁₂ phosphors with varied concentrations have been synthesized through standard solid state reaction technique. The chemicals like Bi₂O₃, TiO₂, Er₂O₃, Yb₂O₃, and Al₂O₃ have been employed as the starting ingredients. Stoichiometric quantities of the respective chemicals have been weighed and mixed constantly around 2 h in an agate mortar and pestle using acetone. To eliminate impurities and produce desired materials, the ground phosphors have been calcined at 1000 °C for 3 h at a heating rate of 5 °C min⁻¹ in a high temperature muffle furnace. The synthesized samples were crushed for a few minutes to get homogeneous and fine powders, which were then utilized for further characterization.

An x-ray diffractometer utilizing Cu-K radiation has been used for phase identification, lattice parameter calculation, and average crystallite size estimation. The x-ray diffraction (XRD) spectra have been collected across a broad range of Bragg's angles, from 10° to 80° (2θ), with 0.02-degree step size. Diffuse reflectance spectra have been monitored by Lambda 950 UV–vis-NIR spectrophotometer (Perkin Elmer) to compute the optical bandgap of the prepared phosphors. Surface morphology has been studied using FESEM. The UC emission spectra have been collected using a triple turret grating monochromator (Princeton) in conjunction with a photomultiplier tube (PMT). 980 nm continuous wave (CW) laser diode has been used to stimulate the prepared samples. A small handmade heater connected with a thermocouple positioned near (2 mm) to the laser point has been utilized to evaluate the thermometric parameters associated with frequency UC emission. To control the temperature, a Variac has been employed.

The structural information and development of the crystalline phase of the synthesized phosphors have been characterized by XRD. Figure 1(a) shows the x-ray diffraction pattern of the synthesized Bi₄Ti₃O₁₂, Er³⁺: Bi₄Ti₃O₁₂, Er³⁺-Yb³⁺: Bi₄Ti₃O₁₂, and Er³⁺-Yb³⁺-Al³⁺: Bi₄Ti₃O₁₂ phosphors, scanned in the range from 10° to 80° (2θ). All the intense diffraction peaks of the prepared phosphors converge to the standard diffraction reference pattern ICSD 98-015-9929 with no extra diffraction peaks, which further confirms the formation of a single phase of the phosphors. The prepared phosphors are thus to have an orthorhombic phase with the Aba2 space group. The maximum diffraction peak associated with all the phosphors is assigned to the (171) hkl plane.

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The lattice constants of the prepared phosphors have been obtained through the Rietveld refinement technique using FULLPROF software and are listed in table 1. The Rietveld refined XRD pattern of Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphors have been depicted in figure 1(b), and all other refined patterns are given in {SI figure 1(a)–(c) (available online at stacks.iop.org/MAF/10/034002/mmedia)}. The average crystallite sizes of the phosphors have been evaluated with Scherrer's equation and are found to lie between ∼56 nm to 59 nm [22, 23]. It is interesting to note that no impurity peaks are obtained despite doping Er³⁺, Yb³⁺, Al³⁺ ions in Bi₄Ti₃O₁₂ phosphors. This may be ascribed to the low concentration of doping ions or the successful substitution of dopant ions in the lattice sites of Bi₄Ti₃O₁₂ phosphors. Based on the R D Shannon's ionic radii database, the effective ionic radii corresponding to the six-coordinated Bi³⁺, Ti⁴⁺, Er³⁺, Yb³⁺, and Al³⁺ are 1.03 Å, 0.605 Å, 0.89 Å, 0.868 Å, and 0.535 Å, respectively [24].

Various researches suggest that all the trivalent ions must replace the Bi³⁺ site due to the similar charge, whereas from the ionic radius point of view, Al³⁺ has more chance of replacing the Ti⁴⁺ site. But several investigations suggest that although the smaller ionic radii of Al³⁺ ions than Bi³⁺, the solution energy to replace Bi³⁺ is smaller than Ti⁴⁺. Hence, the Al³⁺ ions also can replace the Bi³⁺ site [25]. Thus, it should be evident that the substitution of smaller ionic radii in the Bi³⁺ site may result in lattice shrinkage, i.e., Er³⁺ doping causes less lattice shrinkage followed by Yb³⁺ and Al³⁺, which can be verified from SI figure 1(d) [26].

The FESEM images of Bi₄Ti₃O₁₂ phosphors synthesized at 1000 °C for 3h co-doped with Er³⁺, Yb³⁺, and Al³⁺ have been portrayed in figure 1(c). The morphology of the prepared phosphor exhibits plate-like structures [27, 28]. Since the particles shown in the image are indistinct, individual sizes of the particles are very difficult to determine. For the compression purpose, FESEM images of undoped and co-doped with Er³⁺ and Er³⁺-Yb³⁺ Bi₄Ti₃O₁₂ phosphors are also depicted in SI figures 2(a)–(c).

The Raman spectra for the undoped Bi₄Ti₃O₁₂ phosphor have been recorded in the frequency range from 100–1000 cm⁻¹. As shown in SI figure 2(d), various sharp characteristic peaks along with a few broad and weak peaks have also been monitored around 116, 225, 267, 329, 360, 404, 443, 537, 574, 657, 769, and 846 cm⁻¹ that is in good agreement with the previously reported works [29–31]. According to the Raman selection rules, there are 24 Raman active modes possible for the orthorhombic Bi₄Ti₃O₁₂ with a combination of different symmetries (6A_g+2B_1g+8B_2g+8B_3g). Generally, the higher wavenumber phonon modes are assigned to the vibrations corresponding to Ti–O atoms and lower phonon modes are designated to the Bi–O atoms [31]. The 118 cm⁻¹ Raman modes in the Bi₄Ti₃O₁₂ phosphor denote the appearance of the Bi atom in the A-site of the pseudo-perovskite layer [29]. The phonon modes corresponding to 225, 267, 329, 537, and 846 cm⁻¹ have been assigned to the internal vibrational modes of TiO₆ octahedrons [32], in which 225 cm⁻¹ and 267 cm⁻¹ appear due to the distortion in the TiO₆ octahedrons [31]. The modes at 360, 404, 443, and 846 cm⁻¹ arise from the combination of stretching or bending vibrations of Ti-O. In contrast, the 537 cm⁻¹ and 574 cm⁻¹ modes result from the opposite displacement of the apical oxygen atom of TiO₆ octahedral [30]. The mode at 657 cm⁻¹ has been ascribed to the symmetric stretching vibrations of Ti-O, while the 769 cm⁻¹ denotes the vibration associated with oxygen defects [33].

The UV–vis-NIR spectra of the prepared phosphors have been recorded in the diffuse reflectance mode at room temperature. Data has been collected for the undoped and co-doped Bi₄Ti₃O₁₂ phosphors in the range from 200–1800 nm keeping the step size 0.5 nm (figure 1(d)). The BaSO₄ powder has been used as the reference for baseline correction. The broad peak that arises from 200–400 nm has been attributed to the host lattice, whereas the sharp band beyond the 400 nm range is due to the f-f transitions from the rare-earth ions. The peaks around 523 nm, 654 nm, and 1515 nm arise explicitly due to the Er³⁺ activator ions, and the transitions responsible for the above peaks are ⁴I_15/2 → ²H_11/2, ⁴I_15/2 → ⁴F_9/2, and ⁴I_15/2 → ⁴I_13/2, respectively. The 978 nm peak can be simultaneously allocated to the ⁴I_15/2 → ⁴I_11/2 and ²F_7/2 → ²F_5/2 transitions of the Er³⁺ and Yb³⁺ ions, respectively [34]. Besides identifying the peaks, the DRS spectra help find the optical bandgap of the prepared phosphors. For evaluating the optical bandgap of the phosphor, the DRS spectra have been converted to F(R) spectra to obey the following Kubelka-Munk expression [35, 36]:

$$\begin{eqnarray}&&F({R}_{\infty })=\displaystyle \frac{{\left(1-{R}_{\infty }\right)}^{2}}{2{R}_{\infty }}=\displaystyle \frac{K}{S}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{[F({R}_{\infty })h\upsilon ]}^{2}=C{(h\upsilon -{E}_{g})}^{n}\end{eqnarray} \tag{ 2 }$$

where, F(R_∞) is the Kubelka-Munk function, R_∞ is the phosphor's diffuse reflectance, K and S are the absorption and scattering coefficients, respectively, hν is the incident photon energy, E_g is the optical band gap (eV), and the n value indicates the kind of optical transition, with n = 1 indicating direct allowed transitions, 2 indicating non-metallic materials, 3 indicating direct prohibited transitions, 4 indicating indirect allowed transitions, and 6 indicating indirect forbidden transitions [37]. Here, the best fit resulted for n = 1. From the Tauc plot analysis of all synthesized phosphors, and the optical bandgaps are obtained to be 3.23 eV, 3.25 eV, 3.29 eV, and 3.21 eV for Bi₄Ti₃O₁₂, Er³⁺: Bi₄Ti₃O₁₂, Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂, and Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphors respectively. Here, the doping contents in the phosphors are significantly less, so the slight variation in the optical bandgap could be attributed to the fitting and measurement errors. The refractive index (r) corresponding to the direct optical bandgap (E_g) may also be calculated using the equation below [38].

$$\begin{eqnarray}&&\displaystyle \frac{{r}^{2}-1}{{r}^{2}+1}=1-\sqrt{\displaystyle \frac{{E}_{g}}{20}}\end{eqnarray} \tag{ 3 }$$

For doped and co-doped Bi₄Ti₃O₁₂, the refractive index obtained by solving the preceding equation is lying between 1.98 to 2. Because the optical bandgaps of the prepared phosphors are relatively low and they have a high refractive index, they might be potential contenders in light catalytic fields [39, 40].

The upconversion luminescence phenomena of the prepared phosphors have been observed under the 980 nm laser excitation. Figure 2(a) shows the optimized upconversion emission spectra for the 0.5 mol% Er³⁺: Bi₄Ti₃O₁₂, 0.5 mol% Er³⁺−0.75 mol% Yb³⁺: Bi₄Ti₃O₁₂ and 0.5 mol% Er³⁺−0.75 mol% Yb³⁺−0.5 mol% Al³⁺: Bi₄Ti₃O₁₂ phosphors in the range from 450–750 nm at room temperature. The three intense peaks detected ∼525 nm, ∼550 nm, and ∼657 nm can be summarized as the ²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2, and ⁴F_9/2 → ⁴I_15/2 electronic transitions of Er³⁺ ions, respectively. Various research suggests that the Yb³⁺ ion is ideal for sensitizer under 980 nm excitation [41, 42]. Because of the large absorption cross-section of the Yb³⁺ ion around 980 nm, an enhancement of 9.38 times in the green region and 15.47 times in the red region has been observed in Er³⁺–Yb³⁺ co-doped phosphors compared to Er³⁺: Bi₄Ti₃O₁₂ phosphors. Moreover, co-doping Al³⁺ ions in Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphors increases green and red emissions by 3.15 and 2.96 times, respectively. The significant increase in UC emission triggered by Al³⁺ ion doping in the prepared phosphor could be ascribed to crystal field modifications and an increase in asymmetry around the Er³⁺ ions caused by lattice shrinkage owing to the significant differences in ionic radii between Bi³⁺ and Al³⁺ ions [43–45].

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The energy level diagram (ELD) for the Er³⁺-Yb³⁺ system has been introduced to better understand the absorption and emission transition mechanisms of the prepared phosphors. Figure 2(b) depicts the energy level diagram for the 980 nm laser-excited system, including all possible phosphor mechanisms. In the case of singly doped Er³⁺ phosphor, the 980 nm excitation is absorbed via the ground state absorption (GSA) process to the ⁴I_11/2 level, followed by the sequential absorption of another photon via the excited state absorption (ESA₁) process to the ⁴F_7/2 level. Again, few of the excited ions in the ⁴I_11/2 levels relax non-radiatively to the low lying ⁴I_13/2 levels, from which the ESA₂ process to ⁴F_9/2 levels occurs. The ⁴F_7/2 level relaxes further to the thermally coupled levels ²H_11/2 and ⁴S_3/2, after which emission is observed at 525 nm and 550 nm in the green region due to the radiative transitions from the ²H_11/2 and ⁴S_3/2 thermally coupled levels, respectively. Likewise, the red emission ∼657 nm is attributed to a radiative transition from ⁴F_9/2 levels. However, by doping the phosphors with Yb³⁺ ions, the green and red emission improved dramatically, associated with the following energy transfer (ET) processes [46, 47].

$$\begin{eqnarray*}&&\begin{array}{l}{{\rm{ET}}}_{1}{:}^{2}{{\rm{F}}}_{5/2}\left({{\rm{Yb}}}^{3+}\right)\\ \,{+}^{4}{{\rm{I}}}_{15/2}\left({{\rm{Er}}}^{3+}\right){\to }^{2}{{\rm{F}}}_{7/2}\left({{\rm{Yb}}}^{3+}\right){+}^{4}{{\rm{I}}}_{11/2}\left(E{r}^{3+}\right)\\ \,{{\rm{ET}}}_{2}{:}^{2}{{\rm{F}}}_{5/2}\left({{\rm{Yb}}}^{3+}\right)\\ \,{+}^{4}{{\rm{I}}}_{13/2}\left({{\rm{Er}}}^{3+}\right){\to }^{2}{{\rm{F}}}_{7/2}\left({{\rm{Yb}}}^{3+}\right){+}^{4}{{\rm{F}}}_{9/2}\left({{\rm{Er}}}^{3+}\right)\\ \,{{\rm{ET}}}_{3}{:}^{2}{{\rm{F}}}_{5/2}\left({{\rm{Yb}}}^{3+}\right)\\ \,{+}^{4}{{\rm{I}}}_{11/2}\left({{\rm{Er}}}^{3+}\right){\to }^{2}{{\rm{F}}}_{7/2}\left({{\rm{Yb}}}^{3+}\right){+}^{4}{{\rm{F}}}_{7/2}\left({{\rm{Er}}}^{3+}\right)\end{array}\end{eqnarray*}$$

Moreover, the depopulation rates from various metastable states with different pump power density range in the Er³⁺–Yb³⁺ co-doped systems can be theoretically predicted with the help of steady-state rate equations as,

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{d{N}_{Er,1}}{dt}=0={W}_{2}{N}_{Er,\,2}-{W}_{1}{N}_{Er,\,1}\\ \,-{K}_{3}{N}_{Er,1}{N}_{Yb,1}-{\rho }_{p}{\sigma }_{14}{N}_{Er,1}\end{array}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{d{N}_{Er,2}}{dt}=0=\,{\rho }_{p}{\sigma }_{02}{N}_{Er,0}+{K}_{1}{N}_{Er,0}{N}_{Yb,1}\\ \,-{K}_{2}{N}_{Er,2}{N}_{Yb,1}-{\rho }_{p}{\sigma }_{25}{N}_{Er,2}-{W}_{2}{N}_{Er,2}\end{array}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{d{N}_{Er,3}}{dt}=0={K}_{3}{N}_{Er,1}{N}_{Yb,1}+{\rho }_{p}{\sigma }_{13}{N}_{Er,1}\\ \,+{W}_{4}{N}_{Er,4}-{{W}^{{\prime} }}_{3}{N}_{Er,3}\end{array}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{d{N}_{Er,4}}{dt}=0={K}_{2}{N}_{Er,2}{N}_{Yb,1}+{\rho }_{p}{\sigma }_{24}{N}_{Er,2}\\ \,-{W}_{4}{N}_{Er,4}-{{W}^{{\prime} }}_{4}{N}_{Er,4}-{{W}^{{\prime} }}_{41}{N}_{Er,4}\end{array}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{d{N}_{Yb,1}}{dt}=0={\rho }_{p}{\sigma }_{Yb}{N}_{Yb,0}\\ \,-\left({K}_{1}{N}_{Er,0}+{K}_{3}{N}_{Er,1}+{K}_{2}{N}_{Er,2}\right){N}_{Yb,1}-W{{\prime} }_{Yb}{N}_{Yb,1}\end{array}\end{eqnarray} \tag{ 8 }$$

where, N_{Er, k} (k = 0, 1, 2, 3, 4) signifies the population densities for Er³⁺ ions at the ⁴I_15/2, ⁴I_13/2, ⁴I_11/2, ⁴F_9/2 and (⁴S_3/2, ²H_11/2) levels, respectively, while N_Yb,0 and N_Yb,1 signify the population densities for Yb³⁺ ions at the ²F_7/2 and ²F_5/2 levels. W₁, W₂, and W₄ reflect the non-radiative decay rates of ⁴I_13/2, ⁴I_11/2, and (²H_11/2/⁴S_3/2) levels, respectively. The radiative decay rates of the ⁴F_9/2, ⁴S_3/2, and ²H_11/2 states are Wʹ₃, Wʹ₄ and Wʹ₄₁, respectively. W'_Yb represents the radiative decay rate of the Yb³⁺ ion's excited state ²F_5/2. Under 980 nm excitation, K₁, K₂, and K₃ reflect the energy transfer rates of ET₁, ET₂, and ET₃, respectively. σ_ij denotes the absorption cross-section between Er³⁺ ions at the ith and jth levels, whereas σ_Yb denotes the absorption cross-section between Yb³⁺ ions at levels ²F_7/2 and ²F_5/2. The pump power density corresponding to the excitation wavelength of 980 nm is ρ_p. Since the absorption cross-section of the Er³⁺ ions is comparatively low from Yb³⁺ ions, it can be assumed that the processes like GSA and ESA took little part in populating the metastable states and hence can be neglected.

At low pump power density, the non-radiative decays from the ⁴I_11/2 and ⁴I_13/2 levels are dominant over ET₂ and ET₃ from Yb³⁺ ions to Er³⁺ ions. Thus, the energy transfers can be neglected from equations (4) and (5). Equation (8) can be reduced to,

$$\begin{eqnarray}&&\begin{array}{l}{N}_{Yb,1}\\ =\displaystyle \frac{{\rho }_{p}{\sigma }_{Yb}}{{K}_{1}{N}_{Er,0}+{K}_{3}{N}_{Er,1}+{K}_{2}{N}_{Er,2}+{{W}^{^{\prime} }}_{Yb}}{N}_{Yb,0}\propto {I}_{P}\end{array}\end{eqnarray} \tag{ 9 }$$

Considering the above criteria, the equations (4) and (5) can be re-written as,

$$\begin{eqnarray}&&{N}_{Er,1}=\displaystyle \frac{{W}_{2}}{{W}_{1}}{N}_{Er,\,2}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{N}_{Er,2}=\displaystyle \frac{{K}_{1}}{{W}_{2}}\,{N}_{Er,0}{N}_{Yb,1}\propto {I}_{P}\end{eqnarray} \tag{ 11 }$$

The modified equations (7) using equations (10) can be written as,

$$\begin{eqnarray}&&{N}_{Er,4}=\displaystyle \frac{{K}_{2}}{\left({W}_{4}+{W}_{4}^{{\prime} }+{W}_{41}^{{\prime} }\right)}{N}_{Er,2}{N}_{Yb,1}\propto {I}_{P}^{2}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&\begin{array}{l}{N}_{Er,3}=\displaystyle \frac{{K}_{3}}{W{{\prime} }_{3}}{N}_{Er,1}{N}_{Yb,1}+\displaystyle \frac{{W}_{4}}{W{{\prime} }_{3}}{N}_{Er,4}\\ \,=\displaystyle \frac{{K}_{3}{W}_{2}}{{W}_{1}W{{\prime} }_{3}}{N}_{Er,\,2}{N}_{Yb,1}+\displaystyle \frac{{W}_{4}}{W{{\prime} }_{3}}{N}_{Er,4}\propto \left(x{I}_{P}^{2}+y{I}_{P}^{2}\right)\end{array}\end{eqnarray} \tag{ 13 }$$

Equations (14) and (13) represent the population corresponding to the green and red emissions, respectively. As it can be observed that the populations in the respective levels are quadratic in nature, which signifies two photons are required to populate ²H_11/2, ⁴S_3/2 and ⁴F_9/2 levels.

As the pump power density increases gradually, it can be assumed that the ET processes must overcome the non-radiative losses at the ⁴I_11/2 and ⁴I_13/2 levels. Hence, equations (4) and (5) can be reduced by omitting the terms -W₁N_Er,1 and -W₂N_Er,2 as,

$$\begin{eqnarray}&&{N}_{Er,1}=\displaystyle \frac{{W}_{2}}{{K}_{3}{N}_{Yb,1}}{N}_{Er,\,2}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{N}_{Er,2}=\displaystyle \frac{{K}_{1}}{{K}_{2}}\,{N}_{Er,0}\propto {I}_{P}^{0}\end{eqnarray} \tag{ 15 }$$

Further, the equations (7) and (8) can be modified to,

$$\begin{eqnarray}&&{N}_{Er,4}=\displaystyle \frac{{K}_{2}}{\left({W}_{4}+{W}_{4}^{{\prime} }+{W}_{41}^{{\prime} }\right)}{N}_{Er,2}{N}_{Yb,1}\propto {I}_{P}\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&{N}_{Er,3}=\displaystyle \frac{{W}_{2}}{{{W}^{^{\prime} }}_{3}}{N}_{Er,\,2}+\displaystyle \frac{{W}_{4}}{{{W}^{^{\prime} }}_{3}}{N}_{Er,4}\propto (x{I}_{P}^{0}+{I}_{P})\end{eqnarray} \tag{ 17 }$$

Equation (16) defines the population corresponding to the green emission, which turns out to be a single-photon absorption. At the same time, equation (17) represents the red emission, in which the first term is independent of the pump photon, and the second term implies a single-photon absorption. The above result suggests that at high pump power density ET₂ becomes efficient, and non-radiative processes increase rapidly, which eventually causes the saturation effect.

The UC emission has been measured using various laser pump power density ranges (980 nm) to validate the above theoretical assumptions. Earlier studies indicate that the relationship between the UC emission intensity (I_UC) and the input pump power density (p) is not linear, with I_UC∝ pⁿ [48, 49]. The value of 'n' here determines the number of infrared (IR) pump photons necessary to populate certain levels to obtain UC emission. The plot between ln P and ln (I_UC ) is shown in the inset of figure 2(a), with 'n' computed from the slope values. As stated before, the slope value approaches 2 at relatively low pump power density ranges; however, the saturation effect has been detected at higher pump power density ranges.

Chromaticity is defined by the Commission Internationale de l'Eclairage (CIE) as the distribution of colour produced by an object as a function of wavelength (λ) as experienced by human brains. Using the Go CIE software, the CIE colour coordinates of the Er³⁺: Bi₄Ti₃O₁₂, Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂, and Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphors have been determined to be (0.27, 0.71), (0.27, 0.72), and (0.27, 0.72), respectively. Since the doped/co-doped phosphors display dominating green emission, colour purity of the synthesized phosphors under 980 nm excitation has been measured as follows [21],

$$\begin{eqnarray}&&\begin{array}{l}Colour\,Purity\,\left( \% \right)\\ \,=\sqrt{\displaystyle \frac{{({X}_{s}-{X}_{i})}^{2}+{({Y}_{s}-{Y}_{i})}^{2}}{{({X}_{d}-{X}_{i})}^{2}+{({Y}_{d}-{Y}_{i})}^{2}}}\times 100\end{array}\end{eqnarray} \tag{ 18 }$$

where, (X_S, Y_S) symbolizes the sample point, (X_i, Y_i) represents the illumination point and (X_d, Y_d) is the dominating point of the CIE co-ordinates. The specifics of the colour coordinates and purity of the phosphors have been reported in SI tables 1 and 2. As demonstrated in SI figure 3(a), essentially negligible change in the chromaticity between Er³⁺: Bi₄Ti₃O₁₂, Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂, and Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphors has been detected. A modest shift in the colour coordinates towards the green area has been recorded when the pump power density rises in the Er³⁺ –Yb³⁺ –Al³⁺: Bi₄Ti₃O₁₂ phosphor {SI figure 3(b)}.

The thermally coupled levels (TCLs)-based fluorescence intensity ratio (FIR) approach is one of the most generally acknowledged techniques for temperature sensing applications in which the FIRs fluctuate with temperature. The thermally coupled levels of Er³⁺ ions have been identified as the peak at 525 and 550 nm for ²H_11/2 and ⁴S_3/2 levels of Er³⁺ ions in this study. The difference in energy between the ²H_11/2 and ⁴S_3/2 levels is computed as ∼865 cm⁻¹. Owing to the small energy gap (ΔE) between the TCLs, it is believed that the ²H_11/2 levels could be easily populated from ⁴S_3/2 as temperature increases gradually. The UC emission spectra of Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ and Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphors in the range of 505–575 nm have been recorded to explore the temperature sensing behavior of the synthesized phosphors. Because of the low emission intensity, the temperature sensing behavior of Er³⁺: Bi₄Ti₃O₁₂ phosphor has not been investigated.

Mathematically, the FIR between the thermally coupled levels can be represented as [50],

$$\begin{eqnarray}&&FIR=\displaystyle \frac{{I}_{H}}{{I}_{S}}=\displaystyle \frac{N(H)}{N(S)}=A\exp \left(-\displaystyle \frac{{\rm{\Delta }}E}{kT}\right)\end{eqnarray} \tag{ 19 }$$

where I_H and I_S indicate the emission intensities for the G₁ and G₂ levels, respectively. The population density for the ²H_11/2 and ⁴S_3/2 levels is represented by N(H) and N(S), respectively. The fitting energy separation between two thermally connected levels is denoted by ∆E, the Boltzmann's constant is denoted by k, the absolute temperature is denoted by T, and A is a pre-exponential constant. At first, the thermal behaviour of the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor has been witnessed in the temperature range from 300–473 K at ∼5.78 W cm⁻². Beyond 423 K, the UC emission spectra return noisy data. On varying the temperature, the peak positions of ²H_11/2 and ⁴S_3/2 levels didn't alter as the FIR value varies from 0.588 to 1.895. SI figure 4(a) depicts the fitting parameters of FIR vs temperature considering the equation (19). The energy gap (∆E) between the TCLs is found to be 630.46 cm⁻¹. Here, the calculated energy gap differs marginally from the observed energy gap of the UC emission data. Thus, it has been speculated that the decrease in the fitted ∆E value can be attributed to laser-induced heating. Generally, when the laser power increases, the laser itself produces heat around the irradiation spot which the external temperature probe cannot detect that costs difference in the actual and measured ∆E value [51]. Therefore, low laser power is recommended for precise temperature sensing measurement.

Further, to reduce the laser induced heating, the thermometric behaviour of Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor has been monitored at 3.77 W cm⁻². Figure 3(a) displays the variation of FIR as a function of elevating temperature. Starting from 0.45 at ambient temperature, the FIR value raises maximum up to 1.70 at 473 K and thereafter the spectra got noisy. Further, the upper inset of the figure 3(a) reflects the intensity variation of individual states as a function of temperature, which obeys the Boltzmann distribution law [52, 53]. It is no surprise that the ∆E value for the phosphor enhances to 746.91 cm⁻¹ owing to a relatively low thermal effect at low pump power density [51]. Relative and absolute sensitivities, S_r and S_a , has been considered as the two major parameters in temperature sensors which quantity the sensor performance, thus can be stated as [53],

$$\begin{eqnarray}&&{S}_{r}=\left|\left(\displaystyle \frac{1}{FIR}\right)\times \displaystyle \frac{d\left(FIR\right)}{dT}\right|=\displaystyle \frac{{\rm{\Delta }}E}{k{T}^{2}}\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}&&{S}_{a}=\left|\displaystyle \frac{d\left(FIR\right)}{dT}\right|=FIR\times \displaystyle \frac{{\rm{\Delta }}E}{k{T}^{2}}\end{eqnarray} \tag{ 21 }$$

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Further, the equation (21) can be used to evaluate the optimum absolute sensitivity and the corresponding temperature by taking dS_a /dT = 0 as [54],

$$\begin{eqnarray}&&{({S}_{a})}_{{\rm{\max }}}=\displaystyle \frac{0.54A}{{\rm{\Delta }}E/k}\end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray}&&{T}_{{\rm{\max }}}=\displaystyle \frac{1}{2}\times \displaystyle \frac{{\rm{\Delta }}E}{k}\end{eqnarray} \tag{ 23 }$$

Figure 3(b) shows the fitted curve of both relative and absolute sensitivity with increasing temperature. The fitted curve suggests that the value of S_r at ambient temperature is 0.0119 K⁻¹, however, S_a increases gradually with temperature to reach its maximum value ∼0.0084 K⁻¹ at 537 K which is comparable to the experimentally observed value of ∼0.0081 K⁻¹ at 473 K. Temperature resolution (uncertainty; δT), the minimum temperature variation detected by the optical thermometer for a slight change in the FIR can be calculated using the following formula [55, 56],

$$\begin{eqnarray}&&\delta T=\displaystyle \frac{\partial FIR}{FIR\,}\displaystyle \frac{1}{\,{S}_{r}}=\displaystyle \frac{\partial \{\,\mathrm{ln}(FIR)\}}{{S}_{r}}\end{eqnarray} \tag{ 24 }$$

In the present case the temperature resolution of the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor at room temperature has been obtained as 0.4 K. Despite having good temperature sensing properties, the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor could not hold the UC emission shape beyond 473 K even at very low pump power density. Keeping the high UC emission intensity of Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphor in mind, the temperature sensing ability of the phosphor has been examined in the same spectroscopic region under similar laser excitation power. In contrast to the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor, the UC emission spectra in a broader temperature range from 300–573 K for the Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphor has made it possible. The ∆E/k value as shown in figure 3(a) between FIR vs temperature is found to be 1023.12 as the FIR varies from 0.47 to 2.34 with good repeatability as displayed in the inset. The repeatability (R) of the FIR has been calculated as [57],

$$\begin{eqnarray}&&R=1-\displaystyle \frac{{\rm{Max}}({{\rm{\Delta }}}_{m}-{{\rm{\Delta }}}_{i})}{{{\rm{\Delta }}}_{m}}\end{eqnarray} \tag{ 25 }$$

where ${{\rm{\Delta }}}_{m},$ ${{\rm{\Delta }}}_{i},$ represent the mean value of FIR and FIR value in 3 consecutive irradiation cycles, respectively. The calculated R values at 300 K is found to be ∼93% whereas at 573 K it is found to be ∼94%. Although the relative sensitivity has not changed much from the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor due to similar ∆E/k values, the maximum absolute sensitivity changes slightly owing to a relatively small pre-exponential factor (figure 3(b)). The temperature uncertainty for the Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphor has been calculated to be 0.5 K at ambient temperature. All the important sensing parameters for the prepared phosphors have been calculated and listed in table 2 with other reported phosphors for comparison.

Practically, the light output and colour rendering properties of the phosphor-converted light-emitting diodes (pc-LEDs) are greatly influenced by the thermal properties of the phosphor, thus the phosphor used in pc-LEDs should bear high thermal stability. To examine the thermal quenching of the prepared phosphors, the intensity variation as function of the increasing temperature has been monitored in the green region. As the temperature increases monotonically, a gradual dip in the total UC emission has been observed which follows the Boltzmann sigmoidal function [58],

$$\begin{eqnarray}&&y\left(x\right)={A}_{2}+\displaystyle \frac{{A}_{1}-{A}_{2}}{1+{e}^{\{(x-{x}_{0})/dx\}}}\end{eqnarray} \tag{ 26 }$$

Here y(x) is the normalized emission intensity value at a certain temperature (x), A₁ and A₂ represents the initial and final values of asymptotes respectively. x₀ (x₀ = TQ_1/2) is the center of the sigmoid that represents the temperature at which the intensity is reduced to 50% of its initial value. Since the Boltzmann fitting is normalized, A₁ and A₂ values are chosen as 1 and 0 respectively.

Figure 3(c) depicts the Boltzmann sigmoidal fitting curve for Er³⁺-Yb³⁺: Bi₄Ti₃O₁₂ and Er³⁺-Yb³⁺-Al³⁺: Bi₄Ti₃O₁₂ phosphor. Previous reports suggest that the operating temperature for the pc-LEDs could reach up to ∼423 K at higher pump photon excitation. Hence under such operating conditions, the phosphors relax most of their energy through heat causing thermal quenching, which can affect the performance of LEDs. Therefore, it is essential to develop phosphors possessing low thermal quenching so that the phosphor can emit efficiently even at ∼423 K. It is evident that the UC emission intensity for the Er³⁺-Yb³⁺: Bi₄Ti₃O₁₂ phosphor dies out quickly and retained only ∼15% at 423 K. However, with the co-doping of Al³⁺ ion, the phosphor persisted ∼73% of the initial UC emission intensity at 423 K, suggesting the excellent thermal stability of the developed phosphors like the previously reported works [59, 60]. Also, the TQ_1/2 values for the Er³⁺-Yb³⁺: Bi₄Ti₃O₁₂ and Er³⁺-Yb³⁺-Al³⁺: Bi₄Ti₃O₁₂ phosphor has been attained to be ∼374 K and ∼454 K respectively. Additionally, the information about the thermal stability can also be realized by solving the Arrhenius equation [61],

$$\begin{eqnarray}&&{I}_{T}=\displaystyle \frac{{I}_{0}}{\left(1+B\exp \left(\displaystyle \frac{-{E}_{a}}{kT}\right)\right)}\end{eqnarray} \tag{ 27 }$$

where, I₀ and I_T represents the intensities at initial and testing temperature, B is the quenching frequency factor, which is usually referred to the ratio between non-radiative and radiative rates and E_a is the activation energy for the developed phosphors. In the plot between ln(I₀ /I_T –1) and 1/kT, the slope value refers to the activation energy of the phosphor. From figure 3(d), the E_a value for the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ and Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphor have found to be 0.41 eV and ∼0.6 eV respectively. Furthermore, the probability of non-radiative transition per unit time (α) and the activation energy (${E}_{a}$) are related as [62],

$$\begin{eqnarray}&&{\rm{\alpha }}=s\exp \left(\displaystyle \frac{-{E}_{a}}{kT}\right)\end{eqnarray} \tag{ 28 }$$

where, s represents the frequency factor (s⁻¹) and all parameters have their usual meanings. From equation (28) it can be visualized that the lower the activation energy, the higher will be the probability of the nonradiative transitions. Thus, co-doping of Al³⁺ ion in the Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ phosphor provides greater thermal stability by reducing the nonradiative transitions. Again, the TQ_1/2 value can also be achieved using E_a as [63]

$$\begin{eqnarray}&&T{Q}_{1/2}=\displaystyle \frac{-{E}_{a}}{k\times \,\mathrm{ln}(1/B)}\end{eqnarray} \tag{ 29 }$$

All parameters have their usual meanings. The TQ_1/2 values obtained for Er³⁺–Yb³⁺: Bi₄Ti₃O₁₂ and Er³⁺–Yb³⁺–Al³⁺: Bi₄Ti₃O₁₂ phosphor are ∼372 and ∼447 K respectively taking E_a into account. The similar results obtained from both Boltzmann fitting and Arrhenius equation suggest that both approaches are useful for examining the thermal stability behaviour of the prepared phosphors.

Besides having very good thermal stability at low pump power density, the Er³⁺-Yb³⁺-Al³⁺: Bi₄Ti₃O₁₂ phosphors can convert a part of the absorbed NIR excitation to heat apart from generating UC emission at higher pump power. It can be noticed from SI figure 4(b) that the FIR increases linearly with the pump power (P) resulting in the following equation [53],

$$\begin{eqnarray}&&FIR=0.002P+0.31\end{eqnarray} \tag{ 30 }$$

Comparing the equation (30) to the equation (19), we obtained the temperature as,

$$\begin{eqnarray}&&T=\displaystyle \frac{-1023.12}{\mathrm{ln}(1.5\times {10}^{-4}P+0.02)}\end{eqnarray} \tag{ 31 }$$

The equation (31) indicates that corresponding to each pump photon there exists a specific temperature which is generated from the non-radiative relaxation from the upper energy levels. Earlier findings indicate that applications such as photothermal treatment needed temperature between 315 and 318 K to kill cancer cells [53, 64]. Thus, it can be said that by adjusting the laser pump power between 103 mW to 112 mW, the requirements can be fulfilled. However, until the successful implementation of the synthesized phosphor for the in-vivo use, the aforementioned can't be asserted.