Introduction

A new way of measuring temperature and developing temperature probes is important for applications in emerging environments including nanobiotechnology and integrated optics [1,2,3,4,5]. Currently existing temperature measurement technologies or standard thermometers are not able to provide spatial resolution of measurements better than 1 μm, being as such of no use in nanobiotechnology. Further, it is quite difficult to assess inter- or intra-cellular temperature by common thermometers in biological systems. In addition, the ability to remotely detect temperature within the objects volume (unlike from the surface with thermo-vision camera), lack of interference with electrical current and capability to measure temperature of rotating objects are quite important application, which cannot be easily addressed with conventional methods. Therefore, temperature measurements based on changes in the optical properties of materials can overcome these challenges as they offer non-contact measurements. Among all optical methods, temperature dependencies of the luminescent properties of materials have attracted the most attention due to the sensitivity of luminescence and the ease with which luminescence can be detected in comparison to other optical methods [6,7,8,9]. The changes of luminescence properties of nanomaterials with temperature such as changes of absolute and relative emission intensities, lifetime of excited states, emission rise times, peak positions, and emission bandwidths allow them to act as sensitive thermometers. Optical thermometry enables local temperature measurement of a system with sub-micron spatial resolution [10,11,12]. Temperature sensing through photoluminescence (PL) is based on the use of either nanoparticles or luminescent molecular probes as it offers a convenient optical measurement method [6, 13, 14]. Recently, the luminescence ratiometric nanothermometry performed via relative emission intensity measurements or luminescence intensity ratios gained a lot of attention because of its self-referencing capability, high precision, and high reliability [15,16,17]. The ratiometric nanothermometry method is unaffected by the variations in the measurement conditions and changes in the excitation source and can be potentially used in molecular nano thermometers or bioprobes [18,19,20,21,22].

The PL quenching as a function of temperature is strongly associated with the energy difference between transition states and offers high sensitivity in temperature sensing [23,24,25]. Previous studies on ratiometric thermometry were mainly focussed on conventional thermal quenching of semiconductor materials or other nanophosphors where the emission intensities decrease with increase in tempearture [16, 26, 27]. Such PL quenching mechanism in semiconductors is mainly attributed to the delocalization of charge carriers and consequent trapping by non-radiative centers or energy states (with increasing temperature) which would result in decrease in the number of the charge carriers transitioning from the final energy levels to the initial energy levels. Unlike the conventional thermal quenching in most semiconductors, the negative thermal quenching (NTQ) is the phenomenon where the number of charge carriers transitioning between final and initial energy states increase with increase in temperature. This NTQ behaviour in nanoscale semiconductors is mainly due to the characteristic surface states caused by lattice defects which are responsible for releasing trapped charge carriers in the recombination process at high temperatures. In our recent work, we have demonstrated that the semiconductor BFO nanowires show a rare phenomenon of NTQ of emission [28], where emission intensity of certain peaks as a function of temperature shows an increase in luminescence intensity instead of generally observed trend of decrease in intensity. As reported in [28], the emission associated with an energy state of lower activate energy will not affect their emission characteristics of carriers with increase in temperature. On the contrary, the carriers associated with higher activation energy will gain sufficient energy at higher temperatures, the temperature change affects this emission much more. This anomalous NTQ behavior of BFO nanowires was explained using a multi-level model developed by Shibata [29]. The temperature dependent PL intensity and a very long lifetime of ∼ 160 µs was attributed to the trapping and releasing process of the carriers from surface states. In continuation of our published work [28], here, we report on a new way of monitoring temperature variations via NTQ mechanism of BFO nanowires. The multiple ratiometric temperature sensing using a combination of conventional and unconventional (NTQ effect) mechanism offers a promising strategy towards ultrahigh relative sensitivity probing of temperature. Further, we have adopted analytical hierarchy process (AHP) method to validate and strengthen our experimental data.

Experimental procedure

The preparation, structural, optical, and electrical properties characterization of semiconductor BFO nanowires were published by us previously [28, 30,31,32,33]. The temperature sensing via luminescence thermometry was performed using a Fluorolog-3 Model FL3-221 spectrofluorometer system (Horiba–Jobin–Yvon) over the temperature range 300–438 K. For temperature dependent PL studies, the BFO nanowires were deposited both on Pt coated Si (Si/SiO2/Ti/Pt) and quartz substrates. The PL measurements were performed under continuous excitation from a 450 W xenon lamp at a wavelength of 320 nm (3.87 eV). The BFO nanowire samples were placed on a custom-made temperature-controlled platform, and emission spectra were collected via an optical fiber bundle. We have used time-resolved photoluminescence to determine an effective lifetime of minority charge carriers in BFO nanowires as a function of temperature. The temperature dependent time-resolved PL measurements were acquired utilizing a Xenon–Mercury pulsed lamp as excitation source. The temperature of the BFO nanowire sample was controlled by a temperature control system within the accuracy of ± 0.5 K (please refer to the manufacturer’s link to get the product details http://microptik.online/190%d1%81-to-400%d1%81/mhcs400/) employing PID (proportional-integral -derivative) feedback loop equipped with a T-type thermocouple for temperature monitoring. The schematic of the experimental setup used for optical (luminescence) thermometry is shown in Fig. 1. The topography imaging of BFO nanowires on quartz substrate was done using atomic force microscopy (AFM) (Bruker Dimension Icon, USA). The ex-situ ellipsometric spectra (Ψ, Δ) were collected using a J. A. Woollam M2000DI at 70° angle of incidence under 400 mTorr vacuum at 325 K, 375 K, 425 K, 375 K, 525 K, and 575 K.

Fig. 1
figure 1

Schematic of experimental setup used for optical thermometry

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Results and discussions

Temperature dependent optical response

The PL spectra obtained for BFO nanowires at 300 K and at 438 K are presented in Fig. 2a for comparison. The four emission bands with maxima at 2.55 eV (E1), 2.35 eV (E2), 2.27 eV (E3) and 2.23 eV (E4) correspond to the band edge/near band emission (NBE) and defect level/surface state emission (DLE) as reported in our recent work [28]. Inset of Fig. 2a shows room temperature excitation spectrum obtained for BFO nanowires. Figure 2b presents PL spectra of BFO nanowires for E2 defect emission measured in the temperature range of 300–438 K. The PL emission intensity for E2 emission increases with temperatures. Figure 2c shows the evolution of temperature-dependent PL intensity of BFO nanowires for all 4 emissions (E1, E2, E3, and E4) measured at temperatures in the range of 300–438 K. As we can see from Fig. 2c that the PL intensity decreases for E1, E3, and E4 emissions, however, PL intensity increases for E2 emission. Since BFO nanowires provide multiple emission peaks, a ratiometric approach to luminescence thermometry could be used. Since the intensity ratio between two emission bands is calculated from the same measurement, luminescence intensity ratio (LIR) method eliminates errors inherent to temperature readout from the intensity of a single emission band which are caused by fluctuations in excitation intensity or detection system and nonhomogeneous distribution of the probe on the measurement surface and therefore, act as self-referencing (i.e., measurements do not have to be referenced with any temperature standard) [10, 34, 35]. When BFO nanowires are excited with UV light, the photons cause electrons to move into allowed excited states. However, when these electrons return to their equilibrium states, the excess energy is released as photon emission via radiative transition. In our previous work, we have reported that the presence of excess surface states in the band gap of BFO nanowires play an intermediate role during the emission process by capturing the excited carriers and acting as radiation centers with enhanced emission [28]. The increase in temperature results in the release carriers from these surface states and when these carriers again recombine radiatively, they contribute to the green emission.

Fig. 2
figure 2

a PL spectra of BFO nanowires for E1, E2, E3, E4 emissions at 300 K and at 438 K. The spectrum shows increase in luminescence intensity with increase in temperature for 2.35 eV (E2) emission, whereas decrease in PL intensity with temperature is observed for other emissions (E1, E3 and E4) (ref. [21]). Inset of a shows room temperature excitation spectrum showing a peak at 3.8745 eV (b) PL spectra of BFO nanowires for E2 emission over the temperature range of 300–438 K. c Intensity of PL spectra plotted as a function of temperature for E1, E2, E3, and E4 emissions. Luminescence intensity increases with an increase in temperature for 2.35 eV (E2) emission, whereas a decrease in PL intensity with temperature is observed for other emissions (E1, E3 and E4)

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Figure 3a presents optical images of BFO nanowire samples under the sunlight (300 K) and under UV (λlamp = 254 nm) illumination (300 K, 330 K, and 360 K). From the optical images, it can be observed that the BFO nanowires emit green luminescence in the presence of UV light and the intensity of green luminescence decreases as the temperature of the sample is increased from 300 to 360 K. Figure 3b demonstrates an optical transparency of BFO nanowires (deposited on the quartz substrate) under sunlight and under UV illumination at 300 K. Our Institutions’ logo is clearly seen under the ambient sunlight as well as under UV light demonstrating BFO nanowires have good transparency. Moreover, under UV light excitation, beside good transparency, the green photoluminescence from nanowires is clearly visible. The enlarged portion of Fig. 3b shows an AFM image of BFO nanowires. As demonstrated by the AFM topography, high density of nanowires was achieved on the quartz substrate. Generally, the nanowires have a diameter distribution of 90–250 nm with an average length of tens of micrometers. Further, we have investigated the temperature dependent refractive index (n) and extinction coefficient (k) of BFO nanowires using ellipsometry. The ellipsometric spectra of BFO nanowires were evaluated using the Cauchy model for the quartz substrates. A three-medium optical model consisting of substrate/bulk film/ambient was employed. The optical response of the BFO nanowires is described by a Tauc-Lorentz oscillator in the band gap energy region [36, 37]. The Bruggeman Effective Medium Approximation (EMA) was employed to count for the voids between the BFO nanowires. Eventually, substrate back side correction was included. Parameters of Tauc-Lorentz oscillators were fitted with least squares regression analysis leading to low mean square error (< 10). Figure 3c reveals the Psi and Delta with an optical model for BFO nanowires. Parameters of Tauc-Lorentz oscillators were fitted with least squares regression analysis leading to low mean square error (< 10). Figure 3d shows the extracted refractive index (n) and extinction coefficient (k) for BFO nanowires, accordingly. The sub-bandgap extinction coefficient (k) for BFO nanowires can be due to the contribution from surface states. Extracted refractive index (n) values agree with ones found in the literature [38]. The refractive index and extinction coefficient data as a function of temperature reveals very useful conclusions. In our study, both the refractive index and extinction coefficient are insensitive to temperature which implies that the band gap not changing with temperature in this range. Both the extracted refractive index and extinction coefficient seem to be insensitive to temperature (Fig. 3e). Usually, a drastic change in refractive index and extinction coefficient is only expected if we have a phase transition. The temperature independent refractive index and extinction coefficient data suggests and help us to conclude that there is no phase transition happening at higher temperature. Furthermore, band gap also qualitatively does not show a drastic change with temperature in this range.

Fig. 3
figure 3

a Optical images of BFO nanowire samples under the sunlight (300 K) and under UV (λlamp = 254 nm) illumination (300 K, 330 K, and 360 K). b Optical transparency of BFO nanowires under sunlight and under UV illumination (λlamp = 254 nm) at 300 K. Enlarged image shows an AFM image of BFO nanowires. c The raw Psi and Delta measured by ellipsometry and fitted optical model. The real and imaginary component of refractive index with respect to (d) incident photon energy (325 K, 375 K, 425 K, 375 K, 525 K, and 575 K) and (e) temperature (at 2.5 eV)

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Temperature dependent luminescence decay lifetime

The calculated lifetime values of BFO nanowires as a function of temperature for E2 emission is presented in Fig. 4. The error bars in Fig. 4 represent the mean with 4 experimental trials of a data set. As observed from temperature dependant luminescence lifetime studies, the decay time is ~ 160 µs. Such high decay time is expected because the transitions from surface states are forbidden, which results in slow emission rate. This fluorescence decay time of carries does not really signify the sensor response time, rather it signifies the carrier lifetime. In our previous studies, we have calculated the rise time and fall time for carriers in BFO nanowires and found the rise time and decay time constants are about 70 μs and 190 µs, respectively [32]. The carrier lifetimes obtained for BFO nanowires are very high as compared to that of the reported values in bulk or thin films [39, 40]. Usually for a non-passivated surface, the PL decay time decreases more rapidly with increasing temperature. The temperature dependence of carrier lifetimes also depends on the surface recombination velocities [41]. In our case, the carrier lifetime shows only a minor or almost no temperature dependence. This temperature independence is due to less recombination or higher surface recombination velocities. The obtained temperature dependent luminescence lifetime value of ~ 160 μs is close to other luminescence thermometry-based temperature sensors [16, 42, 43]. Further, it can be noted from Fig. 4 that the lifetime is independent of the temperature change, resembling the static quenching behavior and can be explained in terms of multiple trapping and de-trapping process as explained in our earlier work [28].

Fig. 4
figure 4

Lifetime values of BFO nanowires obtained for E2 emission as a function of temperature. The error bars represent the mean with 4 experimental trials of a data set

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Thermal sensitivity analysis

Figure 5a shows a plot of the temperature dependence of the LIR obtained as ratios of E2 emission with other three (E1, E3 and E4). In principle, for the ratiometric sensing, no knowledge regarding the physics underlying the temperature quenching is needed. It is sufficient to approximate the experimental data for further use as a calibration curve [44]. For the case of BFO nanowires, LIR data are fitted with the linear function as shown in Fig. 5b, and fitting parameters are given in the Table 1. The most important Figures of merits for luminescence thermometry are the absolute sensor sensitivity, \(S_{a}\) defined as the rate at which LIR changes with the temperature, and the relative sensor sensitivity, \(S_{r}\) defined as the normalized absolute sensor sensitivity with respect to the measured value: [10]

$$S_{a} = \frac{{\left| {\partial LIR} \right|}}{\partial T}.$$
(1)
$$S_{r} = 100\% \times \left| {\frac{1}{LIR}\frac{\partial LIR}{{\partial T}}} \right|.$$
(2)
Fig. 5
figure 5

a Luminescence intensity ratio (LIR) values of BFO nanowires as a function of temperature (circles). LIR values were obtained as the ratio between peak intensities for E1, E3, and E4 with respect to E2. b Relative and absolute sensor sensitivity obtained from LIR measurements as a function of temperature (300–438 K)

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Table 1 Table summarizing figure of merits of the luminescence thermometry using negative quenching effect of E2 (2.35 eV) emission of BFO nanowires
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The absolute and relative sensitivities of BFO nanowires calculated from Eqs. (1) and (2) are plotted in Fig. 5b and are listed in Table 1. Relative sensitivities achieved with BFO nanowires are similar (slightly lower) but with larger measurement ranges than those reported on ratiometric luminescence thermometry with other semiconductors. However, the observed trend of higher relative sensitivity at lower temperature is in consistent with other reports on ratiometric thermal sensors [9, 16, 45]. Increase in the LIR with increase in temperature in agreement with the argument of transition to the trapped centers before they recombine back radiatively. However, from the relative sensitivity expression, increase in LIR at higher temperatures results decreased relative sensitivity at higher temperatures. Any two energy levels with an energy gap of smaller than 2000 cm1 are usually denoted by the thermally coupled energy levels and the inter carrier population between which is dominated by the Boltzmann distribution [35, 45,46,47]. The gradual decrease in Sr with the increase of temperature, suggests that the thermally coupled energy levels show dominance at relatively low temperatures.

Relative sensitivities of 0.9 and 1.3%K−1 have been found for differently sized nanoparticles of Zn0.99Mn0.01Se/ZnCdSe in the temperature range of 293–373 K [48], and 0.9%K−1 with CdSe/ZnSe and CdTe/ZnS over the narrow temperature range of 293–320 K [49]. It should be note that Zn0.99Mn0.01Se/ZnCdSe luminescence thermometry has been realized for emission from both semiconductors and Mn2+ [10].

Validation of thermal sensitivity using analytical hierarchy process (AHP)

The AHP method deals with linear models (the hierarchy) where the calculations of weights for each LIR and temperature values are based on linear regression to estimate the overall thermal sensitivity of LIR ratio. Therefore, in this paper, we have adopted AHP model to validate and strengthen our experimental data. Based on the data obtained from E2/E4 emission, we have developed intercept equations in \(y=a+bx\) form, where \(y\) represents dependent variable (relative emission intensity) and \(x\) is an independent variable (temperature) through simple linear regression and log value regression. Equation (3) represents linear regression with log value and Eq. (4) represents linear regression with respective evaluated R2 values. The curve fitting plot and as well equations (with and without log value) with R2 values are represented in Fig. 6.

Fig. 6
figure 6

Prediction of relative sensitivity (Sr) for E2/E4 as a function of temperature (300–438 K) using linear regression

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$$\text{y}=-1.313{\text{ln}}\left({{x}}\right)+8.22{; }{\text{R}}^{2}=0.9961.$$
(3)
$$\text{y}=-0.004x+1.94; {\text{R}}^{2}=0.9933.$$
(4)

One of the evaluated parameters will help the expert instantly with linear regression is R2. The statistical significance of R2 is a degree of how well our considered application is appropriately fitting the actual data close to linearity relationship. The linearity relationship in this case is between temperature and E2/E4 emission intensity. The value of R2 should always lies between the spectrum of 0–1. If the value is close to 1, then the observed variance of linearity is high and whereas if it is close to 0 then the linear relationship is considered to be weak or low. However, we can predict the target signal in either of the cases with a high or low linearity relationships. In our case the R2 (log-linear) is calculated to be 0.9961 while in simple linear as 0.9933 (without log). Since, the R2 value is close to 1, we conclude the relationship of sensitivity with temperature is strongly linear. Since, the regression results are found linear, we have further conducted validation of thermal sensitivity of BFO nanowires using LIR ratios at different temperatures via the AHP model [50,51,52,53,54]. The validation model analysis of thermal sensitivity has been accomplished using AHP quantitatively. The AHP, a prominent methodology founded on multi-criteria decision-making model established by Saaty [51] aims at quantifying influencing factors. In our paper, we have quantified emission intensities at different temperatures, in other words at varying levels of abstraction of temperature sensing using semiconductor BFO nanowires and further observed its sensitive analysis. The quantification is performed through the data obtain from LIR ratios (E2/E1, E2/E3, E2/E4) through a series of experiments. Thus, we translate the acquired data patterns into the scale 1 to 9 (based on the emission intensity) of the AHP model suggested by Saaty [50]. To recall, here, we present a brief classification of steps involved in AHP quantitative evaluation through series of steps: (a) defining the objective of the considered application problem, (b) modeling influencing factors into hierarchy at various appropriate levels, (c) forming pair-wise comparison matrices among the factors at each level of the hierarchy, (d) evaluation of the matrices through weigh vectors via principal Eigen vector [51], (e) pooling of all assessed weigh vectors according to the hierarchy model, and lastly (f) final quantification evaluation and sensitivity analysis [55].

Specifically, in this paper, we have investigated the merits of AHP for quantitative validation of the thermal sensitivity of BFO nanowires and performed the following assessments:

  • Quantified and validated thermal sensitivity using LIR ratios (E2/E1, E2/E3, E2/E4) at 300 K.

  • Similarly, further quantified LIR ratios at 346 K and 440 K.

  • Finally, node sensitivities at each of the LIR ratios w.r.t overall temperature range of 300–440 K.

Thus, we applied steps (a–f) AHP algorithm mentioned above to quantify thermal sensitivity of BFO nanowires using LIR ratios. The first step (a) been defining the objective—the validation of thermal sensitivity of LIR ratios quantitatively. In step (b), based on the experimental results for thermal sensitivity of BFO nanowires using LIR ratios at different temperature, we have modelled in a 2 layered hierarchy, shown Fig. 7. The first level consists of considered three temperatures T1 (300 K), T2 (346 K), and T3 (440 K). The second layer and the last level includes LIR ratio (E2/E1, E2/E3, E2/E4).

Fig. 7
figure 7

AHP model for validation of thermal sensitivity

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In the steps (c), formulated pair-wise comparison matrices with one pair matrix at the first level and three pair-wise matrices at the second level. Next in the step (d), assessment of four matrices through weigh vectors evaluations has been performed. The formulation and evaluations of matrices from steps (c) and (d) are shown in the Table 2. All the weight vectors calculated from four matrices in step (d) are pooled and organized via. in the form aggregation matrix shown in the Table 3, this completes the step (e). Finally, in the step (f), we perform concluding evaluation from the aggregation matrix (from step d) through a customized equation to evaluate the overall node sensitivities (at each of the LIR ratios) at the overall temperature range of 300–440 K of the considered application shown in Table 4.

Table 2 Formulation of pair-wise matrices and assessments
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Table 3 Aggregation matrix
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Table 4 Final evaluation
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Based on AHP modelling and assessment, we have validated the following pieces of quantitative analysis: (i) Table 2a validated thermal sensitivity using LIR ratios of E2/E1, E2/E3, E2/E4 at 300 K (room temperature); (ii) Similarly, further quantified LIR ratio at 346 K and 440 K, shown in the Table 2b, c; and (iii) Fig. 8 demonstrates sensitivity analysis through clusters LIR ratios at 300 K, 346 K, and 440 K and finally, Fig. 9 depicts the node sensitivities at p = 0.5 (at each of the LIR ratios) at the overall temperature range of 300–440 K.

Fig. 8
figure 8

Sensitivity analysis through clusters LIR ratios at 300 K, 346 K, and 440 K

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Fig. 9
figure 9

Node sensitivities of LIR ratios (p = 0.5) at the overall temperature range (300–440 K)

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The ultimate aim of validation of the AHP results is to compare the experimental trend of thermal sensitivity of semiconductor BFO nanowires using LIR ratios. For illustrative purpose, we have compared the results of AHP for LIR ratios of E2/E1, E2/E3, E2/E4) at 300 K with the results of Table 1 and Fig. 5a. We found a close match between AHP model with the simulation result (Table 1) and experimental tendency pattern results in Fig. 5a. The comparison of results obtained from these methods are shown in Table 5. Therefore, our analytical validation results endorse the experimental analysis results of thermal sensitivity of semiconductor BFO nanowires.

Table 5 Thermal sensitivity validations
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Conclusion

Multiple peaks in the emission spectrum of BFO nanowires enabled the use of ratio-metric luminescence temperature sensing in the range of 300–438 K with the relative sensitivity as high as 0.75% K−1. Additionally, using a linear regression and AHP, the quantitative validation has been performed for thermal sensitivity of BFO nanowires using LIR ratios at three different temperatures (300 K, 346 K, and 440 K) and as well at overall temperature range of 300–440 K. In order to demonstrate quantitative validation of the AHP model, we have compared LIR ratio (E2/E1) at room temperature (300 K) with the experimental results and found a close match. In conclusion, our studies indicate that BFO nanowires can serve as potential candidate for multiple ratiometric nanothermometry based temperature sensors.