Three-energy-level-cascaded strategy for a more sensitive luminescence ratiometric thermometry

Highlights

• A three-energy-level-cascaded strategy was proposed.

• This strategy reached the maximum sensitivity of 2414/kT².

• The temperature resolution was studied versus the relative sensitivity.

Abstract

Luminescence ratiometric thermometry has gained increasing attention in recent years because of its several merits, such as non-invasive operating mode, fast response time, excellent spatial resolution, and so forth. It can be realized by using the thermally coupled energy levels (TCELs) of rare earth ions. The maximum thermal sensitivity for the TCELs-based luminescence ratiometric thermometry has been found to be ∼2000/kT². Here we show that using a three-energy-level-cascaded strategy can surpass this maximum value. In scheelite host material, the ⁴G_11/2-⁶H_15/2 transition of Dy³⁺ ion was observed successfully upon UV excitation. Moreover, the Dy³⁺ ion’s ⁴G_11/2/⁴I_15/2/⁴F_9/2 excited states were confirmed to be thermally linked with each other by studying on the photoluminescence of the as-prepared Dy³⁺-embedded phosphors at different temperatures. By utilizing the ⁴G_11/2/⁴F_9/2 states, rather than the commonly investigated ⁴I_15/2/⁴F_9/2 ones in the previous literatures, the relative sensitivity was found to as high as 2414/kT² over the experimental temperature range. It surpasses the theoretical maximum value 2000/kT². In the end, we study the relationship between the relative sensitivity and temperature resolution, and find that a higher relative sensitivity cannot always ensure a better temperature resolution. In order to achieve a better temperature resolution in practice, both the relative sensitivity and the relative uncertainty of the luminescence intensity ratio that is used for indicating temperature should be considered simultaneously.

Introduction

Monitoring temperature, although fundamental, is very important in a number of fields [1,2]. It is because temperature can reflect the real-time state of the object of interest and thus provide us much useful information. Therefore, it is necessary to exploit new kinds of temperature measurement methods to meet the needs required by the fast advancement of science and technology [[3], [4], [5]]. So far, dozens of methods have been proposed to measure temperature [6]. Among these possible ways, the luminescence ratiometric thermometry, based on the rare earth ions, becomes a hot research point nowadays as it features short response time, high resolution, non-contact working model and strong immunity to disturbance [[7], [8], [9]]. In general, this technology depends on a pair of TCELs, as presented in Fig. 1(a) [10,11]. When a rare earth ion is excited to its excited state, it relaxes quickly to the lower emitting states. As concluded by Wade et al. and confirmed by many other groups, if two excited states of the trivalent lanthanide ions are thermally linked, their energy gap, ΔE, is always no more than 2000 cm⁻¹ at room temperature [[10], [11], [12], [13], [14], [15]]. It should be emphasized here that the value 2000 cm⁻¹ is not a strict threshold for achieving thermal coupling as it is also influenced by the ambient temperature. Theoretically, there is no limit for the energy gap between one pair of TCELs. However, in practice, the energy gap between one pair of TCELs cannot be too large due to several factors, for instance, the presence of other physical mechanisms like non-radiative relaxation in addition to the Boltzmann distribution for rare earth ions. If the energy gap is too large, there will be de-coupling effect, and the emission emanating from the upper state is not easy to detect. Therefore, most of the previously reported TCELs of the trivalent lanthanide ions are, to the best of our knowledge, smaller than 2000 cm⁻¹. In this case, the luminescence intensity ratio (LIR) between two lines originating from TCELs (1 and 2 in Fig. 1(a)) follows the Boltzmann-type distribution: [[12], [13], [14], [15], [16]]

$$\text{LIR}=A\exp (-\frac{\Delta E}{kT})$$

where A is a pre-exponential constant, k is the Boltzmann constant, and T is absolute temperature. In general, the relative sensitivity, S_r, is used to compare the performance of different temperature sensors. It is defined as [17,18]

$$S_r=\left|\frac{d\text{LIR}}{dT}\frac{1}{\text{LIR}}\right|$$

Combining Eqs. (1) and (2), we have

$$S_r=\frac{\Delta E}{k{T}^2}$$

Eq. (3) reveals clearly that at a certain temperature, the relative sensitivity, S_r, is only related to the energy gap ΔE. To some degree, the larger the ΔE, the higher the S_r. The threshold for a pair of TCELs is confirmed empirically to be 2000 cm⁻¹ for the trivalent lanthanide ions, which means that the maximum relative sensitivity is 2000/kT² [10,11]. This is concluded based on the existing literatures. In addition, it has been found that when a pair of TCELs with a large energy gap (∼2000 cm⁻¹) is used for ratiometric thermal detection, there is usually an offset B in Eq. (1). And in general, the offset B is positive. It has been shown that the presence of B can be attributed to several factors, including the stray light from other excited states or the excitation sources, the overlap between the emission spectra used for thermometry, and other physical mechanisms in addition to the pure Boltzmann distribution [8,10,19]. In this case, the relative sensitivity cannot be expressed by Eq. (3). In our previous work, we have demonstrated that the relative sensitivity can be described as S_r=(LIR-B)/LIR*ΔE/kT² [19]. This corrected sensitivity, due to the presence of the offset B, is smaller than the expected sensitivity ΔE/kT². And at relatively low temperatures, this difference is more obvious.

As is known, in the field of luminescence ratiometric thermometry, there are many parameters to evaluate this optical technology, including absolute sensitivity, relative sensitivity, temperature resolution, spatial resolution, response time, and so forth. Achieving a higher relative sensitivity is always one of the most important things. Therefore, breaking the upper sensitivity limitation 2000/kT² for the trivalent lanthanide ions becomes a challenge. Indeed, some methods are proposed and have been demonstrated to be effective. However, the principles behind these methods are no longer the Boltzmann-type distribution. Can we break the relative sensitivity 2000/kT² for the trivalent lanthanide ions in the scope of the Boltzmann-type distribution? In this paper, we propose a three-energy-level-cascaded strategy to achieve this goal. It is schematically depicted in Fig. 1(b). Above the state 2, there is a state 3. The energy gap between these two states is smaller than the threshold 2000 cm⁻¹ to meet the Boltzmann distribution. The LIR between the thermally coupled states 3 and 2 is dominated by the Boltzmann-type distribution. Therefore, it is not difficult to know that the LIR between the states 3 and 1 should also follow Eq. (1). At this moment, using the thermally coupled states 1 and 3 will easily break the maximum relative sensitivity of 2000/kT² for the trivalent lanthanide ions only if the sum of the energy gap between the states 1 and 2 and that between the states 2 and 3 is larger than 2000 cm⁻¹. In addition to the proposed three-energy-level-cascaded strategy, we also study the relationship between the relative sensitivity and temperature resolution, and find that a higher relative sensitivity cannot always ensure a better temperature resolution. In order to achieve a better temperature resolution in practice, both the relative sensitivity and the relative uncertainty of the LIR that is used for indicating temperature should be considered simultaneously.