1 Introduction

Temperature is one of the most important parameters for design and optimization of combustion systems such as internal combustion and gas turbine engines. To improve their thermodynamic efficiency, engines need to be operated at high temperatures, which affects the thermal load on the components, shortening their lifetime and leading to their failure [1]. Therefore, accurate information about surface temperatures is essential for the design of appropriate cooling schemes, the improvement of predictive design codes and the development of new materials capable of operating in more demanding scenarios (i.e., higher temperatures and longer life cycles).

Spatially and temporally resolved surface temperature measurements in combustion systems are particularly challenging. Thermographic phosphors (TP) have emerged as an alternative to overcome most of the drawbacks of the existing techniques such as thermocouples, thermochromic liquid crystals, temperature-sensitive paints, heat-sensitive paints and non-invasive pyrometry [2]. TP are ceramic materials doped with rare earths or transition metals that exhibit temperature-dependent luminescence characteristics. They offer a semi-intrusive, accurate, temporally and spatially highly resolving technique for remote measurement of surface temperatures over a broad temperature range from cryogenic temperatures up to 2,073 K [3]. This technique is robust against interferences from scattered light, chemiluminescence or soot radiation. With an appropriate handling, its accuracy can be better than 1 % [4].

TP have been used to measure temperatures in a variety of combustion applications such as impinging jet flames [5], gas turbine combustors [6], thermal decomposition of solid materials [7], internal combustion (IC) engines [8, 9], fuel droplets and sprays [10, 11]. However, several factors have to be considered to guarantee the accuracy and robustness of the technique: (1) The intensity of the emitted luminescence signal should be high enough to be distinguished from the background noise and any other kind of radiation; (2) The thickness of the phosphor coating applied on the surface should be minimized to reduce the error induced by the thermal gradient between the surface of the substrate and the top layer of the phosphor coating [12]; (3) The adhesion of the coating to the surface should provide good durability characteristics; and (4) The measurement and calibration strategies have to be handled carefully to reduce systematic errors [4]. Among these factors, the first three are directly related to the coating process of the phosphor.

For most of the common coating methods, TP powders are synthesized separately, then mixed with binders such as polymer binders, silicon resins or other commercially available agents, and finally, the mixture is applied to the substrate using air-brushing or air-spraying [4]. The method usually produces homogeneous coatings with thicknesses ranging from 10 to 60 \(\upmu\)m and with reproducible temporal and spectral luminescence properties [4]. Additionally, this method has the advantages of being very simple to use, and nearly all available phosphors may be bonded by this technique. However, the resistance of these binders against high temperatures, chemically aggressive environments and mechanical stress limits the application of TP for surface temperature measurements in harsh environments such as IC engines and gas turbine combustors. Previous studies using TP in gas turbines report fast degradation of chemically bonded coatings during fired operation of the engine [6, 13–16]. Nevertheless, temperature measurements under controlled experimental conditions have been successfully conducted in fixed and moving parts of gas turbines [17, 18] and internal combustion engines [9, 19].

Alternative coating techniques for TP include thin-film deposition technologies for the production of uniform, homogeneous, well-adhered, high-purity coatings [20]. The sol–gel method [21], Chemical Vapor Deposition (CVD) [22] and Physical Vapor Deposition (PVD) [23] have been evaluated for producing thin films of TP. Among the PVD techniques, sputter deposition could be a choice to overcome the challenges related to the preparation of the coating. Sputter deposition uses the ejection of surface atoms form a source material (target) by ion bombarding (plasma) with the subsequent condensation of those atoms on another surface (substrate) to form a thin film. This is a very versatile process that allows depositing a large variety of materials from the nano to the micro scale [24]. Although sputter deposition has been widely used for the preparation of phosphor thin films in electroluminescence applications [25–33], in the referred literature only sputtered films of \(\hbox {Y}_2\hbox {O}_3{:}\hbox {Eu}^{3+}\) [13, 34] and \(\hbox {YVO}_4{:}\hbox {Eu}^{3+}\) [15] have been evaluated for thermographic applications.

We have evaluated and compared the temperature-dependent luminescence properties of thin films of chromium-doped gadolinium gallium oxide, \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}{:}\hbox {Cr}^{3+}\) (also known as \(\hbox {GGG:Cr}^{3+}\)), deposited by radio frequency (RF) magnetron sputtering. The thin films were deposited on two common substrates used in combustion diagnostics, namely, fused silica and stainless steel. \(\hbox {GGG:Cr}^{3+}\) was selected because it is a TP ideal for temperature measurements in internal combustion engines, due to its appropriate short luminescence lifetimes and insensitivity of its luminescence to the surrounding gas phase in a relatively wide range of temperatures (from 300 to 1,000 K) [35]. To the best of the authors’ knowledge, there is no previous report about sputter deposition of this phosphor. Earlier studies of laser deposition of \(\hbox {GGG:Cr}^{4+}\) [36] and GGG:Nd [37] for laser applications and Electron Beam-PVD of GGG:Ag [38, 39] for electroluminescence applications are state of the art. Additionally, two-dimensional (2D) measurements of the luminescence lifetime, which has not been yet addressed in the literature for thin films of TP, were conducted to evaluate the applicability of thin films for spatially resolved surface thermometry.

2 Materials and methods

2.1 Preparation of the sputter target

A \(\hbox {GGG:Cr}^{3+}\) target, 50 mm in diameter and a Cr doping concentration of 0.5 mol% (with respect to the total content of metals), was prepared by high-temperature solid-state reactions. As represented in Fig. 1, an ammonium hydroxide process was used to guarantee a homogeneous distribution of the dopant in the target. High-purity (99.99 %) gallium oxide (\(\hbox {Ga}_2\hbox {O}_3\)) and gadolinium oxide (\(\hbox {Gd}_2\hbox {O}_3\)) in their stoichiometric proportions were dissolved in hot, concentrated nitric acid \((\hbox {HNO}_3)\) under magnetic stirring. The stoichiometric amount of \(\hbox {Cr}(\hbox {NO}_3)_3\cdot 9\hbox {H}_2\hbox {O}\) was added to the solution. After stirring, the Gd and Cr metal nitrates were in aqueous solution while the \(\hbox {Ga}_2\hbox {O}_3\) remained as solid particles. When \(\hbox {NH}_4\hbox {OH}\) was added to the solution, following reactions took place:

$$\hbox {Gd}^{3+} + 3\,\hbox {OH}^{-} \rightarrow \hbox {Gd}(\hbox {OH})_3 \downarrow$$
(1)
$$\hbox {Cr}^{3+} + 3\,\hbox {OH}^{-} \rightarrow \hbox {Cr}(\hbox {OH})_3 \downarrow$$
(2)

The \(\hbox {Gd(OH)}_3\) and \(\hbox {Cr(OH)}_3\) form an ultrafine precipitate of covering the \(\hbox {Ga}_2\hbox {O}_3\) particles. In this way, the contact area between the metal oxides is increased during the solid-state reactions, guaranteeing a homogeneous distribution of reactants and thus of products. The precipitate was then washed with water and dried in air to remove the \(\hbox {NH}_4\hbox {NO}_3\) by-product and the excess of \(\hbox {NH}_4\hbox {OH}\). After drying, the precipitate was ground, compressed and sintered in air ramped up to 1,373 K for 6 h. At the beginning of the sintering process (low temperatures), the following reactions took place:

$$\begin{aligned}&2\,\hbox {Gd}(\hbox {OH})_3 \rightarrow \hbox {Gd}_2\hbox {O}_3 + 3\,\hbox {H}_2\hbox {O} \uparrow \end{aligned}$$
(3)
$$\begin{aligned}&2\,\hbox {Cr}(\hbox {OH})_3 \rightarrow \hbox {Cr}_2\hbox {O}_3 + 3\,\hbox {H}_2\hbox {O} \uparrow \end{aligned}$$
(4)

At higher temperatures, the Gd and Cr oxides reacted with the \(\hbox {Ga}_2\hbox {O}_3\) core to obtain a crystalline sample of \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}{:}\hbox {Cr}^{3+}\):

$$\begin{aligned} 3\,\hbox {Gd}_2\hbox {O}_3 + (5-x)\,\hbox {Ga}_2\hbox {O}_3 + x\,\hbox {Cr}_2\hbox {O}_3 \rightarrow 2\,\hbox {Gd}_3\hbox {Ga}_{5-x}\hbox {Cr}_x\hbox {O}_{12} \end{aligned}$$
(5)
Fig. 1
figure 1

Flowchart of the ammonium hydroxide process used to prepare the \(\hbox {GGG:Cr}^{3+}\) target

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Fig. 2
figure 2

Experimental setup for the measurement of the luminescence lifetime

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The composition and crystal structure of the target were studied at room temperature by X-ray diffraction (XRD) using a diffractometer in Debye–Scherrer geometry (STOE Stadi P). The diffractometer was equipped with a copper anode and curved germanium (111) monochromator with \(\hbox {Cu}{\text{-}}\hbox{K}_{\alpha 1}\) radiation of wavelength 1.54058 \(\mathring{A}\). The obtained X-ray pattern was analysed and compared with existing crystallographic data.

2.2 Sputter deposition of the thin GGG:Cr\(^{3+}\) films

Thin \(\hbox {GGG:Cr}^{3+}\) films were deposited by RF magnetron sputtering on stainless steel (AISI 304, with 18–20 % Cr content) and fused silica substrates using the parameters summarized in Table 1. High-purity argon was used as sputtering gas. Oxygen (\(\hbox {O}_2/(\hbox {Ar + O}_2\)) ratio of 5 mol%) was added to the sputtering gas with two purposes: (1) avoiding any change of the target oxidation state and (2) restoring the stoichiometry of deposited films which usually have a deficiency of oxygen after sputter deposition when using metal oxide targets [40]. The substrates were located at a distance of about 10 cm above the target in a rotating stage. They were heated to 723 K during the deposition process to facilitate the formation of the films. Prior to each deposition, the target was cleaned by the plasma discharge for 15 min with the shutters closed. Deposition was conducted for several hours to achieve film thicknesses in the range from 1 to 2 \(\upmu\)m. The film thickness was measured with a profilometer (Bruker Dektak XT, vertical resolution 1 \(\mathring{A}\) max. at 6.55 m range) using the film deposited on fused silica.

Table 1 Sputtering parameters for the deposition of the \(\hbox {GGG:Cr}^{3+}\) films
Full size table

X-ray photoelectron spectroscopy (XPS) was used to investigate the chemical composition of the deposited films. The employed XPS system consisted of an \(\hbox {Al}{\text{-}}\hbox{K}_\alpha\) source (operating at 15 kV and 400 W), a monochromator (Specs FOCUS 500), a hemispherical energy analyzer (Specs PHOIBOS 150) with a lens aperture of 1.5 kV and a slit of \(7\,\hbox {mm} \times 20\,\hbox {mm}\), and an electron multiplier detector (Specs MCD-9). The measurements were performed at \(1 \times 10^{-10}\) mbar with an excitation energy of 1,486.61 eV and a pass energy of 20 eV. Survey scans were measured up to binding energies of 1,300 eV with a sampling interval of 0.5 eV.

After deposition, the films were annealed at 1,173 K for 12 h, in \(\hbox {N}_2\) at atmospheric pressure in an electric quartz tube furnace (Carbolite SPLF 77720, \(T_{\mathrm{{max}}} = \hbox {1,673}\) K), to restore their proper crystallinity. The crystallinity of the thin films was studied using XRD in a thin-film configuration before (as deposited) and after annealing. The angle of incidence of the X-ray was \(2.5^{\circ }\) to maximize the XRD signal from the thin film while suppressing the XRD signal from the substrate.

2.3 Evaluation of the luminescence properties of the thin films

To evaluate the luminescence functionality of the \(\hbox {GGG:Cr}^{3+}\) thin films, measurements of the luminescence lifetime at different temperatures were carried out using the setup presented in Fig. 2. The fourth harmonic (266 nm) of a non-focused, pulsed, Q-switched Nd:YAG laser (Quanta Ray, INDI, repetition rate: 10 Hz, pulse width: 5–8 ns) was used to excite luminescence. The pulse energy density was adjusted to \(5\,\hbox {mJ/cm}^{2}\) (measured after the second aperture \(d = 5\) mm) by combining a half-wave plate and a Glan polarizer. For spatial filtering and for minimizing the influence of blackbody radiation and other interfering light, the emitted luminescence light was imaged onto a pinhole (\(d = 100\,\upmu \hbox {m}\)) by a 85-mm Nikkor camera lens. In order to enable homogeneous illumination of the photomultiplier tube (PMT), the signal was collimated by a plano-convex lens (\(f = 30\,\hbox {mm}\)) behind the pinhole. The PMT current was read out by an oscilloscope (Tektronix 5032B, 350 MHz) at an input resistance of 512 Ω and a cable capacity of \(C = 300\,\hbox {pF}\), resulting in a threshold lifetime of 153 ns.

Fig. 3
figure 3

XRD pattern of the \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}{:}\hbox {Cr}^{3+}\) target along with the standard powder diffraction file ICSD 9237 [45]

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Measurements of the temperature-dependent luminescence lifetimes of the \(\hbox {GGG:Cr}^{3+}\) thin films were performed locating the samples within an optically accessible tube furnace (Carbolite, CTF 12/100/900, inner tube diameter: 105 mm, tube length: 900 mm, \(T_{\rm max} = \text{1,473}\) K). The furnace was equipped with a type N thermocouple (TMH GmbH, specified accuracy of 0.4 %), which was directly mounted to the phosphor sample. The measurements were carried out from 1,000 to 310 K, in steps of 10 K while cooling down. At each referred temperature, 100 single shots were recorded by the detection system.

Additional measurements of the luminescence lifetimes were carried out to evaluate the 2D luminescence characteristics of the deposited films. The experimental setup was modified to convert the Gaussian beam profile into a top hat by a beam homogenizer (Holo Or, diffusing angle: \(0.68^{\circ }\)) in order to ensure spatially homogeneous excitation. In this case, the luminescence was monitored by a high-speed CMOS camera (LaVision High Speed Star 6, maximum frame rate: 675 kHz, dynamic range: 12 bit), equipped with a Nikkor 50 mm photo lens. The experiments were conducted at room temperature recording images of 100 single shots with an excitation energy density of \(51\,\hbox {mJ/cm}^2\).

For the evaluation of the temperature-dependent luminescence characteristics, the measured decay signals of the thin films were approximated by a mono-exponential decay and converted to scalar lifetimes, \(\tau\), using the iterative fitting algorithm of Ref. [41], combined with a linear regression of the sum [42, 43]. In the case of the spatially resolved 2D luminescence evaluation, images acquired by the camera have been background-subtracted and subsequently corrected for nonlinearities of the CMOS chip [44] prior to a pixel-wise determination of the luminescence lifetime.

3 Results and discussion

3.1 \(\hbox {GGG:Cr}^{3+}\) target

A \(\hbox {GGG:Cr}^{3+}\) target with a Cr doping concentration of 0.5 mol% (with respect to the total content of metals) was prepared. Figure 3 shows the XRD pattern of the sintered target. The diffraction pattern is consistent with the cubic garnet single phase \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}\) ICSD 9237 [45]. The main reflections (4 0 0), (4 2 0), (4 2 2), (4 4 4), (6 4 0) and (6 4 2) are sharp and well developed, and all the reflections with lower intensities can be easily identified. However, traces of \(\hbox {Gd}_3\hbox {GaO}_6\) as second phase were detected around \(2\theta = 32^{\circ }\). The presence of this second phase is due to the limitation of the sintering temperature to 1,373 K. It is expected that this impurity does not affect the luminescence properties of the material [46].

3.2 Thin \(\hbox {GGG:Cr}^{3+}\) films

After 40 h of sputter deposition, the average thickness of the film deposited on fused silica was measured as \(1.1 \upmu \hbox {m}\). This deposition time is relatively long when compared to other deposition methods [22] and previous sputter depositions [15, 34]. The RF power, which influences the deposition time, was limited to 60 W in order to prevent damages in the target; thus a longer deposition time was required. The chemical composition of the sputtered films was studied using XPS for the film deposited on the stainless steel substrate. The spectrum was compared with standards from a database [47] to identify the elemental components of the film. Figure 4 presents the XPS spectrum of the \(\hbox {GGG:Cr}^{3+}\) thin film deposited on stainless steel. The photoelectron lines of the gadolinium atom \(\hbox {Gd3d}_{3/2}\) (1,218 eV), \(\hbox {Gd3d}_{5/2}\) (1,186 eV), split Gd4p (1/2 at 291 eV and 3/2 at 272 eV), and Gd4d (140 eV), the gallium atom \(\hbox {Ga2p}_{1/2}\) (1,144 eV), \(\hbox {Ga2p}_{3/2}\) (1,117 eV), Ga3s (160 eV), Ga3s (160 eV), split Ga3p (1/2 at 107 eV and 3/2 at 104 eV) and the oxygen atom O1s (531 eV) were distinguished. The Auger peaks O KLL, Gd MNN and Ga LMM were identified at the positions corresponding to \(\hbox {Al}_{k\alpha }\) excitation. The peaks at low binding energies correspond to overlapping signals of photoelectrons from the outer orbitals O2s, Ga3d, Gd5s, Gd5p and Gd4f. The XPS results revealed the presence of all the atoms of the host material in the film (i.e., \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}\)). The photoemission lines from the doping atoms \(\hbox {Cr}^{3+}\) could not be detected by XPS due to its low concentration in the film.

Fig. 4
figure 4

XPS spectrum of the \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}{:}\hbox {Cr}^{3+}\) thin film as deposited on the stainless steel substrate

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After deposition, the films did not show any luminescence signal regardless of the sputtering condition because the dopant atoms are located in a variety of positions within the crystal structure of the host [13]. Consequently, the \(\hbox {Cr}^{3+}\) atoms experience a variety of crystal field effects, which lead to weak emission or non-luminescent relaxation. Therefore, the films were annealed to restore their luminescence properties. Annealing conditions similar to those reported by Chao et al. [48] for \(\hbox {Y}_3\hbox {Al}_5\hbox {O}_{12}\):Ce films were used because YAG and GGG have identical crystal structures. The \(\hbox {GGG:Cr}^{3+}\) films were annealed at 1,173 K for 12 h in \(\hbox {N}_2\) at atmospheric pressure to avoid the oxidation of the stainless steel substrate and the dopant atoms. The crystal structure of the thin film deposited on stainless steel was studied by XRD before and after heat treatment to evaluate the effect of annealing. The crystal structure of the thin film deposited on fused silica was studied by XRD only after annealing to verify the restoration of its crystallinity.

Fig. 5
figure 5

XRD pattern of the \(\hbox {GGG:Cr}^{3+}\) as deposited on stainless steel. The pattern of a polycrystalline stainless steel substrate without annealing is included to facilitate the identification of the XRD reflections

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Figure 5 presents the XRD pattern of the \(\hbox {GGG:Cr}^{3+}\) film as deposited on stainless steel. Figure 6 presents the XRD patterns of the \(\hbox {GGG:Cr}^{3+}\) films deposited on stainless steel and fused silica after annealing. A sample of stainless steel substrate was annealed and analyzed by XRD to identify changes in its diffraction pattern due to the high temperature of the annealing process. The XRD patterns of the stainless steel substrate before and after annealing are included as references in Figs. 5 and 6, respectively. As can be seen in Fig. 5, after deposition at 723 K, the \(\hbox {GGG:Cr}^{3+}\) film is completely amorphous and all the reflections in the pattern correspond to the polycrystalline stainless steel substrate. Since the AISI 304 is an austenitic steel, it is very stable at temperatures up to \(\sim\)1,373 K. This means that annealing at 1,173 K would not cause any change of phase. There are some re-crystallizations at this temperature which are evidenced when comparing the XRD patterns of stainless steel in Figs. 5 and 6.

Fig. 6
figure 6

XRD patterns of the \(\hbox {GGG:Cr}^{3+}\) films deposited on stainless steel and fused silica after annealing. A sample of stainless steel substrate was annealed and analyzed by XRD to identify changes in its diffraction pattern due to the high temperature of the annealing process

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After annealing, the crystal structure of the film was restored and the main reflections of the cubic \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}\) were observed for both films. For the film on stainless steel, all the reflections were identified to belong either to the \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}\) or the substrate structures. It was not possible to determine whether the second phase of \(\hbox {Gd}_3\hbox {GaO}_6\) was also present in the film because of a reflection from the stainless steel substrate around \(2\theta = 30^{\circ }\). In the case of the film deposited on fused silica, the second phase of \(\hbox {Gd}_3\hbox {GaO}_6\) was not present in the film. The annealing process enabled the restoration of the crystal structure of the host material as well as the ordering of the dopant atoms within the host lattice. This resulted in improvements in the coupling of the excitation energy and the electrons, restoring the luminescent properties. On the other hand, the XRD results of the stainless steel substrate suggest a re-crystallization of its structure during the annealing process at high temperatures without any phase change.

3.3 Temperature-dependent luminescence characteristics

Figure 7 shows the temperature-dependent luminescence lifetimes of the thin \(\hbox {GGG:Cr}^{3+}\) films deposited on stainless steel and fused silica (after annealing) in the range between 310 and 1,000 K. Luminescence lifetime measurements of the \(\hbox {GGG:Cr}^{3+}\) target are also included in Fig. 7 to compare the luminescence properties of the source material and the thin films. The calibration curves displayed piecewise linear shapes in the semi-logarithmic plot leveling off at high temperatures due to the low-pass characteristics of the detection system. The film deposited on stainless steel showed luminescence lifetimes of the same order compared to those of the target, with reasonable differences between 600 and 800 K. The corresponding luminescence lifetimes start at \(2.00 \times 10^{-4}\) s and \(1.77 \times 10^{-4}\) s at 310 K and decrease to \(2.50 \times 10^{-7}\) s and \(2.29 \times 10^{-7}\) s at 1,000 K for the thin film and the target, respectively. On the other hand, the film deposited on fused silica exhibited faster decays than those of the target and the film deposited on stainless steel in almost the whole range of temperatures. Its luminescence lifetimes start at \(1.15 \times 10^{-4}\) s at 310 K and decrease down to \(3.13 \times 10^{-7}\) s at 960 K. The differences on the temperature-dependent luminescence behavior of the thin films and the source material could be related to the inherent change in the stoichiometry of the film (i.e., in the atomic concentration of Gd, Ga, O and Cr) during sputter deposition, especially for multicomponent films [40].

The precision of the measurements was estimated by the normalized shot-to-shot standard deviation (\(\sigma _{{\mathrm {S2S}}}\)) of the single-shot temperatures by:

$$\begin{aligned} \sigma _{{\mathrm {S2S}}}\,=\,\frac{\sqrt{\frac{1}{N_s-1}\sum _{s=1}^{N_s} \left( T_s - \frac{1}{N_s} \sum _{s=1}^{N_s} T_s\right) ^2}}{\frac{1}{N_s} \sum _{s=1}^{N_s} T_s} \end{aligned}$$
(6)

where \(s\) and \(N_s\) are the index and number of the single shots (100 in this case) and \(T\) is the temperature, respectively. The results of the normalized shot-to-shot standard deviation are presented in Fig. 8. The thin \(\hbox {GGG:Cr}^{3+}\) films provide standard deviations below 1 % for the entire temperature range resulting in a high temporal precision of the same order as the previous study of Fuhrmann et al. [35] for a thick coating of \(\hbox {GGG:Cr}^{3+}\). The target’s precision behavior is similar, with an increase in standard deviations above 930 K that could be related with a slower response of the target to the temperature change during the cooling down due to its large thickness (4 mm) in comparison with the response of the reference thermocouple. Overall, the results of temperature sensitivity and precision prove the feasibility of high-precision 0-dimensional (0D) single-shot temperature measurements using thin \(\hbox {GGG:Cr}^{3+}\) films in the range from 310 to 1,000 K. However, because the differences of the films and the source material (target) can result in significantly different luminescence lifetimes, it is necessary to record calibration curves for coatings produced by sputter deposition.

Fig. 7
figure 7

Temperature-dependent lifetimes of the \(\hbox {GGG:Cr}^{3+}\) films deposited on stainless steel and fused silica along with the temperature-dependent lifetimes of the \(\hbox {GGG:Cr}^{3+}\) target. Each point represents the mean value of 100 individually evaluated single shots

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3.4 2D luminescence characteristics

Two-dimensional (2D) measurements of the lifetime of the \(\hbox {GGG:Cr}^{3+}\) films were performed at room temperature (\(T=293\) K). Figure 9a presents the 2D distributions of the relative deviation of the local lifetimes with respect to the spatial and temporal mean value for the \(\hbox {GGG:Cr}^{3+}\) film deposited on fused silica. As can be seen, the film exhibited rather uniform lifetimes and the relative deviation lies close to zero in the whole area. For a more detailed evaluation, the one-dimensional (1D) distribution of the relative deviation of the local lifetimes with respect to the mean value at a fixed horizontal position is plotted in Fig. 9b (solid line). As observed, the relative deviations in the film deposited on fused silica at \(x = 1.74\) mm lie between \(-4\,\%\) (12 K) and 2 % (6 K). The spatial precision of the measurements was evaluated by the relative pixel-to-pixel standard deviation (\(\sigma _{{\mathrm {P2P}}}\)) in terms of lifetimes using:

$$\begin{aligned} \sigma _{{\mathrm {P2P}}}\,= \,\frac{\frac{1}{N_{s}} \sum _{s=1}^{N_{s}} \sqrt{\frac{1}{N_{p}-1}\sum _{p=1}^{N_{p}} \left( \tau _{s,p} - \frac{1}{N_{p}} \sum _{p=1}^{N_{p}} \tau _{s,p} \right) ^2}}{\frac{1}{N_{s} \cdot N_{p}} \sum _{s=1}^{N_{s}} \sum _{p=1}^{N_{p}} \tau _{s,p}} \end{aligned}$$
(7)

where \(\hbox {N}_s=100\) is the number of single shots, \(N_p=\hbox {19,044}\) is the number of pixels (\(138 \times 138\)) and \(\tau _{s,p}\) is the luminescence lifetime of the pixel \(p\) at the single shot \(s\). The maximum relative spatial standard deviation for the film deposited on fused silica is \(1.6\,\%\). While the temporal precision is high (max. 1 %), there is a decrease in spatial precision when measuring 2D temperature distributions. Contrary, results for a thick \(\hbox {GGG:Cr}^{3+}\) coating showed that \(\sigma _{{\mathrm {S2S}}}\) and \(\sigma _{{\mathrm {P2P}}}\) are of the same order of magnitude [35]. This difference could be related to a lower signal-to-noise ratio (from a thin film compared to a thick coating) and higher pixel resolution of the present experiment (43 \(\upmu\)m/pixel). For comparison, a \(6 \times 6\) binnig of the 2D data was performed to simulate a pixel resolution similar to Ref. [35] (300 \(\upmu\)m/pixel). As can be observed in Fig. 9b (dashed line), the relative deviation of the local lifetimes with respect to the mean value are further reduced for a lower pixel resolution. Moreover, recalculating \(\sigma _{{\mathrm {P2P}}}\) with Eq. 7 (\(\hbox {N}_s=100\) and \(\hbox {N}_p=529\)) results in a value of 1 %, which is of the same order of magnitude as \(\sigma _{{\mathrm {S2S}}}\). Therefore, the thin \(\hbox {GGG:Cr}^{3+}\) film deposited on fused silica is suitable for temporally and spatially resolved temperature measurements with high spatial resolution and high precision.

Fig. 8
figure 8

Normalized shot-to-shot standard deviations in terms of temperature for the \(\hbox {GGG:Cr}^{3+}\) films deposited on stainless steel and fused silica and for the \(\hbox {GGG:Cr}^{3+}\) target

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In the case of the thin \(\hbox {GGG:Cr}^{3+}\) film deposited on stainless steel, the 2D distribution and 1D distribution at a fixed horizontal position of the relative deviation of the local lifetimes with respect to the spatial and temporal mean value are plotted in Fig. 9c, d, respectively. Clear spatial inhomogeneities of the luminescence lifetime distribution were observed in the film deposited on stainless steel, with local deviations as high as 30 % (88 K). The deviations at \(x = 0.78\) mm range from \(-20\,\%\) (59 K) to \(15\,\%\) (44 K) (solid line in Fig. 9d). In this case, \(\sigma _{{\mathrm {P2P}}}\) in terms of lifetimes is 6.9 % and a \(6\times 6\) binning reduces some local inhomogeneities (dashed line in Fig. 9d) and results in a \(\sigma _{{\mathrm {P2P}}}\) of 4.4 %. Local differences in the Cr doping concentration could be the reason for such a spatial inhomogeneity of lifetimes in the film deposited on stainless steel. Since the films on fused silica and stainless steel were deposited simultaneously using the same sputtering parameters, it is possible that the inhomogeneities are related to the annealing process. Evaporation of atoms from the film or Cr diffusion from the stainless steel substrate, due to the high temperature, could explain the inhomogeneities. However, further studies, including for example the measurement of local doping concentrations, are necessary to clarify these results. The poor homogeneity of the luminescence lifetimes of the film deposited on stainless steel demands improvements for 2D thermometry applications. Nevertheless, because 0D lifetimes are determined collecting the luminescent emission from a spot of \(\sim\)0.8 mm\(^2\), thin \(\hbox {GGG:Cr}^{3+}\) films deposited on stainless steel could be still used as point temperature sensors as long as the measurements are conducted using the same spot used for the calibration.

Fig. 9
figure 9

2D distributions of the relative deviation of local lifetimes with respect to the spatial and temporal mean value for the \(\hbox {GGG:Cr}^{3+}\) thin films deposited a on fused silica and c on stainless steel. 1D distributions at \(x = 1.74\) mm for b the film on fused silica and at \(x = 0.78\) mm for d the film on stainless steel are also included

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4 Conclusions

An evaluation of the physical, chemical and luminescence properties of thin \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}{:}\hbox {Cr}^{3+}\) films, deposited by RF magnetron sputtering, have been conducted to overcome challenges related with the coating process of TP. This study relied on experience of chemistry, materials science and engineering, which involved the preparation of the sputter target, the sputter deposition process and the characterization of the thin films, respectively. From the results, analysis and discussion, the following conclusions are drawn:

  • The annealing process is necessary to restore the crystal structure and the luminescence characteristics of sputtered TP. The complex crystal structure of \(\hbox {Gd}_3\hbox {Ga}_5\hbox {O}_{12}{:}\hbox {Cr}^{3+}\) required annealing at high temperatures (1,173 K) for several hours. Sputter deposition is in general applicable for the coating of TP, except for cases where the substrate cannot resist high temperatures. The exploration of advanced annealing processes such as laser annealing is highly recommended.

  • The thin \(\hbox {GGG:Cr}^{3+}\) film deposited on fused silica exhibited a strong luminescence signal, fast luminescence decays, appropriate temperature sensitivity in a relative wide range of temperatures, adequate precision and spatial homogeneity of luminescent properties. This proves its suitability for point and 2D surface thermometry.

  • The thin \(\hbox {GGG:Cr}^{3+}\) film deposited on stainless steel requires improvements regarding the spatial inhomogeneities in the concentration of the dopant atoms in the film. Nevertheless, it could be still used as high-precision point temperature sensor.