polymers Article Application of Synchrotron Radiation-Based Fourier-Transform Infrared Microspectroscopy for Thermal Imaging of Polymer Thin Films Emigdio Chavez-Angel 1, * , Ryan C. Ng 1 , Susanne Sandell 2 , Jianying He 2 , Alejandro Castro-Alvarez 3 , Clivia M. Sotomayor Torres 1,4 and Martin Kreuzer 5, * 1 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, The Universitat Autònoma de Barcelona Campus, 08193 Barcelona, Spain 2 NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway 3 Laboratorio de Bioproductos Farmacéuticos y Cosméticos, Centro de Excelencia en Medicina Traslacional, Facultad de Medicina, Universidad de La Frontera, Temuco 4780000, Chile 4 Institución Catalana de Investigación y Estudios Avanzados (ICREA), 08010 Barcelona, Spain 5 CELLS-ALBA, Synchrotron Light Source, 08290 Barcelona, Spain * Correspondence: emigdio.chavez@icn2.cat (E.C.-A.); mkreuzer@cells.es (M.K.) Abstract: The thermal imaging of surfaces with microscale spatial resolution over micro-sized areas remains a challenging and time-consuming task. Surface thermal imaging is a very important characterization tool in mechanical engineering, microelectronics, chemical process engineering, optics, microfluidics, and biochemistry processing, among others. Within the realm of electronic circuits, this technique has significant potential for investigating hot spots, power densities, and monitoring heat distributions in complementary metal–oxide–semiconductor (CMOS) platforms. We present a new technique for remote non-invasive, contactless thermal field mapping using synchrotron radiation-based Fourier-transform infrared microspectroscopy. We demonstrate a spatial Citation: Chavez-Angel, E.; Ng, R.C.; resolution better than 10 um over areas on the order of 12,000 um2 measured in a polymeric thin Sandell, S.; He, J.; Castro-Alvarez, A.; film on top of CaF2 substrates. Thermal images were obtained from infrared spectra of poly(methyl Torres, C.M.S.; Kreuzer, M. methacrylate) thin films heated with a wire. The temperature dependence of the collected infrared Application of Synchrotron spectra was analyzed via linear regression and machine learning algorithms, namely random forest Radiation-Based Fourier-Transform and k-nearest neighbor algorithms. This approach speeds up signal analysis and allows for the Infrared Microspectroscopy for Thermal Imaging of Polymer Thin generation of hyperspectral temperature maps. The results here highlight the potential of infrared Films. Polymers 2023, 15, 536. absorbance to serve as a remote method for the quantitative determination of heat distribution, https://doi.org/10.3390/ thermal properties, and the existence of hot spots, with implications in CMOS technologies and other polym15030536 electronic devices. Academic Editor: Alfredo Keywords: thermal imaging; synchrotron radiation; machine learning; temperature dependence; Rondinella FTIR polymer; FTIR thermometry Received: 30 December 2022 Revised: 16 January 2023 Accepted: 16 January 2023 Published: 19 January 2023 1. Introduction The temperature and thermal conductivity of a material are among the most common and important physical measurement parameters. Rapid developments in nanotechnology Copyright: © 2023 by the authors. and biological applications have escalated the ever-growing necessity for contactless and Licensee MDPI, Basel, Switzerland. non-invasive measurements of these parameters [1–3]. Optical measurement techniques This article is an open access article such as fluorescence thermometry [4], optical fiber thermometry [5], Raman thermome- distributed under the terms and try [6], and infrared thermometry based on Planck black-body emission [7] are some of the conditions of the Creative Commons existing techniques that are used to extract the temperature in a remote and non-invasive Attribution (CC BY) license (https:// manner. However, these methods require either very long acquisition times (e.g., Raman creativecommons.org/licenses/by/ thermometry), knowledge of the emissivity which depends on temperature, wavelength 4.0/). and size, or the use of luminescent materials [8]. Polymers 2023, 15, 536. https://doi.org/10.3390/polym15030536 https://www.mdpi.com/journal/polymers Polymers 2023, 15, 536 2 of 13 The extrapolation of temperature from infrared radiation can be achieved by different temperature-dependent features. The most common technique is infrared thermography, in which detecting devices sense the energy radiated from objects in the infrared band region [9]. As the energy emitted by a body is proportional to the fourth power of the temperature rise, the energy values can be converted into the objects surface temperature using Planck’s law of black-body radiation and calibration constants [9]. Infrared thermog- raphy is a contactless technique, which can provide two dimensional thermal images in real time [10]. Thermal cameras, based on these principles, can offer spatially resolved thermal images of a sample or scene. The possible applications for such technologies are very broad, finding utility in areas such as the study of irregularities in building envelopes [11], the testing of aerospace components [12], solar cells [13], microelectronic devices [14], or biomedicine [15]. However, determination of the temperature depends on knowledge of the emissivity of the measured surface. The emissivity is a value ranging from zero to one and is dependent on the specific material, surface, and wavelength, and describes the effec- tiveness of a surface for radiating energy relative to that of a black body [10,15]. In addition to the emissivity, another obstacle to the accurate determination of temperature via infrared thermometry is the complex thermal relationship between a specimen of interest and its surroundings (e.g., convective cooling, ambient humidity, and environmental temperature), which can have a strong effect on measurements [10]. A common approach to obtain thermal maps or local temperatures of a sample is based on Raman spectroscopy. Optothermal Raman or Raman thermometry is one of the most popular and widely used techniques for characterizing the temperature of two- dimensional materials [16], thin films [17,18], substrates [6,19,20], and suspended semicon- ductors [20–25]. Using Raman thermometry, the local temperature can be measured in four different ways: (i) through the ratio of the Stokes and anti-Stokes signal amplitudes and calculation of the temperature based on a Boltzmann distribution of the ground and first excited state populations [26]; (ii) via the analysis of the band position; (iii) linewidth; and (iv) intensity of a Raman mode followed by a determination of the temperature dependence of the associated spectral characteristic [6]. A change in temperature induces changes at the molecular scale, leading to a modification of bond lengths and intermolecular forces. This effect modifies the phonon frequency and its dynamics and gives rise to a shift in the Raman mode frequency (peak position), phonon lifetime (linewidth), and phonon population (amplitude). Consequently, it is possible to extract the local temperature of a sample via the measurement of a Raman band previously calibrated using a reference measurement. Reparaz et al. proposed the measurement of the thermal conductivity via two-laser Raman thermometry. Here, a heating laser creates a temperature gradient in a thin film or membrane and a probing laser locally measures the temperature through Ra- man imaging [22]. However, Raman thermometry requires the presence of a Raman active mode and can be very time-consuming. Moreover, the use of a laser as a heater may induce the injection of photo-excited charge carriers that can alter the measured properties [27] or induce the overpopulation of nonthermal phonons [28]. While infrared (IR) spectroscopy relies on the same effect of temperature on the phonon modes, IR signals are often stronger than Raman signals and can be calibrated for quantitative measurements using multivariate chemometric methods. Temperature- dependent IR spectra have mainly been employed in the determination of the transition temperature and conformational energy of macromolecules [29–32]. This method probes subtle changes in the intensities of individual infrared absorbance bands or band ratios with respect to temperature [32,33]. A potential model system for incorporating variable- temperature Fourier-transform infrared (FTIR) spectroscopy is poly(methyl methacrylate) (PMMA), as the temperature dependence of its infrared absorbance band intensities have been studied in detail in recent years [30,34,35]. For example, the conformational energies for the PMMA backbone and side chains were derived by analyzing changes in the infrared absorbance of PMMA as a function of temperature [29,30]. In another work, the glass transition temperature was derived by analyzing changes in the reflectivity of PMMA thin Polymers 2023, 15, 536 3 of 13 films [31]. Painter et al. studied the thermal transitions of PMMA using the change in width and shape of absorbance bands with increasing temperature [35]. Some PMMA absorbance bands have also been found to be temperature-dependent [29,36]. Due to the stronger signal of IR relative to Raman and the brightness of the synchrotron IR-light source, we propose the exploitation of the temperature dependence of infrared absorbance peaks for thermal imaging in thin films. To our knowledge, the modification of an infrared absorbance band has not been previously used as a metric for the determination of temperature. Thus, we incorporate a simple and fast approach to measure temperature via a linear regression (LR) approach. In addition, we also propose the use of machine learning (ML) algorithms to fully exploit FTIR spectra and apply them to extract tempera- ture information from single peaks or even from a continuous spectral range [37,38]. The development of software, faster computers, and ML enable the application of more general approaches for predicting temperature via measured infrared spectra. In this study, random forests and k-nearest neighbor (k-NN) algorithms were applied to predict the temperature gradient of a test sample using a continuous spectral range. The temperatures predicted by ML were then compared to the LR approach. This work highlights the feasibility of infrared vibrational thermography based on ML approaches and FTIR spectroscopy as a new method for predicting temperatures in polymeric thin films. This approach can be extended to any film with temperature-dependent IR-active modes. Moreover, considering that silicon is transparent to IR excitation, this method could be used to characterize hot spots or power densities in situ. 2. Materials and Methods 2.1. Sample Preparation Samples were fabricated on calcium fluoride (CaF2 ) substrates, a common infrared window transparent to IR light. An initial cleaning step was performed by ultrasonication in acetone and isopropanol for 5 min, followed by a deionized water rinse and N2 drying. Poly(methyl methacrylate) (PMMA) powder was dissolved in anisole (MicroChem Corp (MA, USA)) using magnetic stirring for more than 12 h in a closed container to avoid solvent evaporation. The powder (with an average molecular weight of 15,000 Da and made by gel permeation chromatography) was purchased from Sigma Aldrich (now Merck KGaA, Darmstadt, Germany). The resulting PMMA solution was spin-coated onto CaF2 chips (spin coater from Laurell Technologies) at 4000 rpm and cured at 50 ◦ C for 4 h in a vacuum oven (Binder, Germany). The thickness of the PMMA layer was set to 1 µm. The PMMA layer thicknesses were measured by dual rotating compensator variable angle spectroscopic ellipsometry (VASE) (RC2, J.A. Woollam Co.) over the wavelength range 210–1690 nm with data collected from 55◦ to 70◦ . 2.2. Metal Wire Preparation and Temperature Calibration To create a temperature gradient in the PMMA film, a titanium/gold wire was evapo- rated onto the polymer film and used as a heating element by applying different currents to the wire. The Ti (5 nm) and Au (95 nm) films were deposited using electron-beam evapo- ration (AJA International, Inc., USA) at a deposition rate of 5 Å/s using a mechanical mask. A schematic illustration is shown in Figure 1a. The deposited metallic strip is composed of four rectangular pads connected by pins to the narrow heating wire. The width of the heating line was set to 20 µm and the length to l = 1 mm, the latter being determined by the distance between the inner pads used to measure the voltage. The outer pads were used to inject the current. Since the temperature of the wire is linearly proportional to its electrical resistivity, the temperature can be set by applying the corresponding current/voltage. For the calibration, the electrical resistivity of the wire was measured at different system tem- peratures ranging between 302 and 350 K on a heating stage to obtain the linear correlation between temperature and wire resistivity (Figure S1). A current source with an integrated voltmeter was connected and the corresponding resistivity was set to use the wire as a heating element. Polymers 2023, 15, x FOR PEER REVIEW the linear correlation between temperature and wire resistivity (Figure S1). A Polymers 2023, 15, 536 4 of 13 source with an integrated voltmeter was connected and the corresponding resistiv set to use the wire as a heating element. Figure 1. (a) Schematic Figurerepresentation of representation 1. (a) Schematic the heating device deposited of the on top deposited heating device of the polymer on topfilm. of the polym (b) Optical (b) Optical transmission transmission image image of the sample, of the sample, showing showing the metallic wire the metallic in black wire with the in black with t three infrared infrared measurement measurement areas highlighted areas highlighted in orange. in orange. 2.3. Synchrotron 2.3. Radiation-Based Synchrotron Fourier-Transform Infrared (SR-FTIR) Radiation-Based Fourier-Transform Microspectroscopy Infrared (SR-FTIR) Microspectrosc Synchrotron radiation-based Synchrotron Fourier-transform infrared (SR-FTIR)infrared radiation-based Fourier-transform microspectroscopy (SR-FTIR) microsp measurements were performed at the copy measurements infrared were performedmicrospectroscopy beamline MIRAS of at the infrared microspectroscopy beamline the Spanish synchrotron light synchrotron of the Spanish source ALBA [39].source light The endstation ALBA [39].was The equipped endstationwith was aequipped Vertex 70 spectrometer Vertex 70 coupled to a Hyperion spectrometer coupled3000to avisible/infrared microscope (Bruker, Hyperion 3000 visible/infrared microscope ( Germany). Measurements were carried out in transmission Germany). Measurements were carried out in transmissionmode using × objective a 15mode using a 15× o and matching condenser (numerical and matching aperture condenser = 0.4). Foraperture (numerical each of resulting spectra, = 0.4). For each 256 scans of resulting spec were co-added for the temperature calibration and 64 scans for the line scans and matrix, scans were co-added for the temperature calibration and 64 scans for the line sca with a wavenumber resolution matrix, of 4 cm−1 . The with a wavenumber software of resolution package 4 cm−1.Opus (Version package The software 7.5, Bruker, Opus (Vers Germany) was used for data acquisition. Data was analyzed, fitted, and plotted Bruker, Germany) was used for data acquisition. Data was analyzed, fitted, using a and Python code based on numpy, scipy, and seaborn libraries. Linear using a Python code based on numpy, scipy, and seaborn baselines were calculated libraries. Linear baselin and subtracted in the regions of interest between 2800–3100 cm−1 and 950–1800 cm−1 , −1 calculated and subtracted in the regions of interest between 2800–3100 cm and 95 respectively. The calibration of PMMA between infrared absorbance and temperature was cm−1, respectively. The calibration of PMMA between infrared absorbance and te obtained by using a Linkam FTIR600 temperature control stage mounted in the infrared ture was obtained by using a Linkam FTIR600 temperature control stage mounted microscope with two CaF2 windows of 500 µm thickness and used in a transmission infrared microscope with two CaF2 windows of 500 µ m thickness and used in a tra configuration. The measurements were carried out under atmospheric pressure. sion configuration. The measurements were carried out under atmospheric pressu 2.4. Machine Learning 2.4. Machine Learning Machine learning (ML) was performed with the open source software package Or- ange, BioinformaticsMachine learning Laboratory of the(ML) was performed University with version of Ljubljana, the open3.30.2, source software and the pack ange, Bioinformatics Laboratory of the University of Ljubljana, spectroscopy add-on, version 0.6.2 [40–42]. Within Orange, all spectra were baseline cor- version 3.30.2, a spectroscopy add-on, version 0.6.2 [40–42]. Within Orange, all spectra rected (rubber band) and unit vector normalized in the region of interest after the second were basel rected (rubber derivative was calculated overband) andrange. the total unit vector normalized In addition, in the region a Gaussian of interest smoothing of theafter the data was applied.derivative was calculated over the total range. In addition, a Gaussian smoothing data was applied. 3. Results and Discussion 3. Results The first step and in using Discussion polymer IR modes as a thermometer is to calibrate the IR response with respectThe first step in using to temperature. Some polymer variationsIRofmodes as a thermometer the polymer film such as is to calibrate th density, molecular weight, or polydispersity sponse with respect toindex are relevant temperature. Someto the IR response variations of the film of the polymer film.such as d However, as thismolecular method requires an initial calibration of the IR signal against temperature, weight, or polydispersity index are relevant to the IR response of the film the impact of changing ever, asthese properties this method on the an requires temperature responseofare initial calibration thealready included IR signal againstintemperat the initial calibration. impact Theof calibration step is changing these mandatory properties on to thebetemperature able to exploit an FTIRare response signal already inclu to be used as a thermometer. The infrared the initial calibration. absorbancestep The calibration of the sample wastolocally is mandatory measured be able to exploit an FTIR at different regions, to beasused shownas ain Figure 1b. AThe thermometer. single point absorbance infrared for calibrating thesample of the temperature was locally me response of the at PMMA IR spectra was repeatedly measured at different environmental different regions, as shown in Figure 1b. A single point for calibrating the temp temperatures. Here, the sample response of the was PMMAplaced in a cryostat IR spectra stage and no was repeatedly current was measured applied environ at different to the metal wire. Subsequently, the sample was heated using the metal wire temperatures. Here, the sample was placed in a cryostat stage and no current and the was cryostat stage was kept at room temperature. In this configuration, the infrared response of the PMMA layer was measured along a line scan across the heated metal wire and across a larger area for hyperspectral imaging. to the metal wire. Subsequently, the sample was heated using the metal wire and the c ostat stage was kept at room temperature. In this configuration, the infrared response the PMMA layer was measured along a line scan across the heated metal wire and acro Polymers 2023, 15, 536 a larger area for hyperspectral imaging. 5 of 13 3.1. PMMA Infrared Absorption (Calibration Data) 3.1. PMMA Infrared For Absorption the calibration of the infrared (Calibration Data) absorbance response of PMMA at different te peratures, spectra of the PMMA film were systematically taken at several set temperatu For the calibration of the infrared absorbance response of PMMA at different temper- (Tset) using a cryostat stage (Linkam FTIR600). Measurements were taken between 283 a atures, spectra of the PMMA film were systematically taken at several set temperatures 373 K in 3 K steps during the heating and subsequent cooling cycle. A total of 5 min pass (Tset ) using a cryostat stage (Linkam FTIR600). Measurements were taken between 283 and 373 K in following 3 K stepseach change during in temperature the heating prior to spectrum and subsequent acquisition cooling cycle. A totaltoofallow 5 minfor therm equilibration. Infrared absorbance spectra of PMMA are shown passed following each change in temperature prior to spectrum acquisition to allow for in the C-H stretch regi between 3100–2800 cm −1 (Figure 2a) and the fingerprint region between 1800 and 950 cm thermal equilibration. Infrared absorbance spectra of PMMA are shown in the C-H stretch (Figure region between 2b). All cm 3100–2800 absorption −1 (Figure peaks were 2a) and theidentified and fingerprint associated region betweento the 1800molecular and vib tional 2b). 950 cm−1 (Figure modesAllaccording absorptiontopeaks the literature and were were identified andcompared associatedwith density-functional to the molecular th ory (DFT) simulations (Figure S2) [43-48]. The room temperature vibrational modes according to the literature and were compared with density-functional band assignments a summarized in Table 1. theory (DFT) simulations (Figure S2) [43–48]. The room temperature band assignments are summarized in Table 1. Figureabsorption Figure 2. Infrared 2. Infraredspectra absorption spectrameasured of PMMA of PMMA measured with variablewith variable temperature temperature from 283 andfrom 283 a 373 K in 3 K 373 K in steps. (a)3All K steps. (a)have spectra All spectra have been been baseline baseline corrected in corrected the regioninofthe theregion of the C-H vibratio C-H vibrational peaks between 3100 and 2800 cm and (b) the fingerprint region between 1800 and 950 cm and peaks between 3100 and 2800 cm − 1 −1 and (b) the fingerprint region between 1800 − 1 . 950 cm−1. Table 1. Peak assignment of the measured PMMA absorption peaks compared to literature valu Table 1. Peak assignment of the measured PMMA absorption peaks compared to literature values at at room temperature. room temperature. Fitted Fitted Lit. Values Slope (dIPP/dTse Vibrational Mode Lit.peaks Values Ref. (dIPP/dTset ) Slope Vibrational Mode Peaks [cm −1] Ref. [cm-1/K] [cm [cm −1−1]] [cm-1 /K] [cm−1 ] C-H stretch region: C-H stretch region: C–H C–H stretching stretching vibrations vibrations of the –CH3 of the2995 –CH3 2995 2997 2997 [49] [49] 0.007 0.007 C–H stretching vibrations C–H stretching vibrations of the –CH2 of the –CH2 2951 2951 2952 2952 [49] [49] 0.001 0.001 methoxy carbon methoxy carbon (O–CH3) 2841 2841.6 2841 [50] 2841.6 [50]−0.013 −0.013 (O–CH3) Fingerprint region: C=O stretch (Ketone) Fingerprint region: 1731 1727, 1732 [49–51] 0.001 CH2 bending 1481 1485 [52] −0.014 C=O C–H bending (Alkane) stretch (Ketone) 1448 1731 1450, 1444 1727, 1732 [49,51] [49–51]0.000 0.001 CH2 (CH asymmetrical bending vibration bending 3) 1434 1481 1435.3 1485 [50] [52]−0.008 −0.014 methyl group (C-CH3 ) 1386 1388 [49] 0.009 C-C-O bending 1269 1265 [52,53] −0.032 C-C-O bending 1241 1238 [52,53] −0.029 CH3 wagging 1191 1197 [52] −0.022 C-O-C 1149 1149 [49–51] −0.028 stretching vibration of C–O–C group 1066 1063.6 [49,50] −0.007 C-C stretching 985 990 [52] −0.017 C-C-O bending 1241 1238 [52,53] −0.029 CH3 wagging 1191 1197 [52] −0.022 C-O-C 1149 1149 [49–51] −0.028 stretching vibration of C–O–C group 1066 1063.6 [49,50] −0.007 C-C stretching 985 990 [52] −0.017 Polymers 2023, 15, 536 6 of 13 As Tset was increased, the absorbance of the sample decreased systematically fo wavenumbers. The decrease in amplitude with increasing temperature was caused b As Tset combination was increased, ofthe absorbance different of the sample decreased temperature-dependent systematically phenomena such as for all intermolecular wavenumbers. The decrease in amplitude with increasing temperature teractions, changes in conformational populations, Fermi resonance, and the was caused bydynamic a combination of different temperature-dependent phenomena such as intermolecular molecular groups [30]. A systematic change in the Gaussian amplitude, linewidth ( interactions,width changes halfinmaximum, conformational FWHM), populations, and bandFermi resonance, position andin is observed theFigures dynamicsS3–S5 (from of molecularfitting), groups in [30]. A systematic change in the Gaussian amplitude, linewidth the two-dimensional correlation map (Figure S6), and in simulation (full (Figure width half maximum, FWHM),information in the supporting and band position [54,55]. is observed in Figures S3–S5 (from the fitting), in the two-dimensional correlation map A temperature-dependent shift(Figure in peakS6), and inwas positions simulation (Figure The also observed. S7) PMMA in the Supplementary Materials [54,55]. sorbance peaks listed in Table 1 were individually fitted with Gaussian line shapes (Fig A temperature-dependent S8). To more accurately shiftdetermine in peak positions the peakwas also observed. position, The performed the fits were PMMA ab-only aro sorbance peaks listed in Table 1 were individually fitted with Gaussian line shapes (Figure the peak maxima, typically ± 10 cm−1. The resulting fitting parameters were the maxim S8). To more accurately determine the peak position, the fits were performed only around peak position (peak), amplitude, and FWHM. The temperature dependence of all th the peak maxima, typically ± 10 cm−1 . The resulting fitting parameters were the maximum fitting parameters were plotted against temperature (Figure S3–S5). The impact of peak position (peak), amplitude, and FWHM. The temperature dependence of all three change of all these parameters in the band around 1149 cm−1 is shown in Figure S6 us fitting parameters were plotted against temperature (Figure S3–S5). The impact of the two-dimensional correlation spectroscopy (2DCOS). The synchronous plot (Figure S change of all these parameters in the band around 1149 cm−1 is shown in Figure S6 using shows the typical asymmetrical four-leafed clover pattern which indicates that the two-dimensional correlation spectroscopy (2DCOS). The synchronous plot (Figure S6a) shift of the peak is strongly coupled with peak broadening and decreasing intensity shows the typical asymmetrical four-leafed clover pattern which indicates that the red- temperature increases. The effect of each parameter and its coupling with the measu shift of the peak is strongly coupled with peak broadening and decreasing intensity as signal is also shown in the simulated 2DCOS in Figure S7. A steeper slope correspond temperature increases. The effect of each parameter and its coupling with the measured a more pronounced temperature dependence for the given absorbance band. The IR ba signal is also shown in the simulated 2DCOS in Figure S7. A steeper slope corresponds to a more pronouncedexhibiting the strongest temperature temperature dependence for thevariations are those given absorbance at 1269, band. The IR1241, 1191, and 1 bands cm −1, with temperature dependencies of the peak center positions of 0.032, −0.029, −0. exhibiting the strongest temperature variations are those at 1269, 1241, 1191, and 1149 cm−1 , and −0.028 with temperature cm−1/K, respectively dependencies (Figure of the peak center 3). These positions ofpeaks 0.032, arising −0.029,from the and −0.022, monomer ba − bone 1 units can then be used for the prediction of temperature −0.028 cm /K, respectively (Figure 3). These peaks arising from the monomer backbone on a test sample. units can then be used for the prediction of temperature on a test sample. Figure 3. Temperature dependence of different bands located at: (a) 1269, (b) 1241, (c) 1191, and (d) 1149 cm−1 . The sample has been heated (red) and cooled (blue) over the temperature region between 283 and 373 K. Data points are shown with numerical error from the fit. A linear model has been fitted (grey lines) with the resulting slopes listed in Table 1. The temperature dependencies of the most temperature sensitive peaks (1269, 1241, 1191, and 1149 cm−1 ) are shown in Figure 3. All four peaks possess a linear relationship between Tset and the infrared peak position (IPP) over the measured temperature range. The resulting temperature dependencies (the slope of the linear fit dIPP/dTset) for all peaks are shown in Figures S8 and S9; they have been summarized in Table 1, and are used for the LR approach for the temperature determination. The pronounced redshift of the peaks at 1269, 1241, 1191, and 1149 cm−1 have been previously reported and are in good agreement with our results (Figure 3) [29,36]. 1191, and 1149 cm−1) are shown in Figure 3. All four peaks possess a linear relationsh between Tset and the infrared peak position (IPP) over the measured temperature rang The resulting temperature dependencies (the slope of the linear fit dIPP/dTset) for all pea are shown in Figures S8 and S9; they have been summarized in Table 1, and are used f Polymers 2023, 15, 536 the LR approach for the temperature determination. The pronounced redshift of the pea 7 of 13 at 1269, 1241, 1191, and 1149 cm−1 have been previously reported and are in good agre ment with our results (Figure 3) [29,36]. 3.2. Line Scans (Test Sample) 3.2. Line Scans (Test Sample) Following IR calibration, Following aIRproof-of-concept experiment was calibration, a proof-of-concept performedwas experiment by heating performed the by heatin same film but by using the samea gold film heater but by wire. usingThe wireheater a gold was heated wire. by Thea DC wirecurrent through was heated by the a DC curre Joule effect andthrough then thermal mapping the Joule wasthen effect and realized by measuring thermal mapping was therealized infraredbyabsorbance measuring the infr spectra at different positions along red absorbance spectratheatpolymer. differentThe first measurements positions along the polymer.wereThe taken along first measuremen were taken line scans at positions −200line fromalong scans to 200 µmat relative positionstofrom −200 toof200 the center theµgold m relative to the wire (0.5 mm center of th away from thegold wirepad) voltage (0.5 mm at 5away from with µm steps the voltage a sampledpad) at 5 µof area m 10 × 10 steps withµma2sampled for eacharea of 10 10 µmapping spectrum. All the m2 for each spectrum. lines were takenAll the mapping inside of thelines were with cryostat takenaninside of the cryostat with a environmental temperature set to 318 K. For each line scan, the wire temperature (Twire ) of the temperature environmental temperature set to 318 K. For each line scan, the wire wire was (Twire) left at room temperature (298 K, baseline) or heated to 334 K, 353 K, or 376 K. 334 the wire was left at room temperature (298 K, baseline) or heated to We K, 353 K, or 3 then K. We then calculated the temperature distribution of the calculated the temperature distribution of the PMMA at each measurement position using PMMA at each measureme position linear regression using linear and machine regression and machine learning. learning. 3.2.1.Prediction 3.2.1. Temperature Temperature Prediction by Linear by Linear Regression Regression Model Model Figure 4 showsFigure 4 shows the four the peaks selected four selected peaks with the withtemperature highest the highest temperature responses (126 responses (1269, 1241, − 1191, 1and 1149 cm −1) which were selected and used to calculate the temperature 1241, 1191, and 1149 cm ) which were selected and used to calculate the temperature at each measurementeachposition measurement position by using by using the linear the linear temperature temperature dependencedependence of the absorban of the absorbance peak positions measured in the calibration step (Figure 3). Here, the peak positions measured in the calibration step (Figure 3). Here, the peak positions alone peak positions alon were used as predictors of the temperature, carried out separately were used as predictors of the temperature, carried out separately for each peak. for each peak. Figure Figure 4. Calculated 4. Calculated sample sample temperatures (Ttemperatures (Tcalc calc ) at +/− 200 µm ) atfrom +/− 200 the µheating m fromwire the heating (x = 0), wire using(x = 0), usi the peaks at 1269, 1241, 1191, − 1 and 1149 cm −1, including error bars. For each measurement, the wi the peaks at 1269, 1241, 1191, and 1149 cm , including error bars. For each measurement, the wire temperature (Twire) was left at room temperature (298 K, light blue) or heated to 334 K (blue), 353 temperature (Twire ) was left at room temperature (298 K, light blue) or heated to 334 K (blue), 353 K (purple), or 376 K (red). Prior to each measurement, the wire temperature was given at least 10 min to equilibrate. The room temperature inside of the cryostat is indicated with horizontal red lines. First, the calculated temperatures (Tcalc ) for the measurements at room temperature (298 K) were compared to the set wire temperature (Twire ). The mean temperatures for each of these room temperature measurement points were calculated. The resulting mean values (given with standard derivation) are 309 ± 3, 302 ± 8, 291 ± 4, and 294 ± 3 K for the peaks at 1269, 1241, 1191, and 1149 cm−1 , respectively. As expected, Tcalc calculated for higher wire temperatures (Twire ) increased with increasing Twire . A temperature gradient can be observed with the maximum temperatures close to the wire positions which decays exponentially away from these positions. The decay of the thermal field is given by [56]: r " r # 1 h ∆T = Q exp − x (1) hkd kd Polymers 2023, 15, 536 8 of 13 where Q is power density of the wire, h is the “convection coefficient” (which is the thermal boundary conductance (TBC) between the polymer and the substrate in this case), d is the film thickness, and k is the thermal conductivity of the polymer. From the best fit of (1) (Figure S10), the thermal conductivity and interphase thermal resistance were estimated to be k = 0.28 ± 0.11 WK−1 m−1 and TBC h = 85.30 ± 0.15 × 106 WK−1 m−2 , showing good agreement with the expected values for the thermal conductivity 0.15 < k < 0.25 (WK−1m−1) [57], and the same order for the TBC 60 < h < 150 × 106 WK−1 m−2 for the case of PMMA- metal [58]. An extended description of the fitting procedure is provided in the Supplemen- tary Materials. 3.2.2. Temperature Prediction by Machine Learning Approach In addition to the simple linear regression approach, the measured calibration data enabled the data to be analyzed with ML approaches. Despite the simplicity of linear regression, an important advantage of ML is that multiple complex spectral regions can be simultaneously considered to determine the temperature, rather than only the position of a single peak, as carried out previously in the linear regression approach. Another advantage is that no further knowledge about the temperature sensitivity of individual peaks is necessary and, therefore, the calibration data does not have to be analyzed be- forehand. Moreover, the full spectra can contain subtle temperature-dependent variations that are invisible to the naked eye but detectable by ML. This approach begins with an unsupervised principal component analysis (PCA), applied to identify the temperature- sensitive spectral regions of interest in the fingerprint region from 1550 to 1000 cm−1 (e.g., Figure 2b) for processed second derivative spectra. The resulting scores plot (Figure S11a) shows a clear separation between the line scan data taken at different temperatures (circles) along principal component 2 (PC-2). In addition, the calibration data (stars) also separate temperature dependence along PC-2 with measurements at higher temperatures resulting in a positive PC-2 and those at lower temperatures resulting in a negative PC-2. Consistent with this result, the same trend along PC-2 has been observed for the line scan data. The wavenumber regions with higher intensities of PC-2 (Figure S11b) were used for the following supervised analysis. We identified two spectral regions of interest from 1510–1410 cm−1 and 1300–1120 cm−1 , and we discarded the other wavenumber regions. The pre-processed second derivative spectra were baseline corrected and unit vector normal- ized before further analysis. The random forest and k-nearest neighbor (k-NN) algorithms were applied and compared as supervised models, using the calibration spectra as training data to predict the temperature of the test sample spectra taken close to the heated wire. A total of 1000 trees and 20 neighbors were chosen for the random forest and k-NN algorithms with a Euclidian metric, respectively. The cross validation of the models using 20 folds resulted in high coefficients of determination (R2) of 0.999 and 0.952 and low mean absolute errors (MAE) of 0.691 and 3.477 for the random forest and k-NN algorithms, respectively. The temperatures predicted by the machine learning approaches are plotted in Figure 5 for the two models separately for each applied wire temperature. The temperatures calculated via linear regression for the peak at 1269 cm−1 from Figure 4 are also overlaid onto these plots for direct comparison. 3.3. Hyperspectral Imaging After measuring the line scan in the center of the heater line, we moved to a corner of a voltage pad to take a snapshot of the temperature profile. Measurements at this location were taken due to the possibility of generating non-homogeneous maps due to the influence of the voltage pad. Here, a matrix of 36 × 15 spectra (540) was measured with a step size of 5 µm and a sampled area of 10 × 10 um2 per spectrum (Figure 6c). The black region in the image is due to a mask over the heating wire, which blocked the transmitted IR light. mean absolute errors (MAE) of 0.691 and 3.477 for the random forest and k-NN algo rithms, respectively. The temperatures predicted by the machine learning approaches ar plotted in Figure 5 for the two models separately for each applied wire temperature. Th Polymers 2023, 15, 536 9 of 13 temperatures calculated via linear regression for the peak at 1269 cm−1 from Figure 4 ar also overlaid onto these plots for direct comparison. Figure 5. Temperatures (Tcalc) predicted with linear regression (LR) for the peak at 1269 cm− cated by “●”-markers and temperatures predicted by the machine learning (ML) approaches cated by lines, using the random forest (left) and k-NN (right) algorithms. The data were mea with the gold wire temperature (Twire) at room temperature (298 K) and heated to 334, 353, an K. Room temperature is indicated with horizontal red lines. 3.3. Hyperspectral Imaging After measuring the line scan in the center of the heater line, we moved to a c of a voltage pad to take a snapshot of the temperature profile. Measurements at this tion were taken due to the possibility of generating non-homogeneous maps due t Figure 5. Temperatures (T ) predicted with linear with −1 Figure 5. Temperatures influence ofcalc the (Tcalc voltage ) predicted pad. Here, aregression linearof matrix (LR) 36 ×for15 the regression (LR)peak at peak for the spectra 1269 (540) was cmmeasured at 1269 cm−1 ind w indicated by “•step ”-markers catedsize ofand 5 µtemperatures by “●”-markers m and predicted anda temperatures sampled area byofthe 10machine predicted ×by10the um learning machine (ML) approaches learning 2 per spectrum (ML) approaches (Figure ind 6c). The catedusing indicated by lines, by lines, the using randomthe random forestand (left) and k-NN (right) algorithms. The datawere were measure region in the image is forest due to(left) a mask over k-NN the(right) heatingalgorithms. The wire, which data blocked the transm measured withIR with gold wire temperature (Twire) at room temperature (298 K) and heated to 334,353, and 37 the thelight. gold wire temperature (Twire) at room temperature (298 K) and heated to 334, K. Room temperature is indicated with horizontal red lines. 353, and 376 K. Room temperature is indicated with horizontal red lines. 3.3. Hyperspectral Imaging After measuring the line scan in the center of the heater line, we moved to a corne of a voltage pad to take a snapshot of the temperature profile. Measurements at this loca tion were taken due to the possibility of generating non-homogeneous maps due to th influence of the voltage pad. Here, a matrix of 36 × 15 spectra (540) was measured with step size of 5 µ m and a sampled area of 10 × 10 um2 per spectrum (Figure 6c). The blac region in the image is due to a mask over the heating wire, which blocked the transmitte IR light. Figure 6. Hyperspectral Figure 6. images showing Hyperspectral the temperatures images showing thepredicted by the temperatures (a) random predicted forest by the (a) and random fores (b) k-NN machine(b) k-NN machine learning algorithms. The regions of the metallic gold wire black. learning algorithms. The regions of the metallic gold wire are masked in are masked in (c) Optical image with the metallic gold coating (black) on a PMMA thin film (blue) and the sampled area of the hyperspectral imaging in white. Here, we set the wire temperature to 376 K, measured by the resistance of the wire. For each measurement point, the temperature was predicted using the random forest (Figure 6a) and the k-NN (Figure 6b) algorithms. As previously observed in the line scan predictions (Figure 5), the temperatures predicted by the random forest algorithm were slightly lower Figure 6.by than those predicted Hyperspectral images showing the k-NN algorithm. the temperatures However, predicted this technique by thefor allows (a) a random very forest an quick and direct generation of a thermal map using the raw signal, avoiding the individual in blac (b) k-NN machine learning algorithms. The regions of the metallic gold wire are masked fitting of all 540 spectra while considering the entirety of the frequency windows rather than a single peak. 4. Summary In this work, we presented a novel contactless technique for thermal mapping based on FTIR spectroscopy. For this approach, the temperature dependence of an IR signal of a 1 µm PMMA thin film was used as a local thermometer with a spatial resolution limited by the spot size of the IR source (10 µm in this work). We incorporated machine learning Polymers 2023, 15, 536 10 of 13 methods to directly treat measured raw signals from a sample, avoiding the need for peak fitting and analysis of each individual spectrum. An important advantage of ML is that multiple complex spectral regions can be simultaneously considered to determine the tem- perature, rather than only the position of a single peak. The full spectra can contain subtle temperature-dependent variations that are invisible to the naked eye but detectable by ML. Another advantage is that no further knowledge about the temperature sensitivity of individual peaks is necessary and, therefore, calibration data does not need to be analyzed beforehand. This approach can be extended and adapted to any spectroscopic technique (e.g., Raman, photoluminescence, Brillouin, etc.) and any film can be used as a surface thermometer, as long as it exhibits a temperature-dependent spectroscopic signal. The use of FTIR spectroscopy itself allows for investigation of temperature distributions in CMOS technology, as silicon is transparent and invisible in the IR regime. This opens the possibility to detect hot spots in normal device-operating conditions if they are covered with an IR-active material. This new approach is a step towards a deeper understand- ing of in situ thermal management in electronic devices that can be performed under operating conditions. Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/polym15030536/s1, Figure S1: electrical resistivity of the gold wire measured at different temperatures in a heating stage. Figure S2: simulated IR spectra of PMMA molecules. Figure S3: fitted Gaussian center positions for each PMMA absorbance peak vs temperature. Figure S4: fitted Gaussian amplitudes for each PMMA absorbance peak vs temperature. Figure S5: fitted Gaussian full width at half maximum (FWHM) for each PMMA absorbance peak vs temperature. Figure S6: synchronous (a) and asynchronous (b) two-dimensional correlation spectra obtained from temperature-dependent FTIR spectra of the PMMA film. The red and blue colors represent positive and negative cross peaks, respectively. Figure S7: synchronous two-dimensional correlation spectra obtained from simulated spectra centered at ~1149 cm−1 . (a) Simulated 2DCOS fixing band position and linewidth and varying the intensity. (b) Simulated 2DCOS fixing band intensity and linewidth and varying the peak position. (c) Simulated 2DCOS fixing band position and intensity and varying the linewidth. (d) Simulated 2DCOS varying band position, linewidth, and intensity. Figure S8: PMMA absorbance peaks at 283 K fitted individually using a Gaussian line shape, showing the data points and the fit as black lines. Figure S9: fitting results for a linear fit to the temperature dependence of the peak center positions for different absorbance peaks. The linear fits are shown in red in Figure S1. Figure S10: thermal decay as function of sample position for different temperatures of the heater wire. The solid lines represent the best fit. Figure S11: (a) Transferred data (scores plot) of the PCA with the calibration data (stars) and the line scan data points (circle). (b) Loadings plot of the PCA showing PC-1 (black) and PC-2 (red). Figure S12: simplified workflow of the machine learning approach in this work performed by Orange. Author Contributions: Conceptualization, E.C.-A. and M.K.; formal analysis, E.C.-A., A.C.-A. and M.K.; funding acquisition, J.H., C.M.S.T. and M.K.; investigation, E.C.-A., S.S. and M.K.; methodology, E.C.-A. and M.K.; project administration, C.M.S.T. and M.K.; resources, J.H. and M.K.; software, E.C.- A., A.C.-A. and M.K.; supervision, E.C.-A. and C.M.S.T.; visualization, E.C.-A. and M.K.; writing— original draft, E.C.-A., R.C.N. and M.K.; writing—review and editing, E.C.-A., R.C.N. and M.K. All authors have read and agreed to the published version of the manuscript. Funding: We acknowledge the support from the project LEIT funded by the European Research Coun- cil, H2020 Grant Agreement No. 885689. ICN2 is supported by the Severo Ochoa program from the Spanish Research Agency (AEI, grant no. SEV-2017-0706) and by the CERCA Programme/Generalitat de Catalunya. R.C.N. acknowledges funding from the EU-H2020 research and innovation program under the Marie Sklodowska Curie Individual Fellowship (Grant No. 897148). The Research Council of Norway is acknowledged for the support to NorFab (Grant No. 295864) and the HEFACE project (Grant No. 251068). A.C.-A. acknowledges the support from the Fondecyt Iniciación 11200620. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Polymers 2023, 15, 536 11 of 13 Data Availability Statement: Raw data can be provided by the corresponding author (M.K.) on reasonable request. Acknowledgments: The infrared-spectroscopy measurements were performed at MIRAS beamline at ALBA Synchrotron with the collaboration of ALBA staff. Conflicts of Interest: The authors declare no conflict of interest. References 1. Kim, M.M.; Giry, A.; Mastiani, M.; Rodrigues, G.O.; Reis, A.; Mandin, P. Microscale thermometry: A review. Microelectron. Eng. 2015, 148, 129–142. [CrossRef] 2. 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