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Abstract
To measure the in-plane thermal conductivity and the infrared emissivity of thin films, a steady-state IR micro-thermography with simplified measurement procedure and new data processing method is presented in this paper. Thermal images at different optical heat intensities were collected by an IR camera. By subtracting two measurement results, the background thermal radiation was eliminated. Infrared emissivity, heat flux density and in-plane thermal conductivity were obtained by data fitting. The most important advantages of the proposed method were that the background thermal radiation was eliminated and the complicated optical absorption measurement was replaced by heat power measurement. We have performed measurements on self-suspended polyimide films with different thicknesses. For 504 nm thick film, the thermal conductivity and infrared emissivity in 7∼14 µm were 0.18 Wm−1K−1 and 0.07, respectively. The measurement uncertainty of the thermal conductivity and infrared emissivity were lower than 13% and 10%, respectively, which were much lower than the previous reported value (20%) from the steady-state method. Our measurement procedure was suitable for analyzing thin films with a wide range of thermal properties.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High performance thin films with superior thermophysical properties [1–5] are widely used in photoelectronic devices [6–8]. In fast logic circuits with compact size thermo-physical properties of the thin films govern the operation stability and lifetime of the electric devices. Large temperature rise and gradient in highly integrated devices would cause electric connection failure and lifetime reduction. Various techniques have been developed to determine the thermal-physical properties of thin films [9,10]. Among them, photothermal emission/photothermal radiometry method is the most widely used one because of its simplicities on both sample preparation and data processing [11,12]. Lock-in thermography was introduced in 1979 by Kanstad and Nordal. It was a transient method, where pulsed or modulated laser was used to induce the periodical temperature change of the sample [13]. Based on temperature wave analysis various types of samples including insulating polymers, undoped semiconducting polymers, doped conducting polymers, and one-dimensional carbon fiber bulky papers were evaluated [14]. Recent improvements of this technique include extending the model to extract the optical absorption coefficient of both homogeneous films and multi-layered materials or the effective infrared optical absorption coefficient of samples along with the thermal diffusivity measurements [15–17]. Simultaneous measurement of thermal diffusivity and thermal conductivity relative to a reference sample is also possible [18]. Steady-state infrared (IR) thermography was invented by Anton Greppmair and his coworkers [19]. Compared to lock-in thermography the experimental setup of steady-state IR thermography is much simpler. Because the heating source is continuous and the IR camera does not need to be frequency locked to the modulated laser. The thermal conductivity of poly (3,4-ethylenedioxythiophene): polystyrene sulfonate and polyimide thin films were measured. However, the steady-state measurements are very sensitive to heat losses through convection, radiation, and conduction. Especially for transparent free-standing thin films with large surface area and measured at room temperature; where thermal radiation and convection can not be ignored and the thermal noise is comparable to the signal. So, steady-state IR thermography usually suffered from high measurement uncertainty. In addition, for both transient and steady-state IR thermography the knowledges of the sample absorption and the background IR radiation were necessary for the thermal conductivity calculation [19,20]. However, for transparent thin films with diffusing surface both the transmitted background IR radiation and the incident light absorption can hardly be accurately measured which in turn will reduce the measurement accuracy.
The approach we will present in this paper is an improved steady-state IR thermography method. Instead of using laser as the heat source, the thermal excitation was achieved by using optical projection in visible spectrum. Thus, the interaction between film and laser, such as spontaneous or stimulated emission, was avoided. And 95% optical power intensity uniformity was obtained. The sample was put in a vacuum chamber to prevent the heat convection and sample surface-air conduction. Through adjusting the optical intensity of the projection, the temperature rise of the sample was controlled. So, a linear approximation of the thermal radiation to the surface temperature was valid. The thermal image of the sample was recorded by an infrared (IR) camera with a spatial resolution of 25 µm. To obtain the in-plane thermal conductivity and infrared emissivity a new data processing method was proposed. Two thermal images at different optical heat intensities were detected and their thermal radiation intensity difference was calculated. Based on the analytical solution of a simplified one-dimensional heat equation, infrared emissivity, heat flux density and in-plane thermal conductivity were obtained by data fitting of the intensity difference. A linear relation of optical heat power and heat flux density was used. Neither the background thermal radiation nor the optical absorption of the sample was required in our measurement. As a demonstration, we measured polyimide films with the thickness from 500 nm to 1400 nm. To reduce the thermal noise 50 measured thermal images were averaged and the wavelet denoise technique was applied. The thickness dependence of the infrared emissivity was observed, which fits with Beer-Lambert's absorption law.
2. Measurement theory
The schematic of the measurement setup is shown in Fig. 1. The samples are clamped into a vacuum chamber, which is used to reduce the film thermal loss through heat convection and air-surface conduction. The vacuum chamber has two optical windows. The visible window is a silica window with high transmission in the wavelength range of 400 to 750 nm and low transmission in infrared. It allows the low loss passing of the optical heat light and blocks the infrared radiation at the same time. The infrared window is made by germanium and coated for high transmission in detected Infrared range. The transmitted thermal radiation of the heated film is detected by an IR camera.
Fig. 1. Experimental setup: A projected optical pattern illuminates the backside of a thin film sample. The induced thermal distribution is visualized by an IR camera.
The projector generates a rectangle shape gray scale pattern with uniform gray value. The output of the projector passes through the visible window and is imaged onto the film sample to obtain optical heating. The projection intensity of the pattern can be varied by the gray value and brightness setting. Hence, the temperature rise of the film is controlled. The surface thermal radiation of the sample is detected by an IR camera system equipped with a focal plane array. For the simultaneous deduce of the in-plane thermal conductivity and infrared emissivity the film sample edge temperature is measured by a thermal resistor and fed back to a multimeter.
The choice of the rectangular heat pattern was under the consideration of data processing. As shown in Fig. 2, in order to define the coordinate origin in our model, we needed to locate the heat pattern edge of the thermal image precisely. We chose three rows and calculated the difference of temperature of the adjacent pixels (T(p + 1)-T(p), p is the pixel number). At the pattern edge, the difference of temperature would experience a maximum. So, the mean value of the three pixel numbers of the differential maxima was taken as the edge of the rectangular pattern. When we chose the data of a row the origin was the point, where the edge crossed the row.
In addition, when the in-plan thermal conductivity of the sample was anisotropic, the rectangular pattern could be adjusted to fit the different thermal diffusion length in two perpendicular directions.
When the self-suspended thin film has large surface area and small thickness, the temperature difference along the sample thickness direction can be neglected. In steady-state condition, a two-dimensional heat transfer equation is used to describe the sample surface temperature distribution
Considering high vacuum degree condition the heat conduction between the film sample and the air is not concluded. In Eq. (1), k is the in-plane thermal conductivity, d is the thickness of the sample, ε is the infrared emissivity of the thin film, σ is the Stefan-Boltzmann coefficient, h is the convective heat transfer coefficient. T(x,y) is the sample temperature distribution on the surface and T0 is the initial temperature which is the ambient temperature. Q(x,y) is the heat field distribution.
To realize thermophysical parameters estimation an analytical solution of Eq. (1) is desired. Figure 3 shows a typical temperature distribution in steady-state. We find that near Y = 0 range the temperature gradient along Y-axis is small.
If we define the measurement area to -0.15 mm < Y < 0.15 mm, Eq. (1) can be reduced to one dimension
Due to the geometric symmetry, only the positive part of the X-axis is considered. Moreover, if the measurement area is further confined to the range shown in Fig. 4 (the coordinate origin is shifted to the boundary of the heat load area to build a new x-y coordinate system), then Eq. (2) becomes to a homogeneous differential equation
And the heating will be described by a boundary condition at x = 0. When the temperature rise is small (T(x,y)≈T0), the thermal radiation term can be simplified by
Defining temperature rise by
and inserting Eqs. (4) and (5) into Eq. (3), a linear homogeneous differential equation is obtainedTo validate the model, we carried out a numerical simulation based on a 2D finite-element model. As an example, the temperature distribution of the 2D finite-element model is shown in Fig. 5. The temperature distribution along x-axis at y = 0 is compared with the calculated results with Eq. (9), the comparison is presented in Fig. 6. One can see that they agree well with each other.
Hence, the thermal radiation intensity of the sample in steady-state can be calculated by
When the thermal radiation of the sample is collected by an IR camera, the detected radiation intensity is
where ηt is the transmittance of the measurement system in detective wavelength range and Eb(x) is the background thermal radiation intensity.If two thermal radiation intensity distributions are detected at different heat powers and the heat power change (from P1 to P2) is small, the background thermal radiation intensity can be considered to be equal. Using Eq. (11), the thermal radiation intensity difference of the two measurements are
With the known ηt, M and T0, three coefficients of ε, $\frac{{{q_2}}}{k}$ and $\sqrt \alpha $ can be obtained by fitting the Eq. (14) to the corresponding measurement data. When the vacuum degree inside the chamber is high enough, the air convection can be neglected (h = 0). The in-plane thermal conductivity, heat flux density and infrared emissivity can be obtained simultaneously.
The most important advantage of our method is that the measurement of both the optical absorption of the sample and the background thermal radiation are not required. For a certain thin film sample the heat power ratio (M) can be obtained by measuring the optical heat powers.
3. Experiments
3.1 Measurement setup
The photo of the measurement setup is shown in Fig. 7. The sample was clamped into a vacuum chamber. In all of our experiments, the vacuum degree was kept as 1.5×10−4 Pa. The vacuum degree was determined by the spatial thermal diffusion lengths measured under different cavity pressures. It was found that when the vacuum degree was higher than 5×10−4 Pa the diffusion length did not change anymore. That meant the influence of heat convection (h) could be neglected when the vacuum degree was higher than 5×10−4 Pa.
A projector (C1915 by Epson) with pixel number of 1024×768, pixel size of 14 µm, and maximal luminous flux of 4000 lm was used to generate a heat pattern. The output of the projector passed through the visible window and was imaged onto the thin film sample with 1:1 scale. On the film the optical heat pattern size was 2 mm×4 mm. The intensity uniformity of the projected pattern was 95%. The image gray value of the projected gray scale pattern was fixed to 255 and the optical heat power was varied by the changing the projector brightness. Measured by a calibrated power meter (Thorlabs. PM3), the optical heat power of the projector could be tuned from 69 mW to 107.5 mW. During the whole tuning range, the optical spectrum was unchanged.
Under steady-state condition, the thermal radiation of the sample was detected by an IR camera (VCHD head 680 by Infratec.) with an equivalent blackbody temperature calculation function. The camera was equipped with a focal plane array that consists of 640×480 pixels with the size of 25 µm. The spectral detection range was from 7.5 to 14.0 µm and the frame rate was 60 Hz. The noise equivalent temperature resolution of the IR camera was 30 mK. By using a lens with 1× magnification, a spatial resolution of 25 µm was reached. The acquired thermal images were transported through WLAN port to a personal computer for data analysis. To calculate the thermal conductivity and infrared emissivity using Eq. (14) the film edge temperature (T0) was required, which was detected by a thermal resistor (PT100, Class A) and fed back to a multimeter.
3.2 Setup calibration
To reduce the system error both the IR camera and the thermal resistor have to be calibrated. The calibration of the IR camera was made by the equivalent blackbody temperature measurement of a standard point blackbody. It determined the measurement accuracy of the absolute detected thermal radiation intensity in units of W/m2. The equivalent blackbody temperature from the IR camera was acquired when the point blackbody temperature was set to different values. During the calibration the infrared emissivity of the IR camera was set to 1. A linear fitting yielded a calibration factor a = TIR/TBb=1.009. This calibration factor was used to calculate the detected thermal radiation intensity $E = \sigma \cdot {\left( {\frac{{{T_{IR}}}}{a}} \right)^4}$. The infrared transmittance of the IR camera system was included by this calibration.
The PT100 was calibrated by the resistance measurement of a thermostatic heating plate set at different temperature and the ice water mixture. The linear function $R(\Omega ) ={-} 7.915 + 0.395 \cdot T(K)$ was used to calculate the film edge temperature (initial/ambient temperature).
3.3 Preparation of self-suspended thin film samples
Self-suspended polyimide (PI) film samples with different thicknesses were prepared. Liquid Poly (amic acid) (PAA) solution was used as PI precursor. N-Methyl pyrrolidone (NMP) was used to dilute PAA. To fabricate PI films with lower than 1.2 µm thickness the PAA with 300 cp viscosity was used. The high viscosity PAA with 600 cp was used to fabricate thick PI film. 2-inch one-sided polished thermal oxide wafers (SiO2 300 nm/Si 500 µm) were used as substrates. SiO2 sacrificial layer was wet-etch by Hydrofluoride acid (40%, Macklin) to make the film self-suspending. The photo of the prepared PI thin film sample is shown in Fig. 8.
To satisfy the assumption that the sample radius was much larger than the temperature diffusion length. In our case, the temperature diffusion length of the PI film was estimated. The thermal conductivity of polymer was from 0.1 Wm−1K−1 to 2 m−1K−1. When the initial temperature was 300 K and the infrared emissivity was from 0.1 to 0.8, then the diffusion length was shorter than 1.12 mm. So, the sample radius should be larger than 5 mm. To satisfy the requirement, PI samples with 65 mm diameter were used in our experiments. If the thermal conductivity range was unknown, the temperature diffusion length had to be measured.
4. Results
Figure 9(a) shows a thermal image recorded by IR camera. The thickness of the film sample was 504 nm, which was spin-coated at the speed of 3000 rpm. The equivalent blackbody temperature distribution in x-direction within the measurement area was shown in Fig. 9(b). In the measurement the infrared emissivity of the IR camera was set to 1. In x-axis the x = 0 position was decided by the temperature gradient minimal point.
Fig. 9. The measured data, (a) thermal image, (b) equivalent blackbody temperature distribution in x-direction with y = 0.
To obtain a pair of thermal images the optical heat powers (P1 and P2) of the projector were set to 73.0 mW and 93 mW, which corresponded to a M value of 1.28. The measured equivalent blackbody temperature distributions under the two heat powers are shown in Fig. 10.
Fig. 10. Equivalent blackbody temperature distribution in x-direction with y = 0 under two different optical heating powers.
The transmission of the infrared window of the vacuum chamber was 0.93 in the spectral range of 7.5 to 14.0 µm. Considering the calibration results the fitted data was obtained by
The data from 50 measurements were averaged and the wavelet denoise technique [21,22] was used to reduce the thermal noise. The denoised data was presented in Fig. 11 by blue scatters. During the nonlinear curve fitting, ηt=1, M = 1.28 and T0=311.45 K were used. The fitting curve was shown in Fig. 10 by orange line.
The fitted parameters were ε=0.07 (infrared emissivity), b=$\frac{{{q_2}}}{k}$ = 6.44×10−4 and c=$\sqrt \alpha $=3267; together with h = 0 and T0=311.45 K, the calculated in-plane thermal conductivity of the film sample was 0.18 Wm−1K−1. From Fig. 11 we can see that the fitting results depends strongly on the sharply decay part of the curve. That means that high detective spatial resolution will benefit the reduction of the fitting uncertainty. This is the reason for choosing 25 µm spatial resolution in our experiments. We believe the fitting uncertainty can be improved with higher spatial resolution by using lens system with higher magnification or IR camera with smaller pixel size.
Using the same procedure, the infrared emissivity and the in-plane thermal conductivity of the film samples with different thicknesses were measured. The results are listed in Table 1 and plotted in Fig. 12. We believe that the increasing infrared emissivity with the sample thickness was an evidence of the Beer-Lambert's absorption law in the detected IR wavelength range. In addition, the in-plane thermal conductivity difference between the 504 nm thick film sample and other three thicker samples might be induced by the low signal to noise ratio because of its low infrared emissivity.
Fig. 12. The infrared emissivity and in-plane thermal conductivity for the PI film samples with different thicknesses.
Table 1. The infrared emissivity and the in-plane thermal conductivity for the PI film samples with different thicknesses
To get some knowledge about the measurement uncertainty each sample was measured five times. Type A uncertainty is expressed as
where n is the total measurement times, xi is the measured value of the ith measurement and $\bar x $ is the mean value from n times measurements. The uncertainties for each sample were calculated and the results are shown in Fig. 13. For the infrared emissivity the measurement uncertainty was from 0.04 to 0.10, and for the in-plane thermal conductivity the measurement uncertainty was in the range of 0.09 to 0.13.According to literature, although the thermal conductivity varies when the concrete composition is different, the value is in the range of 0.19 Wm−1K−1 to 0.42 Wm−1K−1 [19,23]. Our measurement results listed in Table 1 located in this range. It is also a verification of our measurements.
5. Conclusion
A method for measuring the thermophysical properties of self-suspended thin film samples under ambient conditions was presented. The procedure was based on a noncontact thermal analysis using a steady-state micro-thermography system. The first time suggested and experimentally verified evaluation procedure permitted the determination of both the infrared emissivity and the in-plane thermal conductivity in a single measurement. A self-suspended 504 nm thick PI sample with as low as 0.07 infrared emissivity and 0.18 Wm−1K−1 in-plane thermal conductivity was successfully measured at room temperature. The spatial resolution and signal to noise ratio was crucial for this measurement technique. The measurement uncertainty was about 10%. This uncertainty results primarily from the background thermal radiation fluctuation and detector noise. The procedure is suitable for analyzing materials with a wide range of thermal properties.
It is expected that a lower uncertainty can be reached by increasing the spatial resolution and signal-to-noise ratio. Furthermore, a post-correction will benefit the accuracy improvement for the materials with low infrared emissivity, where high surface temperature has to be built to generate detectable infrared signal. We believe that besides self-suspended thin films, the proposed method can also be used to measure the thermophysical properties of single-layer films, composite films and multilayer films as long as the total thickness of the film is in the range of nanometers to several micrometers.
Funding
National Natural Science Foundation of China (61704166, 61741502, 61835001, 61875011).
Acknowledgments
Authors are thankful to the Analysis & Testing Center and Micro-fabrication Center in Beijing Institute of Technology for providing the fabrication and characterization facility for this study.
Disclosures
The authors declare no conflicts of interest.
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