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Thermodynamics characteristics of MEMS infrared thin film

Chang Xu, Dan Liu, Lang Zhou, Qingfeng Shi, Yanze Gao, Xin Wang, and Zhuo Li

Open Access Open Access

Abstract

This work demonstrates a micro electro mechanical system (MEMS) technology based infrared thin film, which converts absorbed visible light energy into infrared radiation. The principle of the film and the experiment for studying its thermodynamic characteristics are presented. The radiation spectrum of the thin film conforms to the characteristics of blackbody spectrum, and the average emissivity in infrared band is 0.638. The thermal diffusion distance decreases with the decrease of substrate thickness. Moreover, the fabrication of periodic pixel arrays on substrates can effectively reduce the thermal conductivity. The thermal conductivity of the pixel inscribed thin film with a substrate thickness of 360nm is 0.1W/m·K. The temporal constant decreases with the decrease of substrate thickness. The time constant of the film with a substrate thickness of 360nm is 2.72ms while the working temperature is 5 degrees Celsius. These characteristics indicate that the infrared thin film has a promising application prospect in infrared scene projection.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Infrared scene projection is a technology that simulates the radiation characteristics of infrared scene under laboratory conditions. It transforms the input scene image data into infrared physical radiation and projects to infrared detectors through optical system, provides infrared scene radiation for the development and testing of the infrared imaging system, is a key technology in infrared imaging HWIL (hardware-in-the-loop) simulation [1]. Infrared scene projection technology can be divided into direct radiation type and modulated radiation type according radiation projection mode. The direct radiation infrared scene projection technology does not need additional infrared light source, can directly project intensity distribution adjustable infrared radiation by the emitter array in device. Typical direct radiation devices include resistor array, laser diode array, MEMS infrared thin film, etc. [2–5]. The modulated radiation type projects intensity distribution adjustable infrared radiation by modulating the infrared radiation source. Typical modulated radiation devices include digital micro-mirror array (DMD), IR liquid crystal light valve, and MEMS optical attenuator array [6–8]. The production of resistor array requires more complicated production process, which makes it difficult to achieve large arrays. The infrared radiation of resistor array is concentrated in the high temperature region, and the spatial resolution is limited. Due to the limitation of pixel size, DMD has low resolution and contrast in long-wave infrared band. IR liquid crystal light valve has limitations in frame rate, temperature range and dynamic range. Laser diode is not ideal in spatial uniformity and imaging quality. MEMS optical attenuator array has the limitations of small array size and low frame rate [9–11]. With the advantages of large array size and wide band coverage, the MEMS infrared thin film can meet the requirements of various infrared scene projection.

The MEMS infrared thin film is an optical-thermal-optical converter based on thermal conduction theory. The film converts the absorbed incident light energy into the temperature field distribution, and emit infrared radiation field. Therefore, the thermodynamic characteristics of the film affect the spectral range, spatial resolution and temporal performance of infrared scene projection.

In this work, the radiation, spatial and temporal characteristics of the infrared thin film are studied. The radiation spectrum and emissivity of the film are analyzed by comparing with the standard blackbody radiation spectrum. The thermal conductivity of the film is studied by measuring the linear diffusion function. The temporal constant of the film is analyzed by measuring the impulse response.

2. Principle of MEMS infrared thin film

2.1 Structure of infrared thin film

The MEMS infrared thin film is a large size (3inch) flexible composite film. The substrate is polyimide (PI) macromolecule materials with submicron thickness, which has positive thermal stability, mechanical and optical properties [12,13]. Periodically arranged pixels are fabricated on substrate with the MEMS technology. The pixel is covered with a layer of black material with high absorptivity and low thermal mass. Cr is used as the black material in this work. The structure of the film and pixel is presented in Fig. 1. When the film is irradiated by visible light, its pixels absorb visible light energy and heat up to produce infrared radiation. If the visible energy has spatial distribution, each pixel of the film absorbs different light energy, which generates the temperature distribution corresponding to the incident light and emits infrared radiation scene.

 figure: Fig. 1.

Fig. 1. Schematic diagram of infrared thin film and pixel.

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2.2 Thermodynamic principle of infrared thin film

The film converts absorbed visible light energy into heat energy, and exchanges heat with the environment through three ways: heat conduction, heat convection and heat radiation. The thermodynamic behavior of the film can be described as:

$$d\rho {c_p}\frac{{\partial T}}{{\partial t}} = Q - kd\frac{{{\partial ^2}T}}{{\partial {{\vec{{\mathbf r}}}^2}}} - h({T - {T_\textrm{A}}} )- \varepsilon \sigma ({{T^4} - {T_\textrm{A}}^4} )$$
where ρ is the thin film density, cp is the specific heat capacity of the thin film, T is the thin film temperature, Q is the heat flux absorbed by the thin film, k is the thermal conductivity of the thin film, d is the thin film thickness, h is the heat transfer coefficient of the thin film, ɛ is the thin film emissivity, σ is the Stefan-Boltzmann constant of 5.67 × 10−8W/(m2·K4), and TA is the ambient temperature [14]. The second, third and fourth terms on the right side of the Eq. (1) represent the effects of conduction, convection and radiation on the temperature.

Suppose the incident light is a linear light source (a directional rectangular light source with infinitesimal width). When the thin film thickness d is small enough, it can be considered that there is no temperature gradient on the thickness direction, and the Eq. (1) can be simplified to one-dimensional heat conduction equation. The thin film works in a vacuum environment, the influence of thermal convection can be neglected. The thermodynamic behavior of the thin film can be described as:

$$\begin{array}{l} d\rho {c_p}\frac{{\partial T}}{{\partial t}} = q - kd\frac{{{\partial ^2}T}}{{\partial {x^2}}} - \varepsilon \sigma ({{T^4} - {T_\textrm{A}}^4} )\\ q = \frac{Q}{d}({x = 0} ),q = 0({x \ne 0} )\\ T = {T_\textrm{A}}({x = l} ),T = {T_\textrm{A}}({t = 0} )\end{array}$$
where q is the transverse propagation power density of the illumination on the thin film, and l is the radius of the film. Equation Eq. (2) indicates that the surface temperature of the thin film is related to the absorbed transverse heat flux density q, the ambient temperature TA, the thermal conductivity k, the surface emissivity ɛ and the thermal mass. The thermal mass includes thickness d, specific heat capacity cp and density p.

The steady state solution is used to analyze the thermal diffusion performance of the thin film [15,16]. The steady state heat balance at x distance from the illumination position of the light source is expressed as:

$$kd\frac{{{\partial ^2}{T_x}}}{{\partial {x^2}}} = \varepsilon \sigma ({T_x^4 - {T_\textrm{A}}^4} )$$
The solution of Eq. (3) can be described as:
$$\Delta {T_x} = \Delta {T_{x0}}{e^{ - \gamma |x |}}$$
where ΔTx is the temperature rise at x, ΔTx0 is the temperature rise at x = 0, and γ is the transverse thermal decay coefficient:
$$\gamma = 2\sqrt {\frac{{\varepsilon \sigma {T_A}^3}}{{kd}}}$$
Equation (5) indicates that the temperature of the thin film diffuses to the non-illumination region in the form of e-exponential decay. The thermal diffusion distance is related to the surface emissivity of the thin film ɛ, the thermal conductivity k, the thickness d and the ambient temperature TA.

The transient solution is used to analyze the temporal characteristics of the thin film. The relationship between the surface temperature at a certain position and time is presented as:

$$\Delta {T_t} = \Delta {T_{t0}}{e^{ - {\raise0.7ex\hbox{${({t - {t_0}} )}$} \!\mathord{\left/ {\vphantom {{({t - {t_0}} )} \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}}}$$
where ΔTt is the temperature rise at time t, ΔTt0 is the temperature rise where t = 0, and τ is the time factor:
$$\tau = \frac{{d\rho {c_p}}}{{4\sigma \varepsilon {T_A}^3}}$$
Equation (7) indicates that the temperature of the thin film varies with time in the form of e-exponential decay. The thermal attenuation time factor is related to the surface emissivity of the thin film ɛ, the ambient temperature TA and the thermal mass. When the thermal mass decreases, the thermal attenuation speed increases, the time constant decreases, and the time characteristic of the thin film is improved.

The infrared radiation spectrum of the thin film is blackbody spectrum, which conforms to the Planck’s blackbody radiation law, as presented in Fig. 2. Therefore, the radiation energy and peak position can be modified by the modulation of the incident light energy. And the radiation energy of the radiator in the sampling range of the detector can be simulated also.

 figure: Fig. 2.

Fig. 2. Radiation spectra of blackbodies with different temperatures.

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3. Thermodynamic characteristics

3.1 Experimental setup

The experimental setup for studying thermodynamic characteristics of the infrared thin film is presented in Fig. 3. The input light source is collimated and homogenized 532nm laser. Detectors include spectrometer, point source detector and thermography. PI or infrared thin film is fixed on the inner wall of the vacuum cavity, and the side wall of the cavity has a suction interface, which can be used to connect with the vacuumizing system. A refrigerating chamber is arranged at the back of the vacuum cavity, through which the coolant of the refrigeration system refrigerates the vacuum cavity.

 figure: Fig. 3.

Fig. 3. Experimental setup.

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Visible light is incident on the thin film through the optical window of the vacuum cavity, and the infrared radiation is radiated out through this window. The optical window is made of barium fluoride, which has high transmittance in visible and infrared waveband. The working temperature of the vacuum cavity is 278K, and the vacuum degree is 1 × 10−3Pa. The structure of the vacuum cavity is shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. Structure of vacuum cavity.

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3.2 Spectral characteristics

Omni-lambda 300 scanning grating spectrometer (wavelength response range 2-14µm) is used to measure the radiation spectrum of the infrared thin film in the range of 3-12µm wavelength. The radiation spectrum of the thin film at 383K is measured and compared with the theoretical radiation spectrum of the blackbody at 383K, as shown in Fig. 5. The difference is mainly reflected in the atmospheric absorption, including the strong absorption band of CO2 at 4.3µm, the weak absorption band of CO2 at 4.8µm, 5.2µm and 9.4µm, and the strong absorption band of water vapor at 3.2µm and 6.3µm.

 figure: Fig. 5.

Fig. 5. Radiation spectrum of infrared thin film at 383K.

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By adjusting the power of 532nm laser, the relationship between equivalent blackbody temperature of the thin film and incident light power density is measured by thermography is presented in Fig. 6. The result shows that the relationship between the thin film temperature and the incident light intensity exhibits linear distribution.

 figure: Fig. 6.

Fig. 6. Relationship between equivalent blackbody temperature of infrared thin film and incident light intensity.

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The transmittance of the thin film can be calculated by Eq. (8).

$$\varepsilon ({T_{\textrm{blackbody}}^4 - {T_\textrm{A}}^4} )\textrm{ = }({T_\textrm{S}^4 - {T_\textrm{A}}^4} )$$
where Ts is the apparent temperature of the thin film, Tblackbody is the equivalent standard blackbody temperature, TA is the ambient temperature. The radiation spectra of standard blackbody and infrared thin film at different temperatures are measured and matched to obtain the emissivity of the thin film. The result is presented in Fig. 7.

 figure: Fig. 7.

Fig. 7. (a) Spectrum matching of infrared thin film and blackbody in 3-5µm. (b) Spectrum matching of infrared thin film and blackbody in 8-12µm.

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The results demonstrate that the radiation spectrum of the infrared thin film covers 3-5µm and 8-12µm bands. In the 3-5µm band, the radiation spectrum of the infrared thin film with an apparent temperature of 473K matches the standard blackbody radiation spectrum with a physical temperature of 573K, thus the equivalent blackbody temperature of the thin film is 573K. According to Eq. (8), the average emissivity of the infrared thin film is 0.45 in 3-5µm band. In the 8-12µm band, the radiation spectrum of the thin film with an apparent temperature of 383K matches the standard blackbody radiation spectrum with a physical temperature of 423K. The average emissivity of the thin film in 8-12µm is calculated to be 0.59.

3.3 Thermal characteristics

According to Eq. (5), the thermal diffusivity of the thin film is affected by the emissivity, thickness and thermal conductivity of the substrate. For the same material, k and ɛ remain constant under the same condition. The thermal diffusion distance of the thin film can be modified by changing the substrate thickness. The thermal diffusion characteristics of PI substrates with different thickness and infrared thin film are experimentally studied. The average thicknesses of three PI substrates and one thin film measured by step profiler are presented in Table 1.

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Table 1. Average thicknesses of PIs and infrared thin film

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The homogenized 532nm laser is irradiated on the knife edge and imaged by an optical system to the surface of PI or infrared thin film fixed in the vacuum cavity. The thermal diffusion image of the knife edge is captured by infrared thermometer. The thermal diffusion curve can be obtained by collecting the temperature distribution of the thermal image. The thermal decay coefficients of PI-1, PI-2 and PI-3 are 1.61mm−1, 1.94mm−1 and 2.63mm−1, by fitting the measured thermal diffusion values with e-exponential function, as presented in Fig. 8. The thermal diffusion distance is defined as the distance diffused while the temperature drops from the maximum to 50% of the maximum. Then the thermal diffusion distances of PI-1, PI-2 and PI-3 are 425µm, 350µm and 250µm. The average emissivity of the substrate measured by spectrometer is 0.135, and the thermal conductivity is calculated to be between 0.2 and 0.4W/(m·K), which is consistent with the thermal conductivity of polyimide materials reported in [12].

 figure: Fig. 8.

Fig. 8. Thermal diffusion distances of PIs and infrared thin film.

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In addition to the influence of substrate thickness, the thermal diffusion distance of the thin film is also related to its thermal conductivity. The same method is used to measure the thin film with the thickness of 364nm, and the thermal diffusion curve is presented in Fig. 8. The transverse thermal decay coefficient of the thin film is 5.01mm−1, and the diffusion distance is 125µm. Compared with PI-3 with similar thickness, the thermal diffusivity of the thin film increases significantly, the thermal conductivity decreases to 0.1W/(m·K).

The results show that the thinner the PI substrate, the smaller the thermal diffusion distance. Fabrication of periodic pixels can effectively reduce the thermal conductivity, thereby reducing the thermal diffusion distance. The reduction of thermal diffusion distance can also reduce the thermal crosstalk between pixels and improve the spatial resolution of infrared scene.

3.4 Temporal characteristics

According to Eq. (7), the thermal decay coefficient of the infrared thin film is effected by the emittance and thermal mass. For the same material, the emissivity, heat capacity cp and density p remain constant under the same condition. The thermal decay time of the thin film can be changed by reducing the thickness and the thermal mass of substrate.

The thermal decay characteristics of thin films fabricated on PI substrates with different thickness are experimentally studied. The experiment system is presented in Fig. 2. An infrared point source detector is used to measure the radiation intensity varying with time. The modulated 532nm laser pulse is irradiated on the film fixed in the vacuum cavity. The temperature of the thin film rises rapidly and reaches the thermal equilibrium state while receiving the laser pulse energy. In this state, the temperature remains stable, while the maximum radiation intensity occurs. When the laser pulse intensity is 0, the thermal balance state is broken, the temperature of the thin film begins to decrease, and the radiation intensity decreases accordingly. The time constant is defined as the time takes for radiation intensity decreases from the maximum to e−1 of the maximum. The time constants of thin films with different substrate thicknesses (as presented in Table 1) are 6.56ms, 5.12ms and 2.72ms, by fitting the measured radiation intensity with e-exponential function, as shown in Fig. 9. The results show that the thinner the substrate, the higher the thermal decay rate and the smaller the time constant.

 figure: Fig. 9.

Fig. 9. Time constants of infrared thin films with different substrate thicknesses.

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In addition, the time characteristics of the infrared thin film are also affected by the vacuum cavity temperature. The time constant of the Infrared thin film-3 with refrigeration (working at 278K) is smaller than that without refrigeration (working at 293K). The results show that the supplemental heat rejecter is beneficial to reduce the time constant of the thin film.

4. Application research

Currently, the infrared thin film fabricated by the research team has the pixel size of 35µm×35µm, as presented in Fig. 10. In the view of above characteristics, the thin film can be used as the infrared radiation projection in dynamic infrared scene projection system.

 figure: Fig. 10.

Fig. 10. MEMS infrared thin film and pixels.

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The typical infrared scene projection system consists of image input system, infrared conversion system and projection system. The system structure is presented in Fig. 11.

 figure: Fig. 11.

Fig. 11. Structure of dynamic infrared scene projection system.

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The image input system includes image processing system and synchronizer. The infrared conversion system includes MEMS infrared thin film, vacuumizing system and refrigerating system. The synchronizer receives external sync signal and synchronizes the detector with the image input system, ensures the radiated IR image according to the frame frequency of the detection system. The image input system receives the infrared image data and generates the corresponding gray scale image. Then the gray scale image is projected to the infrared thin film through the optical system. The temperature of the thin film rises when the injected light energy is absorbed and the corresponding infrared radiation is formed. The projection system projects the infrared radiation into the pupil of the detection system and provides dynamic infrared scene for the detector under test.

The working waveband of the dynamic infrared scene projection system based on MEMS infrared thin film is 3-5µm and 8-12µm, the temperature range of infrared radiation is 278K-678K, the time constant is 2.7ms, and the gray scale is greater than 8 bits. The infrared images acquired by thermography are presented in Fig. 12.

 figure: Fig. 12.

Fig. 12. (a), (b) Input images. (c), (d) Infrared images projected by the infrared scene projection system.

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5. Conclusion

In conclusion, the radiation spectrum of the MEMS infrared thin film covers 3-12µm band. The emissivity in 3-5µm band is 0.45, and in 8-12µm band is 0.59. The thermal diffusion distance and temporal constant of the thin film decrease while the substrate thickness decreases. The temporal constant of the thin film with 345nm substrate thickness is 2.72ms in 278K vacuum cavity. By fabricating periodic pixels, the thermal conductivity of the thin film with 360nm can be reduced to 0.1W/(m·K). The results of the experiment indicate that the performance of the infrared thin film can be adjusted by changing the corresponding parameters. The research provide a theoretical and experimental basis for the optimization of the development of the MEMS infrared thin film. At present, the fabrication array size of the film can reach 1539×1539, and the infrared radiation temperature can cover 278K-678K. The dynamic infrared scene projection system based on the MEMS infrared thin film is applied in various hardware-in-loop simulations.

Funding

National Natural Science Foundation of China (61875011).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

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6. A. Khalifa and H. Aly, “Near-infrared video projection system based on digital micromirror devices and digital signal processors,” Opt. Eng. 54(12), 123102 (2015). [CrossRef]  

7. V. Marinove, C. H. Chi, Z. F. Tong, R. C. Liu, N. Berberova, S. H. Lin, E. Stoykova, and K. Y. Hsu, “Liquid crystal light valve operating at near infrared spectral range,” Opt. Quantum Electron. 48(4), 270 (2016). [CrossRef]  

8. X. D. Lv, W. W. Wei, J. Y. Zhang, J. L. Yang, and F. H. Yang, “IR scene Generator Based on MEMS VOA Array,” Aero Weap. 2016(2), 38–41 (2016).

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Figures (12)
Fig. 1.
Fig. 1. Schematic diagram of infrared thin film and pixel.

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Fig. 2.
Fig. 2. Radiation spectra of blackbodies with different temperatures.

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Fig. 3.
Fig. 3. Experimental setup.

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Fig. 4.
Fig. 4. Structure of vacuum cavity.

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Fig. 5.
Fig. 5. Radiation spectrum of infrared thin film at 383K.

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Fig. 6.
Fig. 6. Relationship between equivalent blackbody temperature of infrared thin film and incident light intensity.

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Fig. 7.
Fig. 7. (a) Spectrum matching of infrared thin film and blackbody in 3-5µm. (b) Spectrum matching of infrared thin film and blackbody in 8-12µm.

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Fig. 8.
Fig. 8. Thermal diffusion distances of PIs and infrared thin film.

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Fig. 9.
Fig. 9. Time constants of infrared thin films with different substrate thicknesses.

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Fig. 10.
Fig. 10. MEMS infrared thin film and pixels.

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Fig. 11.
Fig. 11. Structure of dynamic infrared scene projection system.

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Fig. 12.
Fig. 12. (a), (b) Input images. (c), (d) Infrared images projected by the infrared scene projection system.

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Tables (1)

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Table 1. Average thicknesses of PIs and infrared thin film

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

d ρ c p ∂ T ∂ t = Q − k d ∂ 2 T ∂ r → 2 − h ( T − T A ) − ε σ ( T 4 − T A 4 )
d ρ c p ∂ T ∂ t = q − k d ∂ 2 T ∂ x 2 − ε σ ( T 4 − T A 4 ) q = Q d ( x = 0 ) , q = 0 ( x ≠ 0 ) T = T A ( x = l ) , T = T A ( t = 0 )
k d ∂ 2 T x ∂ x 2 = ε σ ( T x 4 − T A 4 )
Δ T x = Δ T x 0 e − γ | x |
γ = 2 ε σ T A 3 k d
Δ T t = Δ T t 0 e − ( t − t 0 ) / ( t − t 0 ) τ τ
τ = d ρ c p 4 σ ε T A 3
ε ( T blackbody 4 − T A 4 )  =  ( T S 4 − T A 4 )
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