Abstract

We present an accurate approach to predict the residual stress in a multilayered mid-infrared long-wave pass filter (MIR-LWPF) by using interfacial stress measurements. Magnesium fluoride (MgF2) and zinc sulfide (ZnS) thin films were used to fabricate 7-layer (MgF2/ZnS)3/MgF2 MIR-LWPF devices by electron-beam evaporation with ion-assisted deposition technique. The interfacial stress between the high-index of ZnS and low-index of MgF2 thin film materials was obtained from the residual stress measurements based on Twyman-Green interferometer and fast Fourier transformation (FFT) method. The modified Ennos formula was used to estimate the residual stress in the (MgF2/ZnS)3/MgF2 multilayered thin films. The difference between the predicted stress value and the measured value is 28 MPa by the proposed method. In the MIR-LWPF design of (MgF2/ZnS)3/MgF2 multilayer structure, the optical transmittance at a near-infrared wavelength of 1.0 µm to 2.5 µm is less than 10%, and the transmittance at a mid-infrared wavelength of 2.5 µm to 7.5 µm is greater than 93%. The proposed method can accurately evaluate and predict residual stress in fabricating mid-infrared long-wave pass filter device which possesses low residual stress as well as lower surface roughness.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In recent years, the demand for infrared optical interference coatings has been increasing, such as in night vision, thermal tracking systems, gas sensing and other applications [1]. The ideal durable infrared anti-reflection coatings require not only low reflectivity in specific infrared bands, but also low scattering and low residual stress. Unfortunately, it is difficult to obtain an excellent infrared anti-reflection coating (ARC) because it is usually composed of two or more multilayer materials during thin film deposition. Generally, the residual stress in a multilayer film stack is not easy to control and to predict accurately. If the residual stress is too large, the film layer will peel off or crack to reduce its performance. Some complex multilayer designs require a total film thickness of up to 10 µm, so they accumulate large mechanical stresses and threaten the durability of the thin films [2]. Residual stress in thin films plays an important role, especially in multilayered thin film deposition. The total residual stress in a multilayered thin film is the contributions of film stresses from each single layer and from interfaces.

Infrared multilayer coatings always use two kinds of high refractive index and low refractive index film materials [3]. Kumar et al. [4] reported that the use of Si/SiO2 multilayer coating in the form of a multicavity Fabry-Perot and long-wave pass filters, in the near-IR region from 1.2 to 2.0 µm. The optical properties remained unchanged, indicating that the filters have a high degree of stability with respect to adverse environmental conditions. However, the evolution details of the residual stresses in multilayer films varying with single layer thickness and microstructure with interfacial stress are not revealed for infrared multilayer coatings.

In this study, magnesium fluoride (MgF2) and zinc sulfide (ZnS) were used to fabricate mid-infrared long-wave pass filter (MIR-LWPF). MgF2 is commonly used as a low refractive index, but the growth microstructure is mostly columnar and contains a large void volume. When the thin film layer is exposed to air, water vapor can occupy the void volume. Under low-energy deposition processes, such as electron-beam or thermal evaporation, the grain size of the columnar structure is large [4]. Increasing the bombardment energy by using ion-assisted deposition or a sputtering technique can reduce the columnar growth size [5]. The columnar structure also exhibits high tensile stress, and thick magnesium fluoride film layers can be used to release compressive stress in multilayer thin films [6].

ZnS is one of the high refractive index materials commonly used in infrared coatings. The ZnS has low optical scattering in the 3-5 µm window and is an excellent mid-infrared material with extremely low absorption [7]. It exhibits compressive stress, which can compensate for the total residual stress of the entire multilayer thin film design [8]. The coating substrates used in thermal imaging systems are mostly germanium or silicon. Germanium has a high transmittance in the 8-12 µm band and has been widely used in the far-infrared band. Silicon is often used in the wavelength range of 3–5 µm. The layer number, film thickness and production cost of the optical interference coatings in the far-infrared band are quite high. The wavelength of 3–5 µm area is an important window in the infrared band, and it has important application significance in the military [9]. In this band, however, less work has been made to fabricate mid-infrared long-wave pass filter deposited on a B270 glass substrate.

Generally, a long-wave pass filter is used to transmit or reflect light for a specific wavelength range. Reflective long-wave pass filters are mainly produced by the thin film interference principle in optical coatings. The long-wave pass filter design needs to increase the transmittance of the passband while blocking visible light, so the film thickness and number of film layers will increase. The deposition of thin films on substrates is usually inherently associated with the development of residual stresses [10]. The residual stress in multilayer coatings is also affected by the number of layers and film thickness. Residual stress is one of major factors to determine the thin-film device performance. Large residual stresses can cause thin film to crack. However, there has been far less research conducted on the residual stresses prediction model for optical thin film coatings. In the present work, we have proposed an experimental analysis approach to predict the residual stresses in fabricating mid-infrared long-wave-pass filter (MIR-LWPF) by using a modified Ennos formula with interfacial stress measurements. Finally, the predicted stress value is compared with the measured value. The proposed residual stresses prediction model can help improve the optical performance of multilayer thin film coatings.

2. Experimental method

The thin film design of optical long-wave pass filters uses the Essential Macleod optical design software [11]. The reference wavelength is 4.0 µm, the initial design is (0.5LH 0.5L)3, and the design specification demands that the transmittance in the range of 3-5 µm must be greater than 95%. The multilayer design can meet specifications after the film thickness is optimized by the Essential Macleod optical design software. A 7-layer thin film design, composed of ZnS and MgF2, with a total film thickness of 2514.32 nm, is shown in Table 1.

Tables Icon

Table 1. The design of mid-infrared long-wave pass filter (MIR-LWPF).

The thin film deposition was performed by using the Showa Shinku dual electron-gun evaporation system. The equipment is described as follows: The vacuum system consists of an oil rotary pump and a mechanical booster pump for rough evacuation and a diffusion pump (DP) for fine evacuation. The helium cold trap captures water vapor in the form of helium condensation in the air compressor to help improve the efficiency of the evacuation rate. The highest vacuum value of the coating system can reach 2.7×10−4 Pa. During the coating process, the pressure was set at 1×10−3 Pa. The gases used in the process were argon (99.999%) and oxygen (99.999%). The maximum output power of the electron gun was 10 kW, the voltage was 10 kV and the current was 1 A. The anode current of the ion-assisted deposition ion source was 0.5–10 A, the anode voltage was 80 - 300 V, and the ion energy was 50-200 eV. Quartz monitoring and optical monitoring were used to control the film’s thickness. The quartz monitoring instrument uses a 5 MHz quartz crystal oscillator. The optical monitoring system used a spectrometer with a wavelength range of 360 nm to 1000 nm and to measure the change in reflectance when the film was deposited on a B270 glass substrate. The extreme point of the reflectivity curves was used to stop the layer deposition.

For the residual stress measurement, a Twyman-Green interferometer combined with a fast Fourier transform (FFT) and MATLAB software program were used to determine the radius of the curvature of the substrate before and after thin film coating. The residual stress value of thin films was obtained from the change in the radius of the curvature. In general, the residual stress in thin films can be determined by using the modified Stoney’s formula [12,13].

$$\sigma = \frac{{{E_s} \cdot t_s^2}}{{6(1 - {\nu _s}){t_f}}}(\frac{1}{{{R_2}}} - \frac{1}{{{R_1}}}),$$
where σ is the residual stress in the thin film; R1 and R2 are the radius of curvature before and after thin-film is deposited on the substrate. Es=71.5 GPa and νs=0.219 are the Young’s modulus and the Poisson’s ratio of the B270 substrate, respectively; ts is the thickness of the substrate and tf (tf << ts) is the film thickness.

A home-made Linnik microscopic interferometer combined with FFT method [14] and a digital Gaussian filter were used to measure the surface roughness of the thin films. First, the height variation of the film surface is obtained by FFT, then, the cutoff wavelength of the signal is defined by a digital Gaussian filter, and the high-frequency roughness signal is separated from the low-frequency surface contour. Finally, the 3D surface contour of the film can be reconstructed, and the surface roughness is calculated by the numerical analysis method [15,16]. For the measurement of mid-infrared transmittance, a Fourier transform infrared spectrometer (FTIR) is used. The manufacturer is Perkin Elmer Frontier, the wave number range is 650 cm−1 to 5000 cm−1, and the resolution can reach 0.008 cm−1. It is mainly composed of a Michelson interferometer and detector, which has high accuracy and fast measurement. For the UV/visible/near-infrared light transmission measurement, a JASCO V770 spectrometer with a wavelength range of 190–2700 nm was used. The spectroscopic ellipsometer used in the experiment was produced by the J. A. Woolam Company, and its model was M2000-UI. The wavelength range is measured from 167 nm to 1800nm, and the incident angle can be adjusted from 45° to 90°. By measuring the amplitude (Psi) and phase (Delta) of the polarized light and using the physical model to fit the data, we can find the optical constants, such as the film thickness, refractive index and extinction coefficient of the thin film.

In this work, we focus on the residual stress and interfacial stress evaluation in multilayer thin film filters. The residual stress estimation in multilayer thin films is helpful for internal stress control. In general, residual stress estimation requires a suitable model. This can help one understand the level of residual stress in multilayer structures. Ennos [17] proposed a simple multi-layer stress formula, which means that the residual stress in multilayer thin films can be obtained by weighting the average residual stress in a single-layer film. The Ennos formula is expressed as follows:

$${\mathrm{\sigma }_{\textrm{avg}}} = \mathop \sum \nolimits_{\textrm{i} = 1}^{\textrm{n} = \infty } \frac{{{\mathrm{\sigma }_{\textrm{Hi}}}{\textrm{t}_{\textrm{Hi}}} + {\mathrm{\sigma }_{\textrm{Li}}}{\textrm{t}_{\textrm{Li}}}}}{{{\textrm{t}_{\textrm{Hi}}} + {\textrm{t}_{\textrm{Li}}}}},$$
where σavg is the average residual stress of the multilayer film, σHi and σLi are the residual stress values of the high and low refractive index thin films, and tHi and tLi are the film thickness values of the high and low refractive index thin films.

We also use Spaepen's method [18] to evaluate the interfacial stress. It is assumed that the multilayer thin film structure is composed of two kinds of thin film materials: H is a high-index thin film and L is a low-refractive-index thin film. It should be noted that the residual stress of both thin film materials can be a tensile or compressive stress. This is determined by an optical interferometer measurement. Once the H thin film material is deposited on the substrate, the bilayer structure of the L material is deposited on the H material. In other words, the surface of the H material is covered by the L material. This means that the surface of the H material disappears, and then, the surface of the L material is formed, and an HL interface is formed with the H material. In this way, a four-layer film is obtained by the LHLH film stack. Figure 1 illustrates a common design of a four-layer film stack. fi is the force per unit width (w) in the i-th layer. fHL and fLH represent the interfacial force per unit width in HL-layer and LH-layer film stacks. Assuming that fHL is not equal to fLH. The change in interfacial force per unit width is defined as the one-dimensional interfacial stress. The measured deflection can be converted into a force per unit width.

 

Fig. 1. Schematic diagram of a four-layer film stack (a) HLHL; (b) LHLH structures.

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Considering a four-layer film stack of HLHL structure, the net interface force per unit length, as shown in Fig. 1(a), in different film stacks can be expressed as

$$\; \delta {\left( {\frac{f}{W}} \right)_{HL}} ={-} {f_H} - {f_L} + {f_{HL,}}$$
$$\delta {\left( {\frac{f}{W}} \right)_{HLH}} ={-} 2{f_H} - {f_L} + {f_{HL}} + {f_{LH,}}$$
$$\delta {\left( {\frac{f}{W}} \right)_{HLHL}} ={-} 2{f_H} - 2{f_L} + 2{f_{HL}} + {f_{LH,}}$$

By subtracting the force per unit length of the four-layer film and the bilayer film, the LH interface stress can be obtained as follows:

$$\; {f_{LH}} = \delta {\left( {\frac{f}{W}} \right)_{HLHL}} - 2\delta {\left( {\frac{f}{W}} \right)_{HL,}}$$
where fLH is the interfacial stress of the low refractive index material deposited on the high refractive index material. Similarly, fHL is the interfacial stress of the high refractive index material deposited on the low refractive index material, as shown in Fig. 1(b). The HL interface stress is given by
$${f_{HL}} = \delta {\left( {\frac{f}{W}} \right)_{LHLH}} - 2\delta {\left( {\frac{f}{W}} \right)_{LH,}}$$
In these formulas, the positive or negative sign of fH and fL is determined by the tensile or compressive stress of the H-layer and L-layer films. If both thin film layers are known to be compressive stress, according to the static force balance, fHL must be a positive tensile stress.

Since the Ennos formula is not complete, and the influence of interface stress on the multilayer film stress is not considered. An accurate approach was proposed to modify the Ennos formulae by including the interface stress components in the computation of total film stress. Therefore, residual stress in multilayered thin films includes the interface stress and the number of interfaces in addition to the residual stress of the single layer film. fHL and fLH, two interface stresses, are multiplied by the number of interfaces and added to the Ennos formula as a correction term, because fHL and fLH have a different number of interfaces when the number of multilayer thin films is odd or even, so the number of layers should be considered. We proposed the modified formulas as shown below:

For a thin-film stack with an odd number of thin films:

$$\begin{aligned}{\mathrm{\sigma}}_{1,3, \ldots 2{\textrm n} + 1} &= \displaystyle{{{\mathrm{\sigma}}_{f1}\cdot t_{f1} + {\mathrm{\sigma}}_{f2}\cdot t_{f2} + \ldots + {\mathrm{\sigma}}_{fn}\cdot t_{fn}} \over {t_{f1} + t_{f2} + \ldots + t_{fn}}} + \displaystyle{{\left( {\displaystyle{{n-1} \over 2}} \right)f_{HL} + \left( {\displaystyle{{n-1} \over 2}} \right)f_{LH}} \over {2\left( {t_{f1} + t_{f2} + \ldots + t_{fn}} \right)}}\\ & = \displaystyle{{\mathop \sum \nolimits_i^n {\mathrm{\sigma}}_{fi}\cdot t_{fi}} \over {\mathop \sum \nolimits_i^n t_{fi}}} + \displaystyle{{\left( {\displaystyle{{n-1} \over 2}} \right)f_{{\textrm {HL}}} + \left( {\displaystyle{{n-1} \over 2}} \right)f_{{\textrm {LH}}}} \over {2\mathop \sum \nolimits_i^n t_{fi}}}.\end{aligned}$$

For a thin-film stack with an even number of thin films:

$$\begin{aligned}{{\mathrm{\sigma}}_{2,4, \ldots 2\textrm{n}}} &= \frac{{{{\mathrm{\sigma}}_{f1}}\cdot {t_{f1}} + {{\mathrm{\sigma}}_{f2}}\cdot {t_{f2}} + \ldots + {{\mathrm{\sigma}}_{fn}}\cdot {t_{fn}}}}{{{t_{f1}} + {t_{f2}} + \ldots + {t_{fn}}}} + \frac{{\left( {\frac{n}{2}} \right){f_{\textrm{HL}}} + \left( {\frac{{n - 2}}{2}} \right){f_{LH}}}}{{2\left( {{t_{f1}} + {t_{f2}} + \ldots + {t_{fn}}} \right)}}\\ & = \frac{{\mathop \sum \nolimits_i^n {{\mathrm{\sigma}}_{fi}}\cdot {t_{fi}}}}{{\mathop \sum \nolimits_i^n {t_{fi}}}} + \frac{{\left( {\frac{n}{2}} \right){f_{\textrm{HL}}} + \left( {\frac{{n - 2}}{2}} \right){f_{\textrm{LH}}}}}{{2\mathop \sum \nolimits_i^n {t_{fi}}}}.\end{aligned}$$

3. Results and discussion

Optical long-wave pass filters (LWPFs) provide a sharp cutoff below a particular wavelength. LWPFs isolate broad regions of the optical spectrum, simultaneously providing high transmission of desired energy, and deep rejection of unwanted energy. As mentioned before, a 7-layer mid-infrared long-wave pass filter (MIR-LWPF) was designed and fabricated in this work. Figure 2 shows the optical spectrum of mid-infrared long-wave pass filter. The optical spectrum for a wavelength of 300–2500 nm could be measured by a visible/near infrared spectrometer, and the mid-infrared spectrum data was measured by a Perkin Elmer Frontier FTIR for a wavelength over 2500 nm. The FTIR results show that the transmittance is greater than 93% at a wavelength of 2.5 to 7 µm, and the transmittance is less than 10% at a wavelength of 1.0 to 2.5 µm. The filter’s performance meets the design specifications.

 

Fig. 2. Transmission spectrum of MIR-LWPF.

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Based on the above interfacial stress formula used for the multilayered film stacks. The interfacial stress fLH between the MgF2 and ZnS layer is 192.28 ± 4.776 Nt/m, and the interfacial stress fHL between the ZnS and MgF2 layer is 28.52 ± 3.954 Nt/m. The measured residual stresses of double-layer films are −0.450 ± 0.003 GPa for MgF2/ZnS/B270 and −0.280 ± 0.002 GPa for ZnS/MgF2/B270, respectively. The measured residual stresses of the four-layer films are −0.244 ± 0.002 GPa for the MgF2/ZnS/MgF2/ZnS/B270 multilayer structure and −0.333 ± 0.003 GPa for the ZnS/MgF2/ZnS/MgF2/B270 structure, as indicated in Table 2. We found that interfacial stress fLH is not equal to fHL. After obtaining the interfacial stress, we substitute it into the modified Ennos formula to estimate the residual stress. Because the influence of the interfacial stress is not considered by Ennos formula, this causes the predicted and measured values for three-layer and four-layer thin films to be significantly different. The prediction results of the modified Ennos formula (namely considering the influence of the interface stress) will be close to the measured value. The difference between the measured stress value and the predicted stress value for the different stacked thin films is compared, as shown in Fig. 3. The residual stress differences between the predicted value and the measured value of the three-layer film are 0.125 GPa for ZnS/MgF2/ZnS/B270 and 0.008 GPa for MgF2/ZnS/MgF2/B270, respectively, as shown in Table 2. The residual stress differences between the predicted and measured values of the four-layer film are 0.001 GPa for MgF2/ZnS/MgF2/ZnS/B270 and 0.013 GPa for ZnS/MgF2/ZnS/MgF2/B270, respectively. The measured value of the residual stress in the mid-infrared long-wave pass filter is −0.206 ± 0.022 GPa. Figure 4 reveals that the predicted stress without considering the interfacial stress is −0.386 ± 0.030 GPa, and the predicted value considering the interfacial stress is −0.276 ± 0.027 GPa. We found that the predicted and measured relative error is 87.4% by using the Ennos formula. After considering the interfacial stress, the relative error can be reduced to 34%. These results show that the predicted stress value for the proposed mid-infrared long-wave pass filter, which shows that the interface stress produced by the thin-film layer numbers’ accumulation is significant.

 

Fig. 3. The difference comparison between the measured stress value and the predicted stress value of (a) LH; (b) HL different stacked thin films.

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Fig. 4. Residual stress prediction for MIR-LWPF

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Tables Icon

Table 2. MgF2 and ZnS four-layer film residual stress measurement and prediction results.

Figures 5(a)–5(c) show the results of measuring the surface roughness of MgF2, ZnS single-layer films and MIR-LWPF by using a home-made Linnik microscopic interferometer. The root-mean-square surface roughness values are 3.32 ± 0.10 nm for MgF2 film, 2.92 ± 0.24 nm for ZnS film, and 1.67 ± 0.19 nm for that of a (MgF2/ZnS)3/MgF2 multilayer film. These results indicate that the MgF2 film's tensile stress is balanced by the ZnS film's compressive stress, after the MgF2 film is deposited on the top of the ZnS film. The surface becomes flatter, and the surface roughness of the thin film is reduced. Figure 6(a) is a FE-SEM micrograph of the mid-infrared long-wave pass filter. Some larger particles can be seen at a magnification of 200 k. In the cross-sectional view of Fig. 6(b), the columnar structures and film interface can be clearly observed, and the film’s surface is flat without bending. Figure 7 shows the XRD pattern of the mid-infrared long-wave pass filter and single-layer film. It can be seen that the single-layer MgF2 film is not crystallized. Although there is no obvious peak in the ZnS film, the trend of the crystal growth appears at 2θ=33.6 degrees. The (110) crystal orientation was found in the (MgF2/ZnS)3/MgF2 multilayer film. This refers to the JCPDS card for MgF2 film crystallization, which may cause an increasing tensile stress of MgF2 film deposited on ZnS thin film.

 

Fig. 5. Surface roughness of the MIR-LWPF (a) MgF2; (b) ZnS; (c) (MgF2/ZnS)3/MgF2

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Fig. 6. FE-SEM image of the MIR-LWPF (a) top view; (b) cross-sectional view.

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Fig. 7. XRD patterns of single layer and multilayer thin films.

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4. Conclusion

In this study, we present a modified Ennos formula to predict the residual stress in multilayered long-wave pass filter (LWPF) for mid-infrared (MIR) applications. A more accurate prediction of the residual stress of multilayered film by considering the interfacial stress effect has been demonstrated experimentally. The MIR long-wave pass filter was prepared by electron beam evaporation with ion-assisted deposition. In the spectral characteristics of mid-infrared long-wave pass filters, the transmittance at a wavelength of 1.0  to 2.5 μm is less than 10%. The average transmission at wavelengths from 2.5  to 7.0 μm is greater than 93%. According to the proposed method and residual stress measurements, the interfacial stress fLH between MgF2 and ZnS is 192.28 ± 4.776 Nt/m, and the interfacial stress fHL between ZnS and MgF2 is 28.52 ± 3.954 Nt/m. The difference between the predicted stress and the measured value of the mid-infrared long-wave pass filter is about 70.3 MPa. The root-mean-square surface roughness is 1.67 ± 0.19 nm, and the fabricated MIR-LWPF has a low stress and low surface roughness that will retain the filter’s high performance.

Funding

Ministry of Science and Technology, Taiwan (106-2221-E-035 -072 -MY2, 108-2622-E- 035-009-CC3); Ministry of Education (20M22026).

Acknowledgments

Authors appreciate the Precision Instrument Support Center of Feng Chia University for providing the FE-SEM measurement, and would like to acknowledge the discussion and support of Dr. Shih-Chin Lin.

Disclosures

The authors declare no conflicts of interest.

References

1. M. Reithmeier and A. Erbe, “Application of thin-film interference coatings in infrared reflection spectroscopy of organic samples in contact with thin metal films,” Appl. Opt. 50(9), C301–C308 (2011). [CrossRef]  

2. R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016). [CrossRef]  

3. Y. Matsuoka, S. Mathonnèire, S. Peters, and W. Ted masselink, “Broadband multilayer anti-reflection coating for mid-infrared range from 7 µm to 12 µm,” Appl. Opt. 57(7), 1645–1649 (2018). [CrossRef]  

4. S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999). [CrossRef]  

5. S. Pimenta, S. Cardoso, A. Miranda, P. De Beule, E. M. S. Castanheira, and G. Minas, “Design and fabrication of SiO2/TiO2 and MgO/TiO2 based high selective optical filters for diffuse reflectance and fluorescence signals extraction,” Biomed. Opt. Express 6(8), 3084–3098 (2015). [CrossRef]  

6. R. Shakouri, “Study of the optical properties of SiO2, and Al2O3 films deposited by electron beam technique,” J. Adv. Phys. 9(3), 2453–2460 (2015). [CrossRef]  

7. M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010). [CrossRef]  

8. D. C. Harris, “Durable 3–5 mm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998). [CrossRef]  

9. A. Piegari and F. Flory, “Optical Thin Films and Coatings: From Materials to Applications,” Woodhead Publishing (2018).

10. K. Jan, P. Sven, and G. Bernd, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012). [CrossRef]  

11. H. A. MacLeod, “Thin-Film Optical Filters, 4th Edition,” CRC Press (2010).

12. C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Opt. Express 18(16), 16594–16600 (2010). [CrossRef]  

13. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909). [CrossRef]  

14. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Appl. Opt. 72(1), 156–160 (1982). [CrossRef]  

15. C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517(17), 5110–5115 (2009). [CrossRef]  

16. C. L. Tien, K. C. Yu, T. Y. Tsai, C. S. Lin, and C. Y. Li, “Measurement of surface roughness of thin films by a hybrid interference microscope with different phase algorithms,” Appl. Opt. 53(29), H213–H219 (2014). [CrossRef]  

17. A. E. Ennos, “Stresses Developed in Optical Film Coatings,” Appl. Opt. 5(1), 51–61 (1966). [CrossRef]  

18. F. Spaepen, “Interfaces and stresses in Thin Films,” Acta Mater. 48(1), 31–42 (2000). [CrossRef]  

References

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  1. M. Reithmeier and A. Erbe, “Application of thin-film interference coatings in infrared reflection spectroscopy of organic samples in contact with thin metal films,” Appl. Opt. 50(9), C301–C308 (2011).
    [Crossref]
  2. R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016).
    [Crossref]
  3. Y. Matsuoka, S. Mathonnèire, S. Peters, and W. Ted masselink, “Broadband multilayer anti-reflection coating for mid-infrared range from 7 µm to 12 µm,” Appl. Opt. 57(7), 1645–1649 (2018).
    [Crossref]
  4. S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
    [Crossref]
  5. S. Pimenta, S. Cardoso, A. Miranda, P. De Beule, E. M. S. Castanheira, and G. Minas, “Design and fabrication of SiO2/TiO2 and MgO/TiO2 based high selective optical filters for diffuse reflectance and fluorescence signals extraction,” Biomed. Opt. Express 6(8), 3084–3098 (2015).
    [Crossref]
  6. R. Shakouri, “Study of the optical properties of SiO2, and Al2O3 films deposited by electron beam technique,” J. Adv. Phys. 9(3), 2453–2460 (2015).
    [Crossref]
  7. M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010).
    [Crossref]
  8. D. C. Harris, “Durable 3–5 mm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).
    [Crossref]
  9. A. Piegari and F. Flory, “Optical Thin Films and Coatings: From Materials to Applications,” Woodhead Publishing (2018).
  10. K. Jan, P. Sven, and G. Bernd, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
    [Crossref]
  11. H. A. MacLeod, “Thin-Film Optical Filters, 4th Edition,” CRC Press (2010).
  12. C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Opt. Express 18(16), 16594–16600 (2010).
    [Crossref]
  13. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909).
    [Crossref]
  14. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Appl. Opt. 72(1), 156–160 (1982).
    [Crossref]
  15. C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517(17), 5110–5115 (2009).
    [Crossref]
  16. C. L. Tien, K. C. Yu, T. Y. Tsai, C. S. Lin, and C. Y. Li, “Measurement of surface roughness of thin films by a hybrid interference microscope with different phase algorithms,” Appl. Opt. 53(29), H213–H219 (2014).
    [Crossref]
  17. A. E. Ennos, “Stresses Developed in Optical Film Coatings,” Appl. Opt. 5(1), 51–61 (1966).
    [Crossref]
  18. F. Spaepen, “Interfaces and stresses in Thin Films,” Acta Mater. 48(1), 31–42 (2000).
    [Crossref]

2018 (1)

2016 (1)

R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016).
[Crossref]

2015 (2)

2014 (1)

2012 (1)

2011 (1)

2010 (2)

M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010).
[Crossref]

C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Opt. Express 18(16), 16594–16600 (2010).
[Crossref]

2009 (1)

C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517(17), 5110–5115 (2009).
[Crossref]

2000 (1)

F. Spaepen, “Interfaces and stresses in Thin Films,” Acta Mater. 48(1), 31–42 (2000).
[Crossref]

1999 (1)

S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
[Crossref]

1998 (1)

D. C. Harris, “Durable 3–5 mm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).
[Crossref]

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Appl. Opt. 72(1), 156–160 (1982).
[Crossref]

1966 (1)

1909 (1)

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909).
[Crossref]

Ahmadvand, H.

R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016).
[Crossref]

Ajith Kumar, S.

S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
[Crossref]

Bandyopadhyay, P. K.

M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010).
[Crossref]

Bernd, G.

Bhatt, M.

M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010).
[Crossref]

Cardoso, S.

Castanheira, E. M. S.

De Beule, P.

Ennos, A. E.

Erbe, A.

Flory, F.

A. Piegari and F. Flory, “Optical Thin Films and Coatings: From Materials to Applications,” Woodhead Publishing (2018).

Ganesha Shanbhogue, H.

S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
[Crossref]

Harris, D. C.

D. C. Harris, “Durable 3–5 mm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).
[Crossref]

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Appl. Opt. 72(1), 156–160 (1982).
[Crossref]

Jan, K.

Jannesari, M.

R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016).
[Crossref]

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Appl. Opt. 72(1), 156–160 (1982).
[Crossref]

Li, C. Y.

Lin, C. S.

Liu, M. C.

C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517(17), 5110–5115 (2009).
[Crossref]

MacLeod, H. A.

H. A. MacLeod, “Thin-Film Optical Filters, 4th Edition,” CRC Press (2010).

Mathonnèire, S.

Matsuoka, Y.

Minas, G.

Miranda, A.

Nagendra, C. L.

S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
[Crossref]

Nautiyal, B. B.

M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010).
[Crossref]

Peters, S.

Piegari, A.

A. Piegari and F. Flory, “Optical Thin Films and Coatings: From Materials to Applications,” Woodhead Publishing (2018).

Pimenta, S.

Reithmeier, M.

Shakouri, R.

R. Shakouri, “Study of the optical properties of SiO2, and Al2O3 films deposited by electron beam technique,” J. Adv. Phys. 9(3), 2453–2460 (2015).
[Crossref]

Spaepen, F.

F. Spaepen, “Interfaces and stresses in Thin Films,” Acta Mater. 48(1), 31–42 (2000).
[Crossref]

Stoney, G. G.

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909).
[Crossref]

Sven, P.

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Appl. Opt. 72(1), 156–160 (1982).
[Crossref]

Ted masselink, W.

Thutupalli, G. K. M.

S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
[Crossref]

Tien, C. L.

Tsai, T. Y.

Yang, H. M.

C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517(17), 5110–5115 (2009).
[Crossref]

Yu, K. C.

Zarei Moghadam, R.

R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016).
[Crossref]

Zeng, H. D.

Acta Mater. (1)

F. Spaepen, “Interfaces and stresses in Thin Films,” Acta Mater. 48(1), 31–42 (2000).
[Crossref]

Appl. Opt. (6)

Biomed. Opt. Express (1)

Infrared Phys. Technol. (3)

M. Bhatt, B. B. Nautiyal, and P. K. Bandyopadhyay, “High efficiency antireflection coating in MWIR region (3.6–4.9 µm) simultaneously effective for Germanium and Silicon optics,” Infrared Phys. Technol. 53(1), 33–36 (2010).
[Crossref]

D. C. Harris, “Durable 3–5 mm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).
[Crossref]

R. Zarei Moghadam, H. Ahmadvand, and M. Jannesari, “Design and fabrication of multi-layers infrared antireflection coating consisting of ZnS and Ge on ZnS substrate,” Infrared Phys. Technol. 75, 18–21 (2016).
[Crossref]

J. Adv. Phys. (1)

R. Shakouri, “Study of the optical properties of SiO2, and Al2O3 films deposited by electron beam technique,” J. Adv. Phys. 9(3), 2453–2460 (2015).
[Crossref]

Opt. Eng. (1)

S. Ajith Kumar, C. L. Nagendra, H. Ganesha Shanbhogue, and G. K. M. Thutupalli, “Near-infrared bandpass filters from Si/SiO2 multilayer coatings,” Opt. Eng. 38(2), 368–380 (1999).
[Crossref]

Opt. Express (1)

Proc. R. Soc. Lond. A (1)

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909).
[Crossref]

Thin Solid Films (1)

C. L. Tien, H. M. Yang, and M. C. Liu, “The measurement of surface roughness of optical thin films based on fast Fourier transform,” Thin Solid Films 517(17), 5110–5115 (2009).
[Crossref]

Other (2)

H. A. MacLeod, “Thin-Film Optical Filters, 4th Edition,” CRC Press (2010).

A. Piegari and F. Flory, “Optical Thin Films and Coatings: From Materials to Applications,” Woodhead Publishing (2018).

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Figures (7)

Fig. 1.
Fig. 1. Schematic diagram of a four-layer film stack (a) HLHL; (b) LHLH structures.
Fig. 2.
Fig. 2. Transmission spectrum of MIR-LWPF.
Fig. 3.
Fig. 3. The difference comparison between the measured stress value and the predicted stress value of (a) LH; (b) HL different stacked thin films.
Fig. 4.
Fig. 4. Residual stress prediction for MIR-LWPF
Fig. 5.
Fig. 5. Surface roughness of the MIR-LWPF (a) MgF2; (b) ZnS; (c) (MgF2/ZnS)3/MgF2
Fig. 6.
Fig. 6. FE-SEM image of the MIR-LWPF (a) top view; (b) cross-sectional view.
Fig. 7.
Fig. 7. XRD patterns of single layer and multilayer thin films.

Tables (2)

Tables Icon

Table 1. The design of mid-infrared long-wave pass filter (MIR-LWPF).

Tables Icon

Table 2. MgF2 and ZnS four-layer film residual stress measurement and prediction results.

Equations (9)

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σ = E s t s 2 6 ( 1 ν s ) t f ( 1 R 2 1 R 1 ) ,
σ avg = i = 1 n = σ Hi t Hi + σ Li t Li t Hi + t Li ,
δ ( f W ) H L = f H f L + f H L ,
δ ( f W ) H L H = 2 f H f L + f H L + f L H ,
δ ( f W ) H L H L = 2 f H 2 f L + 2 f H L + f L H ,
f L H = δ ( f W ) H L H L 2 δ ( f W ) H L ,
f H L = δ ( f W ) L H L H 2 δ ( f W ) L H ,
σ 1 , 3 , 2 n + 1 = σ f 1 t f 1 + σ f 2 t f 2 + + σ f n t f n t f 1 + t f 2 + + t f n + ( n 1 2 ) f H L + ( n 1 2 ) f L H 2 ( t f 1 + t f 2 + + t f n ) = i n σ f i t f i i n t f i + ( n 1 2 ) f HL + ( n 1 2 ) f LH 2 i n t f i .
σ 2 , 4 , 2 n = σ f 1 t f 1 + σ f 2 t f 2 + + σ f n t f n t f 1 + t f 2 + + t f n + ( n 2 ) f HL + ( n 2 2 ) f L H 2 ( t f 1 + t f 2 + + t f n ) = i n σ f i t f i i n t f i + ( n 2 ) f HL + ( n 2 2 ) f LH 2 i n t f i .