Accurate prediction of multilayered residual stress in fabricating a mid-infrared long-wave pass filter with interfacial stress measurements

Chuen-Lin Tien; Chuen-Lin Tien; Hong-Yi Lin

doi:10.1364/OE.411955

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.

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

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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].

(1)$$\sigma = \frac{{{E_s} \cdot t_s^2}}{{6(1 - {\nu _s}){t_f}}}(\frac{1}{{{R_2}}} - \frac{1}{{{R_1}}}),$$

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. E_s=71.5 GPa and ν_s=0.219 are the Young’s modulus and the Poisson’s ratio of the B270 substrate, respectively; t_s is the thickness of the substrate and t_f (t_f << t_s) 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:

(2)$${\mathrm{\sigma }_{\textrm{avg}}} = \mathop \sum \nolimits_{\textrm{i} = 1}^{\textrm{n} = \infty } \frac{{{\mathrm{\sigma }_{\textrm{Hi}}}{\textrm{t}_{\textrm{Hi}}} + {\mathrm{\sigma }_{\textrm{Li}}}{\textrm{t}_{\textrm{Li}}}}}{{{\textrm{t}_{\textrm{Hi}}} + {\textrm{t}_{\textrm{Li}}}}},$$

where σ_avg is the average residual stress of the multilayer film, σ_Hi and σ_Li are the residual stress values of the high and low refractive index thin films, and t_Hi and t_Li 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. f_i is the force per unit width (w) in the i-th layer. f_HL and f_LH represent the interfacial force per unit width in HL-layer and LH-layer film stacks. Assuming that f_HL is not equal to f_LH. 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

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

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

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

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:

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

where f_LH is the interfacial stress of the low refractive index material deposited on the high refractive index material. Similarly, f_HL 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

(7)$${f_{HL}} = \delta {\left( {\frac{f}{W}} \right)_{LHLH}} - 2\delta {\left( {\frac{f}{W}} \right)_{LH,}}$$

In these formulas, the positive or negative sign of f_H and f_L 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, f_HL 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. f_HL and f_LH, two interface stresses, are multiplied by the number of interfaces and added to the Ennos formula as a correction term, because f_HL and f_LH 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:

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

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

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

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 f_LH between the MgF₂ and ZnS layer is 192.28 ± 4.776 Nt/m, and the interfacial stress f_HL 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 f_LH is not equal to f_HL. 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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Table 2. MgF₂ and ZnS four-layer film residual stress measurement and prediction results.

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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 f_LH between MgF₂ and ZnS is 192.28 ± 4.776 Nt/m, and the interfacial stress f_HL 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

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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]

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

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Layer No.	Materials	Refractive Index	Film Thickness (nm)
1	MgF₂	1.383	85.38
2	ZnS	2.199	380.10
3	MgF₂	1.383	487.14
4	ZnS	2.199	232.45
5	MgF₂	1.383	264.26
6	ZnS	2.199	345.44
7	MgF₂	1.383	719.55

Film Stacks	Film Thickness (nm)	Measured Residual Stress (GPa)	Stress Prediction by Ennos Formula (GPa)	Prediction by Modified Ennos Formula (GPa)
ZnS/B270	213	−1.248 ± 0.006
MgF₂/ZnS/B270	443	−0.450 ± 0.003	−0.473 ± 0.010	−0.367 ± 0.009
ZnS/MgF₂/ZnS/B270	656	−0.457 ± 0.003	−0.682 ± 0.007	−0.332 ± 0.006
MgF₂/ZnS/MgF₂/ZnS/B270	869	−0.244 ± 0.002	−0.473 ± 0.004	−0.245 ± 0.005
MgF₂/B270	230	+0.109 ± 0.013
ZnS/MgF₂/B270	443	−0.280 ± 0.002	−0.473 ± 0.003	−0.061 ± 0.007
MgF₂/ZnS/MgF₂/B270	673	−0.062 ± 0.004	−0.269 ± 0.005	−0.070 ± 0.004
ZnS/MgF₂/ZnS/MgF₂/B270	869	−0.333 ± 0.003	−0.473 ± 0.004	−0.320 ± 0.006

Layer No.	Materials	Refractive Index	Film Thickness (nm)
1	MgF₂	1.383	85.38
2	ZnS	2.199	380.10
3	MgF₂	1.383	487.14
4	ZnS	2.199	232.45
5	MgF₂	1.383	264.26
6	ZnS	2.199	345.44
7	MgF₂	1.383	719.55

Film Stacks	Film Thickness (nm)	Measured Residual Stress (GPa)	Stress Prediction by Ennos Formula (GPa)	Prediction by Modified Ennos Formula (GPa)
ZnS/B270	213	−1.248 ± 0.006
MgF₂/ZnS/B270	443	−0.450 ± 0.003	−0.473 ± 0.010	−0.367 ± 0.009
ZnS/MgF₂/ZnS/B270	656	−0.457 ± 0.003	−0.682 ± 0.007	−0.332 ± 0.006
MgF₂/ZnS/MgF₂/ZnS/B270	869	−0.244 ± 0.002	−0.473 ± 0.004	−0.245 ± 0.005
MgF₂/B270	230	+0.109 ± 0.013
ZnS/MgF₂/B270	443	−0.280 ± 0.002	−0.473 ± 0.003	−0.061 ± 0.007
MgF₂/ZnS/MgF₂/B270	673	−0.062 ± 0.004	−0.269 ± 0.005	−0.070 ± 0.004
ZnS/MgF₂/ZnS/MgF₂/B270	869	−0.333 ± 0.003	−0.473 ± 0.004	−0.320 ± 0.006

Accurate prediction of multilayered residual stress in fabricating a mid-infrared long-wave pass filter with interfacial stress measurements

Abstract

1. Introduction

2. Experimental method

3. Results and discussion

4. Conclusion

Funding

Acknowledgments

Disclosures

References

Cited By

Figures (7)

Tables (2)

Equations (9)

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