Stress measurement of thin film on flexible substrate by using projection moire method and heterodyne interferometry

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Stress measurement of thin film on

flexible substrate by using projection

moiré method and heterodyne

interferometry

Kun-Huang Chen

Jing-Heng Chen

Hua-Ken Tseng

Wei-Yao Chang

Kun-Huang Chen, Jing-Heng Chen, Hua-Ken Tseng, Wei-Yao Chang,“Stress measurement of thin film on flexible substrate by using projection moiré method and heterodyne interferometry,” Opt. Eng.

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Stress measurement of thin film on flexible

substrate by using projection moiré method and

heterodyne interferometry

Kun-Huang Chen,a,_*_{Jing-Heng Chen,}b_{Hua-Ken Tseng,}a_{and Wei-Yao Chang}c

a_{Feng Chia University, Department of Electrical Engineering, 100 Wenhwa Road, Seatwen, Taichung 40724, Taiwan} b_{Feng Chia University, Department of Photonics, 100 Wenhwa Road, Seatwen, Taichung 40724, Taiwan}

c_{National Chiao-Tung University, Department of Photonics and Institute of Electro-Optical Engineering, 1001 Ta-Hsueh Road,}

Hsinchu County 30050, Taiwan

Abstract. We propose a stress measurement system based on a projection moiré method and heterodyne interferometry for thin films on a flexible substrate. In the measurement setup, a CMOS camera in which every pixel can receive a series of heterodyne moiré signals by using a continuously relative displacement with a constant velocity is used. Furthermore, the phase of the optimized sinusoidal curve and the surface profile of the flexible substrate are determined using a least-squares sine fitting algorithm. The thin-film stress is obtained by representing the cross-sectional curve of the surface profile by using a polynomial fitting method, estimating the resultant curvature radii of the uncoated and coated substrates, and using these two radii in the corrected Stoney formula. The proposed measurement system has the advantages of high accuracy, high resolution, and high capacity for substrates with high flexibility and a large measurement depth.© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI:10.1117/1.OE.55.6.064102]

Keywords: flexible substrate; thin-film stress measurement; projection moiré; Talbot effect; heterodyne interferometry. Paper 160224P received Feb. 22, 2016; accepted for publication May 5, 2016; published online Jun. 1, 2016.

1 Introduction

The increased demand for light, thin, and flexible electronic devices has caused the flexible electronics industry to grow; examples of such devices are flexible displays,1,2electronic skin,3 flexible luminance,4,5 flexible solar cell,6,7 and bio-logic sensor.8,9 Because flexible substrates on which thin films are fabricated are affected by the stress associated with the fabrication process, the measurement and analysis of thin-film stress are crucial for fabricating and developing flexible electronic devices. Furthermore, in flexible sub-strates coated with a noncrystalline thin film, the thin-film stress can cause large deformations, and, therefore, conven-tional testing techniques, such as optical interferometry10–13 and x-ray diffraction method,14,15cannot be used. The moiré method involves a large measurement depth, high stability, and a simple and economical optical configuration, and, therefore, it is considered appropriate for the stress measure-ment of thin films on flexible substrates. Lee et al.16 _and Huang and Lo17 proposed the methods for measuring the stress in thin films on flexible substrates; the methods involve using the shadow moiré method and analyzing the interval between the moiré fringes. The resolution and accu-racy of these methods are not high because only the maxi-mum and minimaxi-mum of the moiré fringes are measured for determining the fringe contours, and, therefore, the resolu-tion and accuracy can be strongly affected by the uneven spatial distribution of the light intensity. Accordingly, we propose a stress measurement system for thin films on flexible substrates. An expanded and collimated laser light

is passed through a linear projection grating to form a self-image of the grating on a flexible test substrate, and the resultant deformed fringes are obtained on a reference grating to generate moiré fringes that are recorded by a CMOS camera. When the projection grating is moved with a constant velocity in the grating plane, every pixel of the CMOS camera records a series of signals that mimic a heterodyne interferometric signal. Therefore, the phase of the signals can be extracted in a manner identical to that of obtaining the phase of heterodyne interferometric signals. The phases of the optimized sinusoidal curves can be calcu-lated using a least-squares sine fitting algorithm. The phase distribution and resultant surface profile of the uncoated and coated flexible substrates can be reconstructed by employing phase unwrapping and a derived equation. Subsequently, polynomial curve fitting is used to determine the curvature radii of the uncoated and coated flexible substrates, and these radii are used in the corrected Stoney formula for obtaining the thin-film stress. This method has the advantages of high stability and high resolution because of the use of the pro-jection moiré method and heterodyne interferometry.

2 Principle

Figure 1 shows the optical configuration in the proposed method. For convenience, the observation axis of the CMOS camera is considered to be the z-axis, and the y-axis is directed perpendicular to the plane of the paper. A laser beam of wavelengthλ is passed through a beam expander (BE) for expanding and collimating the beam, and then it impinges on a projection grating G₁ at an angleθ to form a self-image of G₁ on the flexible test substrate. The self-image distanceZ₁ can be expressed as18

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EQ-TARGET;temp:intralink-;e001;63;522

Z1¼p 2

λ cos3θ; (1)

wherep denotes the pitch of G₁. The projected fringes of the self-image can be distorted because of the flexibility of the substrate. These distorted fringes are imaged on the reference gratingG₂ of the same pitch with G₁ via a camera lens to form the moiré fringes and captured by the CMOS camera C. The recorded fringe image can be expressed as19

EQ-TARGET;temp:intralink-;e002;63;422 Iðx; yÞ ¼1₄ 1 þ cos 2π p x þ ΨðxÞ þ φ1 þ cos 2π p x þ φ2 þ1₂cos 4π p x þ ΨðxÞ þ φ1þ φ2 þ1₂cos½Ψðx; yÞ þ φ1− φ2 ; (2)

where ϕ₁ and ϕ₂ denote the initial phase of G₁ and G₂. Furthermore, ΨðxÞ is the phase of the height distribution SðxÞ on the substrate and can be written as

ΨðxÞ ¼2π_p SðxÞ tan θ: (3)

In Eq. (2), the second, third, and fourth terms represent the harmonic noise, and the final term describes the desired moiré fringes formed on the surface of the flexible substrate. Hence, the moiré fringes can be obtained by filtering the harmonic noise, and the intensity of the moiré fringe image can be written as

I0_{ðx; yÞ ¼ I}

0ðx; yÞ þ γðx; yÞ cos½ΨðxÞ þ ϕ1− ϕ2; (4) whereI₀denotes the average light intensity,γðx; yÞ denotes the visibility, and ϕ₁− ϕ₂ is the initial phase difference. When the motorized translation stage M, on which G₁ is mounted, is moved along the x-axis at constant velocity v for time t, every pixel of the CMOS camera can receive a continuous sinusoidal signal, whose intensity can be expressed as

I0_{ðx; yÞ ¼ I}

0ðx; yÞ þ γðx; yÞ cos½2πft þ ΨðxÞ; (5) where fð¼ v∕pÞ denotes the heterodyne moiré frequency associated with the time-varying phase. According to Eq. (3), SðxÞ can be expressed as

SðxÞ ¼_{2π tan θ}p ΨðxÞ: (6)

According to this equation, the surface profile corresponding toSðxÞ can be reconstructed by measuring the phase ΨðxÞ.

To determineΨðxÞ, Eq. (5) can be rewritten as

I0_{ðx; yÞ ¼ A cosð2πftÞ þ B sinð2πftÞ þ C;} ₍₇₎ whereA, B, and C are the real numbers. Moreover,

EQ-TARGET;temp:intralink-;e008;326;583 Ψðx; yÞ ¼ tan−1 −B A : (8)

Accordingly, the phase of the moiré fringes on a single pixel can be calculated using a least-squares sine fitting algorithm to obtainA and B. The parameter ΨðxÞ can be obtained by following the aforementioned procedures for the other pixels and unwrapping the obtained phases, and the surface profile can subsequently be reconstructed using Eq. (6).

To obtain the curvature radius of the substrate, the cross-sectional curve (Fig.2) of the reconstructed surface profile in the x-direction and passing through the image center was obtained by using a polynomial fitting method. Let the center of the curve be set as (x₀; h₀), and let (x₁; h₁), (x₂; h₂), and (x₃; h₃) be three points on the curve. The three circular equa-tions can then be expressed as

EQ-TARGET;temp:intralink-;e009;326;396 ðx1− x0Þ2þ ðh1− h0Þ2¼ R2; (9) EQ-TARGET;temp:intralink-;e010;326;363 ðx₂− x₀Þ2_{þ ðh} 2− h0Þ2¼ R2; (10) EQ-TARGET;temp:intralink-;e011;326;335 ðx₃− x₀Þ2_{þ ðh} 3− h0Þ2¼ R2; (11) whereR is the curvature radius. Let x₁− x₂¼ L, h₂− h₁¼ δ₁,x₂− x₃¼ L, and h₃− h₂¼ δ₂, whereL is an arbitrary value. The curvature radius can then be derived as

EQ-TARGET;temp:intralink-;e012;326;276 R ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðδ₁þ δ₂Þðδ₁δ₂þ L2_Þ 2 Lðδ1− δ2Þ ₂ þ ð2 L2_{þ δ}2 1þ δ22Þ 2ðδ1− δ2Þ ₂ s : (12) When L, δ₁, and δ₂ are known, R can be obtained from Eq. (12). Furthermore, the corrected Stoney formula for obtaining the stress in thin films on flexible substrates can be expressed as16 EQ-TARGET;temp:intralink-;e013;326;167 σf¼ðYst 2 s−Yft2fÞ2þ4YsYftstfðtsþtfÞ2 6ð1þνÞY_sY_ft_st_fðt_sþt_fÞ Y f 1þYftf Y sts 1 R− 1 R₀ ; (13) whereσ_f denotes the thin-film stress, t_s and t_f denote the thickness of substrate and thin film, respectively,ν ¼ ½ðν_sþ νfÞ∕2 denotes the average of the Poisson ratios of the y z x θ M G1 Diode laser Z1 G2 L2 Reference plane 2F 2F MO BE L1 C PH

Fig. 1 Optical configuration in the proposed method. BE: beam expander; MO: objective; PH: pinhole; L₁: collimating lens; L₂: imag-ing lens; L₃: camera lens; G₁and G₂: linear gratings; M: motorized translation stage; C: CMOS camera; Z₁: first self-image; and F : focal length of the imaging lens.

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substrate and thin film,Y_sandY_f denote the elastic coeffi-cients of the substrate and thin film, respectively,E_sandE_f denote the Young’s moduli of the substrate and thin film, respectively, and R₀ denotes the curvature radius of the uncoated substrate. When these parameters are known, the desired thin-film stress can be obtained by reconstructing the surface profile by using the heterodyne moiré method, calculating the curvature radii R₀ and R, and using these curvature radii in Eq. (13).

3 Experimental Results and Discussion

To determine the validity of the proposed method, it was applied to a polyimide (PI)-coated flexible substrate. The surface of the PI-coated substrate was coated with a 100-nm thick indium tin oxide (ITO) thin film. The relative param-eters of the PI substrate and ITO thin film are shown in Table 1. The experimental setup included a 473-nm diode laser, two linear gratings with a pitch of 0.2822 mm, an imaging lens with a focal length of 200 mm, a motorized translation stage [Sigma Koki/SGSP(MS)26-100] with a resolution of 0.05 μm for generating heterodyne moiré signals with a frequency (f) of 1 Hz (v ¼ 0.2822 mm∕s), and a CMOS camera (Basler/A504k) with an 8-bit gray level and a resolution of 1280 × 1024. The frame rate of the CMOS camera (f_s) was 15 fps, the exposure time (a) was 66 ms, and the total time (T) taken to record heterodyne moiré signals at different time points was 1 s. Every recorded moiré image was filtered using a3 × 1 window through two-dimensional median filtering for eliminating the harmonic noise in the moiré fringes.20Figures3and4show the exper-imental results. Figures3(a)and4(a)show the moiré patterns on the sample with the uncoated and coated PI substrates. Figures3(b)and4(b)show the reconstructed surface profile of the PI substrate before and after thin-film coating. The

cross-sectional curve of the reconstructed surface profile in the x-direction and passing through the image center is shown. Moreover, the fitting curve of the depicted cross-sectional curve can be obtained through polynomial curve fitting, as shown in Figs. 3(c) and 4(c). The parameters R0 and R of the uncoated and coated substrates can be calculated as 182.7 and 51.3 cm by using Eq. (12). By sub-stituting these values and the parameters in Table 1 into Eq. (13), the stress in the thin film on the PI substrate can be calculated as 43.8 MPa.

According to Eq. (12), the error in the curvature radius in the proposed method can be expressed as

EQ-TARGET;temp:intralink-;e014;326;423 ΔR ¼_∂δ∂R 1 Δδ1þ _∂δ∂R 2 Δδ2; (14)

whereΔδ₁ and Δδ₂ are equal and denote the errors in the height. Therefore, Eq. (14) can be rewritten as

EQ-TARGET;temp:intralink-;e015;326;356 ΔR ¼ 2_∂δ∂R 1 Δδ1¼ 2 _2R1 ∂R_∂δ₁2Δδ1: (15) The error in the curvature radius can be calculated as follows by using Eq. (15):

EQ-TARGET;temp:intralink-;e016;326;288 ΔR ¼_R1 Aδ1 C2 − A2 C3þ BD2 2 L2_C2þ B2_D 2 L2_C2− B2_D2 2 L2_C3 Δδ₁; (16) where EQ-TARGET;temp:intralink-;e017;326;218 A ¼ 2L2_{þ δ}2 1þ δ22; (17) EQ-TARGET;temp:intralink-;e018;326;189 B ¼ δ1þ δ2; (18) EQ-TARGET;temp:intralink-;e019;326;164 C ¼ δ1− δ2; (19) EQ-TARGET;temp:intralink-;e020;326;139 D ¼ L2_{þ δ} 1δ2: (20) and EQ-TARGET;temp:intralink-;e021;326;102 Δδ1¼ ∂δ1 ∂pΔp þ∂δ1 ∂βΔβ þ∂δ1 ∂θ1Δθ1 þ∂δ1 ∂θ2Δθ2 ; (21) L L δ1 δ2 (x1, h1) (x2, h2) (x3, h3) (x0, h0) x h

Fig. 2 Cross-sectional curve of the reconstructed surface profile in thex-direction and passing through the image center; (_x₀_{; h}₀) is the center of the curve, and (_x₁_{; h}₁), (_x₂_{; h}₂), and (_x₃_{; h}₃) are the three points on the curve.

Table 1 Parameters of the PI substrate and ITO thin film.21,22 PI substrate ITO thin film

Thickness,t t_s¼ 75 μm t_f¼ 100 nm

Elastic coefficient,E E_s¼ 2.5 GPa E_f ¼ 116 GPa

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whereΔp, Δβ, and Δθ denote the errors in the grating pitch, projection angle, and phase error, respectively. The errorΔp originates from errors in the grating fabrication. The gratings were fabricated using a mask laser writer on a coated glass substrate, andΔp was estimated as 0.1 μm. The parameter Δβ originates from errors in the axis alignment. For a grating self-image of 110 mm and a projection angle of 30 deg in the experiment, Δβ was estimated as 0.22 deg. The phase error originated from the sampling error, which depends on the frequency and the visibility of the heterodyne inter-ference signal, the camera recording time, the frame expo-sure time, the frame period, and the number of gray levels.23 Considering the related experimental conditions and the visibility of the moiré fringes with a value of 0.3, the phase errorΔθ can be evaluated with a value of 0.32 deg. Substituting the values ofΔp; Δβ, and Δθ, the experimental conditions, and the results into Eqs. (16)–(21), yielded aΔR estimate of5.81 μm.

Furthermore, the error in the thin-film stressΔσ_f originat-ing fromΔR can be derived as

EQ-TARGET;temp:intralink-;e022;326;240 Δσf¼ ∂σf ∂R ΔRþ∂σf ∂R0 ΔR0 ¼ðYst2s_{6ð1 þ vÞY}− Yft2fÞ2þ 4YsYftstfðtsþ tfÞ2 sYftstfðtsþ tfÞ Y f 1 þYftf Y_s_t_s · 1 R2 ΔRþ_R12 0 ΔR0 ; (22)

whereΔR₀is equal toΔR. Substituting ΔR, the experimen-tal conditions, and the results into Eq. (22), yielded a Δσ_f estimate of 7.45 MPa. According to the preceding error analysis, the proposed method has the advantages of high resolution and high accuracy, and the method can be useful Fig. 3 Results for the uncoated PI substrate: (a) moiré pattern on the sample surface, (b) reconstructed

surface profile, and (c) cross-sectional curve and fitting curve of the reconstructed surface profile.

Fig. 4 Results for the coated PI substrate: (a) moiré pattern on the sample surface, (b) reconstructed surface profile, and (c) cross-sectional curve and fitting curve of the reconstructed surface profile.

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in the fabrication and development of flexible electronic devices.

4 Conclusion

This paper proposes a stress measurement system for thin films on flexible substrates by using a projection moiré method and heterodyne interferometry. The phase of the optimized heterodyne moiré signal is determined using a least-squares sine fitting algorithm, and the surface profile of the flexible test substrate is then obtained. The thin-film stress is obtained by representing the cross-sectional curve of the substrate by using a polynomial fitting method, estimating the resultant curvature radii of the uncoated and coated substrates, and using these two radii in the corrected Stoney formula. This method offers the advantages of high accuracy, high stability, high resolution, and high capacity for substrates with high flexibility and a large measurement depth.

Acknowledgments

The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract Nos. MOST 103-2221-E-035-031 and MOST 104-2221-E-035-062.

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Kun-Huang Chen received his BS degree from the Physics Depart-ment of Chung Yuan Christian University, Taiwan, in 2000 and his PhD from the Institute of Electro-Optical Engineering of National Chiao Tung University, Taiwan, in 2004. In 2004, he joined the faculty of Feng Chia University, where he is currently a professor with the Department of Electrical Engineering. His current research activities are optical metrology and optical sensors.

Jing-Heng Chen received his BS degree from the Physics Depart-ment of Tunghai University, Taiwan, in 1997 and his MS and PhD degrees from the Institute of Electro-Optical Engineering, National Chiao Tung University, Taiwan, in 1999 and 2004, respectively. In 2004, he joined the faculty of Feng Chia University, where he is cur-rently a professor with the Department of Photonics. His current research interests are optical testing and holography.

Hua-Ken Tseng received his BS and MS degrees from the Depart-ment of Electrical Engineering of Feng Chia University, Taiwan, in 2012 and 2014, respectively. Currently, he is working at Taiwan Semi-conductor Manufacturing Co., Ltd. His current research interests are biosensors and optical testing.

Wei-Yao Chang received his MS degree from the Department of Electrical Engineering of Feng Chia University, Taiwan, in 2009 and his PhD from the Institute of Electro-Optical Engineering of National Chiao Tung University, Taiwan, in 2015. Currently, he is working in Chroma Ate Inc. His current research interests are biosensors and optical testing.