TW202200976A - System for measuring residual stress in thin films coated on a large substrate - Google Patents

Abstract

Conventionally-used residual stress measuring system is found failing to measure a residual stress in thin films coated on a large substrate owing to the fact that Stoney formula cannot precisely calculate a correct value of the forgoing residual stress. Accordingly, the present invention discloses a system for measuring residual stress in thin films coated on a large substrate. In the present invention, fringe reflection method is adopted for acquiring an x-axis fringe image and a y-axis fringe image from the thin film. After applying a series of signal processes to the x-axis fringe image and the y-axis fringe image, a self-developed residual stress calculating algorithm is adopted for calculating the correct value of the forgoing residual stress in the at least one thin film coated on the large substrate. It is worth mentioning that, experimental data have proved that, this novel system is verified to successfully measure an x-axis residual stress and a y-axis residual stress from the thin films coated on a large substrate compared to the conventionally-used residual stress measuring system.

Description

System for detecting residual stress in large-area thin films

The present invention relates to the related technical field of thin film stress measurement, in particular to a system for detecting residual stress of large-area thin films.

With the high development of smart technology, lightness and thinness have become the basic specifications for portable electronic products. It is conceivable that as the size of portable electronic products continues to become thinner and lighter, various electronic components, electronic chips and/or passive components must also be designed and manufactured in the direction of miniaturization of precision components. Under the trend of miniaturization of precision components, the technology of precision testing related to product quality has also received great attention. For example, in the process of forming a thin film on a substrate, the generation of residual stress may cause the thin film to be defective or deformed, resulting in a decrease in the yield and reliability of the thin film fabrication.

Film residual stress can be divided into tensile stress (Tensile stress) and compressive stress (Compressive stress). The study found that the tensile stress of the film will make the substrate surface concave (Concave), and the compressive stress of the film will make the substrate surface convex (Convex). It is conceivable that excessive residual stress of the thin film will cause excessive voids and cracks at the interface between the thin film and the substrate; in severe cases, part or all of the thin film may be peeled off or cracked from the substrate. The study pointed out that the main causes of film stress are external stress and internal stress. Internal stress, in which internal stress can be subdivided into intrinsic stress and thermal stress. In more detail, the external stress is caused by the external force applied to the film, and the intrinsic stress is caused by the defects derived from the growth of the film. In addition, thermal stress is generated during the cooling process due to the large difference between the expansion coefficients of the film and the substrate.

Figure 1 shows a plane coordinate plot for a biaxial stress analysis. When a thin film is deposited on the surface of a substrate such as a wafer, the stress derived from the difference in the expansion coefficients of the thin film and the substrate is biaxial. As shown in Figure 1. Stress acts on the intimal surface of the membrane along two axes. Although there is no stress in the direction perpendicular to the film surface, there is a strain in the normal direction, and the biaxial stress caused by the strain can be expressed as σ _f = ε _M E _f . where ε _M is the total strain of the film/substrate system, and E _f is the elastic modulus of the film.

Currently, interferometers are widely used to measure the surface topography of substrates and/or thin films. For example, the ROC Patent No. I333059 discloses the use of an interferometer to measure the surface profile and film stress of a rigid substrate or a flexible substrate. However, practical experience has pointed out that when the total stress of the film is too large and the curvature of the substrate is too large, the interference fringes reflected from the surface of the substrate to the (projection) screen will be too dense to be resolved, resulting in the inability to use the existing mathematical formula to calculate Correct value for film stress. Therefore, when using a conventional interferometer to measure the surface profile and film stress of a rigid substrate or a flexible substrate, it is usually necessary to grind the surface of the substrate first to ensure that the surface of the substrate has a considerable flatness. In addition, conventional interferometers cannot be used to detect residual stress in large-area thin films.

As can be seen from the above description, the conventional systems and/or methods for measuring the surface profile and film stress of a substrate still have room for improvement. In view of this, the inventor of this case is After making great efforts to research and invent, a system for detecting the residual stress of large-area thin films of the present invention was finally developed and completed.

The main object of the present invention is to provide a system for detecting residual stress in large-area thin films. For detecting the residual stress of a large-area thin film, the conventional residual stress measurement system of the thin film cannot calculate the correct value of the residual stress of the thin film by using the existing Stoney mathematical formula. Differently, the system for detecting the residual stress of a large-area thin film proposed by the present invention uses the fringe reflection method to obtain an x-axis fringe image and a y-axis fringe image of the film. After a series of signal processing is performed on the fringe image and the y-axis fringe image, the correct value of the residual stress of the accumulated film is calculated by using the self-designed film residual stress algorithm. Furthermore, experimental data show that, compared with the existing commercial film residual stress measurement system, the system proposed by the present invention can accurately measure an x-axis residual stress and a y-axis residual stress of the film.

In order to achieve the above object, the present invention proposes an embodiment of the system for detecting residual stress of a large-area thin film, which includes: a rotating stage on which a substrate is arranged and can be rotated at an angle; a detection light The generating device is arranged along a first optical axis and includes a light source and a grating; a screen is arranged along a second optical axis; an image capturing device faces the screen; and a data processing device is coupled to the an image capturing device, and the data processing device is provided with a phase calculating unit, a phase unwrapping unit, a three-dimensional surface contour establishing unit, a two-dimensional surface contour establishment unit, a curvature radius fitting unit, and a residual stress calculation unit; wherein a detection light of the light source is incident on the top surface of the substrate through the grating, so that the detection light is incident on the top surface of the substrate A first reflected light generated by the top surface is incident on the screen, thereby forming a first striped image on the screen. The image capturing device captures the first striped image to generate and transmit a first image signal to the screen. A data processing device, the data processing device performs a signal processing on the first image signal with its phase calculation unit to obtain a first phase signal, and its phase unwrapping unit performs a phase on the first phase signal Unfolding processing, wherein the three-dimensional surface profile establishing unit establishes a three-dimensional surface profile of a substrate according to the first phase signal that has completed the phase unwrapping process, and the two-dimensional surface profile establishing unit generates the three-dimensional surface profile of the substrate. Perform a curvature calculation and a warp calculation to obtain a two-dimensional surface profile of a substrate, and use the curvature radius fitting unit to perform a curvature radius fitting on the two-dimensional surface profile of the substrate using a contour curve fitting algorithm Calculate the radius of curvature of the surface profile of a substrate; wherein, after a thin film is formed on the top surface of the substrate, the detection light of the light source is incident on a top surface of the thin film through the grating, so that the detection light is incident on the top surface of the thin film. A second reflected light generated by the top surface of the film is incident on the screen to form a second striped image on the screen, and the image capture device captures the second striped image to generate and transmit a second image signal to the data processing device, the data processing device performs the signal processing on the second image signal with its phase calculation unit to obtain a second phase signal, and its phase unwrapping unit for the second phase The signal performs the phase unwrapping process, and its three-dimensional surface profile establishment unit establishes a three-dimensional film according to the second phase signal after completing the phase unwrapping process. The surface profile, the two-dimensional surface profile establishing unit performs the curvature calculation and the warpage calculation on the three-dimensional surface profile of the film to obtain a two-dimensional surface profile of the film, and uses the curvature radius to simulate the surface profile. The combination unit uses the contour curve fitting algorithm to perform the curvature radius fitting calculation on the two-dimensional surface contour of the film to obtain a curvature radius of the film surface contour; wherein, the data processing device uses the residual stress calculation unit to use A film average residual stress algorithm is used to calculate a film average residual stress.

In the aforementioned embodiments of the system for detecting residual stress in large-area thin films of the present invention, the detection light generating device further includes: a light diffusing unit disposed along the first optical axis; and a beam expander disposed along the first optical axis The first optical axis is set; wherein, the light source is a helium-neon laser device or a laser device with other wavelengths, the screen is a smooth plane, and the light diffusing unit is a double concave lens; wherein, the said light source The detection light is propagated to the light diffusing unit after performing a beam expansion process through the beam expander, and then propagates to the grating after performing a light diffusing process via the light diffusing unit.

In the aforementioned embodiment of the system for detecting the residual stress of a large-area thin film of the present invention, when capturing the first stripe image, the image capturing device first performs an image capturing on the screen, and then performs an image capturing on the screen. After the stage is rotated 90 degrees, the image capture device performs another image capture on the screen, thereby obtaining a frame of the first fringe image based on the x-axis direction and a frame of the first fringe image based on the y-axis direction Striped image.

In the above-mentioned embodiment of the system for detecting residual stress of a large-area thin film of the present invention, when capturing the second stripe image, the image capturing device first performs an operation on the screen. and after the rotating stage is rotated by 90 degrees, the image capture device performs another image capture on the screen, so as to obtain a frame of the second texture image based on the x-axis direction and an image based on the A frame of the second stripe image in the y-axis direction.

In the aforementioned embodiment of the system for detecting residual stress of a large-area thin film of the present invention, the phase calculation unit is used for performing the signal conversion process on the first image signal to generate a first frequency domain signal, and then performing the signal conversion process on the first image signal. After performing a frequency shifting and filtering process on the first frequency domain signal, an arctangent function is used to obtain the first phase signal. And, the phase calculation unit is used for performing the signal conversion processing on the second image signal to generate a second frequency domain signal, and then performing the frequency shifting and filtering processing on the second frequency domain signal. , using the arctangent function to obtain the second phase signal.

In the aforementioned embodiments of the system for detecting residual stress in large-area thin films, the three-dimensional surface profile establishment unit is based on the first phase signal after completing the phase unwrapping process, the relationship between the screen and the top surface of the substrate. A first distance between, a first fringe spacing of the first fringe image, and an incident angle of the detection light to establish a substrate surface slope function, and the substrate is respectively in the x-axis direction and the y-axis direction. The surface slope function performs an integral operation to obtain a substrate surface height function, and finally establishes a three-dimensional surface profile of the substrate according to the substrate surface height function and the first phase signal after completing the phase unwrapping process.

In the aforementioned embodiments of the system for detecting residual stress in large-area thin films, the three-dimensional surface profile establishment unit is based on the second phase signal after completing the phase unwrapping process, the relationship between the screen and the top surface of the thin film. a second distance between the A second fringe spacing of the fringe image and the incident angle of the detection light are used to establish a film surface slope function, and after the integral operation is performed on the film surface slope function according to the x-axis direction and the y-axis direction respectively A film surface height function is obtained, and finally the three-dimensional surface profile of the film is established according to the film surface height function and the second-bit signal after completing the phase unwrapping process.

In the aforementioned embodiment of the system for detecting residual stress of large-area thin films of the present invention, after completing the calculation of the curvature and the calculation of the warpage, the two-dimensional surface contour establishment unit is based on the three-dimensional surface contour of the substrate, The data obtained by the curvature calculation and the data obtained by the warpage calculation establish the two-dimensional surface profile of the substrate. And, after completing the calculation of the degree of curvature and the calculation of the degree of warp, the two-dimensional surface profile establishment unit is based on the three-dimensional surface profile of the film, the data obtained by the calculation of the degree of curvature, and the data obtained by the calculation of the degree of warpage Instead, the two-dimensional surface profile of the film is established.

In the aforementioned embodiment of the system for detecting residual stress in large-area thin films of the present invention, the curvature radius fitting unit uses the least squares method as the contour curve fitting algorithm to complete the two substrates. The radius of curvature of the dimensional surface profile is calculated by fitting. And, the curvature radius fitting unit uses the least square method as the profile curve fitting algorithm, so as to complete the curvature radius fitting calculation of the two-dimensional surface profile of the film.

In the foregoing embodiments of the system for detecting residual stress in large-area thin films of the present invention, the algorithm for calculating the average residual stress of thin films includes the following formulas (I), (II) and (III):

；以及

;as well as

；以及

;as well as

其中：σ為該薄膜的殘留應力；σ _x 為該薄膜在所述x軸方向的殘留應力；σ _y 為該薄膜在所述y軸方向的殘留應力；R ₁鍍上該薄膜之前該基板的曲率半徑；R ₂鍍上該薄膜之後該基板的曲率半徑；E_s為該基板2的一彈性模量(elastic modulus)；v為該基板2的一泊松比(Poisson's ratio)；R_x為該薄膜在x軸方向的擬合曲率半徑；R_y為該薄膜在y軸方向的擬合曲率半徑；t_s為該基板2的厚度；以及t_f為該薄膜的厚度。

Wherein: σ is the residual stress of the thin film; σ _x is the residual stress of the thin film in the x-axis direction; σ _y is the residual stress _of the thin film in the y-axis direction; The radius of curvature; R ₂ is the radius of curvature of the substrate after the film is coated; E _s is an elastic modulus of the substrate 2; v is a Poisson's ratio of the substrate 2; R _{x is} the The fitted radius of curvature of the film in the x-axis direction; _Ry is the fitted radius of curvature of the film in the y-axis direction; _ts is the thickness of the substrate 2; and _tf is the thickness of the film.

1: A system for detecting residual stress in large-area thin films

10: Rotary stage

11: Grating

12: Light Divergence Unit

13: Beam Expander

14: Light source

15: Screen

16: Image capture device

17: Data processing device

171: Phase calculation unit

172: Phase Unwrapping Unit

173: 3D Surface Profile Creation Unit

174: 2D Surface Profile Creation Unit

175: Radius of curvature fitting unit

176: Residual stress calculation unit

2: Substrate

S1a-S6a: Steps

S1b-S6b: Steps

S7: Steps

Figure 1 shows a plane coordinate diagram of a biaxial stress analysis;

FIG. 2 shows a schematic diagram of a system for detecting residual stress in large-area thin films according to the present invention;

3 shows a block diagram of a data processing device of the system of the present invention;

FIG. 4 shows a simplified flow chart of performing a measurement of residual stress of a thin film on a thin film plated on a substrate using the system of the present invention;

5 shows a perspective view of a rotating stage, a grating, a light diverging unit, a beam expander, a light source, and a screen using the system of the present invention;

6A shows a side cross-sectional view of the substrate;

6B shows a side cross-sectional view of the substrate;

6C shows a side cross-sectional view of the substrate; and

7 shows a three-dimensional (3D) surface profile, a two-dimensional (2D) surface profile, an x-axis fitting curve, and a y-axis fitting measured from a six-inch sapphire wafer using the system of the present invention Combined graph.

In order to more clearly describe a system for detecting residual stress in a large-area thin film proposed by the present invention, the preferred embodiments of the present invention will be described in detail below with reference to the drawings.

Please refer to FIG. 2 , which is a schematic diagram of a system for detecting residual stress in a large-area thin film proposed by the present invention. As shown in FIG. 2, the system 1 for detecting residual stress of large-area thin films of the present invention includes: a rotating stage 10, a detection light generating device, a screen 15, an image capturing device 16, and a data processing device 17. Wherein, the rotary stage 10 is used for a substrate 2 to be disposed thereon, and the rotary stage 10 can be rotated by an angle. The detection light generating device is disposed along a first optical axis, and includes a grating 11 , a light diffusing unit 12 , a beam expander 13 , and a light source 14 . In more detail, the light source 14 is a helium-neon laser light source with a wavelength of 632.8 nm and a power of 2 mW or a laser light source with other wavelengths for generating a detection light (ie, laser light). Moreover, the beam expander 13 has an optical magnification of 20 times, and is used for performing a beam expansion process on the detection light and then propagating it to the light diffusing unit 12 . In a possible embodiment, the light diverging unit 12 is a double concave lens, which is used for the detection The light is propagated to the grating 11 after performing a light diverging process. The grating 11 has a period of 25 μm and a thickness of 1.5 mm. Thus, the detection light is transmitted through the grating 11 to a top surface of the substrate 2 .

According to the design of the present invention, the image capturing device 16 faces the screen 15 for capturing an image of a striped image formed on the screen 15 . In a possible embodiment, the screen 15 is a smooth plane. Please continue to refer to FIG. 2 and also refer to the block diagram of the data processing device 17 shown in FIG. 3 . As shown in FIG. 2 and FIG. 3 , the data processing device 17 is coupled to the image capturing device 16 . It should be noted that, in the present invention, a phase calculation unit 171 , a phase unwrapping unit 172 , a three-dimensional surface contour establishment unit 173 , a two-dimensional surface contour establishment unit 174 , a curvature radius simulation unit 174 are provided in the data processing device 17 . A combining unit 175 and a residual stress calculating unit 176 are included.

In a possible embodiment, the data processing device 17 is an electronic device, such as a desktop computer, an all-in-one computer, a notebook computer, a tablet computer, or a smart phone. In addition, the phase calculation unit 171 , the phase unwrapping unit 172 , the three-dimensional surface contour establishment unit 173 , the two-dimensional surface contour establishment unit 174 , the curvature radius fitting unit 175 , and the residual stress calculation unit 176 are made of firmware , libraries, variables, or operands are built into the electronic device.

Continue to refer to FIGS. 2 and 3 , and also refer to FIG. 4 , which shows a simplified flow chart of performing a thin film residual stress measurement on a thin film plated on the substrate 2 using the system of the present invention. Engineers who are familiar with the measurement of film residual stress must know that when performing film residual stress, it is usually necessary to first establish a three-dimensional surface profile of the substrate 2, and then perform a thin film on the film plated on the substrate 2. 3D surface contour construction Then, according to the three-dimensional surface contour of the substrate and the three-dimensional surface contour of the film, a curvature radius change before and after the coating is calculated, and finally the correct value of the residual stress of the film is calculated by the Stoney mathematical formula.

As shown in FIG. 2 , FIG. 3 and FIG. 4 , when using the system of the present invention to measure the residual stress of a thin film on a thin film plated on the substrate 2 , a three-dimensional surface of the substrate must also be performed on the substrate 2 first. The contour is established, that is, steps S1a to S5a are performed. In step S1a, a detection light of the light source 14 is incident on the top surface of the substrate 2 through the grating 11, so that a first reflected light generated by the detection light on the top surface of the substrate 2 is incident on the screen 15 , so as to form a first striped image on the screen 15 , the image capture device 16 captures the first striped image to generate and transmit a first image signal to the data processing device 17 . It should be noted that when capturing the first stripe image, the image capturing device 16 first performs an image capturing on the screen 15, and after rotating the rotating stage 10 by 90 degrees, the image capturing device 16 16 Perform another image capture on the screen 15 to obtain a frame of the first fringe image based on the x-axis direction and a frame of the first fringe image based on the y-axis direction.

In step S2a, the data processing device 17 performs a signal processing on the first image signal with the phase calculation unit 171 to obtain a first phase signal. In a possible embodiment, the signal processing is a Fast Fourier Transform (FFT) processing, and the first image signal is converted into a first frequency domain signal. For example, the following equation (1) is used to represent the first image signal, and the following equation (2) is used to represent the first frequency domain signal.

I(x,y)=a(x,y)+b(x,y)cos[2πf ₀ x+Φ(x,y)]................. ..........(1)

I(x,y)=a(x,y)+c(x,y)+c ^* (x,y)...................... ..............(2)

In the above formula (1), Φ(x,y) is the (first) phase signal, I(x,y) is the light intensity distribution function of the first image signal (that is, the first fringe image), a( x, y) is the background signal, b(x, y) is the locally varying contrast in the first fringe image, and f _o is the carrier frequency. After fast Fourier transform processing, in the above formula (2), c(x,y) includes the low-frequency signal, carrier signal and phase information, and c*(x,y) is the conjugate of c(x,y) function. Therefore, in order to extract the phase information, in step S2a, the signal processing further includes a filtering process and a frequency shifting process, so as to effectively separate the background signal and the high frequency noise contained in the first frequency domain signal. At this time, c(x,y) is represented by the following formula (3). Finally, the first phase signal Φ(x, y) can be obtained by using the arc tangent function, and is represented by the following formula (4).

In the above formula (4), Re[c(x,y)] in the arctangent function is the real part, and Im[c(x,y)] is the imaginary part.

Continuing, in step S3a, the data processing device 17 performs a phase unwrapping process on the first phase signal with the phase unwrapping unit 172 thereof. In a feasible embodiment, the phase unwrapping unit 172 uses the phase unwrapping method proposed by Macy in 1983 to complete the aforementioned phase unwrapping process, and must add or subtract 2nπ to solve the discontinuity of the function when unwrapping the phase. Further, in step S4a, the three-dimensional surface profile establishment unit 173 is based on the first phase signal after completing the phase unwrapping process, a first distance between the screen 15 and the top surface of the substrate 2, the first phase A first fringe spacing of a fringe image and an incident angle of the detection light are used to establish a substrate surface slope function, which is obtained after performing an integral operation on the substrate surface slope function in the x-axis direction and the y-axis direction respectively. one The substrate surface height function is finally based on the substrate surface height function and the first phase signal after completing the phase unwrapping process to establish the three-dimensional surface profile of the substrate.

Please also refer to FIG. 5 , which shows a perspective view of the rotating stage 10 , the grating 11 , the light diverging unit 12 , the beam expander 13 , the light source 14 , and the screen 15 . Since the substrate 2 (eg, sapphire substrate) has the reflective property of the polished surface, after the detection light passes through the grating 11 and is directed to the polished surface (ie, the top surface) of the substrate 2 , the detection light is reflected on the polished surface. The light is directed to the screen 15 (ie, a smooth surface), so that the image capture device 16 facing the screen 15 can capture the fringe image. As shown in FIG. 5 , when the slope of θ changes on the surface of the substrate 2 , the reflected light is deflected by 2θ, so that a fringe spacing of the fringe image captured by the image capturing device 16 is shifted by δx. The mathematical relationship between the slope change θ and the displacement amount δx of the fringe spacing can be represented by the following formula (5) after simplification.

δx=2Lθ sec ² β...................................................... ......(5)

In the above formula (5), L is a first distance between the screen 15 and the top surface of the substrate 2 . In addition, as shown in FIG. 5 , β is the incident angle of the detection light (laser light), which is also the reflection angle. Therefore, after obtaining the arc tangent function of the first phase signal Φ(x, y), a substrate surface slope function θ(x, y) can be obtained, which is represented by the following formula (6).

In the above formula (6), p is a first fringe pitch of the first fringe image. To repeat the description, when capturing the first striped image, the image capturing device 16 first performs an image capturing on the screen 15, and after rotating the rotating stage by 90 degrees, the image capturing device 16 Another image capture is performed on the screen 15 to obtain one frame of the first fringe image based on the x-axis direction and one frame of the first fringe image based on the y-axis direction. Therefore, after performing an integral operation on the obtained substrate surface slope function θ(x, y) according to the x-axis direction and the y-axis direction respectively, a substrate surface height function h(x, y) can be obtained, as follows As shown in formula (7) and formula (8),

h(x)=ʃθ(x,y)dx......................................... .................(7)

h(y)=ʃ θ(x,y)dy...................................... ....................(8)

In step S4a, the three-dimensional surface profile of the substrate is finally established according to the substrate surface height function h(x, y) and the first phase signal θ(x, y) after completing the phase unwrapping process. Continuing, in step S5a, the data processing device 17 performs a bow calculation and a warp calculation on the three-dimensional surface contour of the substrate with its two-dimensional surface contour establishing unit 174 to obtain A two-dimensional surface profile of a substrate. 6A , FIG. 6B and FIG. 6C all show side cross-sectional views of the substrate 2 . Generally, sapphire substrates must undergo some surface treatment procedures, such as cutting, lapping, grinding, polishing, surface roughening, and/or patterning (PSS) procedures. Bow and radius of curvature (R) are parameters conventionally used to represent the flatness of a sapphire substrate (wafer). As shown in FIG. 6A , after the center point of the wafer is subtracted from a reference point on a reference surface thereof, a positive value obtained indicates that the surface of the wafer is convex. On the contrary, as shown in FIG. 6B , after subtracting the center point of the wafer from the reference point, the obtained negative value indicates that the surface of the wafer is concave.

Therefore, when calculating the bow of the three-dimensional surface profile of the substrate, first divide the three-dimensional surface profile of the substrate into three blocks, that is, each block has a central angle of 120°. Next, a height value is obtained at the edge of each block, and an average height value of the three height values is the value of the aforementioned reference point. Finally, after subtracting the reference point from a center point of the three blocks, the value of the curvature is obtained. on the other hand. Figure 6C As shown, when calculating the warp degree (Warp) of the three-dimensional surface profile of the substrate, the value of the warp degree is obtained by subtracting the highest point and the lowest point of the three-dimensional surface contour of the substrate.

After the curvature calculation and the warpage calculation are completed, in step S5a, the two-dimensional surface profile establishment unit 174 determines the three-dimensional surface profile of the substrate, the data obtained by the curvature calculation, and the data obtained by the curvature calculation. The obtained data creates a two-dimensional surface profile of a substrate. Finally, in step S6a, the data processing device 17 uses the curvature radius fitting unit 175 to perform a curvature radius fitting calculation on the two-dimensional surface contour of the substrate using a contour curve fitting algorithm to obtain a substrate surface Contour radius of curvature. The contour curve fitting algorithm can perform curve fitting for two-dimensional surface contours in different axial directions to obtain the curvature radius of the surface contour. In a feasible embodiment, the profile curve fitting algorithm is, for example, least squares. Since the two-dimensional surface contour line is composed of a plurality of discrete sampling points, as long as there is a jump of one pixel on the contour curve, noise will be generated, which will affect the value of the radius of curvature. The least square method of fitting curve (least square) is a mathematical optimization technique, which is to minimize the square of the error to find a set of optimal data to obtain the optimized radius of curvature.

Continue to refer to FIGS. 2 , 3 and 4 . After a thin film is formed on the top surface of the substrate 2, in step S1b, a detection light of the light source 14 is incident on a top surface of the thin film through the grating 11, so that the detection light is incident on the top surface of the thin film The generated second reflected light is incident on the screen 15, thereby forming a second striped image on the screen 15. The image capture device 16 captures the second striped image to generate and transmit a second image signal to the screen 15. The data processing device 17 . It should be noted that when capturing the second fringe image, the image capturing device 16 first performs an image capturing on the screen 15 when a rotation angle of the rotating stage 10 is 0 degrees, and in the The rotation angle of the rotary stage 10 After the degree is changed to 90 degrees, another image capture is performed on the screen 15 to obtain a frame of the first fringe image based on the x-axis direction and a frame of the first fringe image based on the y-axis direction.

In step S2b, the data processing device 17 performs the signal processing on the second image signal with the phase calculation unit 171 to obtain a second phase signal. Please refer to the aforementioned equations (1) and (2) repeatedly, the signal processing is a fast Fourier transform (FFT) process, and the second image signal is converted into a second frequency domain signal. In order to extract the phase information, in step S2b, the signal processing further includes a filtering process and a frequency shifting process, so as to effectively separate the background signal and the high frequency noise contained in the second frequency domain signal. Please refer to the aforementioned formula (3) and formula (4).

Continuing, in step S3b, the data processing device 17 performs a phase unwrapping process on the second phase signal with the phase unwrapping unit 172 thereof. In a feasible embodiment, the phase unwrapping unit 172 uses the phase unwrapping method proposed by Macy in 1983 to complete the aforementioned phase unwrapping process, and must add or subtract 2nπ to solve the discontinuity of the function when unwrapping the phase. Further, in step S4b, the three-dimensional surface profile establishment unit 173 is based on the second phase signal after completing the phase unwrapping process, a second distance between the screen 15 and the top surface of the film, the second A second fringe spacing of the fringe image and an incident angle of the detection light are used to establish a film surface slope function, and an integral operation is performed on the film surface slope function according to the x-axis direction and the y-axis direction respectively to obtain a The film surface height function finally establishes a film three-dimensional surface profile according to the film surface height function and the second phase signal after completing the phase unwrapping process.

As can be seen from the aforementioned FIG. 5 , when the slope of θ changes on the surface of the film, the reflected light will be deflected by 2θ, so that one of the second fringe spacings of the second fringe images captured by the image capturing device 16 will be different. Displacement δx. The mathematical relationship between the change θ of the film surface slope and the displacement δx of the second stripe spacing can be represented by the aforementioned formula (5) after simplification. Therefore, after obtaining the arc tangent function of the second phase signal Φ(x, y), a thin film surface slope function θ(x, y) can be obtained, which is represented by the aforementioned formula (6).

To repeat the description, when capturing the second stripe image, the image capturing device 16 first performs an image capturing on the screen 15, and after rotating the rotating stage 10 by 90 degrees, the image capturing device 16 16 Perform another image capture on the screen 15 to obtain a frame of the second fringe image based on the x-axis direction and a frame of the second fringe image based on the y-axis direction. Therefore, after performing an integral operation on the obtained substrate surface slope function θ(x, y) according to the x-axis direction and the y-axis direction respectively, a film surface height function h(x, y) can be obtained. Formula (7) and formula (8) are represented.

In step S4b, the three-dimensional surface profile of the film is finally established according to the film surface height function h(x, y) and the second phase signal θ(x, y) after the phase unwrapping process is completed. Continuing, in step S5b, the data processing device 17 performs a bow calculation and a warp calculation on the three-dimensional surface contour of the film with its two-dimensional surface profile establishment unit 174 to obtain A two-dimensional surface profile of a thin film. After the curvature calculation and the warpage calculation are completed, in step S5b, the two-dimensional surface profile establishment unit 174 uses the three-dimensional surface profile of the film, the data obtained by the curvature calculation, and the data obtained by the curvature calculation. The obtained data creates a two-dimensional surface profile of a thin film.

Finally, in step S6b, the data processing device 17 uses the curvature radius fitting unit 175 to perform a curvature radius fitting calculation on the two-dimensional surface contour of the film by using a contour curve fitting algorithm to obtain a film surface Contour radius of curvature. In a feasible embodiment, the profile curve fitting algorithm is, for example, least squares.

After obtaining the radius of curvature of the film surface contour and the radius of curvature of the surface contour of the substrate, in step S7, the data processing device 17 uses the residual stress calculation unit 176 of the data processing device 17 to calculate a mean residual stress of the film. Mean film residual stress and biaxial residual stress. According to the design of the present invention, the calculation method of the average residual stress of the thin film is represented by the following formula (I).

In the above formula (I), σ is the residual stress of the thin film, R ₁ is the radius of curvature of the substrate before coating the thin film, R ₂ is the radius of curvature of the substrate after coating the thin film, and E _s is the radius of curvature of the substrate 2 An elastic modulus, v is a Poisson's ratio of the substrate 2 , _ts is the thickness of the substrate 2 , and t _f is the thickness of the film. It should be understood that (1/R ₂ -1/R ₁ )=1/R included in the formula (I) is the change in the radius of curvature before and after coating.

In more detail, the above formula (I) is derived from the following formulas (II) and (III).

In the case of considering the anisotropic film stress, as shown in FIG. 1 , the biaxial stress on the film plated on the substrate 2 can be measured according to the biaxial curvature change. Therefore, in the above formulas (II) and (III), σ _x is the residual stress of the film in the x-axis direction, σ _y is the residual stress of the film in the y-axis direction, and R _{x is} the The fitted radius of curvature of the film in the x-axis direction, and R _y is the fitted radius of curvature of the film in the y-axis direction.

From the above formula (I), formula (II) and formula (III), it can be inferred that when the residual stress on the film is an isotropic stress, the residual stress in the x-axis direction is equal to the The residual stress in the y-axis direction is described. At this time, R _x =R _y =R, so σ _x = σ _y = σ , so formulas (II) and (III) can be directly simplified to formula (I).

In more detail, when capturing the surface stripe image of the substrate 2, the present invention particularly utilizes the method of rotating the rotary stage 10 to obtain a frame of the first stripe image based on the x-axis direction and a frame based on the y-axis direction. frame the first fringe image. At the same time, in the case of the surface stripe image of the film, the present invention also uses the method of rotating the rotating stage 10 to obtain one frame of the second stripe image based on the x-axis direction and one frame of the second stripe image based on the y-axis direction. image. In this way, the data processing device 17 uses the two-dimensional surface profile establishment unit 174 to perform the bow calculation and the warp calculation on the three-dimensional surface profile of the substrate and the three-dimensional surface profile of the film. Afterwards, the curvature radius fitting unit 175 can analyze the position with the largest and smallest warpage change, and define the direction with the largest warpage change as the principal stress, and then bend along two perpendicular principal stress directions. rate fitting operation. Finally, the residual stress calculating unit 176 of the data processing device 17 calculates the mean residual stress and/or the global residual stress by using a thin film mean residual stress algorithm; in addition, it can also calculate the x-axis direction and the y-axis direction of the thin film. Residual stress in axial direction (ie σ _x and σ _y ), and determine whether it is non-uniform residual stress (that is, biaxial residual stress can be calculated).

Experimental example

Please refer to Figure 2 and Figure 4 again. In the experimental example, a six-inch sapphire wafer was taken as the substrate 2, and a MgF ₂ film was plated on the sapphire wafer. Next, use the existing commercial film residual stress measuring system KLA-Tencor FLX-2320 and the system of the present invention as shown in FIG. 2 to measure the residual stress in the x-axis and the residual stress in the y-axis. 7 shows a three-dimensional (3D) surface profile, a two-dimensional (2D) surface profile, an x-axis fitting curve, and a y-axis fitting measured from the six-inch sapphire wafer using the system of the present invention Combined graph. In addition, the relevant measurement data are listed in the following table (1).

As shown in Table (1) above, the difference of the x-axis curvature radius is 146.29m, the y-axis curvature radius is 170.56m, the x-axis residual stress difference is 24.30MPa, and the y-axis residual stress difference is 115.85MPa.

Thus, the above has completely and clearly described a system for detecting residual stress in large area thin films disclosed in the present invention. It must be emphasized that the above-mentioned detailed description is directed to a specific description of a feasible embodiment of the present invention, but the embodiment is not intended to limit the present invention. Any equivalent implementation or modification that does not depart from the technical spirit of the present invention shall be included in the patent scope of this case.

1: A system for detecting residual stress in large-area thin films

10: Rotary stage

11: Grating

12: Light Divergence Unit

13: Beam Expander

14: Light source

15: Screen

16: Image capture device

17: Data processing device

2: Substrate

Claims (10)

A system for detecting residual stress in large-area thin films, comprising: a rotating stage for setting a substrate thereon and rotatable in an angle; a detection light generating device, disposed along a first optical axis, and comprising a light source and a grating; a screen, arranged along a second optical axis; an image capture device facing the screen; and A data processing device coupled to the image capture device, and the data processing device is provided with a phase calculation unit, a phase unwrapping unit, a three-dimensional surface contour establishment unit, a two-dimensional surface contour establishment unit, and a curvature radius simulation unit. composite element, and a residual stress calculation element; Wherein, a detection light of the light source is incident on the top surface of the substrate through the grating, so that a first reflected light generated by the detection light on the top surface of the substrate is incident on the screen, thereby forming a a first fringe image, the image capturing device captures the first fringe image to generate and transmit a first image signal to the data processing device, and the data processing device uses the phase calculation unit for the first image signal Perform a signal processing to obtain a first phase signal, perform a phase unwrapping process on the first phase signal with the phase unwrapping unit, and perform a phase unwrapping process on the first phase signal with the three-dimensional surface profile establishment unit according to the first phase unwrapping process completed. A phase signal is used to establish a three-dimensional surface profile of a substrate, and the two-dimensional surface profile establishment unit performs a curvature calculation and a warpage calculation on the three-dimensional surface profile of the substrate to obtain a two-dimensional surface profile of a substrate, and uses The curvature radius fitting unit utilizes a contour curve fitting algorithm to the substrate The two-dimensional surface profile performs a curvature radius fitting calculation to obtain a substrate surface profile curvature radius; Wherein, after a thin film is formed on the top surface of the substrate, the detection light of the light source is incident on a top surface of the thin film through the grating, so that the detection light on the top surface of the thin film generates a second The reflected light is incident on the screen to form a second striped image on the screen. The image capture device captures the second striped image to generate and transmit a second image signal to the data processing device. The data processing device Perform the signal processing on the second image signal with the phase calculation unit to obtain a second phase signal, perform the phase unwrapping processing on the second phase signal with the phase unwrapping unit, and perform the phase unwrapping processing on the second phase signal with the phase unwrapping unit. The three-dimensional surface profile establishing unit establishes a three-dimensional surface profile of the film according to the second phase signal after the phase unwrapping process is completed, and the two-dimensional surface profile establishing unit performs the curvature calculation on the three-dimensional surface profile of the film. Calculate with the warpage degree to obtain a two-dimensional surface profile of a film, and use the curvature radius fitting unit to perform the curvature radius fitting calculation on the two-dimensional surface profile of the film by using the contour curve fitting algorithm Thereby, a radius of curvature of the film surface profile is obtained; Wherein, the residual stress calculation unit of the data processing device uses a thin-film mean residual stress algorithm to calculate a thin-film mean residual stress and a biaxial residual stress. The system for detecting residual stress of a large-area thin film according to claim 1, wherein, when capturing the first stripe image, the image capturing device first executes an image capturing process on the screen. and after the rotating stage is rotated by 90 degrees, the image capture device performs another image capture on the screen, so as to obtain a frame of the first fringe image based on the x-axis direction and an image based on the A frame of the first fringe image in the y-axis direction. The system for detecting residual stress of a large-area thin film according to claim 2, wherein, when capturing the second stripe image, the image capturing device first performs an image capturing of the screen, and after capturing the second fringe image After the stage is rotated 90 degrees, the image capture device performs another image capture on the screen, thereby obtaining a frame of the second texture image based on the x-axis direction and a frame of the second texture image based on the y-axis direction Striped image. The system for detecting residual stress of a large-area thin film according to claim 1, wherein the detection light generating device further comprises: a light diffusing unit disposed along the first optical axis; and a beam expander arranged along the first optical axis; wherein, the detection light of the light source is propagated to the light diffusing unit after performing a beam expansion process through the beam expander, and then propagates to the grating after performing a light diffusing process via the light diffusing unit; Wherein, the light source is a helium-neon laser or other wavelength laser device, the screen is a smooth plane, and the light diffusing unit is a double concave lens. The system for detecting residual stress of a large-area thin film as claimed in claim 1, wherein the data processing device is an electronic device, and the phase calculation unit, the phase unwrapping unit, the three-dimensional surface profile establishment unit, the two-dimensional Surface profile creation unit, this curve The rate-radius fitting unit and the residual stress calculation unit are built in the electronic device in the form of firmware, function library, variable, or operation unit. The system for detecting residual stress of a large-area thin film according to claim 1, wherein the phase calculation unit is used for performing the signal conversion process on the first image signal to generate a first frequency domain signal, and then performing the signal conversion on the first image signal. After performing a frequency shifting and filtering process on the first frequency domain signal, an arctangent function is used to obtain the first phase signal; the phase calculation unit is used for performing the signal conversion process on the second image signal to generate a For the second frequency domain signal, after performing the frequency shifting and filtering processing on the second frequency domain signal, the second phase signal is obtained by using the arctangent function. The system for detecting residual stress in a large-area thin film as claimed in claim 3, wherein the three-dimensional surface profile establishment unit is based on the first phase signal after completing the phase unwrapping process, the relationship between the screen and the top surface of the substrate A first distance between, a first fringe spacing of the first fringe image, and an incident angle of the detection light to establish a substrate surface slope function, and the substrate is respectively in the x-axis direction and the y-axis direction. The surface slope function performs an integral operation to obtain a substrate surface height function, and finally establishes a three-dimensional surface profile of the substrate according to the substrate surface height function and the first phase signal after completing the phase unwrapping process. The system for detecting residual stress in a large-area thin film as claimed in claim 7, wherein the three-dimensional surface profile establishment unit is based on the second phase signal after completing the phase unwrapping process, the relationship between the screen and the top surface of the thin film a second distance between the A second fringe spacing of the fringe image and the incident angle of the detection light to establish a film surface slope function, and after performing the integral operation on the film surface slope function according to the x-axis direction and the y-axis direction respectively A film surface height function is obtained, and finally the three-dimensional surface profile of the film is established according to the film surface height function and the second bit signal after completing the phase unwrapping process. The system for detecting residual stress of a large-area thin film according to claim 1, wherein after completing the calculation of the curvature and the calculation of the warp, the two-dimensional surface contour establishment unit is based on the three-dimensional surface contour of the substrate, The data obtained by the curvature calculation and the data obtained by the warpage calculation establish the two-dimensional surface profile of the substrate and the film. The system for detecting residual stress of a large-area thin film according to claim 3, wherein the algorithm for calculating the average residual stress of the thin film includes the following formulas (I), (II) and (III):

;as well as

;as well as

in: σ is the residual stress of the film; σ _x is the residual stress of the film in the x-axis direction; σ _y is the residual stress of the film in the y-axis direction; R ₁ the radius of curvature of the substrate before coating the film; R ₂ the radius of curvature of the substrate after coating the film; E _s is an elastic modulus of the substrate; v is a Poisson's ratio of the substrate; R _x is the fitted radius of curvature of the film in the x-axis direction; R _y is the fitted radius of curvature of the film in the y-axis direction; _ts is the thickness of the substrate; and t _f is the thickness of the film.

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