TWI874857B - Membrane detecting method - Google Patents

Abstract

A method for detecting membranes is provided. The method includes the following steps: providing a membrane; setting at least one boundary condition of the membrane; establishing an analytical model or a numerical model based on properties of the membrane and the boundary condition; solving the analytical model or the numerical model to obtain at least one frequency response of the membrane; obtaining tensile force of the membrane based on the frequency response; and determining a status of the membrane according to the tensile force.

Description

Thin film testing method

The present invention provides a thin film detection method, and in particular, a thin film detection method that can know the global state of the thin film and prevent the film from being damaged.

Thin films are a very common component in the field of precision electronics and optics, and are widely used. Referring to FIG. 1 , thin film structures can be roughly divided into (a) a covering thin film structure 110 and (b) an independent thin film structure 120 according to the configuration. The covering thin film structure 110 includes a substrate 112 and a thin film 114, and the entire thin film 114 is supported by the substrate 112. For example, thin films used in general semiconductor processes or oxidation processes belong to this category. The independent film structure 120 is substantially similar to the covered film structure 110, and also includes a substrate 122 and a film 124. However, the main difference between the independent film structure 120 and the covered film structure 110 is that the substrate 122 of the independent film structure 120 is formed with at least one cavity 126, so that a part or most of the film 124 is not supported by a component, and only relies on the internal tension of the film 124 to maintain its position and shape, such as a protective film used in a pressure sensor.

Since the price of finished semiconductor products is quite expensive, all major semiconductor foundries with advanced processes around the world will regularly check whether the patterns on the photomask are contaminated. At the same time, the cost of the photomask inspection machine used for inspection is also quite expensive. Taking ASML's exposure machine as an example, during the inspection process, it can only confirm whether there is dust on the surface of the photomask protective film (pellicle) and its specific size and location, but cannot confirm whether the film is damaged or aged. The current common practice is to replace the film regularly to prevent the quality of the manufactured wafers from being affected. However, if the film is contaminated by foreign substances during use, or if it is damaged due to excessive tension caused by poor configuration conditions, the practice of regularly replacing the film cannot prevent or overcome the above situation.

On the other hand, although some manufacturers use frequency measurement to measure the frequency spectrum of a specific point on the film (usually the center point in the case of an independent film structure), and judge whether the film is damaged by the change or drift of the frequency, the above detection method cannot detect the global state of the film at one time, resulting in low detection efficiency. In addition, when the configuration of the film changes, the location where the maximum tension occurs may move from the center point to other places. Therefore, even if the frequency of the center point is measured, it cannot be guaranteed that other locations of the film will not be damaged.

The inventor then devoted all his efforts to research and developed a thin film testing method that can determine the global state of the film and prevent film damage, in order to reduce testing costs and improve testing efficiency.

The present invention provides a film detection method, comprising the following steps: providing a film; giving at least one boundary condition of the film; establishing an analytical model or a numerical model according to the properties of the film and the boundary condition; solving the analytical model or the numerical model to obtain at least one frequency response of the film; obtaining the tension of the film according to the frequency response; and judging the state of the film according to the tension.

In one embodiment, the film detection method further includes the following steps: establishing an experimental model; obtaining at least one experimental frequency response of the film according to the experimental model. In addition, the step of obtaining the tension of the film according to the frequency response includes: comparing the frequency response with the experimental frequency response and obtaining the tension.

In one embodiment, the step of solving the analytical model or the numerical model to obtain the frequency response of the film includes: providing at least one preset load, wherein the preset load is at least one film internal force or at least one linear stress; and obtaining the frequency response according to the preset load. In addition, the step of comparing the frequency response with the experimental frequency response and obtaining the tension includes: increasing or decreasing the preset load by an incremental value; and updating the frequency response according to the preset load after increasing or decreasing the incremental value, until the error between the frequency response and the experimental frequency response is less than a given threshold.

In one embodiment, the frequency response and the experimental frequency response are plural, the frequency response includes a baseband response and a high-frequency response, and the experimental frequency response includes an experimental baseband response and an experimental high-frequency response. In addition, the step of comparing the frequency response with the experimental frequency response and obtaining the tension further includes: comparing the baseband response with the experimental baseband response; and comparing the high-frequency response with the experimental high-frequency response.

In one embodiment, the preset loads are plural, and the preset loads include a first direction preset load acting along a first direction and a second direction preset load acting along a second direction, and the first direction and the second direction are linearly independent of each other.

In one embodiment, the first direction and the second direction are orthogonal to each other, the film is a rectangular film with two long sides and two short sides parallel to the first direction and the second direction respectively, and in the analytical model, the displacement of the film orthogonal to the first direction and the second direction satisfies the following equation: in is the displacement of the film orthogonal to the first direction and the second direction; is the Airy Stress Function of the corresponding film; is the external pressure applied to the film; and are unit vectors in the first direction and the second direction respectively; for time; and They are the density and thickness of the film; and They are the default load in the first direction and the default load in the second direction; is the default linear stress per unit length; and and They are the Young's modulus of the film in the first direction and the second direction respectively.

In one embodiment, the long side and the short side are respectively fixed, and the frequency response satisfies the following equation: in is frequency response; is the initial amplitude of the film perpendicular to the first direction and the second direction; and They are the initial amplitudes of the preset load in the first direction and the preset load in the second direction respectively; and are the lengths of the long side and the short side respectively; and and is the mode of frequency response.

In one embodiment, the film is made of isotropic material, and the frequency response satisfies the following equation: in is the Pusson ratio of the film.

In one embodiment, the film is a circular film, and the step of setting the boundary condition of the film includes: holding the periphery of the circular film.

In one embodiment, the step of judging the state of the film based on the tension includes: judging whether the film is in an elastic deformation region, a plastic deformation region or a damage region based on the tension and the material properties of the film.

In this way, users can analyze the internal tension of the film through analytical models or numerical models according to the properties of the film to be detected and the given boundary conditions, so as to determine whether the film is currently in the elastic deformation zone, plastic deformation zone or damage zone, and replace the film when any position of the film is in the plastic deformation zone, thereby preventing the film from being damaged.

In order to make the above features and advantages of the present invention more clearly understood, embodiments are given below and described in detail with reference to the accompanying drawings.

The above-mentioned and other technical contents, features and effects of the present invention will be clearly presented in the detailed description of the preferred embodiments with reference to the drawings below. It is worth mentioning that the directional terms mentioned in the following embodiments, such as up, down, left, right, front or back, etc., are only referenced to the directions of the attached drawings. Therefore, the directional terms used are for explanation rather than limitation of the present invention. In addition, in the following embodiments, the same or similar components will adopt the same or similar reference numerals.

Please refer to FIG. 2 , which is a schematic diagram of the step flow of an embodiment of the film detection method of the present invention. The film detection method of this embodiment is suitable for judging the state of the film, thereby preventing the film from being contaminated or damaged during use. As shown in FIG. 2 , the film detection method of this embodiment includes the following steps: providing a film (step S210); giving at least one boundary condition of the film (step S220); establishing an analytical model or a numerical model based on the properties and boundary conditions of the film (step S230); solving the analytical model or the numerical model to obtain at least one frequency response of the film (step S240); obtaining the tension of the film based on the frequency response (step S250); and judging the state of the film based on the tension (step S260).

Specifically, when the film is contaminated by external substances or fatigued or damaged due to excessive tension, the internal tension of the film will change accordingly. Thus, the film detection method of this embodiment analyzes a given film through an analytical model or a numerical model, and can grasp the tension at each position on the film. In addition, the properties of the material used to make the film are known. Therefore, by combining the above two pieces of information (such as the tensile curve of the film material), it can be determined whether the film is currently in the elastic deformation area, the plastic deformation area or the damage area, and when any position of the film is in the plastic deformation area, it is replaced to avoid damage to the film.

Please refer to FIG. 3, which is a schematic diagram of a thin film analytical model mechanism of an embodiment of the thin film detection method of the present invention. The thin film analytical model mechanism 300 of the present embodiment may include a thin film 310, wherein the thin film 310 is, for example, a rectangular thin film and has two long sides parallel to each other and two short sides perpendicular to the two long sides, wherein the length of the long side is a , the length of the short side is b , and the thickness of the thin film 310 is h. If the direction parallel to the long side and the direction parallel to the short side are defined as a first direction x and a second direction y , respectively, wherein the first direction x and the second direction y are linearly independent of each other, then according to the von Kármán partial differential equation, the stress and strain of the thin film 310 satisfy the following relationship:

in and They are axial strains in the first direction x and the second direction y respectively; is the shear strain in the first direction x toward the second direction y , and u , v and are the displacements in the first direction x , the second direction y , and a third direction (let it be the z direction) perpendicular to the first direction x and the second direction y . The above three equations can be further derived as follows:

Furthermore, according to the stress-strain relationship of elastic materials:

in and They are axial stress in the first direction x and the second direction y respectively; is the shear stress in the first direction x toward the second direction y ; _Gxy is the shear modulus in the first direction x toward the second direction y ; _Ex and _Ey are the Young's modulus of the material of the film 310 in the first direction x and the second direction y , respectively, and υ is the Pusson's ratio of the material of the film 310. In order to make the film 310 vibrate, at least one preset load can be given to the film 310, wherein the preset load is, for example, a film internal force or a linear stress. Taking the linear stress as an example, let it be:

Assuming that the long side length a and the short side length b of the film 310 are both much greater than the thickness h, the internal shear force can be ignored, i.e.:

At this time, the Airy stress function and the film vibration equation without viscous resistance are introduced, and , , we can get the following three equations:

in is the Airy Stress Function corresponding to the film 310; is the external pressure applied to the film 310 (as a function of position and time); is the default linear stress per unit length; for time; is the density of the film 310. Thus, as long as the above governing equation can be solved, the displacement function of the film 310 in the third direction z can be obtained, and by substituting the specific coordinate position and time of the film 310, the vibration frequency and tension of each point of the film 310 can be obtained. In addition, if the first direction x and the second direction y are partially differentiated according to the tension function, the position where the maximum tension is generated can be further determined, and the critical position where the maximum tension is generated can be more intensively detected.

Please refer to FIG. 4, which is a schematic diagram of a thin film analytical model mechanism of another embodiment of the thin film detection method of the present invention. When solving the above-mentioned vibration equation, in order to avoid too few known conditions and become an indeterminate problem, at least one boundary condition is required for solving. When analyzing an n-gonal covering film structure, at least one side of the film can be fixed by clamping or slightly sticking. Taking the thin film analytical model mechanism 400 shown in FIG. 4 as an example, the two long sides and the two short sides of the film 410 are both fixed. At this time, the boundary condition of the film 410 can be expressed by the following equation:

Thus, the displacement function and stress function can be respectively expressed as:

If the displacement function needs to satisfy the above boundary conditions and be a non-trivial solution, then the mode function corresponding to the displacement function can be assumed to be:

in and is the mode of the vibration frequency function corresponding to the displacement function and is an integer. At this time, let the internal force in the first direction x and the second direction y be , The initial ( t = 0) amplitude is and (As shown in FIG. 4 ), the vibration frequency response of the film 410 satisfies the following equation:

in is the frequency response of the film 410; is the initial amplitude of the film 410 in the third direction z . Thus, the user can substitute any modal parameter to obtain various vibration modal frequencies of the film 410.

Please refer to FIG. 5, which is a schematic diagram of a thin film analysis model mechanism of another embodiment of the thin film detection method of the present invention. The thin film analysis model mechanism 500 of this embodiment is substantially the same as the thin film analysis model mechanism 400 of the previous embodiment, with the main difference being that the thin film 510 is made of an isotropic material, that is:

From the above two relationships, we can infer:

At this time, based on the results of film 410, the frequency response of film 510 will degenerate into:

In another embodiment, in addition to establishing the above-mentioned analytical model, the user can also use commercially available simulation software to establish a numerical model and perform a mechanical analysis on the above-mentioned film 310, film 410, and film 510. The available simulation software includes but is not limited to ANSYS, ABAQUS, COMSOL, or LS-DYNA. According to the software, a film with a given material and size can be established, and a specific boundary can be fixed to achieve the same condition as the film to be analyzed, so that the vibration frequency mode and stress and tension distribution of the entire film can be quickly calculated through the software.

Please refer to Figures 6 to 8, wherein Figure 6 is a schematic diagram of a thin film experimental model mechanism of an embodiment of the thin film detection method of the present invention, Figure 7 is a schematic diagram of a top view of the thin film mechanism in Figure 6, and Figure 8 is a schematic diagram of the experimental frequency response obtained by detecting two different test points in Figure 7. In addition to the above-mentioned analytical model and numerical model, the thin film detection method of this embodiment also establishes an experimental model through real experiments, obtains at least one experimental frequency response of the thin film according to the experimental model, and compares the frequency response obtained by the analytical model or the numerical model with the experimental frequency response as a step of verifying the tension. In detail, the thin film experimental model mechanism 600 is, for example, a confocal microscope (CCM) and may include a perturbation source 610, a spectrometer 620, an optical element 630, a thin film mechanism 640, an optical analyzer 650, and a sensor 660, wherein the perturbation source 610 is, for example, a light source and is suitable for generating white light (white noise). The light waves generated by the perturbation source 610 can be guided through the slit to the spectrometer 620 disposed adjacent to the perturbation source 610, and then emitted from the spectrometer 620 to the optical element 630. In the present embodiment, the optical element 630 is, for example, a convex lens, which can focus the light transmitted by the beam splitter 620 onto the film mechanism 640, thereby disturbing the film 644 on the film mechanism 640; on the other hand, when the film mechanism 640 reflects light of a specific wavelength due to vibration, the reflected light will be emitted toward the beam splitter 620 through the optical element 630, and then emitted from the beam splitter 620 to the optical analyzer 650, wherein the optical analyzer 650 is, for example, a spectrometer or a computer with analysis function, which can analyze the optical intensity of the reflected light and the corresponding relationship between the wavelength through fast Fourier transform. When the disturbance source 610 and the optical analyzer 650 transmit the white light signal and the reflected light signal, which are originally co-localized light, to the sensor 660 , the sensor 660 can confirm the vibration frequency of the thin film 644 in the thin film mechanism 640 according to the wavelength analyzed by the optical analyzer 650 .

As shown in FIG7 , the film structure 640 may include a frame 642 and a film 644, wherein the frame 642 is, for example, an aluminum frame. In order to simulate an independent film structure, the film 644 is fixed on the frame 642 on all sides, and a first test point P1 close to the center point of the film 644 and a second test point P2 offset by 2 mm from the first test point P1 are tested, and the results are shown in FIG8 .

It can be found that the vibration modes and corresponding amplitudes of the first test point P1 and the second test point P2 are different depending on the position. Through the analytical model obtained above, it can be determined that the modal function of the vibration frequency response and the tension function are both continuous functions on the film surface. Therefore, although the experimental model is only suitable for detecting specific points of the film 644, as long as the experimental frequency response results obtained at the two detected positions are the same as the frequency response obtained by the analytical model or the numerical model, or the baseband response (m=n=1) and the high-frequency response (m＞1, n＞1) obtained at the same test position are the same, it can be determined that the film frequency function or tension distribution function obtained by the analytical model or the numerical model is credible and true.

It is worth mentioning that since there will inevitably be errors between the actual values measured in the experiment and the results obtained by theory or software calculation, the user can set a given threshold in advance, such as 1~5%. When the error between the experimental frequency response and the frequency response obtained by the analytical model or numerical model is less than the given threshold, the two frequencies can be considered the same.

If the theoretical solution and experimental solution for the same test position are different, it means that the analytical model or numerical model needs to be modified. At this time, the user can increase or decrease the above-mentioned preset load by an incremental value, and iterate and update the frequency response according to the preset load after increasing or decreasing the incremental value, until the error between the obtained frequency response or tension value and the experimental frequency response or experimental tension value is less than a given threshold. In this way, the user only needs to detect the frequency modes of two different positions of the film to be tested through actual experiments, or the fundamental frequency and high-frequency responses at the same position, and then compare them with the analytical model or numerical model to obtain the global results of the film to be tested.

Please refer to Fig. 9, which is a schematic diagram of a thin film mechanism of another embodiment of the thin film detection method of the present invention. The thin film mechanism 900 of this embodiment is substantially the same as the thin film mechanism 640 of the previous embodiment, and the main difference between the two is that the substrate 910 and the thin film 920 included in the thin film mechanism 900 are both circular.

In detail, in order to simultaneously establish the boundary conditions and maintain the geometric symmetry of the various physical conditions of the circular film, whether simulating a covered film structure or an independent film structure, the film mechanism 900 of this embodiment will fix the periphery of the circular film 920. Since independent films generally have a larger tension distribution than covered films, when the circular film to be tested is still in the elastic region under the boundary conditions of the independent film structure, it can be ensured that the covered film is also in the elastic region, and thus the film 920 can be prevented from being damaged.

The present invention has been disclosed in the above with the preferred embodiments, but those skilled in the art should understand that the above embodiments are only used to describe the present invention and should not be interpreted as limiting the scope of the present invention. It should also be noted that all changes and substitutions equivalent to the above embodiments should be considered to be within the scope of the present invention. Therefore, the protection scope of the present invention shall be based on the scope defined by the patent application.

110: covered film structure 112: substrate 114: film 120: independent film structure 122: substrate 124: film 126: cavity 300, 400, 500: film analysis model mechanism 310, 410, 510: film 600: film experimental model mechanism 610: disturbance source 620: spectrometer 630: optical element 640: film mechanism 642: frame 644: film 650: optical analyzer 660: sensor 900: film mechanism 910: substrate 920: film a , b : length m, n: mode _Nx , _Ny , _N0x , _N0y , _N0 : film internal force P1, P2: test point S210~S260: step x _, y : direction λ1 _, λ2 , λ ₃ : wavelength

FIG. 1 is a schematic side view of (a) a covered film structure and (b) an independent film structure in the prior art. FIG. 2 is a schematic diagram of the step flow of an embodiment of the film detection method of the present invention. FIG. 3 is a schematic diagram of a film analysis model mechanism of an embodiment of the film detection method of the present invention. FIG. 4 is a schematic diagram of a film analysis model mechanism of another embodiment of the film detection method of the present invention. FIG. 5 is a schematic diagram of a film analysis model mechanism of another embodiment of the film detection method of the present invention. FIG. 6 is a schematic diagram of a film experimental model mechanism of an embodiment of the film detection method of the present invention. FIG. 7 is a schematic diagram of a top view of the film mechanism in FIG. 6. FIG. 8 is a schematic diagram of the experimental frequency response obtained by detecting two phase-different test points in FIG. 7. Figure 9 is a schematic diagram of a thin film mechanism of another embodiment of the thin film detection method of the present invention.

S210~S260: Steps

Claims (10)

A film detection method comprises the following steps: Providing a film; Giving at least one boundary condition of the film; Establishing an analytical model or a numerical model based on the properties of the film and the at least one boundary condition; Solving the analytical model or the numerical model to obtain at least one frequency response of the film; Obtaining the tension of the film based on the at least one frequency response; and Judging the state of the film based on the tension. The film detection method as described in claim 1 further includes the following steps: Establishing an experimental model; and Obtaining at least one experimental frequency response of the film based on the experimental model; Wherein, the step of obtaining the tension of the film based on the at least one frequency response includes: Comparing the at least one frequency response with the at least one experimental frequency response and obtaining the tension. The thin film detection method as described in claim 2, wherein the step of solving the analytical model or the numerical model to obtain at least one frequency response of the thin film includes: Give at least one preset load, wherein the at least one preset load is at least one film internal force or at least one linear stress; and According to the at least one preset load, the at least one frequency response is obtained; Wherein, the step of comparing the at least one frequency response with the at least one experimental frequency response and obtaining the tension includes: Increasing or decreasing the at least one preset load by an incremental value; and The at least one frequency response is updated according to the at least one preset load after increasing or decreasing the incremental value until the error between the at least one frequency response and the at least one experimental frequency response is less than a given threshold. The thin film detection method as described in claim 3, wherein the at least one frequency response and the at least one experimental frequency response are plural respectively, the plural frequency responses include a baseband response and a high-frequency response, the plural experimental frequency responses include an experimental baseband response and an experimental high-frequency response, and the step of comparing the at least one frequency response with the at least one experimental frequency response and obtaining the tension further includes: Comparing the baseband response and the experimental baseband response; and Comparing the high-frequency response and the experimental high-frequency response. A thin film inspection method as described in claim 3, wherein the at least one preset load is plural, the plural preset loads include a first direction preset load acting along a first direction and a second direction preset load acting along a second direction, and the first direction and the second direction are linearly independent of each other. The film detection method as described in claim 5, wherein the first direction and the second direction are orthogonal to each other, the film is a rectangular film with two long sides and two short sides parallel to the first direction and the second direction respectively, and in the analytical model, the displacement of the film orthogonal to the first direction and the second direction satisfies the following equation: in is the displacement of the film orthogonal to the first direction and the second direction; is the Airy Stress Function corresponding to the film; is the external pressure applied to the film; and are unit vectors in the first direction and the second direction respectively; for time; and They are respectively the density and thickness of the film; and The first direction preset load and the second direction preset load are respectively; is the default linear stress per unit length; and and They are respectively the Young's modulus of the film in the first direction and the second direction. The thin film inspection method as described in claim 6, wherein the two long sides and the two short sides are respectively held, and the at least one frequency response satisfies the following equation: in for the at least one frequency response; is the initial amplitude of the film perpendicular to the first direction and the second direction; and The initial amplitudes of the first direction preset load and the second direction preset load respectively; and are the lengths of the two long sides and the two short sides respectively; and and is the mode of the at least one vibration frequency. The thin film detection method as described in claim 7, wherein the thin film is made of isotropic material, and the at least one frequency response satisfies the following equation: in is the Pusson's ratio of the film. The film detection method as described in claim 1, wherein the film is a circular film, and the step of determining at least one boundary condition of the film includes: Holding the periphery of the circular film. The thin film detection method as described in claim 1, wherein the step of judging the state of the thin film according to the tension includes: Judging whether the thin film is in an elastic deformation region, a plastic deformation region or a damage region according to the tension and the material properties of the thin film.

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