JP2009053058A - Method of measuring young's modulus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of measuring a Young's modulus without deforming a measuring object. <P>SOLUTION: By an optical lever method of making a laser beam come into a thin film formed on a substrate, for example, and of measuring the angle variation of the reflected light, deflection of the substrate is measured and internal stress σ of the thin film is determined. Next, by an in-plane method as one type of the X-ray diffraction method, the lattice surface interval of the horizontal surface direction of the thin film is measured, and distortion ε is determined. The Young's modulus E is determined based on the stress σ and distortion ε determined in that manner. This optical lever method allows the Young's modulus to be measured with the laser beam without deforming the measuring object because measurement is performed with X-rays in the in-plane X-ray diffraction method. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a method for measuring Young's modulus.

  Conventionally, Young's modulus is also referred to as a longitudinal elastic modulus, and is a numerical value representing material characteristics, and is widely used when designing machines and structures. Young's modulus is a constant determined from the relationship between elongation and force when pulled or compressed in one direction. Further, when the Young's modulus of a certain material is large, it means that the material does not deform much with respect to external stress, in other words, the material is hard. On the contrary, when the Young's modulus is small, it means that the deformation is large with respect to the external stress, that is, it is soft.

As a method for measuring the Young's modulus, as disclosed in Patent Document 1, a method is known in which a load is deformed by applying a load to an object to be measured and the amount is determined from the amount of deformation. In addition, a so-called nano-intention method is also known. The nanointention method is a method in which a regular triangular pyramid indenter is pushed into a thin film, and a Young's modulus is obtained by calculation from a load applied to the indenter and a projected area opened in the film under the indenter.
JP-A-6-3236

  By the way, the nanointention method has a problem that the Young's modulus cannot be measured without deforming the film because the Young's modulus is obtained by calculation from the projected area opened on the film under the indenter. Furthermore, in the case of a film having a thickness of nanometer order, the indenter reaches the substrate surface. As described above, the nano-intention method has a problem that it is difficult to measure a nano-order film, particularly a film thinner than 100 nm.

  Further, even in the method disclosed in Patent Document 1, it is difficult to measure the Young's modulus without deforming the film because one side of the paper sheet is pressed and the other is loaded and the amount of deformation is measured. Further, it is difficult to measure a nano-order film as in the nano-intention method.

As described above, the conventional Young's modulus measurement method has a problem that it is difficult to measure the Young's modulus without deforming the object to be measured.
In particular, the conventional Young's modulus measurement method has a problem that it is difficult to measure the Young's modulus of a nano-order thin film.

  The present invention has been made in view of the above-described circumstances, and an object of the present invention is to provide a method capable of measuring Young's modulus without deforming an object to be measured.

In order to achieve the above object, the Young's modulus measurement method according to the first aspect of the present invention comprises:
By measuring the reflection angle of the laser light incident on the film to be measured for which the stress is to be obtained, the stress of the film to be measured is obtained,
By measuring the lattice spacing in the in-plane direction of the film to be measured, the strain of the film to be measured is obtained,
The Young's modulus of the film to be measured is obtained by dividing the stress of the film to be measured by the strain of the film to be measured.

  The film to be measured may be formed on a substrate.

  The stress of the film to be measured is obtained by measuring a reflection angle of a laser beam incident on the film to be measured in a state where the film to be measured is not formed on the substrate, and then on the substrate. The method may include measuring a reflection angle of laser light incident on the film to be measured in a state where the film to be measured is formed.

  The substrate may be a transparent substrate.

  A reflective film having light reflectivity may be provided on one main surface or the other main surface of the substrate or the surface of the film to be measured.

  The substrate may be a glass substrate.

  The substrate may be a substrate having light reflectivity.

  The substrate may be a silicon substrate.

  One main surface and the other main surface of the substrate may be mirror-polished.

  The same film may be formed on one main surface and the other main surface of the substrate except for the film to be measured.

  The film to be measured may contain ZnO.

  The film to be measured may be crystalline.

  According to the present invention, the Young's modulus can be obtained without deforming the object to be measured by obtaining the stress and strain existing in the film (for example, residual stress and residual strain existing in the state). A rate measurement method can be provided.

  A method for measuring Young's modulus according to an embodiment of the present invention will be described below with reference to the drawings. In the present embodiment, a method for measuring the Young's modulus of a thin film when a thin film is formed on a substrate will be described as an example. Further, a silicon substrate will be described as an example, and a thin film will be described using ZnO as an example.

  First, in the present embodiment, the Young's modulus is calculated using Equation 1 indicating the relationship between the Young's modulus, stress, and strain. When the Young's modulus is σ (Pa) for stress, ε for strain, and Ε (Pa) for Young's modulus, these values satisfy the following formula.

(Formula 1)
σ = Ε ・ ε

As a method for measuring stress, an optical balance (optical lever method) is used. In the optical balance, the radius of curvature is measured by irradiating the object to be measured with laser light or the like and detecting the reflected light from the object to be measured. When the object to be measured, for example, the substrate bends and the radius of curvature changes, the angle of the reflected light slightly changes as shown in FIGS. 1B and 1C, and the detector detects light such as laser light. Can detect this change in angle as a change in the detection position of light (light lever). The angle change of the reflected light is detected by a sensor, and the curvature radius of the substrate surface is measured. Specifically, as shown in FIG. 1A, a substrate 11 is supported by, for example, three points by a support member 12, and a laser is irradiated to the substrate at a predetermined angle θ ₀ , and the reflected light angle θ Detect ₁ This is repeated for the entire substrate to measure the radius of curvature of the film.

In this embodiment, in order to obtain the stress of the ZnO film (film to be measured) formed on the substrate, first, as shown in FIG. 1B, an initial state (first state) in which no ZnO film is formed. The surface of the silicon substrate 21 is irradiated with a laser beam at a predetermined angle θ ₀ and the angle θ _{1 of the} reflected light is detected to measure the curvature radius R ₁ of the silicon substrate surface (first curvature radius measurement). Next, as shown in FIG. 1C, a ZnO film 22 is formed on the silicon substrate 21, and in this state (second state), a laser beam is irradiated at a predetermined angle θ ₀ , and reflected light By detecting the angle θ ₂ , the curvature radius R ₂ of the silicon substrate is measured (second curvature radius measurement). Next, R can be obtained from the amount of change in the radius of curvature before and after the film formation according to the following equation 2, and the internal stress σ of the film can be obtained from the equation 3 using this R.

_Assuming that the internal stress σ, the substrate Young's modulus E _Si , the substrate thickness d _Si , the substrate Poisson's ratio ν _Si , the film thickness d _M , and the radius of curvature R, these satisfy the following expressions 2 and 3.

(Formula 2)

(Formula 3)

Here, the Young's modulus E _{Si of} the substrate, the thickness d _{Si of} the substrate, the Poisson's ratio ν _{Si of the} substrate, and the film thickness d _M are constants given in advance. Therefore, the stress can be calculated by detecting the radius of curvature R. The stress obtained at this time is a stress in the in-plane direction of the film. Here, the in-plane direction of the film is a direction perpendicular to the substantial normal direction of the film.

  In the present embodiment, since the ZnO film is transparent, it is preferable to form the ZnO film on the silicon substrate because the laser beam is favorably reflected on the surface of the silicon substrate.

  In the case of using the optical lever method, it is preferable that the warpage of the substrate occurs concentrically like, for example, a record board from the viewpoint of ensuring the reproducibility and reliability of measurement data. In general, a silicon wafer used for LSI (Large Scale Integration) is mirror-polished on one side only, the front and back surfaces are asymmetrical, and it is bent in a bowl shape, but no concentric warpage occurs. For this reason, it is preferable that the silicon substrate is mirror-polished on both the front and back sides, that is, both main surfaces of the silicon substrate, whereby the substrate can be warped substantially concentrically. Accordingly, it is preferable to use a silicon substrate having both main surfaces that are subjected to the same surface processing and that both surfaces are symmetrical.

  Next, as a strain measuring method, an in-plane method which is a kind of X-ray diffraction method is used. A commonly used X-ray diffraction method is called an out-of-plane method, in which X-rays are incident from a direction inclined by a predetermined angle from the normal direction of the film, that is, the substantial normal direction of the film, that is, This is a method of measuring the lattice spacing in the direction parallel to the substantial normal. On the other hand, in-plane method, as shown in FIG. 2B, X-rays are emitted from a substantially horizontal direction of the ZnO film 22 formed on the substrate 21, that is, from a direction substantially perpendicular to the normal direction of the film. Make it incident. This measures the lattice spacing in the direction (in-plane direction) perpendicular to the substantial normal of the film. That is, according to the in-plane method, the strain in the in-plane direction of the film can be measured. Specifically, as shown in FIG. 2A, for lattice planes arranged in a direction perpendicular to a substantial normal (corresponding to lattice planes arranged in the in-plane direction in the in-plane method). When X-rays are incident from a predetermined angle θ, the lattice spacing is d, the X-ray incident angle is θ, the X-ray wavelength is λ, and n is an integer. When the angle qc (Bragg's diffraction angle) satisfies the diffraction formula 4, the X-rays diffracted at each lattice plane are strengthened and detected as a peak shown in FIG. Here, the direction perpendicular to the paper surface in FIG. 2A is the above-described substantially normal direction. The spectrum shown in FIG. 3 was measured with a 100 nm ZnO film formed on a silicon substrate as will be described in detail later.

(Formula 4)
2dsinθc = nλ

  Next, using the spectrum from the lattice spacing d obtained by the in-plane method in this way, the strain (ε) is calculated by the Willson-Hall plot (Equation 5). In the following formula, λ is the wavelength of the X-ray, and in FIG. 3, copper is used for the X-ray source, and λ is 0.154184 nm of the Cu-ka line. β is the expansion of the diffraction angle (in radians) due to the size and strain of the crystallite, and is the half width of the diffraction peak of the X-ray diffraction spectrum shown in FIG. θc is the Bragg diffraction angle, and D is the crystallite size.

(Formula 5)
1 / λ ・ β ・ cosθc = 1 / λ ・ 2ε ・ sinθc + 1 / D

  In Equation 5, λ is a constant in the present embodiment. Then, when each diffraction angle θc corresponding to at least two diffraction peaks, that is, a plurality of lattice spacings is measured and the y-axis is βcosθc and the x-axis is sinθc, the strain ε is obtained from the inclination, and the y-axis The crystal grain size D is obtained from the above section.

  The Young's modulus Ε is calculated by substituting the stress σ and the strain ε obtained in this way into Equation 1 above.

  As described above, in this embodiment, the Young's modulus can be calculated by obtaining the stress by the optical lever method and the strain by the in-plane method. Further, as described above, in this embodiment, in the optical lever system, the stress is obtained by scanning a film formed on the substrate with a laser beam. In the in-plane method, strain can be obtained by making X-rays incident. Thus, in this embodiment, Young's modulus can be measured without deforming the film.

  In particular, in the nano-indentation method, the Young's modulus is obtained from the load applied to the indenter and the projected area opened to the film under the indenter. It was difficult to measure the Young's modulus. However, as described above, in this embodiment, stress and strain can be measured by laser light or X-ray irradiation, and the film is not physically deformed or destroyed. The Young's modulus can be measured nondestructively even with an extremely thin thin film, particularly a thin film of 100 nm or less.

  In addition, as a method for measuring without breaking the film, there is also a method of measuring Young's modulus by applying ultrasonic waves to one point of the film and measuring at another point on the film away from one point. However, there are a density, a thickness, and a Young's modulus as parameters. Since each value is obtained by fitting the measured sound wave spectrum, there is a problem that it is difficult to accurately obtain the Young's modulus.

  However, as described above, in the present invention, the Young's modulus is calculated by the stress and strain obtained by the above-described method. Therefore, unlike the ultrasonic method, the Young's modulus can be directly obtained without depending on the fitting. The rate is uniquely determined.

(Example)
First, a ZnO film was formed on a silicon substrate. The ZnO film was formed by a reactive plasma deposition apparatus. As the film forming conditions in the reactive plasma deposition apparatus, the ZnO raw material has a Ga ₂ O ₃ concentration of 4 wt%, the substrate temperature is 200 ° C., and the pressure in the film forming apparatus is about 3 × 10 ⁻¹ (Pa). Set. In this example, a silicon oxide film having a thickness of about 8 nm was formed on a silicon substrate, and a ZnO film having a thickness of 100 nm was formed at a deposition rate of 170 nm / min under the above conditions. Then, the Young's modulus of this film was measured using both the optical lever method and the in-plane X-ray diffraction method.

First, the stress of the ZnO film formed under the above conditions was measured.
As described above, first, with the silicon oxide film formed on the silicon substrate (before the ZnO film was formed), the substrate surface was scanned to obtain the curvature radius.

Next, a ZnO film was formed, the curvature radius after the film formation was determined in the same manner, R was determined using Expression 2, and the film stress was calculated according to Expression 3. The internal stress of the ZnO film was determined to be 9.406 × 10 ⁸ (Pa) as shown in FIG.

  Next, the X-ray diffraction spectrum of the ZnO film in the horizontal plane direction was measured with an X-ray diffractometer. The spectrum shown in FIG. 3 was obtained.

  Based on this spectrum, the diffraction angle spread β was calculated, and the strain (ε) was calculated by the equation of the Willson-Hall plot. In this embodiment, the X-ray wavelength λ is 0.154184 nm. From these, the strain ε was determined to be 0.0069.

The stress and strain thus obtained were substituted into the above-described formula 1, and the Young's modulus was obtained as 1.3632 × 10 ¹¹ (Pa).

Similarly, for a ZnO film having a thickness of 30 nm, the curvature radius R of the silicon substrate before film formation and the curvature radius of the silicon substrate after film formation were determined by the optical lever method, and the stress σ was determined. Next, the diffraction angle spread β was determined by the in-plane X-ray diffraction method, and the strain ε was determined. As shown in FIG. 4, the Young's modulus of 1.3108 × 10 ¹¹ (Pa) is obtained by dividing the stress by the strain using the stress of 1.088 × 10 ⁹ (Pa) and the strain of 0.0083 obtained as described above. )was gotten.

  Thus, in the present invention, it was possible to measure the Young's modulus even in a very thin film having a film thickness of 30 nm.

The present invention is not limited to the above-described embodiments, and various modifications and applications are possible.
For example, in the above-described embodiment, the configuration in which the ZnO film is formed on the silicon substrate has been described as an example. However, it is possible to use other than the silicon substrate. For example, a transparent substrate made of glass or the like can be used. As shown in FIG. 5A, when a transparent substrate 21a made of glass or the like is used, when measuring stress by an optical lever method as described above, in order to improve the reflection of laser light, In addition to the film to be measured such as a ZnO film, a reflective film 23 made of Cr or the like having light reflectivity such as laser light may be formed on the surface, the other main surface, or the surface of the film. When a substrate made of a material other than silicon is used, the value of the substrate material is used as the silicon-related material constant in Equation 3.

  Also, when using a substrate other than a silicon substrate such as a transparent substrate made of glass or the like, from the viewpoint of ensuring measurement reliability in the optical lever method, for example, as shown in FIG. Reflective films 23a and 23b having light reflectivity are preferably formed on the main surface, so that warpage of the substrate can be generated substantially concentrically. Therefore, it is preferable to use the both main surfaces of the glass substrate in which the same film is formed except for the thin film to be measured and the both surfaces are symmetrical.

  In the present embodiment, the configuration in which the ZnO film, which is the object to be measured, is formed on the silicon substrate has been described as an example. However, the present invention is not limited to this, and the object to be measured may be formed on another substrate. Good.

  In the X-ray diffraction method used in the above-described embodiment, only a crystalline material can be measured because a diffraction phenomenon is used, and an amorphous film cannot be measured. However, even when an amorphous film is formed, when a crystalline substrate is used, the strain (first strain) in the vicinity of the substrate surface before forming the amorphous film is reduced as described above. An amorphous film is obtained indirectly by measuring the strain (second strain) in the vicinity of the surface of the substrate after the amorphous film is formed, and obtained by the in-plane X-ray diffraction method and Equation 5. It is possible to measure the strain. As a result, the Young's modulus can be measured for an amorphous film.

(A) thru | or (c) is a figure explaining the optical lever method. (A) And (b) is a figure explaining the in-plane X-ray-diffraction method. It is the X-ray diffraction spectrum which measured the ZnO film | membrane by the in-plane X-ray-diffraction method. It is a table | surface which shows the relationship of the stress concerning the embodiment of this invention, distortion, and Young's modulus. (A) And (b) is a figure explaining the optical lever method in the case of providing a reflecting film.

Explanation of symbols

    11, 21 ... substrate, 21a ... transparent substrate, 12 ... support member, 22 ... ZnO film (film to be measured), 23, 23a, 23b ... reflective film

Claims (12)

By measuring the reflection angle of the laser light incident on the film to be measured for which the stress is to be obtained, the stress of the film to be measured is obtained,
By measuring the lattice spacing in the in-plane direction of the film to be measured, the strain of the film to be measured is obtained,
A Young's modulus measuring method, wherein the Young's modulus of the film to be measured is obtained by dividing the stress of the film to be measured by the strain of the film to be measured.   The method for measuring Young's modulus according to claim 1, wherein the film to be measured is formed on a substrate.   The stress of the film to be measured is obtained by measuring a reflection angle of a laser beam incident on the film to be measured in a state where the film to be measured is not formed on the substrate, and then on the substrate. 3. The Young's modulus measurement method according to claim 2, further comprising measuring a reflection angle of laser light incident on the film to be measured in a state where the film to be measured is formed.   The method for measuring Young's modulus according to claim 2 or 3, wherein the substrate is a transparent substrate.   5. The Young's modulus measurement method according to claim 4, wherein a reflection film having light reflectivity is provided on one main surface or the other main surface of the substrate or the surface of the film to be measured.   6. The Young's modulus measurement method according to claim 4, wherein the substrate is a glass substrate.   4. The Young's modulus measurement method according to claim 2, wherein the substrate is a substrate having light reflectivity.   The method for measuring Young's modulus according to claim 7, wherein the substrate is a silicon substrate.   The method for measuring Young's modulus according to any one of claims 2 to 8, wherein one main surface and the other main surface of the substrate are mirror-polished.   10. The Young's modulus according to claim 2, wherein the same film is formed on one main surface and the other main surface of the substrate except for the film to be measured. Measuring method.   The method for measuring a Young's modulus according to claim 1, wherein the film to be measured contains ZnO. The method of measuring a Young's modulus according to any one of claims 1 to 11, wherein the film to be measured is crystalline.

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