JPH0613964B2 - Film thickness measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION <Industrial field of application> The present invention relates to a thin film formed on a substrate, for example, plating,
The present invention relates to a method for measuring the thickness of a thin film formed by coating, painting, etc. by ultrasonic waves.

<Prior Art> Conventionally, a method of measuring the thickness of a film formed on a substrate by using ultrasonic waves is known, and ultrasonic waves are usually generated through a liquid for ultrasonic wave propagation through the film and the film. The reflected ultrasonic wave or transmitted ultrasonic wave is irradiated onto the substrate and detected by an appropriate means.

As a measurement method using ultrasonic waves, a method of irradiating a film with pulsed ultrasonic waves and measuring the film thickness from the time delay of the reflected ultrasonic pulse, an ultrasonic wave with which the film thickness of the film to be measured is irradiated. Method that uses the phenomenon that ultrasonic waves resonate when it is an integer multiple of 1/4 wavelength, or the method that the sound velocity of surface acoustic waves changes depending on the film thickness It has been known. There is a method of using a so-called V (Z) curve showing an interference relationship between a reflected wave from a film surface and a surface acoustic wave, as a method of measuring using a change in sound velocity of a surface acoustic wave.

Further, as one method for measuring the film thickness using an ultrasonic microscope, the method disclosed in Japanese Patent Application Laid-Open No. 61-20803 is known. This method is
When ultrasonic waves are radiated at an incident angle θ peculiar to the combination consisting of the substrate, the film, and the ultrasonic transmission medium, the ultrasonic wave is generated when the product of the frequency of the ultrasonic wave and the film thickness reaches the value H peculiar to the combination. The phenomenon in which the reflectance of is extremely small is used.
Therefore, according to this method, the incident angle θ and the value H are obtained in advance for the combination body having the film and the substrate made of the same substance as the subject, and the ultrasonic wave is applied to the film of the subject at the incident angle θ. The film thickness can be calculated from this frequency and the value H by measuring the frequency of the incident ultrasonic wave at which the reflection intensity is minimized.

(Problems to be Solved by the Invention) According to the measuring method disclosed in Japanese Patent Laid-Open No. 61-20823, as described above, ultrasonic waves are applied to the film of the subject at a predetermined incident angle. After irradiation, the frequency of the reflected wave from the film is analyzed to detect the frequency of the ultrasonic wave that minimizes the reflection intensity, and the film thickness is calculated from the detected frequency. However, in the above-described measuring method, the film thickness cannot be measured unless a wave having a constant product of the frequency and the film thickness that minimizes the reflection intensity occurs in the subject.

That is, the film thickness cannot be calculated by the above method when a wave having another functional relationship in which the frequency at which the reflection intensity is minimum and the film thickness are not inversely proportional to each other in the subject is generated.

An object of the present invention is to provide a film thickness measuring method capable of measuring film thickness if there is a certain functional relationship between the frequency and the film thickness at which the reflection intensity of the object is minimum and the film thickness is not inversely proportional.

(Means and Actions for Solving Problems) Variables are the incident angle θ of ultrasonic waves and the frequency f of the minimum portion when a complicated or single minimum portion appears in the reflection intensity frequency distribution of the reflected ultrasonic waves from the subject in advance. The functional relationship d = g () with the film thickness d is obtained, and when measurement is performed, d is obtained from the minimum frequency of the reflection intensity.

Embodiments of the Invention Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

First, it will be explained how the minimum reflection intensity phenomenon, which is the basis of the present invention, changes according to the film thickness.

As shown in FIG. 1, the substrate 12, the film 14, the ultrasonic wave propagation medium 16 in contact with the film surface, and the object 17 in contact with the substrate surface are combined, and the incident angle of the ultrasonic waves incident on the combination from the substrate side. As a result of measuring the ultrasonic wave reflection intensity from the combination by varying θ over a wide range, the incident angle θ _o peculiar to the combination of the combination of the substrate, the film, and the propagation medium is θ _o.
When an ultrasonic wave was applied to the substrate at, a frequency distribution of the reflection intensity having a plurality of or one minimal portion was obtained as shown in FIG. Then, when the incident angle θ was kept constant and only the thickness of the film of the combination was changed to examine the frequency distribution of the reflection intensity, as shown in FIGS. 3A to 3B, the frequency at each local minimum portion was the film thickness. It turned out to change according to the change of.

In addition, L. M. "Waves in Layered Media" by Brekovsky, Academic Press,
By applying the calculation method disclosed in New York, 1980 to the above combination to irradiate ultrasonic waves from the film side at an incident angle θ to obtain the reflection intensity, the frequency distribution of the reflection intensity of a general layered material is obtained. As a result of examination, when the incident angle θ has a value peculiar to the above combination, a plurality of or one local minimum appears in the frequency distribution of the reflection intensity, and the frequency of each local minimum is the film thickness. It was found to change depending on the value of.

Next, the above method for calculating the reflection intensity will be described in detail.

As shown in FIG. 4, the reflectance when the layered material sandwiched by the semi-infinite medium is irradiated with ultrasonic waves at the incident angle θn + 1 is calculated. In FIG. 4, the thickness of the i-th layer is d _i ,
The angle between the traveling direction of the longitudinal wave and the z axis in the layer is represented by θ _i , the angle between the traveling direction of the transverse wave in the i-th layer and the z axis is represented by γ _i , and the n + 1-th layer is a liquid.

First, the coordinate origin is set on the boundary surface between the first layer and the second layer,
The positive direction of the z axis is perpendicular to this boundary surface and in the direction of the nth layer. Here, it is assumed that the first layer and the (n + 1) th layer are semi-infinite media, while the other i-th layers are media having a finite thickness d _i . That is, the boundary between the mth layer and the m + 1th layer is Becomes

Further, the two-dimensional problem is treated as the minimum reflectance phenomenon does not depend on the y coordinate.

Let ρ be the density, λ and μ be the Lame constant, b be the sound velocity of the transverse wave, and c be the sound velocity of the longitudinal wave, and the quantities relating to the i-th layer are represented by the upper and lower suffixes i.

When the longitudinal wave velocity potential is φ and the transverse wave velocity potential is ψ, x components u and z components of the displacement vector and stresses σ _zz and σ _xy are represented by the following equations. Σ for simplicity
_{If zz} ≡ s and σ _xy ≡ σ, The lame constants λ and μ are the sound velocity c of the longitudinal wave and the sound velocity b of the transverse wave.
And the density ρ have the following relationship.

Further, the potentials φ and ψ satisfy the following wave equation.

Here, k and κ have the following relationship with the frequency ω and the sound velocities b and c.

The displacement amount and the stress must satisfy the continuity condition at the boundary between elastic bodies. Therefore, considering the boundary between the j-th layer and the j + 1-th layer, The relationship must always be established.

On the other hand, each potential of the j-th layer can be expressed as Φ _j ≡e ^{i (ξx−ωt)} Ψ _j ≡e ^{i (ξx−ωt)} because the dependences on x and t are sinusoidal. Therefore, the displacement amounts U _j and W _j can be _calculated from the equations (1) and (2) as follows. Becomes Also, the stresses S _j and σ _j are Then, from equations (3), (4), (5) and (6), Becomes

Therefore, if we write the continuous condition (7) using the above potential, it becomes as follows.

About U About W About S About σ Here, ξ, θ _j , γ _j , k _j , and κ _j satisfy the following relationship because ξ is an x component of the wave vector and is an invariant.

ξ = k _{n + 1} · sin θ _{n + 1} = k _j sin θ _j = κ _j sin γ _j (j = 1, 2 ... n) θ _{n + 1} is an incident angle, and when this incident angle is determined, θ _{i of} all layers and γ _i will be decided. However, Then θ _j becomes a complex number, To put As Becomes

Next, consider the m-th layer. Denoting the potential of incident and reflected at the coordinate origin at the boundary between the m-th layer and the m-1 _{layer, Φ m = (φ m '} e iαmz + φ m "e -iαmz) · e i (ξx-ωt ⁾ [psi _m = a ^{_{(ψ m 'e βmz + ψ}} m "e -iβmz) · e i (ξx-ωt). However, α _m and β _m are Where φ _m ′ and ψ _m ′ are the potentials of the traveling wave in the positive z-axis direction, and φ _m ″ and ψ _m ″ are the potentials of the traveling wave in the negative z-axis direction. U _m using these potentials, w _m, s _m, to represent the sigma _m, omit the subscripts m, Becomes Each quantity at the boundary between the m-1th layer and the mth layer is
It is obtained by setting z = 0 in the equation (8). Similarly, each quantity at the boundary between the mth layer and the m + 1th layer is
It is obtained by setting z = d. First, in equation (8), z
== d Becomes P = αd and θ = βd.

Next, considering the boundary condition (7), at z = 0, Becomes In this equation (10), φ ′ + φ ″, φ′−φ ″, ψ′−ψ ″, ψ ′ + ψ ″ are u
Solving for _m−1 , w _m−1 , s _m−1 , σ _m−1 Becomes

Thus, (9) from the equation and the equation (11) _{(u m, w m, s} m,
σ _m ) is (u _m−1 , w _m−1 , sm ₋₁ ,
σ _m−1 ) can be expressed as follows.

However, a _m is a matrix of 4 rows and 4 columns, and each component is as follows.

When ξ / κ = ζ and ξ / k = η are set, a ₁₁ = 2ζ cos p + (1-2ζ ² ) COS θ a ₂₂ = (1-2ζ ² ) cosP + 2ζ ² cosQ a ₃₃ = (1-2ζ ² ) cosP + 2ζ ² cos θ = a ₂₂ a ₄₄ = 2ζ ² cosP + (1-2ζ ² ) cosQ = a ₁₁ .

If is a complex number, choose a positive pure imaginary number, And

Here, if Equation (12) is repeatedly used, Can be expressed as However, a _{A = a m a m-1} ...... a 2.

, Ψ _{n + 1} because the _{n +} 1th layer is a liquid
= 0. Therefore, the traveling wave and the reflected wave that enter the elastic body from the (n + 1) th layer at the incident angle θ _{n + 1} are represented by the following equations.

Φ _{n + 1} = Re ^{iαn + 1 (z−H)} + e
^{-Iαn + 1 (z-H)} where: And

The transmitted wave is represented by the following formula.

Φ ₁ = φ ₁ e ^−iα1z , Ψ ₁ = ψ ₁ e ^−iβ1z where: And

Considering that the _{n + 1} - _th layer is a liquid, the continuous condition in the plane of z = H is: w _{n + 1} = w _n s _{n + 1} = s _n σ _{n + 1} = σ _n = 0 (14) When w _n , s _n , and σ _n on the right side are expressed using However, A _ij indicates the i-th row and j-th column component of the matrix A. (1
When u ₁ is removed from the equations (4) and (15), w _{n + 1} = M ₂₂ w ₁ + M ₂₃ s ₁ + M ₂₄ σ ₁ s _{n + 1} = M ₃₂ u ₁ + M ₃₃ w ₁ + M ₃₄ σ ₁ . However, Is.

Here, from equations (1), (2), (3), and (4), w _{n + 1} = iα _{n + 1} (R-1) s _{n + 1} = -ρ _{n + 1} ω ² (R + 1) u ₁ = i (ξφ + β ₁ ψ _{) w 1 = i (-α 1} φ 1 + ξψ 1) Becomes From the above equation, the reflectance R is represented by the following equation.

here, Is.

Also, this z'is Expressed as here, And ψ _{1 /} φ ₁ is Is.

When the semi-infinite medium of the first layer is liquid or gas, ψ _{1 /} φ ₁ = 0 and E = α ₁ M ₃₂ −iρ ₁ ω ² M ₃₃ F = α ₁ M ₂₂ −iρ ₁ It becomes ω ² M ₂₃ . From this, z'is Becomes However Is.

Therefore, the reflectance R is calculated from equation (14) as Becomes here Is.

Furthermore, when the first layer and the (n + 1) th layer are the same liquid,
From ρ ₁ = ρ _{n + 1} , c ₁ = c _{n + 1} , α ₁ = α _{n + 1} ,
z ₁ = z _{n + 1} . Therefore, the reflectance R is Becomes However, Is.

A procedure for actually calculating the reflection intensity using the above calculation method will be described.

First, as shown in FIG. 5, the n + 1th layer is the ultrasonic wave propagation medium 16, the nth layer is the film 14, the n-1st layer to the second layer 12 are the base 12, and the first layer is the contact object 17, such as air. Therefore, the thicknesses of the film and the substrate are d and D, respectively.

Subsequently, the incident angle theta, ultrasonic transmission medium 16, film 12, base 14, the density of the object 17, Lame constant, the speed of sound or the like are substituted into the above equation a _1, a ₂ ····· a _n Ask. Furthermore, A =
a _n a _n-1 ... A ₂ , M _ik , ψ _{1 /} φ ₁ , E, F, and z ′ are sequentially obtained. Then, using these values, the reflectance R is obtained from the equation (17).

Next, the measuring method of the present invention for measuring the film thickness by utilizing the above-mentioned minimum phenomenon of reflection intensity will be described.

FIG. 1 shows a measuring device for carrying out the measuring method. First, the subject 10 measured by this device is
It has a base 12 and a thin film 14 formed on the base, and water 16 as an ultrasonic wave propagation medium is placed on the base.
Then, the measuring device is in contact with the water 16 and the base 12
Of the first and second piezoelectric transducers 18 and 20 mounted above. The first transducer 18 irradiates the base 12 of the subject 10 with ultrasonic waves through the water 16, and the second transducer 20 receives the ultrasonic waves reflected from the subject. The transducer 18 is connected to the pulse generator 22. Further, the transducer 20 is connected to a fast Fourier transformer 28 via an amplifier 24 and an A / D converter 26.

Next, a method of measuring the film thickness using the measuring device configured as described above will be described.

<Example 1> In this example, the film thickness of the chromium plating layer of the subject 10 in which the chromium plating 14 is applied on the base 12 made of copper is measured by using water as the ultrasonic wave propagation medium 16 and the contact object 17.

First, regarding the combination of copper, chromium, and water, the reflection intensity is calculated by using the above calculation method with the incident angle and the film thickness as variables. The density and sound velocity of each element of the above combination are shown in the following table.

From the results obtained by the above calculation, FIG. 6 shows the relationship between the frequency of the minimum reflection intensity and the film thickness d of the chrome plating for each incident angle θ. In this figure,
A plurality of characteristic lines obtained by plotting the frequencies of the respective minimum portions in the film thickness of the respective minimum portions in various film thicknesses and connecting the plot points of the corresponding minimum portions are shown. Note that the incident angle was calculated with θ = 40 °.

Then, in FIG. 6, the minimum portion where the frequency changes most sensitively to the change of the film thickness, that is, the minimum portion where the slope of the characteristic line is the largest is found. In this embodiment, it can be seen that the _first minimum portion ₁ having the lowest frequency corresponds to the above condition.

Then, the reflection intensity of the subject 10 is measured by the measuring device. In this case, first, planar ultrasonic waves including a plurality of frequency components are emitted from the first transducer 18 to the base 12 through the water 16 at an incident angle θ = 40 °. Subject 1
The ultrasonic wave reflected at 0 is received by the second transducer 20. The frequency of the reflected ultrasonic wave is measured from this received signal, and the frequency distribution of the reflection intensity shown in FIG. 7 is obtained. Then, from FIG. 7, the frequency ₁ of the _first minimum portion from the lowest frequency is read, and ₁ = 32.2 MHz is obtained. Therefore, this ₁ = 32.2 MHz is set to the characteristic line l _{1 in} FIG.
By corresponding to, the film thickness d of the chrome plating 14 =
4 μm is obtained.

Further, the measuring device may be configured as shown in FIG. According to this apparatus, the ultrasonic microscope lens 34 is used as the ultrasonic wave generating means. This microscope lens 34
Is provided with an acoustic lens 36 having a wedge-shaped recess formed of a propagating material such as fused quartz or sapphire, and a piezoelectric film 38 attached to the upper end of the acoustic lens. The ultrasonic microscope lens 34 transmits ultrasonic waves at a predetermined incident angle θ to the subject 1
The reflected ultrasonic waves reflected from the subject are received while irradiating the film 0 of 0. In FIG. 8, reference numeral 16 indicates water as an ultrasonic wave propagation medium that is in contact with the acoustic lens 42 and the film 14.

(Effect of the invention) The reflected wave is obtained by irradiating the surface of the film with the ultrasonic wave, measuring the reflected ultrasonic wave from the object on the surface side of the film, and examining the frequency distribution of the reflected intensity from the measured ultrasonic wave. The film thickness d can be obtained from the frequency at which the reflection intensity of is minimal. Therefore, according to the present invention, the film thickness can be measured even if the frequency at which the reflection intensity of the reflected wave is minimum and the film thickness d are not in inverse proportion.

[Brief description of drawings]

FIG. 1 is a partially cutaway side view showing a measuring device for carrying out the measuring method of the present invention, FIG. 2 is a diagram showing a frequency distribution of reflection intensity, and FIGS. 3A to 3B are respectively different film thicknesses. Showing the frequency distribution of the reflected wave in FIG. 4, FIG. 4 and FIG. 5 are cross-sectional views showing different layered bodies for explaining the calculation method of the reflection intensity, and FIG. 6 is the frequency of the reflected wave at a certain incident angle. FIG. 7 is a characteristic diagram showing changes in distribution, FIG. 7 is a diagram showing a frequency distribution of reflected waves of the subject, and FIG. 8 is a sectional view showing a different modification of the measuring apparatus. DESCRIPTION OF SYMBOLS 10 ... Subject, 12 ... Base | substrate 14 ... Membrane 16 ... Ultrasonic propagation medium 17 ... Contact object

Claims (1)

[Claims] 1. A method for measuring a film thickness of a subject having a substrate and a film formed on the substrate, comprising: a substrate and a film made of the same material as the substrate and the film of the subject; and ultrasonic waves. Regarding a combination with a propagation medium, when the film of the combination is irradiated with ultrasonic waves through the ultrasonic propagation medium, the reflection intensity frequency distribution of the reflected ultrasonic waves from the combination has a plurality of or a single minimum portion. A step of obtaining a function d = g (f) of the film thickness d with the incident angle θ of the sound wave and the frequency f of the ultrasonic wave at the minimum portion as variables; and an ultrasonic wave propagation medium of the combination based on the substrate of the subject. A step of contacting an ultrasonic wave propagation medium made of the same substance as the above; a step of irradiating ultrasonic waves at the incident angle θ on the substrate of the subject through the propagation medium; and an ultrasonic wave reflected from the subject The frequency distribution of Constant and,
A step of detecting a frequency at which the reflection intensity becomes minimum; and a step of calculating the film thickness of the film of the subject from the detected frequency and the function; .