JP2967159B2 - Film thickness measurement method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a highly accurate film thickness measuring method.

(Prior Art) Conventional measuring methods used for measuring the thickness of a thin film formed by vapor deposition, sputtering, or CVD method include the following two methods.
There are types. One of them is a thin film formed on the surface,
This is a method of measuring the thickness of a thin film by using a step with a portion where a substrate surface where a thin film is not formed is exposed. These include (1) a stylus type that converts the change in surface irregularities into a change in capacitance while taking the surface with a thin needle and extracts and measures the signal. (3) Laser reflection by irradiating the surface with laser light and measuring the change in the intensity of light reflected from the surface by projecting an optical interference pattern and measuring the amount of change in the interference pattern Law, (4)
A method of directly measuring and measuring steps with an electron microscope, etc.
and so on. Another method is to measure the thickness of an optically transparent thin film, (5) an optical interference method using interference between light reflected on the surface of the thin film and light reflected from the surface of the substrate, and (6). There are an optical deflection method (ellipso method) for measuring the change in the deflection angle of light to measure the film thickness, and (7) a method for irradiating characteristic X-rays and measuring the film thickness from the attenuation factor.

(Problems to be Solved by the Invention) In the film thickness measurement (1) to (4) for measuring a step between a thin film and a substrate surface, it is necessary to form a step on a sample to be measured. For this purpose, when forming a thin film, the surface of the sample under the thin film is exposed by masking the sample surface to form a step, or etching or mechanically removing a part of the formed thin film. Must be measured. These methods can measure metals, inorganic substances, and organic substances irrespective of the material of the thin film. However, it takes time to prepare a sample for measurement, which is not easy. Further, when the roughness of the substrate is large, or when the sample is distorted at the boundary between the thin film and the substrate due to the stress acting between the thin film and the substrate, it becomes difficult to measure with high accuracy when the thickness is 10 nm or less.

In the optical methods (5) and (6), the film thickness is 10
The measurement can be performed sufficiently even at nm or less, and there is no need to create a step for measuring the film thickness. However, it is limited to a material that transmits light, and the target whose film thickness can be measured is narrow, and measurement cannot be performed with a metal thin film or the like.

In the method (7) for measuring the thickness of a thin film based on the transmittance of X-rays, first, it is necessary to form the thin film on a thin substrate that sufficiently transmits X-rays. Is very limited.

From these results, conventionally, regardless of the film material and substrate,
In addition, there is no need to form a step in the sample, and there is no measurement method capable of measuring a film thickness of 0.1 nm to 100 nm with high accuracy. In particular, the thickness of an optically opaque metal thin film is measured using a step, and it is difficult to measure with a thickness of 10 nm or less with high accuracy.

The present invention has been proposed in order to improve the above-mentioned drawbacks, and its purpose is to measure the film thickness with high accuracy without depending on the material and substrate of the film, and it is not necessary to form a step on the sample, and the thin film is used. To provide a method for measuring the film thickness.

(Means for Solving the Problems) In order to achieve the above object, the present invention irradiates the film to be measured with X-rays from an oblique direction, measures the X-ray reflectance, and calculates the film thickness d by the following formula: Here, r ₀₁ is the X-ray reflectivity of the complex refractive index n ₁ in vacuum r ₀₂ is the X-ray reflectivity of the complex refractive index n ₂ in vacuum λ is the wavelength of X-rays δ ₁ is a constant β ₁ determined by a substance Is a constant determined by the substance φ is a value determined by n ₀ cos θ = n ₂ cos φ n ₁ , n ₂
Is a complex refractive index, and θ is an incident / reflection angle.

(Operation) It is known that the reflectance r ₀₂ between media having different complex refractive indices is expressed by the equation (1) of the complex amplitude of Fresnel.

Where θ is the oblique incidence angle, Is a refraction angle, and the relationship is shown in FIG. 1. n ₀ and n ₂ are complex refractive indices, which are expressed by equation (2) using optical constants δ and β of the substance.

δ and β are values specific to the element. Further, the angle φ can be obtained from Snell's law (3).

n ₀ cos θ = n ₂ cos φ (3) Although δ and β differ depending on the substance or the wavelength of the X-ray, Henke [Atomik Data and
NIUCLEA DATA TABLE (ATOMIC DATE AND NUCL
EAR DATA TABLES 27.1-144) (1982)]. In addition, since a compound composed of several kinds of elements can be calculated, it can be used as a known value.

Usually, what can be measured as the X-ray reflectivity is the square of the absolute value of the complex amplitude, and is expressed by equation (4).

The reflectance between the media having complex refractive indices n ₀ and n ₁ (FIG. 2) is similarly represented. Expressions (5) to (8) are used.

n ₁ = 1−δ ₁ −iβ ₁ (6) n ₀ cos θ = n ₁ cos φ (7) Next, on the substrate complex refractive index of n _2, as shown in FIG. 3, if there is a single layer film of n ₁ the reflectance (in vacuo both membranes). According to burning, when r ₀₁ and r ₀₂ are used, the reflectance from the single-layer film is expressed by Expression (9).

Here, δ is assuming that the thickness of the single-layer film having the complex refractive index n ₁ is d. Is represented by

Oblique oblique angle theta is, if smaller than a certain angle theta _c, X-rays are hardly reflected. . This area is called a total reflection area.
The critical angle θ _c is expressed by equation (11) using the optical constant δ of the substance.

cos θ _c = 1−δ (11) In the X-ray region (wavelength 0.1 nm to 10 nm), δ is small (<10
^{-3), θ} _c has a value of 3.0 ° or less in most materials.

For angles greater than θ _c , the X-ray reflectivity sharply decreases. Therefore, the assumption of | r ₀₁ |, | r ₀₂ | ≪1 holds in the region of θ> θ _c . Based on this assumption, to expand the section r ₀₁ (9) below as follows.

O (r ₀₁ ³ ) is a term of third or higher order with respect to r ₀₁ . ｜ r ₀₁
Since |, | r ₀₂ | ≪1, ignoring terms of second and higher order, it is expressed as r ₀₁₂ = r ₀₂ e− ^iδ + (1−e− ^iδ ) r ₀₁ (13) The reflectivity _R012 of the single-layer film that can be measured is | r
₀₁₂ | ² .

Therefore, It is. Therefore, R ₀₁₂ vibrates as φ increases. Since the cycle of the vibration is proportional to the film thickness d, the film thickness can be obtained by measuring the vibration.

Furthermore, in the X-ray region, δ is almost
Since it is very small at 10 ^-3 or less, 1
-Δ ~ 1 can be similar.

Therefore, from formulas (14) and (7), the X-ray reflectivity is measured at an angle equal to or larger than the critical angle, and the period ω of the vibration is obtained, whereby the film thickness d can be accurately obtained regardless of the type of the substance. Can be. At this time, ω It is expressed as

Where ω: period of vibration d: film thickness θ: oblique oblique angle n ₁ : complex refractive index.

(Example) Next, an example of the present invention will be described.

The embodiment is merely an example, and it goes without saying that various changes or improvements can be made without departing from the spirit of the present invention.

First Example Pt (platinum) was formed on a substrate made of Si (silicon), and the film thickness was measured from X-ray reflectivity.

FIG. 4 shows the configuration of an apparatus used for measuring the X-ray reflectivity. In the figure, 1 is an electron gun, 2 is a metal target, and in this example, Al (aluminum) was used. Reference numeral 3 denotes an X-ray filter made of, for example, thin Be. 4 is a slit,
5 are collimated. The wavelength of X-ray 5 is 8.34Å
(1-K line). Reference numerals 6 and 7 denote rotating stages, 6 rotates the sample 8, and 7 rotates the X-ray detector 9 at θ−2θ, and measures the X-ray reflectance of the sample 6. 10 is a container. When measuring with soft X-rays of about 10 ° attenuated by air, the container 10 is evacuated to a vacuum. The optical constants of Pt and Si with respect to λ = 8.34Å are δ _Pt = 1.064 × 10 ^-3 β _Pt = 3.085 × 10 ^-4 δ _Si = 1.897 × 10 ^-4 β _Si = 8.452 × 10 ^-6 (16) Very small. These values were determined from the Henkc table. The critical angles of Si and Pt are 1.12 ° and 2.64, respectively.
°. Therefore, at angles above the critical angle of Pt, γ ₀₁ ≫γ
₀₂ holds. Equation (14) is simplified as follows.

When the Pt film thickness is d = 300 ° and the X-ray reflectivity is measured with an X-ray of λ8.34 °, the vibration shown in FIG. 5 should be observed. When the film thickness d is 100 °, the cycle of vibration becomes small as shown in FIG. Therefore, the film thickness can be obtained from this cycle.

FIG. 7 shows the reflectivity of the Pt film to X-rays at λ = 8.34 °. At θ _c = 2.64 ° or more, the reflectance shows oscillation. The oblique incident angles giving one cycle (2π) of this vibration are denoted by θ ₁ and θ ₂ , respectively. Therefore, from equation (17) And m ₂ = m ₁ +1 (m ₁ and m ₂ are integers) Given θ ₁ = 3.5 ° and θ ₂ = 4.15 °, The points in FIG. 7 are the measured values, and the solid line is the X-ray reflectivity calculated with d = 264 °, which agrees well.

[Second Embodiment] FIG. 8 shows the result of forming an optically transparent thin film of quartz (SiO ₂ ) as an insulator on a Si substrate and measuring the X-ray reflectivity. The optical constant of SiO ₂ is Is the optical constant of Si It is a material very close to and optically almost the same material. Even with such a combination of substances, the critical angle of SiO ₂
Above 1.15 °, a beat with a reflectance can be observed.
From the width of the beat And the film thickness.

Therefore, according to the method of the present invention, it is possible to measure the film thickness in the order of Å if there is a slight difference in optical constant regardless of the type of the substance.

Third embodiment] First, two sheets of Si substrates A, on the B film thickness d ₁ Cr (chromium)
Form a film. The substrate A was taken out, to form a Cr film having a thickness d ₂ thereon putting board C instead. Accordingly, three types of film thicknesses d ₁ (A), d ₂ (C), and d ₁ + d ₂ (B) are obtained.

The X-ray reflectivities of these three types of films were calculated as ninth, tenth,
As shown in FIG. For the sake of clarity, both the experiment (dotted line) and the calculated value (solid line) are logarithmic.

From FIG. 9, d ₁ = 110 °, and from FIG. 10, d ₂ = 290 °
Å, from Figure 11 determined to be d ₁ + d ₂ = 400Å, good agreement.

Therefore, according to the method of the present invention, a film thickness of the order 膜厚 can be accurately measured.

Fourth Embodiment According to the present invention, the resolution of the film thickness measurement depends on the resolution of the oblique incident angle. To determine the film thickness, Δθ = θ _{i + 1}
It is necessary to observe the vibrations of one period in the - [theta] _i. In the region where θ is small, it is sin θ ~ θ For example, if it is difficult to measure a period of vibration smaller than 0.2 °, it is impossible to measure a film thickness of 1200 ° or more with an X-ray of λ = 8.337 °. In addition, it is difficult to measure the vibration period larger than 10 ° because the X-ray reflectivity sharply decreases. Therefore, it is difficult to measure a film thickness of 24 ° or less with an X-ray of λ = 8.337 °. However, if a CuK line of λ = 1.54 ° is used, it is possible to measure a film thickness of about 4.4 °, and if an L line of Cu of λ = 13.3 ° is used,
It can measure up to a thickness of 1900 mm.

Therefore, when, for example, Cu (copper) is used as the X-ray source in FIG. 4, X-rays of K-ray (wavelength 1.54 °) and L-ray (13.3 °) are generated at the same time. By measuring the reflectance of each of the K and L lines using a detector that can separate and measure the K and L lines, 4Å to 2000
The film thickness of 膜厚 can be measured. As a target of the X-ray source, any substance can be used as well as Mo, W, Al, and Cu.

Fifth Embodiment FIG. 12 shows a measured value of the X-ray reflectivity of Pt obtained by performing a Fourier transform. The horizontal axis is the cycle of vibration. From the position of the peak,
The thickness d can be determined.

The use of this method has an advantage that d can be obtained even when the measurement range is narrow and there is no one-cycle vibration in the measurement range. If the measurement range is narrow, the peak is broad and broad, so that the required film thickness accuracy is poor. However, by increasing the measurement range and sharpening the peak, the accuracy of film thickness measurement can be improved.

(Effects of the Invention) As described above, according to the present invention, the film thickness can be accurately obtained in the order of Å by measuring the period of the vibration with respect to the oblique incident angle of the X-ray reflectance. X-rays
Since most substances are transmitted, the thickness of a film made of any substance can be measured, and further, there is no need to make a step on the sample.

Further, by changing the wavelength of the X-ray, a film thickness of 1 to 2000 ° can be accurately measured. Further, by using the Fourier transform, there is an effect that the film thickness can be obtained even if one cycle of vibration cannot be measured.

[Brief description of the drawings]

FIG. 1 shows that the complex refractive indices are n ₀ (= 1) and n ₂ (= 1−δ ₂ −).
The figure which showed the relationship between the oblique incidence angle (theta) and angle (phi) when X-rays were incident on the interface of i (beta) ₂ ). FIG. 2 shows that the complex refractive index is n ₀ (=
1) shows the relationship between the oblique incidence angle θ and the angle φ when X-rays enter the interface between n ₁ (= 1−δ ₁ −iβ ₁ ), and FIG. 3 shows that the complex refractive index is n. FIG. 6 is a diagram showing a relationship between an oblique incident angle θ and an angle φ when X-rays enter a film having a complex refractive index of n ₁ on a substrate ₂ . FIG. 4 is a view showing a structure of an X-ray reflectivity measuring device.
FIG. 5 is a diagram showing the relationship between the calculated value of the X-ray reflectivity at an angle equal to or larger than the critical angle of Pt of Pt having a thickness of 300 ° and the oblique incident angle. FIG. 6 is a diagram showing a relationship between Pt having a film thickness of 100 °, a calculated value of X-ray reflectivity at an angle equal to or larger than the critical angle of Pt, and an oblique incident angle. FIG. 7 is a diagram showing the relationship between the X-ray reflectivity of the Pt film and the oblique incident angle.
FIG. 8 is a diagram showing the relationship between the X-ray reflectivity of the SiO ₂ film and the oblique incident angle. FIG. 9 is a diagram showing the relationship between the X-ray reflectivity and the oblique incident angle of a 110 ° -thick Cr film. Figure 10 shows a 290 mm thick Cr film.
The figure which showed the relationship between the X-ray reflectance of a film, and the oblique incidence angle. FIG. 11 is a diagram showing the relationship between the X-ray reflectivity and the oblique incident angle of the 400 ° -thick Cr film, and FIG. 12 is a diagram showing the relationship between the Fourier transform intensity of the X-ray reflectivity and the period of vibration. FIG. 1 ... Electron gun, 2 ... Target, 3 ... X-ray filter, 4 ... Slit, 5 ... X-ray, 6 ... θ rotation stage, 7 ... 20 rotation stage, 8 ... Sample, 9 ... ... X
Line detector, 10 …… Container.

Claims (1)

(57) [Claims] 1. A film to be measured is irradiated with X-rays from an oblique direction, the reflectance of the X-rays is measured, and the film thickness d is calculated by the following equation: Here, r ₀₁ is the X-ray reflectivity of the complex refractive index n ₁ in vacuum r ₀₂ is the X-ray reflectivity of the complex refractive index n ₂ in vacuum λ is the wavelength of X-rays δ ₁ is a constant β ₁ determined by a substance Is a constant determined by the substance. Φ is a value determined by n ₀ cos θ = n ₂ cos φ, where n ₁ and n ₂ are complex refractive indices, and θ is an incident / reflection angle.