JP3339243B2 - X-ray reflectance analysis method and apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for analyzing X-ray reflectivity, and more particularly to an evaluation of the quality and thickness of a thin film by measuring X-ray reflectivity.

With the recent high integration of MOS devices, gate oxide films have been reduced in thickness to several tens of degrees, and metal films for wiring have also been reduced in thickness. Evaluation of film quality is important for improving the quality and reliability of these thin films.

[0003]

2. Description of the Related Art The X-ray reflectivity method uses X-rays having a wavelength of about 1 mm, so that coatings of several to several thousand mm can be evaluated.
This is an evaluation method capable of accurately evaluating the film density, the roughness of the surface and between the films and the interface with the substrate.

In this method, even for a multilayer film, the film quality can be evaluated nondestructively by using an appropriate model. When evaluating a single-layer thin film formed on a substrate by using this method, the reflection intensity of the measured X-ray has a vibration curve that depends on the incident angle due to the interference between the thin-film surface and the reflected X-ray from the substrate surface. can get.

The amplitude intensity of the vibration is proportional to the density difference between the substrate and the thin film, and the interval between the vibrations is inversely proportional to the film thickness. Therefore, a film having a small density difference from the substrate, for example, silicon (S
i) Silicon oxide (SiO ₂ ) film on the substrate (silicon density is 2.
33g / cm ³ , the density of silicon oxide film is 2.20g / cm ³ )
It was difficult at the time of fitting the measurements with the model.

As a method of analyzing the X-ray reflectivity from a multilayer film, a calculation method based on the complex refractive index and Fresnel's equation has been almost established.

[0007]

As described above, in the X-ray reflection curve, the quality of the thin film is reflected as interference vibration,
Other changes in the reflectance due to the incident angle mainly reflect the reflectance of the substrate.

The dependence of the reflectivity on the incident angle is larger than the change in the interference vibration in a film whose density is close to the substrate, and this may cause the result to be unstable in the nonlinear least squares optimization in the data optimization by the model. I was

As described above, in the prior art, it is difficult to evaluate a thin silicon oxide film or a liquid crystal substrate which is important in the manufacture of a semiconductor device. SUMMARY OF THE INVENTION It is an object of the present invention to speed up processing and increase reliability when optimizing measurement data using a model in thin film evaluation by the X-ray reflectivity method.

[0010]

Means for solving the above problems are as follows: 1) The intensity of the reflected X-rays from the surface of the coating film deposited on the substrate .
The X-ray reflection curve showing the incident angle dependence is plotted from the surface of the substrate.
Divide by the X-ray reflection curve showing the incident angle dependence of the reflected X-ray intensity
First data and the thickness, density, surface and
X-ray wavelength calculated using the roughness of the interface as a parameter
The reflectivity for the incident angle at
The second divided by the X-ray reflection curve representing the incident angle dependence of the intensity
Find the square of the difference with the data at multiple angles of incidence,
The parameter is set so that the sum of the square values is minimized.
By optimization, the density, surface and boundary of the coating
X-ray reflectance analysis method for evaluating the roughness of the surface , or 2) X-ray reflectance analysis method according to 1 above, wherein the reflectance from the substrate surface is measured after removing the coating, or 3) The reflectance from the substrate surface is determined by the unevenness of the substrate surface.
Incident angle at X-ray wavelength calculated using roughness as a parameter
X-ray reflectivity analysis method of the 1, wherein using the reflectivity for, or 4) the data 1 wherein 1 X-ray reflectivity analysis method according to Fourier transform determine the thickness of the coating, or 5) on the substrate means for determining the X-ray reflection curve from the surface of the coatings deposited, and means for obtaining the data obtained by dividing the X-ray reflection curve of the X-ray reflection curve from the surface of the coating from the surface of the substrate possess, According to the analysis method described in 1 above, the density of the coating
Degree, roughness of surface and interface, and analysis method described in 4 above
It is achieved by X-ray reflectance analyzer for have a means for determining the coating thickness by law.

[0011]

According to the present invention, by removing the overall reflectance from the substrate from the measured reflectance, and using only the remaining vibrating portion for optimizing the model, it is possible to speed up the processing and increase the reliability. I have.

More specifically, the vibration part can be enlarged by dividing the measured reflectance of the thin film by the reflectance of the substrate and normalizing it. In this case, the reflectance of the substrate can be obtained by measuring the thin film after removing it, or by optimizing the thin-film measurement data with a model of only the substrate that does not include vibration, to obtain an approximate value of the vibration data. Data can be obtained.

FIG. 1 is a diagram for explaining the principle of the present invention.
Fig. 1 (A) shows the path of light incident on a thin film deposited on a substrate at an angle of incidence 注 (Note: The angle of incidence here refers to the angle of incident light to the substrate, usually the depression angle). It is. In the figure, ρ ₁ is the density of the thin film, ρ ₂ is the density of the substrate, σ ₀ is the roughness of the thin film surface, σ ₁ is the roughness of the interface between the substrate and the thin film, and t ₁ is the thickness of the thin film.

FIG. 1B shows measured data of the reflectance R of the thin film, and is an X-ray reflection curve showing the relationship between the reflectance and the incident angle. Here, R is expressed as follows. R (Ψ, t ₁ , ρ ₁ , ρ ₂ , σ ₀ , σ ₁ ) Note that the calculation for determining the reflectance R including the composite film is shown in the following paver, for example. do not do. LGParatt, Phys. Rev., 95, 359 (1954) .L. Nevot and P. Croce, Rev. Phys. Appl., 15, 761 (19
80) .B. Vidal and P. Vincent, Appl. Optics, 23, 1794 (198
4). SKSinha, EBShirota and S. Garoff, Phys. Rev. B,
38, 2297 (1988) .H. Chen and M. Heald, J. Appl. PHys., 66 (4), 15, 1793.
FIG. 1C shows measurement data of the reflectance R of the substrate, showing the relationship between the incident angle and the reflectance. Here, Rs is expressed as follows.

Rs (Ψ, ρ ₂ , σ ₀ ′) Here, σ ₀ ′ is the roughness of the substrate surface. As the reflectance R of the substrate, an X-ray reflection curve data-fitted with a model of the substrate alone may be used as described in the embodiment.

FIG. 1 (D) shows the relationship between the value I (Ψ) obtained by dividing the reflectance of the thin film by the reflectance of the substrate and the angle of incidence. I (Ψ) = R (Ψ, t ₁ , ρ ₁ , ρ ₂ , σ ₀ , σ ₁ ) /
Rs (Ψ, ρ ₂ , σ ₀ ′) In this figure, the vibrating part of FIG. 1B is extracted.

The thickness t ₁ can be obtained by Fourier transforming this data. Next, ρ ₁ , ρ ₂ , σ ₀ ,
In order to obtain σ ₁ and σ ₀ ′, the vibration part is subjected to least-squares optimization using a model. The sum of squares χ ² of the residual (I _data −I _fit ) can be expressed as χ ² = Σ (I _data −I _fit ) ² . Here, Σ represents the sum of the squares of the residuals of the data value I _data and the value I _fit obtained by the _data fitting for each point.

Since the optimization by the model is a nonlinear least squares method, the reflection curve from the coating surface in the conventional example has a point that the sum of squares of the residual χ ² is locally reduced in addition to the actual solution. When the vibration structure is small, the local minimum point is determined by the global structure of the reflectivity, and a correct result may not be obtained, or the visibility in selecting the initial value of the optimization may be very poor.

On the other hand, in the present invention, since the global structure of the reflectance is largely eliminated and only the vibrating part is extracted, the prospect of data optimization is remarkably improved, and the reliability of the obtained result is improved. The nature also increases. Also, the background noise included in the measurement data is canceled by this processing, and the effect is eliminated.

[0020]

2 to 4 are explanatory diagrams of the first embodiment. Figure 2
Numeral 3 indicates the relationship between the common logarithm of the reflectance and the incident angle 2 °.

FIG. 2 shows the calculated values of the X-ray reflection curve of the silicon (Si) substrate. There is no vibration structure in the reflection curve. The parameters are roughness 0, 2, 4Å. FIG. 3 is a reflection curve of a silicon oxide film having a thickness of 324 °. In the figure, the solid line (1) shows the value calculated by this method and the dotted line (2) shows the data value.

FIG. 4 (A) shows the result obtained by fitting the above-mentioned reflectance with the model of the silicon substrate and dividing the reflectance of the silicon oxide film by the reflectance of the silicon substrate. Good prospects for squared optimization.

FIG. 4A shows (Ψ ² −Ψc ² ) ^1/2 / λ.
Shows the Log ₁₀ (R / R _Si ) value with respect to. Here, Ψ is the incident angle, Ψc is the critical angle for total reflection, and λ is the X-ray wavelength of 1.3 °. Approximate film thickness can be obtained by Fourier transforming this data [Fig. 4 (B) and K. Sakurai and
A. Iida, Jpn. J. Appl. Phys. Lett., Vol. 31, 113 (1992).
reference〕.

In FIG. 4B, a peak indicating the film thickness is seen at a distance d = 324 °. 5 and 6 are explanatory diagrams of the second embodiment of the present invention. FIG. 5 shows a native oxide film formed by treating a silicon substrate with hydrochloric acid / hydrogen peroxide solution.
FIG. 7 is a graph plotting the reflectance (expressed as Nox in the figure) (dotted line), the reflectance (solid line) of the silicon substrate from which the natural oxide film has been removed with hydrofluoric acid, and the ratio Log ₁₀ (Nox / Si).

FIG. 6 shows the calculated values of the reflectance when various natural oxide film densities are assumed and the reflectance of the silicon substrate from which the natural oxide film is removed. Here, for example, N
ox 1.9-Si indicates a natural oxide film having a density of 1.9 g / cm ² on a silicon substrate. The simulation was performed with the thickness of the native oxide film as t = 10Å, the surface roughness as σsurf = 3Å, and the interface roughness as intint = 2Å.

When the above ratio of raw data is compared with this simulation, its density can be easily estimated. Density obtained by least squares optimization is 2.07 g / cm ² , thickness is 11
Was Å.

By incorporating these data processing methods into the X-ray reflectivity measuring device, the extraction of the desired result can be speeded up and the reliability can be increased.

[0028]

According to the present invention, in the evaluation of film quality and film thickness by X-ray reflectivity measurement, the accuracy of data analysis is improved, and even when the film density is close to the substrate density or when the film thickness is small. Can be evaluated appropriately, and the derivation of the results can be made faster and more reliable.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is an explanatory view (1) of the first embodiment of the present invention.

FIG. 3 is an explanatory view (2) of the first embodiment of the present invention.

FIG. 4 is an explanatory view (3) of the first embodiment of the present invention.

FIG. 5 is an explanatory view (1) of the second embodiment of the present invention.

FIG. 6 is an explanatory diagram (2) of the second embodiment of the present invention.

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G01N 23/207 G01B 15/02 H01L 21/66

Claims (5)

(57) [Claims] 1. Reflection from the surface of a coating deposited on a substrate
The X-ray reflection curve showing the dependence of the X-ray intensity on the incident angle
X-ray reflection representing the incident angle dependence of the reflected X-ray intensity from the surface
The first data divided by the curve and the thickness, density, surface and interface roughness of the coating are
To the incident angle at the X-ray wavelength calculated as a parameter
The reflectivity depends on the incident angle dependence of the intensity of the reflected X-rays from the substrate surface.
The square value of the difference between the second data divided by the X-ray reflection curve and the angle is obtained at a plurality of incident angles, and the parameter is set so that the sum of the square values is minimized.
By optimization, the density, surface and
An X-ray reflectance analysis method characterized by evaluating the roughness of a surface . 2. The X-ray reflectance analysis method according to claim 1, wherein the reflectance from the substrate surface is measured after removing the coating. 3. The method according to claim 1, wherein the reflectance from the surface of the substrate is
X-ray wavelength calculated using surface roughness as a parameter
2. The X-ray reflectivity analysis method according to claim 1, wherein the reflectance with respect to the incident angle at the point is used. 4. The X-ray reflectivity analysis method according to claim 1 , wherein said data 1 is subjected to Fourier transform to determine the thickness of the coating. 5. A means for determining an X-ray reflection curve from the surface of a coating film deposited on a substrate, and data obtained by dividing the X-ray reflection curve from the surface of the coating film by an X-ray reflection curve from the surface of the substrate. have a means for determining, in the analyzing method according to claim 1, wherein
More coating density, surface and interface roughness, and claims
An X-ray reflectivity analyzer comprising means for determining the thickness of a film by the analysis method according to 4 .