JPH116804A - Method of improving detection sensitivity of thin film and analysis method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accurately determine the thickness, surface roughness, interface roughness, density, composition and the like of a very thin oxide film formed on a silicon substrate by an X-ray reflection factor method. SOLUTION: An X-ray wavelength 3 near a silicon K absorption end is used to allow increase in the amplitude of a vibration component in a reflection factor data even when the density is closer as between a silicon substrate 1 and an oxide film 2. The thickness of an oxide film 2 is determined from the frequency of the vibration component or the accuracy is improved for determining parameters of the thickness, the surface roughness, the interface roughness, the density and the like of the oxide film 2 by a parameter fitting. In addition, the refractive indexes of the oxide film 2 are determined based on the amplitude of the vibration component in a reflection factor data obtained using two X-ray wavelengths 3 or more near the silicon K absorption end and simultaneous equations are solved by using the refractive indexes obtained to determine the densities and the contents of silicon of the oxide film 2. This also enables determining of a composition of even a very thin oxide film 2.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to an X-ray reflectance method for determining the thickness, density, surface roughness, interface roughness, composition, etc. of an ultrathin film such as an ultrathin silicon oxide film formed on a silicon substrate. The present invention relates to a method for improving the detection sensitivity of a thin film and an analysis method which are suitable for obtaining the above.

[0002]

2. Description of the Related Art Conventionally, an X-ray reflectivity method has been used for structural analysis of a layered material sample or a film sample.

For example, Japanese Patent Application Laid-Open No. 3-146846 discloses a method of measuring the density of a thin film by parameter fitting using the X-ray reflectivity method. A method and an apparatus for extracting a vibration component from X-ray reflectance data from a body to obtain a film thickness and other physical quantities are disclosed.

Further, for example, N. Awaji et al. "High-Ac
curacy X-ray Reflectivity Studyof Native Oxide For
med in Chemical Treatment "(Jpn. J. Appl. Phys. Vo
l.34 (1995) pp.L1013-L1016), N. Awaji et al. "Hig
h-Density Layer at the SiO ₂ / Si Interface Observed
by Difference X-Ray Reflectivity "(Jpn. J. Appl. P
hys.Vol.35 (1996) pp.L67-L70), Y.Sugita et al.
"X-Ray Reflectometry and Infrared Analysis of Nat
ive Oxides on Si (100) Formed by Chemical Treatmen
t "(Jpn. J. Appl. Phys. Vol. 35 (1996) pp.5437-544
As reported in 3) and the like, the X-ray reflectivity method is also used for analyzing a silicon oxide film.

[0005]

The X-ray reflectivity method is expected to be applied to the analysis of an ultra-thin oxide film having a thickness of 1 to 4 nm, which is used as a next-generation gate oxide film, with respect to a silicon oxide film. However, in the conventional X-ray reflectivity method, if the refractive index of the film is close to the refractive index of the substrate, it is difficult to obtain physical information of the film from the measurement data, so that measurement and analysis are difficult. In particular, in the case of an ultra-thin silicon oxide film formed on a silicon substrate, the conditions are severe because the density of the oxide film is close to that of the substrate and the refractive index is also close.

Here, the principle of measurement by the X-ray reflectivity method will be described.

The complex refractive index n can be written as n = 1−δ + iβ (1), where i is an imaginary unit. 1-δ is a real part and β is an imaginary part.

At this time, δ and β are respectively λ: X-ray wavelength,
r _e : classical electron radius, v _c : unit cell volume, Z _k : atomic number of the k-th atom of the unit cell, f _k ': real component of the anomalous dispersion term of the k-th atom, f _k ″: same imaginary number Ingredients, N _A :
Avogadro constant, ρ: density, M _k : atomic weight of k-th atom,

[0009]

(Equation 1)

## EQU1 ##

When the wavelength of the X-ray used is far from the X-ray absorption edge of the constituent element of each layer of the sample, the value of the real component f _k ′ of the anomalous dispersion term is sufficiently smaller than the atomic number Z _k. small. Therefore, at this time, ど の (Z _k
+ F _k ') / ΣM _k can be considered to be substantially equal to 、, and the equation (2) can be written as follows. ^{_{δ = (N A λ 2 r}} e / 4π) ρ ... (4)

That is, when this approximation holds, it can be said that δ is proportional to the density ρ of the film if the wavelength λ of the X-ray is determined regardless of the composition of the film (the kind of element).

Here, in order to clarify the conventional problems, a theoretical formula of the X-ray reflectivity for a layered material will be described.

Consider a case in which X-rays are incident on a sample as shown in FIG. 6 from the air side at an oblique angle (the complementary angle of the incident angle) θ.
In the following description, the effect of the roughness of the interface in each layer is neglected, and only the case where the polarization is σ polarization is considered.

Now, let the complex refractive index of the j-th layer be n _j and the film thickness be d
_j, and X incident on the (j + 1) th layer from the jth layer
If the viewing angle of the line is θ _j , the Fresnel coefficient (amplitude reflectance) F for the reflection at the interface between the j-th layer and the (j + 1) -th layer
_{j, j + 1} are δ _j , β like n _j = 1−δ _j + iβ _{j
If j} is taken, cos θ = n _j cos θ _j , so that g _j = n _j sin θ _j = (n _j ² −cos ² θ) ^1/2 ≒ (θ ² −2δ _j + 2iβ _j ) ^{1 / 2} ... (5), and given by F _{j, j + 1} = (g _j −g _{j + 1} ) / (g _j + g _{j + 1} ) (6)

In a multilayer film, the reflectance from the sample including the influence of reflection from the lower layer is calculated by the Fresnel coefficient F
_{Using j, j + 1} , the following recurrence equation is solved | R _0,1
| ² .

[0017]

(Equation 2)

Here, γ _j = 2πg _{j dj} / λ (8) (λ: X-ray wavelength in vacuum).

In the actual analysis, the recurrence formula of the formula (7) is directly calculated by a computer. Here, the approximate calculation will be described.

In a structure having only one oxide film on the substrate,
In equation (7), approximation as F _0,1 , F _1,2 ≪1 gives

[0021]

(Equation 3)

And the reflectance is | R _0,1 | ^{2 2} | exp (2iγ ₁ ) F _1,2 + F _0,1 | ² (10)

Here, the Fresnel coefficients F _0,1 and F _1,2 are
As given by equations (5) and (6), it is a complex number having an imaginary component, but in a range where the viewing oblique angle θ of the X-ray is sufficiently larger than the critical angle for total reflection, the equation (5) is used. , Θ ² -2δ
_{Since j} ≫ 2β _j , it can be regarded as a real number.

[0024]

(Equation 4)

## EQU1 ## Therefore, the reflectance is

[0026]

(Equation 5)

Can be approximated by

Here, the reflectance in the case of only the substrate from which the film has been removed is | R ₁ | ² ≒ (δ ₂ / 2θ ² ) ² (13) In a range where the viewing angle θ is sufficiently larger than the critical angle for total reflection, in equation (4), g _j = θ, and γ _j = (2πd _j / λ) θ (14) The vibration component of the value (normalized reflectance) obtained by normalizing the value of the expression (11) using the value of the reflectance (13) of the substrate as the baseline is:

[0029]

(Equation 6)

## EQU2 ##

When measuring the X-ray reflectivity of a multilayer sample as shown in FIG. 6, information on physical quantities such as the film thickness and density of the j-th layer is included in g _j and γ _j . . Therefore, in order to obtain the physical quantity information as described above for the layer, the amplitude reflectance of X-rays at the interface between the (j-1) th layer and the jth layer and at the interface between the jth layer and the (j + 1) th layer Must be sufficient. For this purpose, from the Fresnel coefficient equation (6), it is a condition that there is a sufficient difference in refractive index between adjacent layers. That is, in order for the information of the j-th layer to be sufficiently reflected in the X-ray reflectivity measurement data, the (j-
It is necessary that the refractive indices of the 1) layer and the (j + 1) th layer are sufficiently separated from the refractive index of the jth layer.

This is because when only one film is formed on the substrate, the amplitude of the equation (15) is obtained.

[0033]

(Equation 7)

That is, (1) the difference between δ ₁ and δ ₂ is not zero, that is, there is a difference in the refractive index between the substrate and the film. (2) δ ₁ is not zero, that is, This means that there is a need for a difference in refractive index between the film and vacuum (air).

From the above, the anomalous dispersion can be ignored,
For a general X-ray wavelength for which the approximation of the formula (4) is established, the density is closely related to the refractive index. Therefore, if the density between the layer to be measured and the adjacent layer is close, the conventional X
It can be said that the linear reflectance method makes it difficult to obtain information on physical quantities such as film thickness. That is, Problem 1: The closer the density is to the adjacent layer, the more information about that layer
Is hard to find.

Further, even if there is a certain difference in the density between the layer to be measured and the layer adjacent thereto, and it is not necessary to consider the problem 1, measurement is performed using only one X-ray wavelength. Is obtained, only the information of the density ρ given by approximation of the equation (4) can be obtained by obtaining δ, and the information of the composition cannot be obtained. That is, Problem 2: Information on composition cannot be obtained.

The above two problems exist in the conventional X-ray reflectivity method. In particular, in the analysis of an ultra-thin oxide film on the silicon surface, which is expected to be used, these two points have been major obstacles.

On the other hand, recently, in the structural analysis by the X-ray reflectivity method, by using the wavelength near the X-ray absorption edge of the component element, the change from the critical angle of total reflection to the depth of about the X-ray penetration length. A method for determining the average number density and composition of elements is described in AGXR (Anomalous Grazing X-ray Reflectomet
ry) method ”(“ Solid State Physics ”Vol. 32,
No.3 (1997) pp.161-170).

This method utilizes the fact that the magnitude of the total reflection critical scattering vector changes due to the anomalous dispersion effect when the X-ray wavelength near the X-ray absorption edge of the constituent element is used. In this method, the number density of the constituent elements in the surface region is determined, and the composition is determined.

However, in this method, as described in the literature, the number density of the element to be obtained is determined when the X-ray oblique angle is equal to the critical angle for total reflection. This is an average value in a penetration depth (for example, about several tens of nm) region.

Therefore, according to the known AGXR method, a composition of a uniform film sufficiently thicker than the penetration depth of X-rays can be obtained. However, it is extremely difficult to accurately determine the composition of a film thinner than the penetration depth, for example, a film having a thickness of several nm. For example, in the field where the establishment of analysis technology is currently required in the semiconductor industry,
The thickness of the silicon gate oxide film is an extremely thin film of 1 to 4 nm, and therefore, the known AGXR method can hardly be used for these analyses.

Accordingly, an object of the present invention is to provide a conventionally known AG
Detection of a thin film that solves the disadvantage that only average information in the X-ray penetration depth region can be obtained in the XR method and that can solve the above-described problems 1 and 2 in the conventional X-ray reflectivity method It is to provide a sensitivity improvement method and an analysis method.

[0043]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems, a method for improving the detection sensitivity of a thin film according to the present invention employs a method in which a density close to a substrate A formed on a substrate (referred to as "A") is measured. When analyzing the physical properties of the target thin film (referred to as “B”) based on the X-ray reflectivity method, the period of the vibration is obtained from the measurement data of the vibration component of the X-ray reflectivity intensity, and the period of the vibration is determined. In a method of obtaining the thickness of a thin film to be measured from the obtained period using a relational expression with the thickness of the thin film, the volume of the substrate A and the thin film B among the main constituent elements of the substrate A or the thin film B is determined. X of any of the elements with different contents per unit
By using the wavelength near the X-ray absorption edge as the wavelength of the incident X-ray, the difference between the refractive indices of the substrate A and the thin film B is enlarged, whereby the Fresnel coefficient (amplitude) of X-ray reflection at the interface between the substrate A and the thin film B is increased. (Reflectance), thereby increasing the amplitude of the obtained reflectance intensity vibration component, thereby improving the sensitivity of detecting the reflectance intensity vibration component.

Further, in the method for improving the detection sensitivity according to another aspect of the present invention, a method for forming a substrate on a substrate (referred to as “A”).
When analyzing the physical properties of a thin film to be measured (referred to as “B”) having a density close to that of the substrate A based on the X-ray reflectivity method, parameter fitting is performed on the measurement data of the vibration component of the X-ray reflectivity intensity. In the method for obtaining one of the parameters of the thickness of the thin film to be measured, or the roughness of the film surface, or the roughness of the interface between the film and the substrate, or the method of obtaining a plurality of parameters simultaneously, the substrate A or the thin film B Of the main constituent elements having different contents per volume in the substrate A and the thin film B, X
By using the wavelength near the X-ray absorption edge as the wavelength of the incident X-ray, the difference between the refractive indices of the substrate A and the thin film B is enlarged, whereby the Fresnel coefficient (amplitude) of X-ray reflection at the interface between the substrate A and the thin film B is increased. (Reflectance), thereby increasing the amplitude of the obtained reflectance intensity vibration component, thereby improving the sensitivity of detecting the reflectance intensity vibration component.

In the method for analyzing a thin film according to the present invention, the physical properties of a thin film to be measured (hereinafter, referred to as "B") formed on a substrate ("A") having a known composition and density. To
When analyzing based on the X-ray reflectivity method, reflectivity measurement is performed at two or more wavelengths, and at least one of the wavelengths is measured in a certain region (referred to as “R”) in the sample. Using a wavelength close to the absorption edge of any of the contained elements (referred to as “X”), a change in the refractive index of the region R when the wavelength λ is changed is obtained from the measurement data. In the method for determining the content of element X per volume, and thus the composition, the change in the refractive index is determined from the change in the amplitude of the reflectance intensity vibration component, or
The region R is matched with the thin film B to be measured by determining the refractive index of the film B to be measured from the parameter fitting, and the content per unit volume of the element X in the thin film B to be measured and the measurement object Find the density of the area.

[0046]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described according to preferred embodiments.

[First Embodiment] In a first embodiment of the present invention, for example, a sample having a thin film 2 formed on a substrate 1 as shown in FIG. X-ray reflectivity of any of the main constituent elements having different contents per volume using X-rays 3 having a wavelength near the X-ray absorption edge (generally within ± 0.02 °). Perform the measurement by the method.

Therefore, in this case, in δ shown in the equation (2), the term of f _k ′ due to anomalous dispersion cannot be ignored compared to Z _k . From equation (2), it can be seen that the change Δδ in δ when f _k ′ is ignored and when it is not ignored depends on the number of atoms of the selected component element per volume. That is, even if the densities ρ of the substrate 1 and the thin film 2 are close to each other, a component element whose content per volume is relatively different from each other is selected, and X of the wavelength near the X-ray absorption edge is selected.
If a line is used, the difference in the refractive index between the substrate 1 and the thin film 2 can be increased.

For example, when the substrate 1 has a density of 2.33 g / cm
³ silicon substrate, thin film 2 was formed to a thickness of 2 nm and a density of 2.3.
FIGS. 2 and 3 show the results of theoretical calculations for a silicon oxide film of 0 g / cm ³ .

In this calculation, the roughness of the surface of the thin film 2 and the roughness of the interface between the thin film 2 and the substrate 1 are each set to 0.3 nm. The calculation is a recurrence formula of the reflectance (6).
The value is obtained by directly solving the equation and the equation (7), and the imaginary component of the complex refractive index of silicon is also taken into consideration. However, the anomalous dispersion term of oxygen atoms having little effect was ignored, and the anomalous dispersion term for oxygen atoms was set to zero for both the real part and the imaginary part.

FIG. 2 shows a silicon K absorption edge (6.738).
Å) The reflectance calculation results at each wavelength in the vicinity are shown in FIG.
The calculation results of the normalized reflectance obtained by standardizing the reflectance of the substrate with the substrate reflectance are shown. 2 and 3, the horizontal axis represents the oblique angle [mrad] of the X-ray, and the vertical axis represents the reflection intensity and the normalized reflection intensity, both expressed as relative values.

As can be seen from FIG. 2, since the wavelength is long,
At a viewing angle of about 300 mrad, the reflectivity attenuation is about 8 digits.

For comparison, X for the same sample
FIG. 4 shows the calculation result of the reflectance at a line wavelength of 1.54 °, and FIG. 5 shows the calculation result of the normalized reflectance. Viewing angle 80mra
About d, and the reflectance attenuation is about eight digits.

From these results, comparing FIGS. 3 and 5 in particular, it can be seen that the amplitude of the vibration component of the reflection intensity can be increased by using the wavelength near the silicon K absorption edge.

[0055] That is, because the density of the substrate 1 and the thin film 2 is close, in the example of FIG. 4 and FIG. 5, the difference between the real component [delta] ₂ of the refractive index of the real component [delta] ₁ and the thin film 2 having a refractive index of the substrate 1 is Therefore, the amplitude of the vibration component expressed by the equation (15) becomes smaller. On the other hand, in the examples of FIGS. 2 and 3 according to the present embodiment, by using X-rays having a wavelength near the K absorption edge of silicon, even if the density of the substrate 1 and the thin film 2 is close, the refraction of the substrate 1 is reduced. The difference between the real component δ ₁ of the refractive index and the real component δ ₂ of the refractive index of the thin film 2 can be made large.
A vibration component having a large amplitude can be obtained.

Therefore, for example, from the equation (15), the period of the vibration of the vibration component is λ / (2d ₁ ).
In FIG. 3, when the period of the vibration is examined for the data at the X-ray wavelength λ = 6.742ｒａ, it is about 170 mrad, and therefore, d ₁ = 6.742 / (2 × 0.17) ≒ 19.8 [Å It can be seen that the thickness of the thin film 2 is about 2 nm.

On the other hand, even in the case of FIG. 5, the X-ray wavelength λ = 1.
For 54 ° data, the oscillation period is about 40 mr
Since ad is determined, d ₁ = 1.54 / (2 × 0.04) ≒ 19.25 [Å], and it can be seen that the thickness of the thin film 2 is also about 2 nm.

However, as can be seen by comparing the data of FIGS. 3 and 5, for example, 6.7 having the largest amplitude in FIG.
With the data of 42 °, it is possible to obtain data whose amplitude is 100 times or more as compared with the case of FIG. Therefore, in order to check the period of the vibration component, it is better to use the data of FIG.
Clearly, it is much easier and more accurate than using the data of FIG.

As described above, in the present embodiment, when the measurement is performed by the X-ray reflectivity method, among the main constituent elements of the substrate 1 or the thin film 2, the content per volume differs between the substrate 1 and the thin film 2. By using incident X-rays having a wavelength near the X-ray absorption edge of the element, measurement data in which the amplitude of the vibration component of the reflection intensity data is relatively large, and from the period of the vibration component,
The thickness of the thin film 2 is determined.

Therefore, when checking the period of the vibration component from the measurement data, an accurate value can be obtained relatively easily because the amplitude of the vibration component is large.

In particular, when the density of the substrate 1 and that of the thin film 2 are close to each other, if the conventional X-ray wavelength is used, the amplitude of the vibration component becomes small, so that it is difficult to measure the period (in some cases, Impossible), but in the present embodiment, the substrate 1
Even when the density of the thin film 2 is close to that of the thin film 2, the amplitude of the vibration component of the reflection intensity data can be increased, so that the period can be measured easily and accurately.

The vibration component of the reflection intensity data is caused by interference between the light reflected on the surface of the thin film 2 and the light reflected on the interface between the thin film 2 and the substrate 1 shown in FIG. The value of the obtained film thickness is hardly influenced by the X-ray wavelength or the penetration depth of the X-ray. Therefore, in the first embodiment, for example, since the density of the substrate 1 and the thin film 2 is close to each other, when a normal X-ray wavelength is used, the amplitude of the vibration component of the reflection intensity data becomes too small. When it becomes difficult to measure the period, the X-ray wavelength near the X-ray absorption edge of an element having a different content between the substrate 1 and the thin film 2 is used. Is relatively enlarged, making the measurement of its period easier and more accurate.

In the above example, the period of the vibration component is checked from the measured data, and from the result, the film thickness is obtained based on an approximate expression such as Expression (15).
Thickness of the thin film 2, density of the thin film 2, surface roughness of the thin film 2,
Physical quantities such as interface roughness between the thin film 2 and the substrate 1 can be obtained individually or simultaneously by parameter fitting.

In this case, for example, the theoretical formula of the reflectance given by the recurrence formula of the formula (7) is used, and each parameter in the theoretical formula is measured by, for example, the nonlinear least square method by the Marquardt method. Each parameter can be obtained by optimizing the data. When calculating the roughness, instead of equation (6),

[0065]

(Equation 8)

By using, the term σ of roughness can be included in the theoretical formula.

Even in the case of this parameter fitting, using the wavelength near the silicon K absorption edge, for example, as the X-ray wavelength λ, the actual measurement data in which the vibration component of the reflectance is emphasized is obtained. JP-A-6-221
By performing optimization such that the data of the emphasized vibration component is effectively reflected as in the method described in JP-A-841, the calculation efficiency and accuracy can be improved.

[Second Embodiment] Next, a second embodiment of the present invention will be described.
In the second embodiment, for example, the composition of the thin film 2 is obtained from a sample in which the thin film 2 is formed on a substrate 1 as shown in FIG. However, the composition and density of the substrate 1 are assumed to be known.

For this purpose, in the second embodiment, the value of the real component f ′ of the anomalous dispersion term of the element whose content is to be determined (“X”) among the component elements of the thin film 2 Are measured at two or more wavelengths such that At this time, at least one wavelength is a wavelength near the X-ray absorption edge of the element X (generally within ± 0.02 °), and therefore, the absolute value of f ′ cannot be ignored compared to the atomic number Z _X of the element X. Choose a wavelength under such conditions.

In equation (2), since M _k ≒ 2Z _k , this equation (2) is

[0071]

(Equation 9)

Can be obtained. Deform,

[0073]

(Equation 10)

Is as follows.

[0075] In this equation (19), r _e, N _A is known, [rho is unknown for the thin film 2. If X-ray reflectance measurement is performed with λ determined, δ can be determined from, for example, the amplitude of the vibration component of the reflection intensity data.

Now, a wavelength λ ₁ close to the X-ray absorption edge of the element X is selected, and f ′ can be ignored for the constituent elements other than the element X, and f ′ cannot be ignored for the element X. (M + 2f ′) = AM (A ≠ 1) (20)

Here, if the mass ratio of the element X is X, the mass ratio of the elements other than the element X is (1-X), so that δ obtained from the reflectance measurement at the wavelength λ ₁ is δ. as _{L1, {AX + (1-} X)} ρ = {1+ (A-1) X} ρ = 4πδ L1 / (λ 1 2 r e N A) ... (21)

Similarly, when a wavelength λ ₂ (which does not have to be close to the X-ray absorption edge of the element X, but f ′ can be ignored for at least the constituent elements other than the element X), For the element X, if (M + 2f ′) = BM (22), δ obtained from the reflectance measurement at the wavelength λ ₂ is converted to δ.
As _{L2, {BX + (1-} X)} ρ = {1+ (B-1) X} ρ = 4πδ L2 / (λ 2 2 r e N A) ... (23)

The values of A and B are calculated by using a numerical table of the anomalous dispersion terms of elements (eg, S. Sasaki "Numerical Tables of Ano
malous Scattering Factors Calculated by the Cromer
andLiberman's Method "KEK Report 88-14 (1989)).

At this time, since the unknowns in the equations (21) and (23) are two of X and ρ, the equations (21) and (2)
By solving equations 3) simultaneously, the values of X and ρ can be determined.

When the density of the substrate 1 and the density of the thin film 2 are not so close and therefore it is not necessary to take measures against the above-mentioned problem 1, the wavelength λ ₂ is shifted from the X-ray absorption edge of the element X. You may be away. At this time, since B = 1 can be set,
The density ρ is immediately obtained from the equation (23).
X can be obtained from equation (21).

On the other hand, when the density of the substrate 1 is close to that of the thin film 2, if the wavelength λ ₂ is far from the X-ray absorption edge of the element X, as described in the first embodiment, Since the amplitude of the vibration component of the reflection intensity data becomes small, it becomes difficult (or impossible) to determine δ _L2 therefrom. Therefore, in this case, it is necessary to use a wavelength close to the X-ray absorption edge of the element X as the wavelength λ ₂ .

As a specific example of the second embodiment, the case where the composition of the silicon oxide film on the silicon substrate described in the first embodiment is obtained will be described.

For example, the composition is calculated from the data of the wavelength 6.743 ° and the data of the wavelength 6.750 ° in the normalized reflectance curve shown in FIG.

First, the number table of the anomalous variance term described above (S. Sas
aki: From KEK Report 88-14), as the real component f ′ and the imaginary component f ″ of the anomalous dispersion term of silicon, f ′ (Si) f ″ (Si) 6.743Å−9.887 0.353 6.750Å -7.532 0.353 is obtained.

In order to obtain δ, usually, a known parameter fitting algorithm is used for the actually measured data. Here, δ is obtained from the approximate expression of Expression (15).

[0087] First, r _e = 2.8179 × 10 ^-13 (cm) N _A = 6.022 × 10 ²³ [/ mol] M _Si = 28.086 (silicon atomic weight) M _O = 15.9994 (oxygen Ρ _Si = 2.33 [g / cm ³ ] (density of the silicon substrate 1).

The value of δ of the silicon substrate 1 at the wavelength of 6.743δ (= λ ₁ ) is given by the following equation (2).

[0089]

[Equation 11]

Is as follows. From the data in FIG. 3, the maximum value of the vibration is about 12.5 and the minimum value is about 0.994. Therefore, when this is compared with the approximate expression of Expression (15),

[0091]

(Equation 12)

From the condition having a solution, δ ₂ <δ ₁ , and δ ₂ <δ _1
1 , δ ₂ > 0, so solve this and

[0093]

(Equation 13)

Therefore, δ ₁ = 2.268 × 4.19 × 10 ⁻⁵ ≒ 9.503 × 1
0 ⁻⁵ is δ ₁ of the thin film 2 easily obtained from the approximate expression.

On the other hand, when the wavelength is 6.750 ° (= λ ₂ ), the value of δ of the silicon substrate 1 is given by the following equation (2).

[0096]

[Equation 14]

Is as follows. From the data in FIG. 3, the maximum value of the vibration is about 4.94 and the minimum value is about 0.997. Therefore, when this is compared with the approximate expression of Expression (15),

[0098]

(Equation 15)

From the condition having a solution, δ ₂ <δ ₁ , and δ ₂ <δ _1
1 , δ ₂ > 0, so solve this and

[0100]

(Equation 16)

Therefore, δ ₁ = 1.611 × 6.602 × 10 ⁻⁵ ≒ 10.63
7 × 10 ⁻⁵ is δ ₁ of the thin film 2 easily obtained from the approximate expression.

Using these values, equation (21) and (2)
Solving the simultaneous equations of the expression 3), A = (M _Si + 2f ′) / M _Si = (28.086−2 × 9.887) /28.086≒0.29595 B = (M _Si + 2f ′) / Since M _Si = (28.086−2 × 7.532) /28.086≒0.46365, the expression (21) is given by: (1−0.740505) ρ = 1.5477 and the expression (23) Is (1−0.53635X) ρ = 1.7288. The solution of this simultaneous equation is X ≒ 0.4679 ρ ≒ 2.3080.

Since X is the mass ratio of silicon, if it is converted to a composition ratio (however, the constituent elements of the thin film 2 are only Si and O), Si: O = (0.4679 / 28.086): {(1-0.4679) /15.9994} {1: 1.996}, which indicates that the composition formula of the thin film 2 is substantially SiO ₂ . Also, the density ρ is found to be about 2.31 g / cm ³ .

In this example, δ at each wavelength is
Although calculated using the approximate expression of Expression (15), δ at each wavelength may be calculated by well-known parameter fitting described in the first embodiment. In this case, the accuracy can be further improved by performing the calculation using the equation (17) described above and including the roughness term σ in the theoretical equation.

In the above example, the substrate 1 and the thin film 2 have close densities (2.33 g / cm ³ and 2.30 g / cm ³ ).
Therefore, in each case, two wavelengths close to the K absorption edge of silicon were used. However, when the density of the substrate 1 and the thin film 2 is not so close, even if one wavelength is not close to the X-ray absorption edge of the target element X. good. In other words, in this case, even if a wavelength away from the X-ray absorption edge of the target element X is used, δ can be measured sufficiently, and the density ρ of the thin film 2 can be immediately obtained from δ. Then, using the value of the density ρ, the mass ratio X of the target element X can be obtained from δ measured at a wavelength close to the X-ray absorption edge of the target element X.

Furthermore, in the above example, simultaneous equations were constructed using δ measured with X-rays of two wavelengths. However, δ was measured with X-rays of three or more wavelengths, and three or more obtained as a result. Of the thin film 2 by simultaneous equations
Alternatively, a plurality of values of the mass ratio X of the target element X may be obtained, and for example, the density ρ of the thin film 2 and the mass ratio X of the target element X may be determined as their average values.

As described above, in the second embodiment, the composition of the thin film 2 formed on the substrate 1 having a known composition and density is applied to the X-ray absorption edge of the constituent elements of the thin film 2. It is determined by an X-ray reflectivity method using two or more wavelengths including near wavelengths. That is, at each wavelength, the real component δ of the complex refractive index n of the thin film 2 is obtained from the amplitude of the vibration component of the measured reflectance data or by parameter fitting that effectively reflects the amplitude of the vibration component. Using the value
For example, the mass ratio of the constituent elements in the thin film 2 and the thin film 2
Solves a system of equations containing the density of
, The mass ratio of the constituent element and the density of the thin film 2 are determined. Thereby, the composition of the thin film 2 can be obtained.

Here, the method according to the second embodiment,
The difference from the known AGXR method described above will be described.

In the known AGXR method described above, two wavelengths near the X-ray absorption edge of an element whose number density is to be obtained are used, and the number density of the element is obtained from the shift amount of the critical angle of total reflection. However, in this method, since the number density is obtained from the shift amount of the critical angle of total reflection, as described in the literature, the obtained result is about the penetration depth of X-rays (generally, several tens of (about nm). Therefore,
For example, if this method is used as it is for measuring an ultra-thin oxide film having a thickness of about several nm on a silicon substrate, information from the silicon substrate is also collected, and it is not possible to obtain an accurate composition of the oxide film.

On the other hand, in the second embodiment, the mass ratio of the element X whose wavelength is close to the X-ray absorption edge is determined.
X-ray reflectance measurement is performed using the above wavelengths, and the refractive index (real number component δ) of the thin film 2 is determined from the amplitude of the vibration component of the reflection intensity data obtained by the X-ray reflectance measurement. Using the values, the mass ratio X of the element X and the density ρ of the thin film 2
Ask for each. The vibration component of the reflection intensity data is shown in FIG.
The component reflected on the surface of the thin film 2 shown in FIG.
Caused by interference with components reflected at the interface with
When the refractive index of the substrate 1 is known, the refractive index obtained from the amplitude of the vibration component is the refractive index of the thin film 2 itself.

That is, in the method of the second embodiment,
Regardless of the penetration depth of the X-rays, the refractive index of the thin film 2 itself can be obtained. Therefore, the mass ratio X of the element X and the density ρ of the thin film 2 determined using the refractive index are as follows:
Each of them is physical property information of the thin film 2 itself which does not include information of the substrate 1.

As described above, according to the method of the second embodiment of the present invention, it is possible to relatively easily and accurately determine the composition of an ultrathin film, which has been difficult (or impossible) by the known AGXR method. It becomes possible.

In the first and second embodiments described above, for example, synchrotron radiation can be used as the X-ray source.

[0114]

According to the present invention, when the thickness of a thin film formed on a substrate is determined by the X-ray reflectivity method, the content of the main constituent elements of the substrate or the thin film per volume in the substrate and the thin film is determined. By using the wavelength near the X-ray absorption edge of one of the elements having different amounts as the wavelength of the incident X-ray, measurement data having a large amplitude of the vibration component of the reflection intensity data is obtained. Find the thickness. Therefore, for example, even when the density of the thin film is close to that of the substrate, it is possible to obtain the reflection intensity data having a relatively large amplitude of the vibration component, and the measurement of the period is easy and accurate.

When physical parameters such as the film thickness, film surface roughness, and film-substrate interface roughness of the thin film formed on the substrate are determined by parameter fitting based on the X-ray reflectivity method, Among the main constituent elements, the vibration component of the reflection intensity data obtained by using the wavelength near the X-ray absorption edge of any of the elements having different contents per volume in the substrate and the thin film as the wavelength of the incident X-ray By using measurement data having a large amplitude and performing parameter fitting so that the vibration component is effectively reflected, calculation efficiency and accuracy can be greatly improved.

Further, when the composition of a thin film formed on a substrate having a known composition and density is determined based on the X-ray reflectivity method, two or more wavelengths including wavelengths close to the X-ray absorption edge of the constituent elements of the thin film are obtained. Of the refractive index of the thin film according to the wavelength is obtained from the amplitude of the vibration component of the reflection intensity data at each wavelength, or the amplitude of the vibration component of the reflection intensity data is effectively reflected. By determining the content of the element and the density of the thin film from the variation in the refractive index of the obtained thin film, for example, by obtaining the parameter fitting, for example, to obtain a film thickness such as an ultrathin oxide film formed on a silicon substrate. Even the composition of an extremely thin film can be determined relatively easily and accurately.

[Brief description of the drawings]

FIG. 1 is a schematic diagram showing a thin film on a substrate to be measured in an embodiment of the present invention.

FIG. 2 is a graph showing a relationship between a viewing angle and a reflection intensity when an X-ray wavelength near a K absorption edge of silicon is used.

FIG. 3 is a graph showing data obtained by normalizing the data of FIG. 2 with the reflection intensity of a substrate.

FIG. 4 is a graph showing the relationship between the viewing angle and the reflection intensity when an X-ray wavelength away from the K absorption edge of silicon is used.

FIG. 5 is a graph showing data obtained by normalizing the data of FIG. 4 with the reflection intensity of a substrate.

FIG. 6 is a schematic diagram illustrating the principle of reflection in a multilayer film.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Substrate, 2 ... Thin film, 3 ... X-ray, θ ... Oblique angle

Claims (3)

[Claims] 1. A physical property of a thin film to be measured (hereinafter, referred to as “B”) having a density close to that of a substrate A formed on a substrate (hereinafter, referred to as “A”) is analyzed based on an X-ray reflectivity method. In this case, the period of the vibration is obtained from the measurement data of the vibration component of the X-ray reflectivity intensity, and the relationship between the period and the film thickness of the thin film is used. In the method for obtaining the thickness, of the main constituent elements of the substrate A or the thin film B, the wavelength near the X-ray absorption edge of any of the elements having different contents per volume in the substrate A and the thin film B is calculated as By using the wavelength as the wavelength, the difference between the refractive indices of the substrate A and the thin film B is enlarged, thereby increasing the Fresnel coefficient (amplitude reflectance) of X-ray reflection at the interface between the substrate A and the thin film B. Reflectivity by increasing the amplitude of the reflected vibration component Improve the detection sensitivity of intensity vibration components,
A method for improving detection sensitivity for measuring the thickness of a thin film by an X-ray reflectivity method. 2. A physical property of a thin film to be measured (hereinafter, referred to as “B”) having a density close to that of the substrate A formed on the substrate (hereinafter, referred to as “A”) is analyzed based on an X-ray reflectivity method. In this case, by performing parameter fitting on the measurement data of the vibration component of the X-ray reflectance intensity, the parameters of the film thickness of the thin film to be measured, the film surface roughness, or the interface roughness between the film and the substrate are obtained. Or the method of obtaining a plurality of parameters simultaneously. Among the main constituent elements of the substrate A or the thin film B, the X-ray absorption of any of the elements having different contents per volume in the substrate A and the thin film B By using the wavelength near the edge as the wavelength of the incident X-ray, the difference between the refractive indices of the substrate A and the thin film B is enlarged, whereby the Fresnel coefficient (amplitude inverse) of the X-ray reflection at the interface between the substrate A and the thin film B is increased. Allowed a larger rate), than Te, improve the detection sensitivity of the reflectance intensity vibration components by expanding the amplitude of the reflectance intensity vibration component obtained,
A method for improving detection sensitivity for measuring a film thickness of a thin film, a film surface roughness, or an interface roughness between a film and a substrate by an X-ray reflectivity method. 3. A physical property of a thin film to be measured (hereinafter, referred to as “B”) formed on a substrate (hereinafter, referred to as “A”) whose composition and density are known, based on an X-ray reflectivity method. In the case where the analysis is performed, the reflectance measurement is performed at two or more wavelengths, and at least one of the wavelengths includes any one of the elements (referred to as “R”) included in a certain region (“R”) in the sample. Using a wavelength close to the absorption edge of “X”), a change in the refractive index of the region R when the wavelength λ is changed is obtained from the measurement data. In the method of obtaining the content, and thus the composition, the change in the refractive index is obtained from the change in the amplitude of the reflectance intensity vibration component, or from the parameter fitting using the value to obtain the refractive index of the film B to be measured. , Region R to be measured Determining the composition and density of the thin film by the X-ray reflectance method, wherein the content and the density of the element X in the measurement target thin film B are determined in conformity with the thin film B. analysis method.