JP5424239B2 - LAYER STRUCTURE ANALYSIS METHOD, DEVICE, AND PROGRAM USING X-RAY REFLECTIVE METHOD - Google Patents

Description

  The present invention relates to a method, apparatus, and program for analyzing a layered structure in which a layered structure such as a single layer film, a multilayered film, or a non-uniform density layer is formed on a substrate using an X-ray reflectivity method. Is.

  The refractive index of a substance with respect to X-rays has a value slightly smaller than 1, and X-rays incident on a flat and smooth material surface at an angle shallower than the total reflection critical angle cause an optical total reflection phenomenon outside the substance. . When the incident angle θ is equal to or greater than the total reflection critical angle θc, specular reflection X-rays reflected at the scattering angle 2θ with respect to the incident X-rays and refraction X-rays penetrating from the medium surface into the medium are generated. However, the ratio between the specular reflection X-ray intensity and the incident X-ray intensity is referred to as X-ray reflectivity.

  Further, the refractive X-ray intensity penetrating from the medium surface into the medium attenuates exponentially in the depth direction from the surface. For this reason, X-rays scattered inside the medium and emitted from the surface are mainly X-rays scattered near the surface, and reflect information near the surface.

  In the X-ray reflectivity method, it is possible to nondestructively determine the surface of the substance and the internal structure in the depth direction of the thin film using this feature. Specifically, when the laminate is a multilayer film, the intensity of the reflected X-rays changes with the incident angle due to the interference effect of the X-rays reflected at the surface or the multilayer film interface. In the X-ray reflectivity method, the thickness and density, surface roughness (roughness), and interface roughness (roughness) of each layer of the surface multilayer film are determined nondestructively by analyzing the incident angle dependence of the X-ray reflectivity. be able to.

  In recent years, the X-ray reflectivity method has been widely used for analysis of multilayer films such as semiconductors. For example, Patent Document 1 discloses a thin film density measurement method by parameter fitting using an X-ray reflectivity method.

  Moreover, in patent document 2, a vibration component is extracted from the X-ray reflectivity data from a laminated body using Fourier transform, the film thickness of each layer is calculated | required, the result, the curve of the theoretical value of X-ray reflectivity, and a measured value A method of obtaining interface roughness and other physical quantities using fitting together is disclosed.

  In Patent Document 3, an X-ray reflection curve representing the incident angle dependence of the logarithmic value of the reflected X-ray intensity from the surface of the coating deposited on the substrate is used as the logarithmic value of the reflected X-ray intensity from the surface of the substrate. Discloses a method for evaluating the coating film based on the data divided by the X-ray reflection curve representing the incident angle dependency of the film.

  Further, in Patent Document 4, when the density of the substrate and the oxide film is close and the refractive indexes of both are close like the silicon oxide film, the vibration component of the X-ray reflectivity intensity is calculated based on the X-ray reflectivity method. Performing parameter fitting of theoretical values and measured values, and improving the fitting accuracy by selecting the X-ray wavelength that expands the difference in refractive index when determining the film thickness, surface roughness, and interface roughness parameters of the thin film to be measured And a method for improving the detection sensitivity of the vibration component of the X-ray reflectivity is disclosed.

  Further, in Patent Document 5, the material properties (film thickness, density, surface and interface roughness) of a material in which a single-layer or multilayer thin film is formed on a substrate are easily and shortly determined from an X-ray reflectivity curve. As a method of analyzing by time, a method of refining parameter fitting by the least square method of the X-ray reflectivity curve based on the optimum value obtained by the maximum entropy method is disclosed.

  Moreover, in patent document 6, regarding the film structure analysis method using the X-ray reflectivity method, the vibration component of the obtained reflected X-ray intensity is Fourier-transformed, and the obtained film thickness of each constituent layer is used as an initial value. A method for analyzing the film structure of a thin film sample by performing a least square fitting analysis of the X-ray reflectivity curve is disclosed.

  In Patent Document 7, in a film structure analysis method for analyzing the structure of a film sample composed of a single layer film or a multilayer film by an X-ray reflectivity measurement method, the same film sample is selected from at least one of resolution and dynamic range. A method for determining a film structure by simultaneously analyzing a plurality of measured measurement data under different measurement conditions is disclosed.

  In Patent Document 8, the depth distribution of the impurity element injected into the sample to be measured is replaced with a multilayer film layer having a different density, and analysis is performed by parameter-fitting an interference vibration curve to an analytical expression representing the X-ray reflectivity. A method is disclosed.

  As described above, the analysis method of the laminated structure by the X-ray reflectivity method is an analysis method for obtaining the film structure by comparing the measurement result of the X-ray reflectivity with the theoretical calculation value of the X-ray reflectivity. In X-ray reflectivity theoretical calculation, a model with the density, film thickness, surface roughness (roughness), and interface roughness (roughness) of the laminated film as parameters is obtained, and a theoretical calculation value is obtained for the model. A method for determining a parameter of a film structure by performing parameter fitting with a measured value is employed.

  Here, the theoretical formula of the X-ray reflectivity used for the data analysis is, for example, as shown in Non-Patent Documents 1 to 4, in the Parratt multilayer film model (Non-Patent Document 5), the Nevot-Croce A theoretical formula combining the roughness formula (Non-Patent Document 6) is used. In addition, Sinha (Non-patent Document 7) reports an equation for obtaining diffuse scattering due to surface roughness by detailed analysis of a Nevot-Cross roughness equation. Also, Vidal (Non-Patent Document 8) reports an equation that combines the roughness equation with the matrix method instead of the recurrence method for the Parratt multilayer model.

  The theoretical formula of the X-ray reflectivity obtained by combining the Nertot-Cross roughness formula with the Parratt multilayer film model is expressed by the following formulas (7) and (17) in Patent Document 4. As a non-patent document in which the inventor explains the contents of the invention of Patent Document 9 cited in Patent Document 7 as Expression (2) and Expression (3) of (Equation 2) in Patent Document 8 Reference 9 includes Formula (1), Formula (2), and Formula (7), and Non-Patent Document 2 includes Formula (1.69), Formula (1.116), Formula (3.8), and Formula (3.15). ) As disclosed in Non-Patent Document 3 in section (2.4) and Non-Patent Document 4 as equations (1) to (5).

  Here, the basic principle and theoretical formula of the X-ray reflectivity method will be described. In the following, in order to simplify the description, the case where the electric field amplitude of the incident X-ray is S-polarized light parallel to the surface will be described as an example. The coordinate axes of the multilayer film as a medium through which X-rays travel are defined as shown in FIG.

Here, the size k ₀ of the wave vector of the X-ray as the X-ray wavelength lambda,
Indicated by

The refractive index of the j layer is n _j , and the average roughness of the interface between the j−1 layer and the j layer is σ _{j−1, j} . Further, it is assumed that the incident X-ray amplitude from the j layer to the j + 1 layer is E _j , the wave number vector is k _j , the reflected X-ray amplitude is E _j ′, the transmitted X-ray amplitude is E _{j + 1} , and the wave vector is k _{j + 1} .

Here, the wave vector of incident X-rays before entering the sample is k ₀ = (k _{0, x} , 0, k _{0, z} ), and n ₀ regarding the X-ray refractive index in the space of the incident part.
= 1, the component parallel to the surface of the wave vector of X-rays in the medium is not different from the component parallel to the surface of the wave vector of incident X-rays, and k _{j, x} = k _{0, x} , The component in the depth direction perpendicular to the surface of the wave vector of X-rays in the medium is
Indicated by

Further, the Fresnel reflection coefficient r _{j, j + 1} indicating the reflectivity at the j, j + 1 interface of X-rays incident on the j + 1 layer from the j layer in the depth direction of the multilayer film is:
Indicated by

Further, the Fresnel transmission coefficient t _{j, j + 1} indicating the transmittance at the j, j + 1 interface of X-rays incident on the j + 1 layer from the j layer in the depth direction of the multilayer film is
Indicated by

Then, as shown in FIG. 7, when there is an X-ray of amplitude E _{j + 1} ′ from the j + 1 layer to the j layer in addition to the X-ray of amplitude E _j from the j layer to the _{j + 1} layer, Line amplitude E _j
, E _j ′, and the amplitude E _{j + 1 of the} j + 1 layer X-ray
, E _{j + 1} '
Indicated by Here, h _j is the thickness of the j layer, and this relational expression is
The relationship is used.

When the thickness h _N of the lowermost substrate layer is infinite, since the X-ray amplitude E _N ′ = 0 at that time, the X-ray amplitude in each layer is sequentially obtained from the matrix from the bottom. Line reflectivity
Can be requested. This method is a theoretical calculation method of the X-ray reflectivity from the surface of the multilayer film by the matrix method. For example, as formula (1.76) of Non-Patent Document 2 and as Formula (5) of Non-Patent Document 8 It is shown.

However, this formula does not take into account the surface roughness or interface roughness at all, so it is not realistic. Therefore, when there is surface roughness or interface roughness, it is approximated that the Fresnel reflection coefficient r _{j, j + 1} and the Fresnel transmission coefficient t _{j, j + 1} change according to the roughness, and the Fresnel reflection coefficient r ′ having roughness is approximated. _The calculation is performed by replacing _{j, j + 1 with} a rough Fresnel transmission coefficient t ′ _{j, j + 1} .

  The theoretical formula is shown as, for example, Formula (22) of Non-Patent Document 8, and the calculation program code according to the theoretical formula is shown as Appendix A of Non-Patent Document 2. Examples of the calculation are shown in FIGS. 1.13 and 1.18 of Non-Patent Document 2, for example.

How to approximate the rough Fresnel reflection coefficient r ′ _{j, j + 1} and the rough Fresnel transmission coefficient t ′ _{j, j + 1} will be described later. It can be seen that the coefficients t ′ _{j, j + 1} are not related to the X-ray reflectivity.

  In the matrix method, the perspective between the X-ray reflectivity and the reflection X-ray amplitude at each layer is poorly seen. Therefore, the Parratt multilayer film model expressed in the form of a recurrence formula of the X-ray reflection amplitude at each layer ( Non-patent document 5) is used. Next, the Parratt recursion formula method will be described.

the amplitude _{E j} of X-rays incident to the j + 1 Layers j layer, the ratio of _{R j} between the amplitude _{E j} 'of X-rays emitted to j layer from j + 1 _layer, when _{j + 1,}
And
It is.

In the bottom layer,
And the X-ray reflectivity is
Is required. These formulas are theoretical formulas of the X-ray reflectivity according to the Parrat multilayer model. From this equation, it can be seen that the Fresnel transmission coefficient t ′ _{j, j + 1} is not related to the X-ray reflectivity, and when there is surface roughness or interface roughness, the Fresnel reflection coefficient r _{j, j + 1 is set} to a rough Fresnel reflection coefficient r. 'It can be seen that the calculation should be performed with _{j and j + 1} .

About the approximation method of the Fresnel reflection coefficient r ′ _{j, j + 1 having} roughness, it is approximated that the Fresnel reflection coefficient indicating the reflectance at the surface or interface is exponentially attenuated by the surface roughness or interface roughness. Multiplying the Fresnel reflection coefficient r _{j, j + 1} at the interface between the j layer and the j + 1 layer expressed by the equation (3) by an attenuation term due to the surface roughness or the interface roughness,
The Nevot-Cross roughness equation (Non-patent Document 6) is widely used.

  The theoretical formula of the X-ray reflectivity obtained by combining the Nertot-Cross roughness formula with the Parratt multilayer film model is expressed by the following formulas (7) and (17) in Patent Document 4. As a non-patent document in which the inventor explains the contents of the invention of Patent Document 9 cited in Patent Document 7 as Expression (2) and Expression (3) of (Equation 2) in Patent Document 8 Reference 9 includes Formula (1), Formula (2), and Formula (7), and Non-Patent Document 2 includes Formula (1.69), Formula (1.116), Formula (3.8), and Formula (3.15). ) As disclosed in Non-Patent Document 3 in section (2.4) and Non-Patent Document 4 as equations (1) to (5).

  A calculation program code according to this theoretical formula is shown as Appendix A of Non-Patent Document 2, and an example of the calculation is shown in FIGS. 1.13 and 1.18 of Non-Patent Document 2, for example. Has been.

That is, if the Fresnel reflection coefficient in consideration of surface roughness and interface roughness is r ′ _{j, j + 1} ,
It is said.

However, in the calculation method for reducing the reflectance only by applying an attenuation term to the Fresnel reflection coefficient when the incident X-ray is specularly reflected as described above, the interface is rough as shown in FIG. The model is merely calculated as a model in which the density ρ _e continuously changes at the interface as shown in FIG. 8A (FIG. 1.16 of Non-Patent Document 2).

This calculation method is indistinguishable from a model in which a rough interface is replaced with a multi-layer structure of a large number of thin flat films having a continuous density, and is reflected from X-rays transmitted through each interface. All X-rays are calculated on the assumption that they contribute to interference. That is, at the continuous density multilayer structure interface, there is no model of X-rays scattered and diffused in directions other than the specular reflection direction and X-rays scattered and diffused in directions other than the refractive transmission direction. It does not take into account the reduction of the sum of the interference component of reflected X-rays and the interference component of transmitted X-rays due to the amount of X-rays that are non-interference components as diffusely scattered X-rays. In a paper (Non-Patent Document 9) in which the inventor has explained the contents of the invention of Patent Document 9 cited in Patent Document 7, a diffuse caused by non-uniform density due to nanoparticles and pores in each layer of the multilayer film In consideration of scattering, when the surface / interface of each layer of the multilayer film has roughness, as shown in Equation (1), Equation (2), and Equation (7) in Non-Patent Document 9, It does not take into account the reduction of the sum of the interference component of reflected X-rays and the interference component of transmitted X-rays due to diffuse scattering caused by irregularities at the surface / interface.

The recurrence formula of the reflectance is
It is.

Therefore, as shown in FIG. 3, the present inventor, for a sample in which a W film is formed on a Si substrate, the average roughness σ _0,1 of the W film surface and the average roughness of the interface between the W film and the Si substrate. The reflectance was calculated according to the conventional calculation method by changing σ ₁ and ₂ as follows. The incident X-ray is S-polarized light and the wavelength is 0.154 nm (CuKα ray). The incident angle is θ, the average roughness of the W film surface is σ _0,1 , the average roughness of the Si substrate interface is σ _1,2 , and the depth of the W film is 10 nm. The calculation results are shown in FIG. 9, FIG. 10, FIG. 11 and FIG.

FIG. 9 shows a case where both the surface and the substrate are flat and smooth (ideal plane) (σ _0,1 = σ _1,2 = 0 nm). Since the X-ray reflected from the sample surface interferes with the X-ray reflected from the interface, it attenuates while vibrating. The amplitude of this vibration corresponds to the surface roughness and the interface roughness, and the rougher (the more blurred the interface), the smaller the vibration amplitude, so that both the surface and the substrate are flat and smooth (ideal plane). In the case (σ _0,1 = σ _1,2 = 0 nm), the vibration amplitude does not decrease as shown in FIG.

As shown in FIGS. 10 and 11, when both the surface and the substrate are rough by the same amount (σ _0,1 = σ _1,2 = 0.3 nm, σ _0,1 = σ _1,2 = In the case of 0.5 nm), as the roughness increases, the decrease in reflectivity increases as the incident angle increases, but the amplitude of vibration due to interference between the X-ray reflected at the sample surface and the X-ray reflected at the interface decreases. Instead, both the surface and the substrate interface interfere and vibrate as if they were ideal planes. This is because the conventional calculation method is a calculation method in which the sum of the transmitted wave and the reflected wave contributing to the interference does not change although the reflectance is lowered by applying an attenuation term to the Fresnel reflection coefficient. If both the surface and the substrate are rough, the interference due to multiple reflections in the specular reflection direction should be weaker and a smooth graph with smaller vibration amplitude should be obtained.

In addition, as shown in FIG. 12, when only the surface is rough (σ _0,1 = 0.5 nm, σ _1,2 = 0 nm), the incident angle has an extremely large amplitude from 1 degree to 1.5 degrees. It is vibrating. This amplitude is larger than the vibration amplitude when both the surface and the substrate are flat and smooth (ideal plane) (σ _0,1 =, σ _1,2 = 0 nm). When the surface roughness increases, the amplitude of vibration due to the interference between the X-rays reflected at the sample surface and the X-rays reflected at the interface should decrease, but the rough surface acts like an interference mirror on the substrate interface. It is vibrating. This is a rough calculation because the conventional calculation method uses a damping term for the Fresnel reflection coefficient to reduce the reflectivity, but the sum of the transmitted wave and reflected wave that contribute to interference does not change. The calculation shows that the transmitted wave increases in response to a decrease in the reflected wave on the surface, indicating that the interference effect is strengthened at a specific angle. When the surface is rough, the calculation result that the interference due to multiple reflections is stronger than the flat and smooth (ideal plane) case is not realistic, and it should be a smooth graph with smaller vibration amplitude Conceivable.

  Therefore, none of the conventional methods accurately detects roughness.

  This invention is made | formed in view of such a situation, and it aims at providing the method, apparatus, and program which can analyze the layer structure of a laminated body correctly using a X-ray reflectivity method. .

In the conventional calculation method, the X-ray reflectivity in the multilayer film has been calculated by applying an attenuation term to the Fresnel reflection coefficient at the surface or interface when considering the roughness. The reflectance obtained by this calculation method is obtained by reducing the value by applying an attenuation term to the reflectance when a rough surface or interface is considered, and does not correspond to irregularities on the surface or interface. The surface or interface is actually the roughness, the surface or interface, resulting X-ray component as a non-interfering component as a diffuse scattering by the surface or interface roughness, interference of the transmitted X-ray interference components of the reflected X-ray Since the reduction of the sum with the component occurs, the vibration amplitude accompanying the incident angle of the reflected wave intensity in the specular reflection direction becomes smaller corresponding to the size of the unevenness at the surface or interface. The present invention has been made paying attention to this point.

That is, in the layered structure analysis method using the X-ray reflectivity method according to the present invention, the X-ray from the X-ray source is applied to the layered body in which the layer structure is formed on the substrate. An irradiation step of irradiating at an incident angle θ, a detection step of detecting, with a detector, specular reflection X-rays reflected at a scattering angle 2θ with respect to the incident X-rays that are the irradiated X-rays from the laminate; A measuring step of measuring the X-ray reflectivity, which is a ratio of the intensity of the specular reflection X-ray detected with respect to the intensity of the incident X-ray, by a measuring device, and an analyzing step of analyzing the measured X-ray reflectivity by the analyzer A layer structure analysis method of a laminate using an X-ray reflectivity method, wherein the analysis step is performed by the analyzer when the laminate has surface roughness or interface roughness. X-rays in a direction other than the specular reflection direction on the surface or interface of the body due to the unevenness of the surface or interface The X-ray reflectivity is analyzed in consideration of the fact that the sum of the interference component of the reflected X-rays and the transmitted X-rays at the surface or interface is reduced by the scattering than the incident component. It is characterized by this. Note that the laminate includes a substrate in which a layer structure such as a single layer film, a multilayer film, and a density non-uniform layer is formed (hereinafter the same).

  According to the present invention, in the analyzer, when the laminate has a surface roughness or an interface roughness, the surface or interface of the laminate has an X in a direction other than the specular reflection direction due to irregularities at the surface or interface. The X-ray reflectivity is analyzed by taking into account the reduction of the interference component between the reflected X-rays and the transmitted X-rays at the surface or interface due to diffuse scattering, and the reflected wave intensity in the specular reflection direction is An analysis result is obtained in which the vibration amplitude associated with the incident angle becomes smaller corresponding to the size of the irregularities at the surface or interface. As a result, the layer structure of the laminate can be accurately analyzed.

  As in the invention described in claim 2, it is preferable that the inside of the laminate is non-uniform in density in the depth direction from the surface.

  According to the invention of claim 2, since the inside of the laminate is non-uniform in the depth direction from the surface, the layer structure of the laminate having such a non-uniform density layer can be analyzed more accurately. Will be able to.

  By the way, in the conventional calculation method, although the reflectance is lowered by applying an attenuation term to the Fresnel reflection coefficient, the total of the transmitted wave and the reflected wave contributing to the interference is not changed. When the intensity of diffuse scattering increases due to surface roughness or interface roughness, the total of all X-ray intensities, including the intensity of X-rays reflected from the laminate and transmitted through the laminate, increases. This is a phenomenon that is impossible in practice. Therefore, as in the invention according to claim 3, the analysis step includes a Fresnel reflection coefficient indicating a reflectance at a surface or an interface of the laminated body when taking into account a decrease in the interference component in the analyzer. It is preferable to take into account that the sum of the Fresnel transmission coefficient indicating the transmittance at the surface or interface of the laminate is less than 1 at the surface or interface where the roughness of the laminate is present.

  According to a third aspect of the present invention, the analysis step includes a Fresnel reflection coefficient indicating a reflectance at a surface or an interface of the laminated body when taking into account a decrease in the interference component in the analyzer, Since the sum of the transmittance and the Fresnel permeability coefficient indicating the transmittance at the surface or interface of the laminate is less than 1 at the surface or interface where the roughness of the laminate is taken into account, the surface roughness is added to the laminate. When the intensity of diffuse scattering increases due to roughness or interfacial roughness, the total of the X-ray intensities including the X-ray reflected from the laminate and the intensity of the X-ray transmitted through the laminate increases. Therefore, it is possible to accurately analyze the layer structure of the laminated body, excluding phenomena that are impossible.

  According to a fourth aspect of the present invention, the analysis step includes the X-ray intensity reflected at the surface or interface of the laminate when the analyzer takes into account the reduction of the interference component, It is preferable to take into account that the sum of the X-ray intensity transmitted through the surface or interface is lower than the X-ray intensity incident on the surface or interface of the laminate.

  According to the invention of claim 4, the analysis step includes the X-ray intensity reflected on the surface or interface of the laminate when the analysis device takes into account the reduction of the interference component, Considering that the sum of the X-ray intensity transmitted through the surface or interface is smaller than the X-ray intensity incident on the surface or interface of the laminate, when the diffuse scattering intensity is increased, Accurately analyze the layer structure of the laminate by reliably excluding phenomena that are not possible in practice, such as the total X-ray intensity, including the intensity of reflected X-rays and the intensity of X-rays transmitted through the laminate. Will be able to.

  As in the invention of claim 5, in the analysis step, the X-ray intensity transmitted through the surface or interface having the roughness of the laminate when taking into account the reduction of the interference component in the analyzer, It is preferable to take into account that the X-ray intensity reflected at the surface or interface of the laminate does not increase due to a decrease in surface roughness or interface roughness.

  According to the invention of claim 5, in the analysis step, the X-ray intensity transmitted through the surface or interface having the roughness of the laminate when taking into account the reduction of the interference component in the analyzer. X-rays reflected from the laminate when the intensity of diffuse scattering increases because the X-ray intensity reflected at the surface or interface of the laminate does not increase with the surface roughness or decrease due to the interface roughness. It is possible to accurately analyze the layer structure of the laminate by reliably excluding phenomena that are impossible in practice, such as the increase in the total intensity of X-rays including the intensity of X-rays transmitted through the line and the laminate. become able to.

  According to a sixth aspect of the present invention, in the analysis step, the X-ray intensity transmitted through the surface or interface of the laminate is taken into account when the analyzer takes into account the reduction of the interference component. It is preferable to take into account that surface roughness or interface roughness decreases due to surface roughness or interface roughness.

  According to the invention of claim 6, when the analysis step takes into account the reduction of the interference component in the analyzer, the X-ray intensity transmitted through the surface or interface of the laminate is In consideration of the decrease in surface roughness or interface roughness due to surface roughness or interface roughness, when the intensity of diffuse scattering increases, X-rays reflected from the laminate or transmitted through the laminate It is possible to accurately analyze the layer structure of the laminate by reliably excluding a phenomenon that is impossible in practice, such as an increase in the total of the X-ray intensity including the intensity.

  As in the invention of claim 7, the analysis step includes the X-ray intensity reflected at the surface or interface of the laminate when taking into account the reduction of interference components accompanying the diffuse scattering in the analyzer. Considering that the sum of the X-ray intensity transmitted through the surface or interface of the laminate is smaller than the X-ray intensity incident on the surface or interface of the laminate corresponding to the intensity change of the diffuse scattering. It is preferable.

  According to the invention of claim 7, the analysis step includes the X-ray intensity reflected at the surface or interface of the laminate when taking into account the reduction of the interference component accompanying the diffuse scattering in the analyzer. Considering that the sum of the X-ray intensity transmitted through the surface or interface of the laminate is smaller than the X-ray intensity incident on the surface or interface of the laminate corresponding to the intensity change of the diffuse scattering. Therefore, when the intensity of diffuse scattering increases, a phenomenon that is impossible in practice, such as the total of all X-ray intensities, including X-rays reflected from the laminate and X-rays transmitted through the laminate, increases. It is possible to accurately exclude the layer structure of the laminated body by excluding it with certainty.

  According to an eighth aspect of the present invention, the measuring step measures the X-ray reflectivity with the measuring instrument and also measures the intensity of diffuse scattered X-rays, and the analyzing step includes the analyzer. Then, when taking into account the reduction of the interference component, the sum of the X-ray intensity reflected at the surface or interface of the laminate and the X-ray intensity transmitted through the surface or interface of the laminate is It is preferable to take into account that the X-ray intensity incident on the surface or interface decreases corresponding to the intensity change of the measured diffuse scattered X-ray.

  According to an eighth aspect of the present invention, the measuring step measures the X-ray reflectance with the measuring instrument and also measures the intensity of diffuse scattered X-rays, and the analyzing step includes the analyzer. Then, when taking into account the reduction of the interference component, the sum of the X-ray intensity reflected at the surface or interface of the laminate and the X-ray intensity transmitted through the surface or interface of the laminate is Reflecting from the laminated body when the intensity of diffuse scattering increases, since the X-ray intensity incident on the surface or interface is taken into account in accordance with a decrease in the intensity of diffuse scattering X-rays measured. Accurately analyze the layer structure of the laminate by reliably excluding phenomena that are not possible in practice, such as the increase in total X-ray intensity, including the intensity of X-rays and X-rays that pass through the laminate. Will be able to.

  As in the invention described in claim 9, based on the analysis result of the X-ray reflectivity in the analysis step in the invention described in any one of claims 1 to 8 by the evaluator, It is preferable to further include an evaluation step for obtaining at least one of the film thickness, the surface roughness, and the interface roughness.

  According to invention of Claim 9, it is an evaluator, Based on the analysis result of the X-ray reflectivity in the analysis process in the invention of any one of Claims 1-8, Since the method further includes an evaluation step for obtaining at least one of the film thickness, surface roughness, and interface roughness, when the intensity of diffuse scattering increases, X-rays reflected from the laminate or X transmitted through the laminate It is possible to accurately evaluate the physical properties of the laminate by reliably excluding a phenomenon that is impossible in practice, such as an increase in the total X-ray intensity including the line intensity.

  As in the invention described in claim 10, an X-ray reflectivity analysis formula using the film thickness, surface roughness and interface roughness of the layered body as parameters is created by an evaluator, and the X-ray reflectivity is calculated. The thickness of the layer of the laminate is adjusted by a fitting method using the least squares method or the maximum entropy method so that the X-ray reflectivity theoretical value of the X-ray reflectivity analysis formula matches the incident angle dependency measurement value. It is preferable to determine at least one of surface roughness and interface roughness.

  According to the invention described in claim 10, an X-ray reflectivity analysis formula using the film thickness, surface roughness, and interface roughness of the layered product as parameters is established by the evaluator, and the X-ray reflectivity is calculated. The film thickness of the layer of the laminate by a fitting method using the least square method or the maximum entropy method so that the X-ray reflectivity theoretical value of the X-ray reflectivity analysis formula matches the measured value of the incident angle dependency of Since at least one of the surface roughness and the interface roughness is required, the physical properties of the laminate can be more accurately evaluated by performing a good fitting between the measured value and the theoretical value. Become.

According to an eleventh aspect of the present invention, there is provided an apparatus for analyzing a layer structure of a laminate using an X-ray reflectivity method. An incident angle of X-rays to a surface of a laminate having a layer structure formed on a substrate. an X-ray source irradiated at θ, a detector for detecting specularly reflected X-rays reflected at a scattering angle 2θ with respect to incident X-rays that are the irradiated X-rays from the laminate, and the detected mirror surface An X-ray reflectivity method comprising: a measuring device that measures an X-ray reflectance that is a ratio of reflected X-ray intensity to the incident X-ray intensity; and an analyzer that analyzes the measured X-ray reflectance. The layered structure analysis apparatus of the used laminate, wherein the analyzer performs specular reflection on the surface or interface of the laminate due to irregularities on the surface or interface when the laminate has surface roughness or interface roughness. Interference of reflected X-rays at the surface or interface due to scattering of X-rays in directions other than the direction The sum of the interference components of the component and the transmitted X-rays, is characterized in that it is intended to analyze the X-ray reflectance in consideration of reducing than the incident component.

  According to invention of Claim 11, there exists an effect similar to the said this invention (method).

  As in the invention of claim 12, based on the analysis result of the X-ray reflectivity in the analyzer in the invention of claim 11, of the layer thickness, surface roughness and interface roughness of the layered product It is preferable to further comprise an evaluator that obtains at least one of

  According to invention of Claim 12, there exists an effect similar to invention of Claim 9.

According to a thirteenth aspect of the present invention, there is provided a program for analyzing a layer structure of a laminated body using the linear reflectance method, wherein X-rays from an X-ray source are applied to a laminated body having a layer structure formed on a substrate. This is detected when the detector detects specular reflection X-rays reflected at a scattering angle 2θ with respect to the incident X-rays that are the irradiated X-rays from the laminate. The first function of measuring the X-ray reflectivity, which is the ratio of the intensity of specular reflection X-rays to the intensity of the incident X-ray, and the surface of the laminate when the laminate has surface roughness or interface roughness or by X-ray in a direction other than the specular reflection direction by the surface or interface roughness is scattered at the interface, the sum of the interference component of the interference component and transmitted X-ray of the reflected X-ray at the surface or interface, the incident the second function and analyzing the X-ray reflectance in consideration of reducing than component Is realized by a computer.

According to the thirteenth aspect of the present invention, the laminate having a layer structure formed on the substrate is irradiated with X-rays from an X-ray source to the surface of the laminate at an incident angle θ, and the irradiation is performed from the laminate. When the specular reflection X-ray reflected at the scattering angle 2θ is detected by the detector with respect to the incident X-ray that is the generated X-ray, the intensity of the detected specular reflection X-ray with respect to the intensity of the incident X-ray The first function of measuring the X-ray reflectivity as a ratio, and when the laminate has a surface roughness or an interface roughness, the surface or interface of the laminate has an irregularity on the surface or interface other than the specular reflection direction. by X-ray in a direction to the scattering of the sum of the interference component of the interference component and transmitted X-ray of the reflected X-ray at the surface or interface, the X-ray reflectance in consideration of reducing than incident component The second function of analyzing An analysis result is obtained such that the amplitude of the reflected wave in the direction becomes small. As a result, the layer structure of the laminate can be accurately analyzed.

  As in the invention of the fourteenth aspect, based on the analysis result of the X-ray reflectivity in the second function in the invention of the thirteenth aspect, the film thickness, surface roughness, and interface roughness of the layer of the laminate. It is preferable that the computer further realizes a third function for obtaining at least one of them.

  According to the invention of claim 14, based on the analysis result of the X-ray reflectivity in the second function in the invention of claim 13, the film thickness, surface roughness and interface roughness of the layered body. Since the third function for obtaining at least one of these is further realized by the computer, an analysis result is obtained such that the amplitude of the reflected wave in the specular reflection direction is reduced. As a result, the layer structure of the laminate can be accurately analyzed.

According to the present invention, in the analyzer, when the laminate has a surface roughness or an interface roughness, an X-ray is emitted in a direction other than the specular reflection direction on the surface or interface of the laminate due to the unevenness of the surface or interface. by but scattered, the sum of the interference component of the interference component and transmitted X-ray of the reflected X-ray at the surface or interface, so are consideration to decrease the X-ray reflectance is analyzed than incident component Thus, an analysis result is obtained in which the vibration amplitude accompanying the incident angle of the reflected wave intensity in the specular reflection direction becomes smaller corresponding to the size of the irregularities on the surface or interface. As a result, the layer structure of the laminate can be accurately analyzed.

It is a block diagram which shows the whole structure of the laminated body layer structure analysis apparatus using the X-ray reflectivity method which concerns on one Embodiment of this invention. It is a flowchart which shows the calculation procedure of the layer structure analysis of a laminated body using a X-ray reflectivity method. It is a model figure which shows the cross-sectional structure of a sample typically. It is a graph which shows the analysis result (when both the surface and a board | substrate are rough: (sigma) _0,1 = (sigma) _1,2 = 0.3nm) by this apparatus. It is a graph which shows the analysis result (When both the surface and a board | substrate are rough: (sigma) _{0, 1} = (sigma) _1,2 = 0.5nm) by this apparatus. It is a graph which shows the analysis result (when both the surface and a board | substrate are rough: (sigma) _0,1 = 0.5nm, (sigma) _1,2 = 0nm) by this apparatus. It is a conceptual diagram of the multilayer film for calculating a reflectance. It is a model figure which shows the cross-sectional structure of a sample typically, Comprising: (a) is a model figure in which the density is changing continuously, (b) is a model figure in which the interface is rough. It is a graph which shows the analysis result (when both the surface and a board | substrate are flat and smooth: (sigma) _0,1 = (sigma) _1,2 = 0nm) by the conventional method. It is a graph which shows the analysis result by the conventional method (when both the surface and the substrate are rough: σ _0,1 = σ _1,2 = 0.3 nm). It is a graph which shows the analysis result by the conventional method (when both the surface and the substrate are rough: σ _0,1 = σ _1,2 = 0.5 nm). It is a graph which shows the analysis result by the conventional method (when both the surface and the substrate are rough: σ _0,1 = 5 nm, σ _1,2 = 0 nm).

  The features of the present invention will be specifically described below with reference to the drawings. In addition, the following description is for making an understanding of this invention easy, and is not restrict | limited to this. That is, modifications, embodiments, and other examples based on the technical idea of the present invention are included in the present invention.

  FIG. 1 is a block diagram showing the overall configuration of a layered structure analysis apparatus (hereinafter referred to as “the present apparatus”) 10 using a X-ray reflectivity method according to an embodiment of the present invention. As shown in FIG. 1, this apparatus 10 generates a goniometer 2 on which a sample 1 that is a laminate is rotatably mounted at a predetermined pitch angle, and X-rays that irradiate the sample 1 placed on the goniometer 2. The X-ray source 3 to be detected, the monochromator 4 which splits the X-rays irradiated from the X-ray source to make the X-rays incident on the sample 1 (Xi), and the reflected X-rays (Xr) from the sample 1 are detected. The detector 5 and the computer 8 are provided. Commercially available hardware can be used for the goniometer 2, the X-ray source 3, the monochromator 4, the detector 5, and the computer 8 themselves. The detector 5 rotates in conjunction with the rotation of the goniometer 2, so that the incident angle θ of incident X-rays irradiated from the X-ray source 3 through the monochromator 4 to the sample 1, and the detector 5. The operation is set so that the elevation angle θ ′ is equal to each other. By this operation setting, the detector 5 detects the specular reflection X-ray reflected from the sample 1 with respect to the incident X-ray at the scattering angle 2θ. Be able to.

  For example, the computer 8 includes a CPU (Central processing unit) 81a for executing various calculations, a ROM (Read-only memory) 81b for storing various programs in advance, and a RAM (temporarily storing various data). Randam-access memory) 81c, to which an input unit 6 such as a keyboard and a mouse and a display unit 7 such as a CRT and a liquid crystal are electrically connected.

  Then, by reading various programs stored in the ROM 81b into the CPU 81a and executing them, a detection data processing unit 82 and an X-ray reflectivity calculation unit (corresponding to a measuring instrument and an analyzer) 83 are obtained. A physical property evaluation unit (corresponding to an evaluator) 84, an X-ray source control unit 85, a goniometer control unit 86, and a detector control unit 87 are constructed.

  The detection data processing unit 82 calculates the intensity of the reflected X-ray using the detection data acquired from the detector 5.

The X-ray reflectivity calculation unit 83 functions as a measuring instrument (corresponding to a first function) that measures the X-ray reflectivity using the intensity of the reflected X-ray calculated by the detection data processing unit 82. When the sample 1 has surface roughness or interface roughness, X-rays are scattered in the direction other than the specular reflection direction by the unevenness of the surface or interface on the surface or interface of the sample 1, thereby Considering that the sum of the interference component of the reflected X-ray and the interference component of the transmitted X-ray is smaller than the incident component, it functions as an analyzer for analyzing the calculated X-ray reflectivity (second Corresponding to a function). Examples of a technique that takes into account the reduction in interference components associated with diffuse scattering in the X-ray reflectivity analysis step include the following (1) to (6).

(1) When taking into account the reduction of interference components due to diffuse scattering, the Fresnel reflection coefficient indicating the reflectance at the surface or interface of the sample 1 and the Fresnel transmission coefficient indicating the transmittance at the surface or interface of the sample 1 In the surface or interface is less than 1.

(2) The sum of the X-ray intensity reflected from the surface or interface of the sample 1 and the X-ray intensity transmitted through the surface or interface of the sample 1 when taking into account the reduction of the interference component accompanying diffuse scattering is the sample. Considering that the X-ray intensity incident on the surface or interface of 1 is reduced.

(3) The surface roughness or interface roughness of the X-ray intensity reflected at the surface or interface of the sample 1 in the X-ray intensity transmitted through the surface or interface of the sample 1 when taking into account the reduction of interference components due to diffuse scattering Taking into account that there is no increase due to the decrease.

(4) When taking into account the reduction of interference components due to diffuse scattering, the X-ray intensity transmitted through the surface or interface of the sample 1 depends on the surface roughness or interface roughness at the surface or interface where the sample 1 is rough. Take into account the decrease.

(5) When taking into account the reduction of interference components associated with diffuse scattering, the sum of the X-ray intensity reflected at the surface or interface of sample 1 and the X-ray intensity transmitted through the surface or interface of sample 1 is the diffuse In consideration of the change in the intensity of scattering, the X-ray intensity incident on the surface or interface of the sample 1 is taken into account.

(6) In addition to measuring the X-ray reflectivity, the diffuse scattered X-ray intensity is also measured and reflected at the surface or interface of the sample 1 when taking into account the reduction of interference components accompanying diffuse scattering. The sum of the X-ray intensity and the X-ray intensity transmitted through the surface or interface of the sample 1 is more dependent on the intensity change of the diffuse scattered X-ray measured than the X-ray intensity incident on the surface or interface of the sample 1. Take into account the corresponding decrease.

  The physical property evaluation unit 84 is based on the X-ray reflectivity calculated by the X-ray reflectivity calculation unit 83 and the rotation angle information of the goniometer 2 (that is, the incident angle θ of the X-ray to the sample 1). It has a function (corresponding to a third function) as an evaluator for obtaining at least one of the film thickness, surface roughness, and interface roughness of the layer of Sample 1. That is, from the X-ray reflectivity and the incident angle θ of the X-ray to the sample 1, as shown in FIGS. 4, 5, and 6 to be described later, when the sample 1 has surface roughness or interface roughness As the incident angle θ of X-rays to the sample 1 increases, the X-ray reflectivity attenuates while vibrating, and the film thickness of the sample 1 is obtained from the period of the vibration amplitude at that time. Surface roughness and interface roughness are determined from the state of attenuation. The physical property evaluation unit 84 may be a graph display that can evaluate the physical properties of the sample 1 on the display unit 7. The user can visually recognize the graph display and the like, and the film of the layer of the sample 1 At least one of thickness, surface roughness and interface roughness can be determined.

  The X-ray source control unit 85 controls the X-ray irradiation timing at the X-ray source 3, and the goniometer control unit 86 controls the rotation timing of the sample 1 placed on the goniometer 2, and the detector control unit 87. Controls the detection timing of the reflected X-rays from the sample 1 under the operation settings. Each control unit 85 to 87 may be separately provided as an external controller of the computer 8.

Subsequently, an X-ray reflectivity method that takes into account the reduction of the sum of the interference component of the reflected X-ray and the interference component of the transmitted X-ray at the surface or interface due to diffuse scattering due to the unevenness of the surface or interface that characterizes the present invention Will be described in detail. As a technique for taking into account the reduction of interference components due to diffuse scattering, the above (4) will be described as an example.

  In the conventional calculation method, the X-ray reflectivity in the multilayer film has been calculated by applying an attenuation term to the Fresnel reflection coefficient at each interface when considering the roughness. The reflectance obtained by this calculation method is obtained by reducing the value by applying an attenuation term to the reflectance when an interface having no roughness is considered. In fact, diffuse scattering occurs at the rough interface, so that the amplitude of the reflected wave in the specular reflection direction becomes small. Here, diffuse scattering refers to weak X-rays that appear around specular reflection spots due to unevenness on the surface or interface when there is surface roughness or interface roughness. The fact that this diffuse scattering is occurring means that X-rays scattered and diffused in directions other than the specular reflection direction or X-rays scattered and diffused in directions other than the refractive transmission direction, that is, diffuse scattered X-rays, which are non-interference components. It is conceivable to consider the reduction of reflected X-rays contributing to interference and the intensity change of transmitted X-rays contributing to interference due to the amount of rays. In the following, considering this point, the theoretical formula of reflectance will be reviewed.

It is a matrix recurrence formula of the reflectance described above
As mentioned above, this relational expression includes
The relationship is hidden. As can be seen, this equation is the result of the reflected and refracted wave energy matching the incident wave.

When there is surface roughness or interface roughness and diffuse scattering occurs, this value is smaller than 1 when the above equation is an equation showing only a coherent X-ray component contributing to the specular reflection X-ray intensity. That is,
It is. Therefore, returning to the theoretical formula that accurately describes this, the theoretical formula of reflectance is reexamined.

Put this and write the matrix recurrence formula of reflectance,
And the recurrence formula of the reflectance is
It becomes.

In this precisely described theoretical formula, the Fresnel reflection coefficient is calculated at the rough interface.
Then, in the conventional method, since the coefficient in parentheses () to be considered in the equation (19) is stored as 1, the Fresnel transmission coefficient t is used to compensate for the decrease in the Fresnel reflection coefficient r ′. '
On the contrary, it can be seen that the calculation is increasing. In practice, rough scattering of the interface will cause diffuse scattering and the amount contributing to interference should both decrease. Therefore, it is necessary to consider the transmission coefficient as well as the reflection coefficient.

Regarding the Fresnel transmission coefficient at the interface with roughness, the interface roughness varies with the roughness correlation distance in the direction parallel to the surface. For example, in Nevot-Croce (Non-Patent Document 6) and Vidal (Non-Patent Document 8), when the spatial frequency of the uneven distribution of the interface is high, the Fresnel transmission coefficient at the rough interface is
It is reported that. That is, this indicates that the Fresnel transmission coefficient at the rough interface is larger than the Fresnel transmission coefficient at the smooth interface, and when the spatial frequency of the uneven distribution at the interface is high, the interface is uniform. It shows that the transmission is close to that when the density changes.

However, even in this case, the term (r ′ _{j, j + 1} ² + t ′ _{j, j + 1} t ′ _{j + 1, j} ) is smaller than 1. Also, de Boer (Non-Patent Document 10) shows that when the spatial frequency of the uneven distribution at the interface is small, that is, the Fresnel transmission coefficient at the interface with gentle roughness,
It is reported that. That is, when the distribution in the direction parallel to the uneven surface of the interface increases, the Fresnel transmission coefficient decreases.

Sinha (Non-Patent Document 7) uses a DWBA calculation including dynamical first order approximation to determine the damping factor.
Is obtained.

Therefore, in general, a recurrence formula for reflectance
In the surface Fresnel reflection coefficient r when there is roughness and surface roughness _{'j, j + 1,} the Fresnel transmission coefficient t' _{j, j + 1} and the Fresnel reflection coefficients _{r j} in a smooth surface _{interface, j + 1,} the Fresnel transmission coefficient _{t j,} The relationship with _{j + 1}
Put like. Here, Γ is an attenuation factor of the Fresnel reflection coefficient when there is roughness, and T is a change factor of the Fresnel transmission coefficient when there is roughness. C _{j, j + 1} is a correlation function in a direction parallel to the surface of the interface roughness and a function indicating the distribution of the uneven structure at the interface.

  The functions Γ and T have a physical meaning as a function indicating the ratio of X-rays that are coherently reflected or transmitted at the uneven surface interface. By analyzing the measurement result of the X-ray reflectivity using the general function model of the X-ray reflectivity as described above, not only the surface roughness and the interface roughness, but also the distribution of the uneven structure at the surface interface can be obtained. It can be determined accurately.

For example, the transmitted X-rays also consider models that there is a similar attenuation and reflection X-ray by the unevenness of the surface interface, the interference component of the interference component and transmitted X-ray of the reflected X-ray at the surface or interface due to diffuse scattering Taking into account the reduction of the sum , that is, what results will be obtained if the attenuation factor derived by Sinha (Non-Patent Document 7) is adopted as the attenuation factor of the reflection Fresnel reflection coefficient and the change factor of the Fresnel transmission coefficient. To find out
Then, according to (Equation 19), calculation is performed for the two-layer film using the apparatus 10. In addition, through this calculation, each step of the layer structure analysis method of the laminated body using the X-ray reflectivity method of the present invention is realized.

FIG. 2 is a flowchart showing the calculation procedure of the layer structure analysis of the laminate using the X-ray reflectivity by the apparatus 10, FIG. 3 is a schematic diagram showing the cross-sectional structure of the sample 1, and FIG. FIG. 5 is a graph showing the case where both the surface and the substrate are rough: σ _0,1 = σ _1,2 = 0.3 nm, and FIG. 5 shows the analysis result of the apparatus 10 (both the surface and the substrate are rough). Case: σ _0,1 = σ _1,2 = 0.5 nm), FIG. 6 is an analysis result by the apparatus 10 (when only the surface is rough: σ _0,1 = 0.5 nm, σ _{1, 2} = 0 nm).

In the multilayer structure as shown in FIG. 3, the reflectance is calculated by changing the average roughness of the W film surface and the average roughness of the interface between the W film and the Si substrate by the same amount. The incident X-ray is S-polarized light and the wavelength is 0.154 nm (CuKα ray). The incident angle is θ, the average roughness of the W film surface is σ _0,1 , the average roughness of the Si substrate interface is σ _1,2 , and the depth of the W film is 10 nm.

  In FIG. 2, when the apparatus 10 is turned on by, for example, an instruction from the input unit 6, the computer 8 performs various programs stored in the ROM 81 b in advance (layer structure analysis of the laminate using the X-ray reflectivity method). Program) is read into the CPU 81a, and initial setting is made so that the units 82 to 87 can be executed. Thereby, the X-ray source control unit 85 controls the X-ray irradiation timing in the X-ray source 3. Then, X-rays generated from the X-ray source 3 are spectrally separated by the monochromator 4 to be incident X-rays on the sample 1 (step S1: equivalent to an irradiation step).

  The goniometer control unit 86 rotates the sample 1 placed on the goniometer 2 at a predetermined angular pitch. Then, the angle of incidence of X-rays on the sample 1 is changed, and the rotation angle information is stored in the RAM 81c.

  The detector control unit 87 controls the detection timing of the reflected X-ray from the sample 1 by the detector 5. Detection data from the detector 5 is taken into the computer 8 (step S2: corresponding to a detection step).

  The detection data processing unit 82 calculates the intensity of the reflected X-ray based on the detection data from the detector 5 and stores it in the RAM 81c (step S3: corresponding to the detection step).

  The X-ray reflectivity calculation unit 83 uses the intensity of the reflected X-ray calculated by the detection data processing unit 82 to calculate an X-ray reflectivity that takes into account the reduction of interference components due to diffuse scattering as described above (step) S4: corresponds to a measurement process and an analysis process).

  The physical property evaluation unit 84 uses the X-ray reflectivity calculated by the X-ray reflectivity calculation unit 83 and the rotation angle information of the goniometer 2 (incident angle θ of X-rays to the sample 1) stored in the RAM 81c. In this case, at least one of the film thickness, surface roughness, and interface roughness of the layer of the sample 1 is obtained. Here, for easy understanding, the X-ray reflectance and the incident angle θ of the X-ray to the sample 1 are determined. Is displayed on the display unit 7 and the physical property of the sample 1 can be evaluated by the user visually recognizing the graph display (step S5: corresponding to an evaluation step). The calculation results are shown in FIGS.

  In FIG. 4, FIG. 5 and FIG. 6, the solid line is the current calculation result, and the dotted line is the conventional calculation result. The solid line graphs of FIGS. 4 and 5 have smaller amplitudes of vibration due to interference than the broken line graphs. Both the surface and the interface are rough, which means that the intensity of diffuse scattered waves is stronger than when both are smooth, the interference due to multiple scattering in the specular reflection direction is weakened, and the amplitude of vibration is small. Since it should be a graph, unlike the conventional calculation result, this calculation result is considered to represent the experimental value well.

The solid line graph of FIG. 6 eliminates the vibration of the abnormal amplitude with the incident angle θ of about 1 to 1.5 degrees, which is seen in the conventional calculation result, as compared with the broken line graph. The amplitude of is small. This amplitude is smaller than the vibration amplitude when both the surface and the substrate are flat and smooth (ideal plane) (σ _0,1 = σ _1,2 = 0 nm). As the surface roughness increases, the amplitude of vibration due to the interference between the X-rays reflected from the sample surface and the X-rays reflected from the interface should be reduced, so the results of this calculation are considered to represent experimental values well.

  As described above, according to the present embodiment, X-rays from the X-ray source 3 are incident on the surface of the sample 1 on the sample 1 which is an example of a laminate having a layer structure formed on the substrate. , And the specular reflection X-ray reflected from the sample 1 with respect to the incident X-ray that is the irradiated X-ray at a scattering angle 2θ is detected by the detector 5, and the intensity of the detected specular reflection X-ray is detected. The X-ray reflectivity, which is a ratio of the incident X-ray to the intensity of the incident X-ray, is measured by the X-ray reflectivity calculation unit 83, and the sample 1 also has a surface roughness or an interface roughness by the X-ray reflectivity calculation unit 83. In this case, the measured X-ray is obtained by taking into account the reduction of the interference component between the reflected X-ray and the transmitted X-ray at the surface or interface due to diffuse scattering due to the surface or interface irregularities on the surface or interface of the sample 1. Since the reflectivity is analyzed, the vibration vibration associated with the incident angle of the reflected wave intensity in the specular direction is reflected. An analysis result is obtained in which the width becomes smaller corresponding to the size of the unevenness at the surface or interface. As a result, the layer structure of the laminate can be accurately analyzed.

  In the present embodiment, the physical property evaluation unit 84 further obtains at least one of the layer thickness, surface roughness and interface roughness of the sample 1 based on the analysis result of the X-ray reflectance. When the intensity of diffuse scattering increases, a phenomenon that is impossible in practice, such as the total of all X-ray intensities, including the X-ray reflected from the sample 1 and the intensity of the X-ray transmitted through the sample 1 is surely increased. By excluding it, the physical properties of the sample 1 can be accurately evaluated.

In the above embodiment, as the sample 1 which is an example of the laminated body, the two-layer structure in which the W film is formed on the Si substrate is illustrated as shown in FIG. 3, but the single layer is formed on the other substrate. The present invention can be similarly applied to a laminate in which a film, a multilayer film, a non-uniform density layer, or the like is formed. When there is a surface roughness also planar substrate injected impurities, considering the reduction of the sum of the interference component of the interference component and transmitted X-ray of the reflected X-ray at the surface due to diffuse scattering due to the unevenness of the surface It can be applied in the same way.

Moreover, in the said embodiment, although (4) was mainly demonstrated among methods (1)-(6) which considered the reduction | decrease of the interference component by diffuse scattering, it can apply similarly to others. However, in method (6), X-ray reflectivity is measured and diffuse scattered X-ray intensity is also measured. However, diffuse scattered X-ray intensity is measured simultaneously with X-ray reflectivity measurement. It is preferable to carry out as well. The measurement result of diffuse scattered X-ray intensity improves the accuracy of determining the correlation function C _{j, j + 1 in} the direction parallel to the surface of the interface roughness.

  In the above embodiment, the detection data processing unit 82, the X-ray reflectance calculation unit 83 corresponding to the measuring instrument and the analyzer, and the physical property evaluation unit 84 corresponding to the evaluator are all stored in the ROM 81b of the computer 8 in advance. Although illustrated as one of various programs (software) that are stored and read by the CPU 81 and executed, it is needless to say that all or part of them may be configured by hardware.

  Moreover, although the case where the program for exhibiting each function of this invention was previously memorize | stored in ROM81b of the computer 8 was illustrated in the said embodiment, this program is computer using external media, such as CD. 8 can be installed easily. This is very convenient because the method of the present invention can be performed using an existing apparatus.

10 Layer structure analysis apparatus 1 of laminate using X-ray reflectivity method Sample (an example of laminate)
2 Goniometer 3 X-ray source 4 Monochromator 5 Detector 6 Input unit 7 Display unit 8 Computer 82 Detection data processing unit 83 X-ray reflectivity calculation unit (corresponding to measuring instrument and analyzer)
84 Physical property evaluation unit (corresponds to an evaluator)
85 X-ray source controller 86 Goniometer controller 87 Detector controller

Japanese Patent Laid-Open No. 3-14684 JP-A-6-221841 JP-A-8-254509 Japanese Patent Laid-Open No. 11-6804 JP-A-11-258185 JP 2000-35408 A JP 2005-114475 A JP 2007-51955 A JP 2001-349849 A

Kenji Sakurai; Regarding the application of X-ray reflectivity method, Applied Physics, Vol. 78, No. 3 (2009) pp. 224-230 Kenji Sakurai; Introduction to X-ray reflectivity method (Kodansha, 2009) Pavel Karimov et al .; multilayer X-ray reflectivity simulation program, The Rigaku-Denki Journal 33 (1) (2002) pp. 20-24 Y. Kojima; Precise structural evaluation of thin films by X-ray reflectivity method, The Rigaku-Denki Journal 30 (2) (1999) pp. 4-13 L. G. Parratt; Surface Studies of Solids by Total Reflection of X-Rays, Phys. Rev. 95 (1954) pp. 359-369 L. Nevot et P.M. Croce; Caracterization des surface par reflexion rasante de rayons X. Application a l'ete du policeage de queues verres silicates, Rev. Phys. Appl. (Paris) 15, 761-779 (1980) S. K. Sinha, etc. X-ray and neuron scattering from rough surfaces, Phys. Rev. B Vol. 38, no. 4 (1988) p. 2297-2311 B. Vidal and P.I. Vincent; Metallic multilayers for X rays using classical thin-film theory, Applied Optics, Vol. 23, Issue 11 (1984) pp. 199. 1794-1801 Table Kazuhiko, Ito Yoshiyasu; Nanoparticle / hole size measurement in thin film by reflection X-ray small angle scattering method, Advances in X-ray analysis, 33 (2002) pp. 185-195 D. K. G. de Boer; X-ray reflection and transmission by rough surfaces, Phys. Rev. B51 (1995) pp. 5297-5305

Claims (14)

An irradiation step of irradiating the surface of the laminated body with an incident angle θ to the laminated body having a layer structure formed on the substrate from the X-ray source;
A detection step of detecting, with a detector, specular reflection X-rays reflected at a scattering angle 2θ with respect to the incident X-rays that are the irradiated X-rays from the laminate;
A measuring step of measuring an X-ray reflectance, which is a ratio of the intensity of the detected specular reflection X-ray to the intensity of the incident X-ray, with a measuring instrument;
An analysis step of analyzing the measured X-ray reflectance with an analyzer, and a layer structure analysis method for a laminate using an X-ray reflectance method,
In the analyzing step, when the laminate has a surface roughness or an interface roughness, X-rays are emitted in a direction other than the specular reflection direction on the surface or interface of the laminate due to unevenness of the surface or interface. The X-ray reflectivity is analyzed in consideration of the fact that the sum of the interference component of the reflected X-rays and the transmitted X-rays at the surface or interface is reduced by the scattering than the incident component. A layer structure analysis method for a laminate using an X-ray reflectivity method.   2. The layer structure analysis method of a measurement object using an X-ray reflectivity method according to claim 1, wherein the inside of the laminate is non-uniform in density from the surface in the depth direction.   In the analysis step, when the reduction of the interference component is taken into account by the analyzer, the Fresnel reflection coefficient indicating the reflectance at the surface or interface of the laminate and the transmittance at the surface or interface of the laminate The X-ray reflectivity method according to claim 1, wherein the sum of the Fresnel transmission coefficient and the Fresnel transmission coefficient is less than 1 at the surface or interface where the laminate is rough. The layer structure analysis method of the used laminated body.   In the analysis step, when the analyzer is used to reduce the interference component, the X-ray intensity reflected at the surface or interface of the laminate, and the X-ray intensity transmitted through the surface or interface of the laminate The layer structure of the laminate using the X-ray reflectivity method according to claim 1 or 2, taking into account that the sum of the values decreases from the X-ray intensity incident on the surface or interface of the laminate. analysis method.   In the analysis step, when taking into account the reduction of the interference component in the analyzer, the X-ray intensity transmitted through the surface or interface having the roughness of the laminate is reflected at the surface or interface of the laminate. The layer structure analysis method for a laminate using the X-ray reflectivity method according to claim 1 or 2, taking into account that there is no increase due to a decrease in surface roughness or interface roughness of the X-ray intensity.   In the analysis step, the X-ray intensity transmitted through the surface or interface of the laminate is roughened at the surface or interface where the laminate has roughness when taking into account the reduction of the interference component. The layer structure analysis method for a laminate using the X-ray reflectivity method according to claim 1 or 2, taking into account a decrease due to roughness or interface roughness.   In the analysis step, when the analyzer is used to reduce the interference component, the X-ray intensity reflected at the surface or interface of the laminate and the X-ray intensity transmitted through the surface or interface of the laminate are The X-ray according to claim 1, wherein the sum of the X-rays is smaller than the X-ray intensity incident on the surface or interface of the laminate in accordance with the intensity change of the diffuse scattering. A layer structure analysis method of a laminate using a reflectance method. The measuring step is to measure the X-ray reflectivity with the measuring device and also measure the intensity of diffuse scattered X-rays.
In the analysis step, when the analyzer is used to reduce the interference component, the X-ray intensity reflected at the surface or interface of the laminate and the X-ray intensity transmitted through the surface or interface of the laminate are The sum of the above is taken into account that the X-ray intensity incident on the surface or interface of the laminate is reduced corresponding to the intensity change of the measured diffuse scattered X-ray. 3. A layer structure analysis method of a laminate using the X-ray reflectivity method described in 2.   In the evaluator, based on the analysis result of the X-ray reflectivity in the analysis step according to any one of claims 1 to 8, the layer thickness, surface roughness and interface roughness of the layered product A method for analyzing the layer structure of a laminate using an X-ray reflectivity method, further comprising an evaluation step for obtaining at least one of the above.   With an evaluator, an X-ray reflectivity analytical expression using the film thickness, surface roughness, and interface roughness of the layered product as parameters was established, and the measured value of the incident angle dependence of the X-ray reflectivity was Of the layer thickness, surface roughness, and interface roughness of the laminate, the fitting method using the least squares method or the maximum entropy method is used so that the theoretical X-ray reflectance values of the X-ray reflectance analysis formula match. The layer structure analysis method for a laminate using the X-ray reflectivity method according to claim 9, wherein at least one is obtained. An X-ray source that irradiates the surface of the laminate with an incident angle θ on the laminate having a layer structure formed on the substrate;
A detector that detects specular reflection X-rays reflected at a scattering angle 2θ with respect to incident X-rays that are the irradiated X-rays from the laminate;
A measuring instrument for measuring an X-ray reflectivity which is a ratio of the intensity of the detected specular reflection X-ray to the intensity of the incident X-ray;
An apparatus for analyzing a layer structure of a laminate using an X-ray reflectivity method, comprising an analyzer for analyzing the measured X-ray reflectivity;
When the analyzer has a surface roughness or an interface roughness, the analyzer scatters X-rays in a direction other than the specular reflection direction due to the unevenness of the surface or interface at the surface or interface of the laminate , the sum of the interference component of the interference component and transmitted X-ray of the reflected X-ray at the surface or interface, characterized in that in consideration of reducing than incident component is intended to analyze the X-ray reflectance Layered structure analysis device of laminate using X-ray reflectivity method.   An evaluator that obtains at least one of the film thickness, surface roughness, and interface roughness of the layer of the laminate based on the analysis result of the X-ray reflectivity in the analyzer according to claim 11. A structural analysis apparatus for a measurement object using an X-ray reflectivity method, characterized in that it is provided. X-rays from an X-ray source are applied to the laminate having a layer structure formed on the substrate at an incident angle θ on the surface of the laminate, and the incident X-rays that are the irradiated X-rays are emitted from the laminate. On the other hand, when specular reflection X-rays reflected at a scattering angle 2θ are detected by a detector, an X-ray reflectance that is a ratio of the intensity of the detected specular reflection X-rays to the intensity of the incident X-rays is measured. The first function and
By X-ray is scattered in a direction other than the specular reflection direction by the surface or interface roughness at the surface or interface of the laminate when there is surface roughness or surface roughness to the laminate, in surface or interface wherein the sum of the interference component of the interference component and transmitted X-rays of the reflected X-rays, than incident component to achieve the second function of analyzing the X-ray reflectance in consideration of reducing the computer A layer structure analysis program for a laminate using the X-ray reflectivity method.   A third method for obtaining at least one of the film thickness, surface roughness and interface roughness of the layer of the laminate based on the analysis result of the X-ray reflectance in the second function according to the invention of claim 13. The structure analysis program of the measurement object using the X-ray reflectivity method characterized by further realizing the function of the above in a computer.