JP4764208B2 - Method for evaluating the orientation of polycrystalline materials - Google Patents

Description

  The present invention relates to a method for evaluating the orientation of a polycrystalline material using an X-ray diffraction method, and more particularly to a method for quantitatively evaluating the orientation.

  The X-ray diffraction phenomenon is used to evaluate the orientation of polycrystalline materials. The method is to qualitatively measure the half-width of the rocking curve, and the quantitative method is pole measurement. There is a method for calculating an orientation distribution function (ODF).

  The former method for obtaining the half-value width has a problem that the orientation cannot be quantitatively grasped and a weak orientation that does not become a peak in the rocking curve cannot be evaluated. Nevertheless, as a practical method, many samples have been measured under the same measurement conditions using the same measurement device, and the obtained half-value widths have been relatively compared. It is difficult to compare with the half-value width obtained under the conditions. The reason is that the half-value width varies depending on the measurement optical system, and the absolute value is not reliable.

  The latter extreme point measurement requires a complicated goniometer with a chi-axis and has a problem that the measurement takes time. In this case as well, in the evaluation of weak orientation, it is difficult to evaluate the quantitativeness because the correction of the X-ray irradiation area and the calculation of the background are complicated.

Therefore, an evaluation method described in the following Patent Document 1 has been developed as a method capable of quantitative orientation evaluation.
JP 2004-45369 A

  The evaluation method described in Patent Document 1 assumes an orientation density distribution function (including characteristic parameters characterizing the shape of the function) that is axially symmetric around the normal direction of the surface of the sample. The theoretical diffraction X-ray intensity is obtained based on the orientation density distribution function. The characteristic parameters are determined so that the theoretical rocking curve including the characteristic parameters is closest to the measured rocking curve. As a result, the orientation state of the sample can be quantitatively evaluated.

  The evaluation method described in the above-mentioned Patent Document 1 uses an orientation density distribution function. This orientation density function indicates that the normal line of the measured lattice plane of the sample crystallite is the normal line of the sample surface. It is a function for the angle “tilt with respect to”. Here, the “lattice surface to be measured of the crystallite of the sample” refers to a lattice surface that contributes to diffraction (hereinafter referred to as a diffraction surface). When the normal of the diffraction surface coincides with the normal of the sample surface, the tilt angle φ is zero. Assuming a Gaussian function as the orientation density distribution function, this Gaussian function has the highest orientation density when the tilt angle φ of the diffraction surface is zero, and the orientation density decreases as the tilt angle φ increases.

  However, considering the actual diffraction phenomenon, the situation where the diffraction X-ray intensity depends on the tilt angle φ differs from the Gaussian function in the following two points.

  The first point is the presence or absence of periodicity. In an actual diffraction phenomenon, if the tilt angle φ is 360 degrees (2π radians), that is, if the diffraction surface rotates once and returns, the diffraction intensity becomes the same as when φ is 0 degrees. On the other hand, in the Gaussian function, even when φ reaches 360 degrees, the value of the function remains reduced and does not return to the value when φ is 0 degrees. That is, in the actual diffraction phenomenon, the diffracted X-ray intensity exhibits periodicity with a period of 2π radians, but the Gaussian function does not have such periodicity.

  The second point is the presence or absence of overlapping of diffraction peaks due to crystal symmetry. In the actual diffraction phenomenon, another diffraction surface having a mirror index different from that of the considered diffraction surface may cause the diffraction phenomenon at the same diffraction angle. That is, there are equivalent diffractive surfaces with different Miller indices. Therefore, in reality, when the diffracted X-ray is measured at a specific diffraction angle while the inclination angle φ is changed, the diffracted X-ray intensities from the equivalent diffracting surfaces are detected in an overlapping manner. . Even if the crystal system has the lowest symmetry, a diffraction phenomenon from another diffractive surface having a mirror index opposite to the considered diffractive surface should occur at φ = 180 degrees. The Gaussian function does not take into account the overlap of diffracted X-rays caused by such crystal symmetry. In crystals with high symmetry such as hexagonal crystals and cubic crystals, the number of equivalent diffractive surfaces increases, and depending on the Miller index of the diffractive surface being considered, it is also diffracted when the tilt angle φ is 60 or 90 degrees. A peak may appear.

  Since the above two differences exist, when the Gaussian function is simply selected as the orientation density distribution function, the theoretical rocking curve and the measured rocking curve are not consistent in principle as the tilt angle φ increases. come. Therefore, the reliability of the quantitative evaluation of the orientation is poor particularly for a sample with a low degree of orientation (a sample in which the diffraction X-ray intensity spreads to a point where the inclination angle φ is large).

  The present invention has been made in order to solve the above-mentioned problems, and an object of the present invention is to give an appropriate periodicity to the orientation density distribution function and to take into consideration the symmetry of the diffraction surface (lattice surface to be measured). Thus, an object of the present invention is to provide a method for evaluating the orientation of a polycrystalline material so that the reliability of quantitative evaluation of the orientation is improved even when the inclination angle φ is large.

The method for evaluating the orientation of a polycrystalline material according to the present invention comprises the following steps (a) to (d). (A) A step of assuming a diffraction surface normal distribution function P that is axially symmetric around the normal direction of the surface of the sample made of the polycrystalline material. This diffraction surface normal distribution function P is obtained by (a1) expressing the orientation density distribution function ρ at an angle φ at which the normal of the measured lattice plane of the crystallite of the sample is inclined with respect to the normal of the surface of the sample. The angle φ is periodic with a period of 2π radians, (a2) the periodic orientation density distribution function ρ is added to the measured lattice plane and its equivalent lattice plane , and , (A3) includes characteristic parameters that characterize the shape of the function. (B) An X-ray is incident on the surface of the sample at an incident angle α, the intensity of the diffracted X-ray reflected from the measured grating surface of the sample is measured, and the incident angle α is changed to change the measured grating. Obtaining the measurement rocking curve by determining the change in the intensity of the diffracted X-ray from the surface. The diffracted X-ray from the measured grating surface forms an angle 2θ0 with respect to the incident X-ray, and the incident angle α has a relationship of α = θ0 + φ. (C) calculating a theoretical diffracted X-ray intensity based on the diffractive surface normal distribution function P, and obtaining a theoretical rocking curve in a state including the characteristic parameter. (D) determining the characteristic parameter so that the theoretical rocking curve is closest to the measured rocking curve, thereby determining the diffraction surface normal distribution function P;

As described above, the diffraction surface normal distribution function P is obtained by periodicizing the orientation density distribution function and adding the orientation density distribution function to the measured lattice plane and its equivalent lattice plane as described above. When the theoretical diffraction X-ray intensity distribution is calculated based on the diffraction surface normal density distribution function P, the rocking curve well reflects the actual diffraction phenomenon. By fitting the theoretical rocking curve thus obtained to the measured rocking curve and obtaining the characteristic parameters, the reliability of quantitative evaluation of orientation is improved.

  Note that at the stage of obtaining the measurement rocking curve, it is not necessary to actually connect the measured values with the curve, and it is sufficient if there is measurement data that can be fitted to the theoretical rocking curve. Therefore, discrete measurement data is sufficient.

The method for evaluating the orientation of the polycrystalline material according to the present invention includes a periodic distribution of the orientation density distribution function and the addition of the orientation density distribution function with respect to the measured grating plane and its equivalent grating plane to the diffraction plane normal distribution. Since the theoretical rocking curve is calculated based on the diffraction surface normal distribution function, the theoretical rocking curve is more faithful to the actual diffraction phenomenon than the conventional method using the orientation density distribution function as it is. This improves the reliability of quantitative evaluation of orientation.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. First, a method for obtaining a measurement rocking curve will be described. FIG. 1 is a plan view showing one embodiment of an X-ray diffraction apparatus for carrying out the present invention. The incident X-ray 10 formed of a parallel X-ray beam is incident on the surface of the sample 12 at an incident angle α, and the diffracted X-ray 14 reflected by the sample 12 passes through the light receiving slit 16 and the solar slit 18 to be crystal analyzer 19 It is detected by the X-ray detector 20 via (Ge (111)). That is, this X-ray diffractometer is a parallel beam method. By using a crystal analyzer 19 in addition to the solar slit 18, higher resolution is realized. In the measurement examples described later, two types of synchrotron radiation and X-ray tube are used as the X-ray source. However, only when synchrotron radiation is used, a crystal analyzer 19 is used as shown in FIG. ing. When an X-ray tube is used, the crystal analyzer 19 is omitted and the X-rays emitted from the solar slit 18 are directly incident on the X-ray detector 20. This is because when an X-ray tube is used, sufficient X-ray detection intensity cannot be obtained when the crystal analyzer 19 is used.

The light receiving system (light receiving slit 16, solar slit 18, crystal analyzer 19, X-ray detector 20) is disposed at an angle of 2θ ₀ with respect to the incident X-ray 10. The Bragg angle (depending on the wavelength of the incident X-ray 10) of the measurement surface of the sample 12 is θ ₀ . The sample 12 is placed on a sample turntable 22, and the sample turntable 22 can rotate around a goniometer center 24 (perpendicular to the paper surface of FIG. 1). Also, the sample 12 can rotate about a horizontal rotation axis 28 (perpendicular to the goniometer center 24). That is, the sample 12 can be rotated in the plane. The light receiving system is mounted on a detector turntable 26, and this detector turntable 26 can also rotate around the goniometer center 24.

If the measurement lattice plane of the sample 12 is determined and the wavelength of the X-ray to be used is determined, the aforementioned Bragg angle θ ₀ is determined. In FIG. 2A, when the incident angle α is made equal to θ ₀ , the measured grating surface 30 that contributes to diffraction is parallel to the surface of the sample 12. Naturally, the normal line of the measured grating surface 30 is parallel to the normal line of the sample surface. In other words, only crystallites having a measured lattice plane parallel to the sample surface contribute to diffraction. Then, the diffracted X-ray 14 from such a crystallite is detected. On the other hand, in FIG. 2B, when the sample 12 is rotated by an angle φ so that the incident angle α = θ ₀ + φ, the crystallite in which the measured lattice plane 30 is inclined by the angle φ with respect to the sample surface. Only contributes to diffraction. Thus, when the sample 12 is rotated with the detector fixed at the position of 2θ ₀ , the incident angle α changes, and the crystallites corresponding to the respective inclination angles φ (ie, the angle φ relative to the sample surface). Diffracted X-ray intensity information from crystallites that are only oriented.

  By the way, the present invention assumes an orientation density distribution function ρ that is axially symmetric around the normal direction of the sample surface. Therefore, in measuring the diffraction intensity, the sample is rotated in-plane. This makes it possible to compare the theoretical rocking curve with the measured rocking curve. Note that if it is expected that the orientation of the sample is originally axially symmetric, the sample need not be rotated in-plane.

As described above, if the position of the detector is fixed at 2θ ₀ and the diffraction X-ray intensity I is measured by changing the incident angle α, a rocking curve of α-I can be obtained. In order to accurately determine the diffraction X-ray intensity, it is preferable to determine the integrated intensity of the diffraction peak. The calculation of the integrated intensity is described in the above-mentioned Patent Document 1.

Next, a method for obtaining the theoretical rocking curve will be described. FIG. 3 is a perspective view in which the normal vector n of the measurement lattice plane of the crystallite is displayed in polar coordinates. An XY plane is assumed on the surface of the sample 12 , and the normal direction of the sample surface is the Z axis. The normal vector n of the measured lattice plane of the crystallite can be expressed by polar coordinates (φ, ξ). The angle φ is an angle at which the normal vector n is inclined from the Z axis (the normal of the sample surface). The angle ξ is an azimuth angle from the X axis when the normal vector n is projected onto the XY plane.

  The orientation density distribution function ρ of a crystallite having a normal vector n is generally a function of φ, ξ, and z. z is the depth from the surface of the sample. That is, ρ = ρ (φ, ξ, z). The existence probability (orientation probability) of such a crystallite is expressed by equation (1) in FIG. If this orientation probability is integrated in all directions, it should be 1, which is a normalization condition as shown in equation (2). For polycrystalline materials that are perfectly randomly oriented, ρ = constant. Assuming that ρ is axisymmetric about the Z axis, ρ does not depend on ξ.

  In this embodiment, a Gaussian function periodicized with a period of φ = 2π radians is used as the orientation density distribution function. The periodic Gaussian function is expressed by equation (3) in FIG. In Equation (3), G is a normalization factor, H is the half width (FWHM) of a periodic Gaussian function, and has an angle dimension. This H becomes a characteristic parameter characterizing the shape of the function. Once H is determined, the function form of ρ is determined, and once the function form is determined, the theoretical diffraction X-ray intensity can be calculated as will be described later.

  N is a value related to the multiplicity of periodicity, and is an integer that changes by one. Strictly speaking, equation (3) becomes a periodic function when N is infinite. In actual calculations, N is a finite value, but how much N should be increased depends on the degree of orientation of the measurement sample (the magnitude of H) and the value of φ. Since the range of φ is “0 to π” radians, in Eq. (3), items in Σ are added sequentially as k = 0, ± 1, ± 2,. However, when the value of the expression (3) hardly changes (for example, even if k is increased, the change of the value of the expression (3) becomes smaller than 10 minus 5), the increase of k is discontinued. Yes.

  Since H is assumed to depend on the depth z from the sample surface, it is expressed as H (z). This H can also be handled as not depending on the depth z. G is a function of H and can be calculated by the equations (4) to (6) in FIG. When H is sufficiently large, that is, when there is almost no orientation, G becomes as shown in Equation (7), and at this time, the orientation density distribution function ρ becomes as shown in Equation (8) and becomes an unoriented model. Transition continuously. When there is no orientation, the orientation density distribution function ρ is a uniform constant (1 / 4π) independent of the tilt angle φ.

  FIG. 6 is a graph of the orientation density distribution function ρ using a periodic Gaussian function. Using the magnitude of H as a parameter, the horizontal axis represents the inclination angle φ and the vertical axis represents the value of the function ρ. It can be clearly seen that the function ρ approaches non-orientation as H increases. When H is infinite, ρ does not depend on φ and becomes a constant value (1 / 4π).

Next, consider the actual diffraction phenomenon. Diffracted X-rays are observed from all diffractive surfaces having the same diffraction angle (that is, all diffractive surfaces having the same lattice plane spacing). Therefore, what is reflected in the actual diffracted X-ray intensity is a superposition of orientation density distributions of all diffractive surfaces (equivalent diffractive surfaces) having different Miller indices and having the same diffraction angle (ie, addition). the combined one) (this is hereinafter is referred to as a diffraction plane normal distribution). The function shown in the graph of FIG. 6 is a periodic orientation density distribution function ρ for a diffractive surface of one Miller index. The diffractive surface normal distribution function P is what the crystal system of the sample is (such as hexagonal or cubic), and what is the Miller index of the diffractive surface to be measured (measured grating surface) , Depends on This determines how many diffractive surfaces (diffractive surfaces with different Miller indices and equal diffraction angles) are present, and where they appear at the tilt angle φ. Because. The diffractive surface normal distribution function P is the sum of the orientation density distribution functions ρ for those equivalent diffractive surfaces. Therefore, the diffractive surface normal distribution function P reflecting the actual diffraction phenomenon can be obtained for the first time by specifying the crystal system of the sample and the mirror index of the diffractive surface of measurement symmetry. The shape of the diffraction surface normal distribution function P will be described below by designating the crystal system and Miller index.

  The first example is a sample in which the crystal system of the sample is a hexagonal crystal, and the (001) plane normal is oriented so that there is a high probability of facing the sample plane normal direction. That is, the sample has an orientation such that the (001) plane is parallel to the surface of the sample. In order to quantitatively evaluate whether the degree of orientation is strongly oriented or weakly oriented, a diffractive surface normal distribution function P is obtained.

  Another diffraction plane equivalent to the (001) plane is (00-1). It should be understood that the minus sign is attached to the number on the right side of the minus sign as a method of expressing the Miller index. When the (001) plane is at a position of φ = 0 degrees, the (00-1) plane is at a position of φ = 180 degrees (π radians). The diffraction surface normal distribution function P (φ, z) for the diffraction phenomenon arising from these two equivalent diffraction surfaces is the (001) plane orientation density distribution function ρ and the (00-1) plane orientation density distribution. Functions ρ (shifted by π radians) are superimposed on each other, as shown in equation (9) in FIG. The diffractive surface normal distribution is assumed to be axially symmetric around the normal direction of the sample surface and therefore does not depend on the azimuth angle ξ. When the diffractive surface normal distribution function P is integrated in all directions, Equation (10) is established.

  FIG. 8 is a graph showing the diffractive surface normal distribution function P of the above equation (9). This graph has a peak at φ = 180 degrees in addition to a peak at φ = 0 degrees. Compared with the graph of the orientation density distribution function ρ in FIG. In the graph of FIG. 8, H = 180 degrees, and it is already approaching the non-oriented model, ρ = (1 / 2π). On the other hand, in the graph of FIG. 6, at H = 180 degrees, it is still far from the non-oriented model, ρ = (1 / 4π).

  Considering the actual diffraction phenomenon, when a sample having a hexagonal (001) plane parallel to the sample surface as described above is assumed, a diffraction peak appears at φ = 0 degrees, and , A diffraction peak also appears at φ = 180 degrees (if the sample holder or the like does not interfere with X-rays). Therefore, the diffraction surface normal distribution function P as shown in the graph of FIG. 8 represents the actual diffraction phenomenon better than the orientation density distribution function ρ of FIG.

  Whatever the crystal system and what the Miller index of the diffractive surface is, considering the diffraction phenomenon from the diffractive surface, at least at φ = 180 degrees There is another diffraction peak. Therefore, even for the diffraction surface with the lowest symmetry, a graph of the diffraction surface normal distribution function P as shown in FIG. 8 is obtained.

Next, a method for obtaining the theoretical diffraction X-ray intensity (theoretical rocking curve) from the diffraction surface normal distribution function P will be described. The diffracted X-ray intensity I can be obtained by equation (11) in FIG. The diffracted X-ray intensity I varies depending on the incident angle α (see FIG. 2). C in the right side of the equation (11) is a constant part that does not depend on the incident angle α. The constant C does not affect the shape of the rocking curve, but only affects the strength of the entire rocking curve. t is the thickness of the thin film sample when it is assumed to measure diffracted X-rays from the thin film sample, θ ₀ is the Bragg angle, z is the depth from the sample surface, and μ is the linear absorption coefficient of the sample. Α is an incident angle, α = θ ₀ + φ, β is an emission angle, and β = θ ₀ −φ.

  Even if the crystal system and the diffraction surface of the sample are different types, only the function form of the diffraction surface normal distribution function P in the equation (11) is different, and the equation (11) itself is common. Therefore, the following description will focus on how the functional form of the diffraction surface normal distribution function P differs when the crystal system of the sample and the diffraction surface are different.

The second example is a sample in which the crystal system of the sample is cubic and oriented so that the normal of the (111) plane is high in the sample surface normal direction. There are eight diffractive surfaces equivalent to the (111) plane, including itself. In addition, (-1-1-1), (11-1), (1-11), (-111), (-1-11), (-11-1), and (1-1-1). When the (111) plane is oriented at φ = 0 degrees, the (-1-1-1) plane is oriented at φ = π radians. The three planes (11-1), (1-11), and (−111) are oriented at φ = 70.5 degrees, and (−1-11), (-11-1), (1-1 The three planes of -1) are oriented at φ = 109.5 degrees. The diffraction surface normal distribution function P (φ, z) for the diffraction phenomenon generated from these eight equivalent diffraction surfaces is expressed by the equation (12) in FIG. Ρ ₍₁₁₁₎ and ρ _(11-1) in the equation (12) are expressed by the equations (13) and (14) in FIG. G ₍₁₁₁₎ in the equation (13) and G _(11-1) in the equation (14 ₎ are expressed by the equations (15) and (16) in FIG.

  FIG. 12 is a graph showing the diffractive surface normal distribution function P of the above equation (12). This graph shows that when H is small (the degree of orientation is strong), in addition to the peak at φ = 0 °, φ = 70.5 °, φ = 109.5 °, and φ = 180 °. Even has a peak. When H = about 30 degrees, a distribution having a peak of φ = 0 degrees and a distribution having a peak of φ = 70.5 degrees overlap each other. When H = 90 degrees, reflecting the overlap of diffraction peaks, the overall distribution becomes a gentle peak centered at φ = 90 degrees, and thereafter, as H increases, the non-oriented model, ρ = 2 / π , Approaching.

The third example is a sample in which the crystal system of the sample is cubic and oriented so that the normal of the (110) plane is high in the sample surface normal direction. There are twelve diffractive surfaces equivalent to the (110) plane including itself, and in addition, (-1-10), (101), (10-1), (011), (01-1) , (1-10), (−110), (−101), (−10-1), (0-11), and (0-1-1). When the (110) plane is oriented at φ = 0 degrees, the (−1-10) plane is oriented at φ = π radians. The four surfaces (101), (10-1), (011), and (01-1) are oriented at φ = 60 degrees, and the two surfaces (1-10) and (−110) are φ = It is in the direction of π / 2 radians (90 degrees), and the four surfaces (−101), (−10-1), (0-11), and (0-1-1) are in the direction of φ = 120 degrees. is there. The diffraction surface normal distribution function P (φ, z) for the diffraction phenomenon generated from these 12 equivalent diffraction surfaces is expressed by equation (17) in FIG. Ρ ₍₁₁₀₎ , ρ _(101), and ρ _(1-10) in the equation (17) are expressed by the equations (18), (19), and (20) in FIG. Normalization factors G ₍₁₁₁₎ , G ₍₁₀₁₎ and G _(1-10 ) in equations (18) to (20) should be obtained by the same method as equations (15) and (16) in FIG. Can do.

  FIG. 15 is a graph showing the diffraction surface normal distribution function P of the above-described equation (17). This graph has peaks at φ = 60 °, 90 °, 120 °, and 180 ° in addition to the peak at φ = 0 ° when H is small (where the degree of orientation is strong). Due to the overlapping of diffraction peaks, the non-oriented model, ρ = 3 / π, is already approached at H = 60 degrees.

The fourth example is a sample in which the crystal system of the sample is cubic and oriented so that the normal of the (100) plane is high in the sample surface normal direction. There are six diffractive surfaces equivalent to the (100) plane, including itself, and there are (-100), (010), (0-10), (001), and (00-1). . When the (100) plane is oriented at φ = 0 degrees, the (−100) plane is oriented at φ = π radians. The four surfaces (010), (0-10), (001), and (00-1) are in the direction of φ = π / 2 radians (90 degrees). A diffraction surface normal distribution function P (φ, z) for a diffraction phenomenon generated from these six equivalent diffraction surfaces is expressed by equation (21) in FIG. Ρ ₍₁₀₀₎ and ρ ₍₀₁₀ ) in equation (21) are expressed by equations (22) and (23) in FIG. The normalization factors G ₍₁₀₀₎ and G ₍₀₁₀ ) in the equations (22) and (23) can be obtained by the same method as the equations (15) and (16) in FIG.

  FIG. 18 is a graph showing the diffraction surface normal distribution function P of the above equation (21). This graph has peaks at φ = 90 ° and 180 ° in addition to the peak at φ = 0 ° when H is small (where the degree of orientation is strong). At H = 90 degrees, it approaches the non-oriented model, ρ = 3 / (2π).

  Next, a specific measurement example will be described. FIG. 19 shows an example in which (111) reflection of a 30 nm thick Au (gold) polycrystalline thin film (crystal system is cubic) formed by sputtering on a glass substrate is measured. As an X-ray source, synchrotron radiation is used. The X-ray with a wavelength of 0.12 nm is extracted and used. The circles in the graph are the diffracted X-ray intensities obtained by the integrated intensity for each incident angle α. Further, the curve in the graph is a theoretical rocking curve, and the diffraction surface normal distribution function shown in the equation (12) of FIG. 9 and the graph of FIG. 12 is assumed, and the diffraction X-ray is expressed by the equation (11) of FIG. The intensity (rocking curve) is calculated, and the half width H of the Gaussian distribution is determined so that this theoretical rocking curve matches the measured value. In this case, curve fitting was performed using the least square method. The measured value and the theoretical curve agree very well. At that time, H was 69 ± 4 degrees. This is a crystal with very weak orientation. Thus, the degree of orientation can be quantitatively evaluated even with a sample having very weak orientation.

  On the other hand, the theoretical rocking curve is obtained by using the orientation density distribution function without periodicity (that is, the theoretical rocking curve is obtained using the conventional technique described in Patent Document 1), and this is the same measurement. When fitted to a rocking curve, H was 81 ± 16 degrees.

  Further, with respect to the measurement rocking curve measured with the CuKα ray for the same sample, H was 68 ± 5 ° when fitting was performed by obtaining a theoretical rocking curve using a periodic Gaussian function. On the other hand, when the theoretical rocking curve was obtained using the conventional technique and fitting was performed, H was 89 ± 25 degrees.

  The above orientation evaluation results are shown in the list of FIG. According to the method of the present invention, the acquired half-value width H is smaller than that of the prior art method. In the prior art, the periodicity of the orientation density distribution function and the overlap of diffraction peaks due to equivalent diffraction surfaces are not taken into consideration, so the theoretical rocking curve has a smaller width than the actual rocking curve (diffraction peak). Tend to be sharp). When such a theoretical rocking curve is fitted to the measured rocking curve, the obtained evaluation result tends to be larger than the actual half-value width H. The list of FIG. 20 is a result that matches such a tendency. Naturally, the value of H obtained by the present invention (that is, the orientation degree index) is more reliable.

  In the conventional method described above, a periodic Gaussian function is used as the distribution function of the diffractive surface normal, but a Lorentz function or a pseudo-void function can be used in addition to the Gaussian function.

It is a top view which shows one Example of the X-ray-diffraction apparatus for implementing this invention. It is explanatory drawing which shows a mode that X-ray | X_line is diffracted by the to-be-measured lattice plane in a sample. It is the perspective view which displayed the normal vector of the to-be-measured lattice plane of a crystallite in the polar coordinate. It is a mathematical formula related to the orientation density distribution function. It is a mathematical expression of the normalization factor. It is a graph of orientation density distribution function (rho). It is a numerical formula of a diffractive surface normal distribution function of hexagonal crystal (001) and a numerical formula of diffracted X-ray intensity. It is a graph of the diffraction surface normal distribution function of a hexagonal crystal (001). It is a numerical formula of a diffractive surface normal distribution function of a cubic crystal (111). It is a mathematical formula related to the diffraction surface normal distribution function of cubic (111). It is a mathematical formula related to the diffraction surface normal distribution function of cubic (111). It is a graph of the diffraction surface normal distribution function of a cubic crystal (111). It is a numerical formula of a diffractive surface normal distribution function of a cubic crystal (110). It is a mathematical formula related to the diffraction surface normal distribution function of the cubic crystal (110). It is a graph of the diffraction surface normal distribution function of a cubic crystal (110). 3 is a mathematical expression of a cubic (100) diffraction surface normal distribution function. It is a mathematical formula related to the diffraction plane normal distribution function of cubic (100). It is a graph of the diffraction surface normal distribution function of a cubic crystal (100). It is a measurement example of (111) reflection of an Au thin film having a thickness of 30 nm. It is a list of measurement results.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Incident X-ray 12 Sample 14 Diffraction X-ray 16 Light receiving slit 18 Solar slit 20 X-ray detector 22 Sample turntable 24 Goniometer center 26 Detector turntable 28 Rotating shaft 30 Measurement lattice plane

Claims (2)

A method for evaluating the orientation of a polycrystalline material comprising the following steps.
(A) A step of assuming a diffraction surface normal distribution function P that is axially symmetric around the normal direction of the surface of the sample made of the polycrystalline material. This diffraction surface normal distribution function P is obtained by (a1) expressing the orientation density distribution function ρ at an angle φ at which the normal of the measured lattice plane of the crystallite of the sample is inclined with respect to the normal of the surface of the sample. The angle φ is periodic with a period of 2π radians, (a2) the periodic orientation density distribution function ρ is added to the measured lattice plane and its equivalent lattice plane , and , (A3) includes characteristic parameters that characterize the shape of the function.
(B) An X-ray is incident on the surface of the sample at an incident angle α, the intensity of the diffracted X-ray reflected from the measured grating surface of the sample is measured, and the incident angle α is changed to change the measured grating. Obtaining the measurement rocking curve by determining the change in the intensity of the diffracted X-ray from the surface. The diffracted X-ray from the measured grating surface forms an angle 2θ0 with respect to the incident X-ray, and the incident angle α has a relationship of α = θ0 + φ.
(C) calculating a theoretical diffracted X-ray intensity based on the diffractive surface normal distribution function P, and obtaining a theoretical rocking curve in a state including the characteristic parameter.
(D) determining the characteristic parameter so that the theoretical rocking curve is closest to the measured rocking curve, thereby determining the diffraction surface normal distribution function P; 2. The method for evaluating orientation according to claim 1, wherein the diffraction surface normal distribution function P is obtained by adding a periodic Gaussian function to the lattice surface to be measured and its equivalent lattice surface. .

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