JP6314778B2 - Crystallite diameter calculation method - Google Patents

Description

  The present invention relates to a crystallite diameter calculation method for calculating the crystallite diameter of a thin film formed on the surface of an amorphous substrate.

  One method for obtaining information on the crystallinity of a substance contained in a material (hereinafter referred to as “crystal information”) is X-ray diffraction. In X-ray diffraction, when X-rays with the same wavelength as the distance between atoms are incident on a material with regularly arranged atoms, the X-rays scattered by each atom interfere with each other in a specific direction. Is a phenomenon that generates intense X-rays (hereinafter referred to as “diffracted X-rays”), and is one of the analysis methods used to grasp the characteristics of materials. In this document, measurement using such an X-ray diffraction phenomenon is called “X-ray diffraction measurement”.

  The crystallite diameter which is one of the crystal information of the substance can be obtained from the measurement result of the X-ray diffraction measurement. Specifically, when a diffraction peak derived from a target substance is included in a diffraction pattern (X-ray diffraction pattern) obtained as a measurement result of X-ray diffraction measurement, the degree of spread of this rotational peak Increases as the crystallite size of the substance decreases. For this reason, the crystallite diameter of the substance can be determined by examining the extent of the diffraction peak derived from the substance.

  The Scherrer method is widely used for calculating the crystallite diameter. In the Scherrer method, the half width of the diffraction peak is employed as an index for determining the spread of the diffraction peak. Based on the assumption that the half-width broadening of the diffraction peak resulting from subtracting the half-width broadening due to the measurement optical system is caused by the crystallite diameter, the crystallite diameter of the substance contained in the material is calculated. (For example, see Patent Document 1).

JP 2013-145188 A

  When determining the half width of a diffraction peak, if the intensity of the diffraction peak is sufficiently higher than the intensity of the background of the diffraction pattern obtained by X-ray diffraction measurement, the half width can be determined with high accuracy. However, when the target of the X-ray diffraction measurement is a thin film, the number of crystal lattice planes contributing to the X-ray diffraction phenomenon is reduced, so that the intensity of the diffraction peak is often low as a whole. Moreover, the thin film used as the object of X-ray diffraction measurement is formed on the surface of a base material. In that case, if the substrate is a material having crystallinity, the crystallite diameter can be correctly calculated by selecting the diffraction peak derived from the thin film so as not to overlap the diffraction peak derived from the substrate.

  However, in the evaluation of the crystallite diameter, for example, a combination of a base material and a thin film material is often designated in advance, such as a product that is actually being commercialized or a prototype. In such a case, when the substrate is an amorphous material such as glass or an amorphous polymer, a broad diffraction peak (halo pattern) derived from the substrate is detected in a wide range of diffraction angles. For this reason, it becomes very difficult to select a diffraction peak derived from a thin film so as not to overlap with a diffraction peak derived from a substrate. Then, in many cases, in the diffraction pattern obtained by X-ray diffraction measurement, the diffraction peak derived from the thin film is observed to overlap the diffraction peak derived from the base material, which causes an error in the calculation result of the crystallite diameter. Can be a factor.

  The main object of the present invention is to calculate the crystallite diameter that can accurately calculate the crystallite diameter of the thin film even when the diffraction peak derived from the thin film is superimposed on the diffraction peak derived from the amorphous base material. It is to provide a method.

(Background of the invention)
In general, when X-ray diffraction measurement is performed using a thin film formed on the surface of an amorphous substrate as a test sample, a diffraction pattern including a diffraction peak derived from the substrate and a diffraction peak derived from the thin film is obtained. In this diffraction pattern, a background is generated in addition to the diffraction peak derived from the thin film. The background generated here is mainly derived from the amorphous base material, and in many cases, it is observed overlapping the diffraction peak derived from the thin film. Therefore, when obtaining the half width of a diffraction peak derived from a thin film, the diffraction peak derived from the thin film is extracted after removing the intensity of the diffraction peak as the background intensity in order to remove the influence of the diffraction peak derived from the substrate. Then, the half width is obtained, and the crystallite diameter of the thin film is calculated by applying the obtained half width of the diffraction peak.

By using the above method, when the diffraction peak derived from the amorphous substrate does not overlap with the diffraction peak derived from the thin film, a crystallite diameter with less error is calculated.
On the other hand, when a part of the diffraction peak derived from the thin film (bottom part) is buried due to the influence of the diffraction peak derived from the amorphous substrate, the diffraction peak derived from the amorphous substrate is used as the background. When the above method for calculating the crystallite diameter by processing is used, there is a possibility of calculating a crystallite diameter including a lot of errors. Particularly in recent years, the intensity of diffraction peaks derived from thin films tends to decrease due to the ultrathinning of thin films with the progress of film formation technology, and the proportion of diffraction peaks derived from thin films that are buried in the diffraction peaks derived from the base material is thereby reduced. If the number is increased, the calculation error of the crystallite diameter may become larger.

  Therefore, the present inventor says that the waveform separation processing is performed on the diffraction peak derived from the amorphous substrate and the diffraction peak derived from the thin film without processing the diffraction peak derived from the amorphous substrate as a background. The idea was completed and the present invention was completed.

The first aspect of the present invention is:
A diffraction peak derived from the amorphous substrate and the thin film are obtained by performing X-ray diffraction measurement using a Bragg-Brentano concentrated optical system on a test sample having a thin film formed on the surface of the amorphous substrate. A measurement step for obtaining a diffraction pattern including a diffraction peak derived from
Of the diffraction pattern obtained in the measurement step, the diffraction pattern is derived from the amorphous substrate within a diffraction angle range including a diffraction peak derived from the amorphous substrate and a diffraction peak derived from the thin film. A waveform separation step for separating a diffraction peak and a diffraction peak derived from the thin film,
Obtaining the half-value width of the diffraction peak derived from the thin film obtained in the waveform separation step, and calculating the crystallite diameter of the thin film based on the half-value width;
Is a crystallite diameter calculation method.

The second aspect of the present invention is:
In the measurement step, X-ray diffraction measurement is performed on a test sample having a thickness of the thin film of 10 nm or more and 500 nm or less. In the crystallite diameter calculation method according to the first aspect, is there.

  According to the present invention, even when a diffraction peak derived from a thin film is observed superimposed on a diffraction peak derived from an amorphous substrate, the crystallite diameter of the thin film can be accurately calculated.

It is a schematic sectional drawing which shows the structure of the test sample used as the object of X-ray diffraction measurement by this invention. It is a process flow figure showing a crystallite diameter calculation method concerning an embodiment of the invention. It is a figure which shows an example of the diffraction pattern obtained by X-ray-diffraction measurement. It is the P section enlarged view of FIG. It is a figure which shows an example of a waveform separation process result. It is a figure which shows an example of the diffraction peak obtained at a waveform separation process. It is a figure which shows the diffraction pattern obtained at the measurement process of an Example. It is a figure which shows the peak waveform obtained at the waveform separation process of the Example.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
The present invention performs X-ray diffraction measurement using a Bragg-Brentano concentrated optical system on a test sample in which a thin film is formed on the surface of an amorphous substrate, and based on the measurement results, the thin film crystallites This relates to a method for calculating the diameter.
In the embodiment of the present invention, description will be given in the following order.
1. 1. Test sample 2. About Bragg-Brentano optical system 3. Calculation method of crystallite diameter 4. Effects of the embodiment Examples and comparative examples

<1. About the test sample>
FIG. 1 is a schematic cross-sectional view showing the configuration of a test sample to be subjected to X-ray diffraction measurement in the present invention.
The illustrated test sample 1 is obtained by forming a thin film 3 on the surface (upper surface) 2 a of an amorphous substrate 2. The amorphous substrate 2 is made of an amorphous material such as glass or an amorphous polymer. The thin film 3 is made of a material having a crystal structure. The thin film 3 is made of, for example, a metal such as copper, nickel, cobalt, gold, silver, titanium, tantalum, or niobium, or a metal compound such as ITO (Indium Tin Oxide) (metal oxide, metal nitride, or the like). Can be formed.

  In the embodiment of the present invention, the test sample 1 in which the thin film 3 having a thickness of 1000 nm (1 μm) or less is preferably formed on the surface 2a of the amorphous substrate 2 is measured, and more preferably, the thin film 3 A test sample 1 having a thickness of 10 nm or more and 500 nm or less is set as a measurement object. The reason for this is that when the thickness of the thin film 3 is less than 10 nm, the intensity of the diffraction peak derived from the thin film is too low to make it difficult to calculate the crystallite diameter, and when the thickness of the thin film 3 exceeds 500 nm, it is derived from the thin film. This is because the intensity of the diffraction peak is sufficiently high, and the diffraction peak derived from the base material hardly affects the calculation result of the crystallite diameter.

<2. About Bragg-Brentano Concentrating Optical System>
The Bragg-Brentano concentrated optical system is a concentrated optical system configured such that the relationship between the incident angle of X-rays and the diffraction angle satisfies a relationship of 1: 2. The incident angle is an angle of X-rays (incident X-rays) incident on the test sample, and the diffraction angle is an angle formed by incident X-rays and diffracted X-rays. In this Bragg-Brentano concentrated optical system, an X-ray source that generates X-rays, a sample surface of a test sample, and a light-receiving slit that limits diffracted X-rays are arranged on the same circumference. Then, the intensity of the X-ray that has passed through the light receiving slit is detected by an X-ray detector.

<3. About calculation method of crystallite size>
In this embodiment, the crystallite diameter of the thin film is obtained by the Scherrer method. The Scherrer method is a method for obtaining the crystallite diameter of a certain substance by the following equation (1).
D = 0.9λ / (βcos θ) (1)
This equation (1) is called Scherrer's equation, where D is the crystallite diameter (unit is nm), λ is the X-ray wavelength (unit is nm), and β is the diffraction peak due to the crystallite diameter. The spread width (unit: rad.) And θ is the diffraction angle (unit: deg.) Of the diffraction peak.

Here, β in the above equation (1) employs a value obtained by subtracting the spread width b ₀ by the optical system from the half-value width b of the actually measured diffraction peak. There are two approximate formulas for obtaining β: Gaussian approximation shown in the following equation (2) and Cauchy approximation shown in the following equation (3).
β = (b−b ₀ ) × π ÷ 180 (2)
β = √ (b ² −b ₀ ² ) × π ÷ 180 (3)
Note that the b _0, using the half width of a diffraction peak derived from a standard powder samples were measured by the same inclination angle. As the standard powder, for example, LaB6 powder made by NIST or Si powder made by NIST is preferably used.

FIG. 2 is a process flow diagram showing the crystallite diameter calculation method according to the embodiment of the present invention.
The crystallite diameter calculation method according to the embodiment of the present invention mainly includes a measurement step S1, a waveform separation step S2, and a calculation step S3. Hereinafter, each step will be described.

(Measurement step S1)
In the measurement step S1, the amorphous substrate 2 is obtained by performing X-ray diffraction measurement with the Bragg-Brentano concentrated optical system on the test sample 1 in which the thin film 3 is formed on the surface of the amorphous substrate 2. And a diffraction pattern including a diffraction peak derived from the thin film 3 and a diffraction peak derived from the thin film 3.
When the X-ray diffraction measurement is actually performed on the test sample 1, for example, a measurement result as shown in FIG. 3 is obtained. The measurement results shown in the figure represent diffraction patterns with the diffraction intensity (I) on the vertical axis and the diffraction angle (2θ) on the horizontal axis. However, the diffraction pattern in the figure is greatly simplified from the diffraction pattern obtained by actual X-ray diffraction measurement. Moreover, the diffraction pattern when X-ray diffraction measurement is performed in the range of angles θ1 to θ2 is shown. In the illustrated diffraction pattern, a diffraction peak 11 derived from the amorphous substrate 2 and a diffraction peak 12 derived from the thin film 3 are included. Further, the diffraction peak 12 derived from the thin film 3 overlaps the diffraction peak 11 derived from the amorphous substrate 2.

  When a diffraction pattern in which the diffraction peak 11 derived from the amorphous substrate 2 and the diffraction peak 12 derived from the thin film 3 are thus superimposed is obtained (particularly, the shoulder of the diffraction peak 11 as shown in the figure). For example, if the diffraction peak 11 derived from the amorphous substrate 2 is processed as a background, the half width of the diffraction peak 12 cannot be accurately obtained. The reason is described below.

  In the background treatment, the intensity of the diffraction peak 11 derived from the amorphous substrate 2 is removed as the background intensity. Then, the shape (waveform) of the diffraction peak 12 derived from the thin film 3 superimposed on the diffraction peak 11 is shown in FIG. It is recognized as At this time, a part 12 a of the diffraction peak 12 derived from the thin film 3 is buried under the influence of the diffraction peak 11 derived from the amorphous substrate 2. For this reason, when the intensity of the diffraction peak 11 derived from the amorphous substrate 2 is removed as the background intensity as shown by the broken line in the figure, a part 12a of the diffraction peak 12 derived from the thin film 3 is missing. The shape of the diffraction peak 12 is recognized. Therefore, the half width is obtained in a manner that does not reflect the shape of the original diffraction peak 12 derived from the thin film 3. As a result, the crystallite diameter of the thin film 3 calculated using the half width of the diffraction peak 12 is also inaccurate.

  In contrast, in the present embodiment, the processing proceeds to the next waveform separation step S2 without processing the diffraction peak 11 derived from the amorphous substrate 2 as a background.

(Waveform separation step S2)
The waveform separation step S2 includes a diffraction angle (2θ) range including the diffraction peak 11 derived from the amorphous substrate 2 and the diffraction peak 12 derived from the thin film 3 among the diffraction patterns obtained in the previous measurement step S1. In this step, the diffraction peak 11 derived from the amorphous substrate 2 and the diffraction peak 12 derived from the thin film 3 are waveform-separated.

  In this waveform separation step S2, first, the range of the diffraction angle (2θ) including the diffraction peak 11 derived from the amorphous substrate 2 and the diffraction peak 12 derived from the thin film 3 is determined. For example, when the diffraction pattern shown in FIG. 3 is obtained in the measurement step S1, the range of the diffraction angle so as to include both the broad diffraction peak 11 derived from the substrate and the diffraction peak 12 derived from the thin film superimposed thereon. Is determined in the range of θ3 to θ4, for example. The range of the diffraction angle determined here is narrower than the measurement range θ1 to θ2 of the X-ray diffraction measurement described above.

  Next, waveform separation processing is performed for each of the diffraction peak 11 derived from the base material and the diffraction peak 12 derived from the thin film within the range of the diffraction angle determined above. This waveform separation processing can be performed using waveform separation software for separating the Kα1 line and the Kα2 line. This type of waveform separation software uses the diffraction peak of the Kα1 line (λ = 1.54059Å) and the diffraction peak of the Kα2 line (λ = 1.544441Å) when using CuKα rays for the characteristic X-rays of X-ray diffraction. Used for waveform separation.

When performing waveform separation processing, it is necessary to refine the diffraction angle, diffraction intensity, half-value width, peak shape parameter, and asymmetric parameter of the diffraction peak to be subjected to waveform separation. The refinement described here refers to changing each parameter that determines the calculation data so that the difference between the actual data and the calculation data is minimized. The peak shape parameter is a parameter that determines the shape of the peak, and the asymmetric parameter is how much the peak center is asymmetric from the center of the half-value width (the difference between the width at the low angle side and the high angle side) ) Is a parameter that determines. In the case of actual refinement, the predetermined parameter is changed repeatedly by the least square method or the like until the difference between the data is minimized. The peak shape parameter and the asymmetric parameter will determine whether or not to refine according to the shape of the actual data. However, it is generally better to fit the calculation data to the actual data if both are targeted for refinement. Tend to be.
In the present embodiment, the above-described refinement is performed not only on the diffraction peak derived from the thin film but also on the diffraction peak derived from the amorphous substrate. That is, the diffraction peak derived from the amorphous substrate is regarded as one broad diffraction peak instead of the background, and the above-described refinement is performed on the diffraction peak. As a result, the diffraction peak 11 derived from the amorphous substrate 2 and the diffraction pattern 12 derived from the thin film 3 are separated into waveforms as shown in FIG. 5, for example.

  When the Kα1 line and the Kα2 line separated using the waveform separation software are compared, the relationship between the diffraction intensities is Kα1 line> Kα2 line. For this reason, the Kα2 line is removed in the waveform separation step S2, and the peak waveform of the Kα1 line is used in the next calculation step S3.

(Calculation step S3)
In the calculation step S3, first, the half width b of the diffraction peak 12 is obtained using the diffraction peak 12 derived from the thin film obtained in the waveform separation step S2. The diffraction peak 12 derived from the thin film used at this time is obtained in the waveform separation step S2, and, as shown in FIG. 6, the portion buried under the influence of the diffraction peak 11 derived from the base material before the waveform separation process ( 12a). Further, the half width b of the diffraction peak 12 to be obtained here is “when the β included in the equation (1) is obtained by an approximate expression of Gaussian approximation or Cauchy approximation,“ the half width b of the actually measured diffraction peak b. Is equivalent to. Next, based on the half-value width b of the diffraction peak derived from the thin film obtained previously, the crystallite diameter of the thin film is calculated by the above formula (1).

<4. Effects of the embodiment>
According to the embodiment of the present invention, even when the diffraction peak 11 derived from the thin film 2 is observed superimposed on the diffraction peak 11 derived from the amorphous substrate 2, the diffraction peak derived from the amorphous substrate 2 is observed. The half-value width b of the diffraction peak 12 can be obtained based on the entire shape of the diffraction peak 12 derived from the thin film without losing a part 12a of the diffraction peak 12 derived from the thin film buried under the influence of 11. For this reason, the crystallite diameter of the thin film can be accurately calculated.

<5. About Examples and Comparative Examples>
(Example)
A test sample was prepared by using a glass flat plate as an amorphous substrate and forming a composite oxide film A with a thickness of 50 nm on the surface of the glass flat plate. Next, the above-described measurement step (X-ray diffraction measurement) S1 was performed on the test sample on which the complex oxide film A was formed. Thereby, a diffraction pattern as shown in FIG. 7 was obtained. In this diffraction pattern, a diffraction peak 14 derived from an amorphous substrate and two diffraction peaks 15 and 16 derived from a thin film appear. One diffraction peak 15 overlaps the diffraction peak 14.

Next, by performing the waveform separation step S2 and the calculation step S3 described above in order, 2θ = 30.6 deg. The crystallite diameter was determined using a nearby diffraction peak. FIG. 8 shows the result of the waveform separation process performed on the composite oxide film A. In this example, the range of diffraction angles was determined so as to include both a broad diffraction peak (what was regarded as a diffraction pattern) 14 derived from a glass flat plate and a diffraction pattern 15 overlapping therewith. And in the range of the determined diffraction angle, not only the diffraction peak derived from the complex oxide film A but also the broad diffraction peak 14 derived from the glass flat plate was subjected to waveform separation processing. For this reason, in FIG. 8, the waveform 17 is refined from the diffraction peak derived from the amorphous substrate, and the waveform 18 is refined from the diffraction peak derived from the thin film. Thereby, the diffraction peak shape derived from the composite oxide film A that was buried in the diffraction peak derived from the glass plate before the waveform separation process can be extracted including the buried part after the waveform separation process. confirmed. Accordingly, by obtaining the half width according to the diffraction peak shape derived from the complex oxide film A obtained by waveform separation, the half width indicates the original half width of the diffraction peak due to the complex oxide film A. it is conceivable that.
Note that a straight line 20 descending to the right passing through the lower side of the waveforms 17 and 18 in FIG. 8 shows a background of a broad diffraction peak due to a glass plate used as an amorphous substrate. The two left and right vertical lines 21 and 22 that are present indicate the start point and the end point of a broad diffraction peak due to the glass plate.

The above is for the composite oxide film A. In this embodiment, however, the composite oxidation is performed by changing only the film formation conditions with a combination of the same amorphous substrate and the same composite oxide film. The measurement process S1, the waveform separation process S2, and the calculation process S3 were performed on the material films B, C, and D. As for the composite oxide films A to D, those in which the magnitude relation of the crystallite size was confirmed in advance as A <B <C <D were used. The calculation results of the crystallite diameters of the composite oxide films A to D obtained by this method are shown in Table 1 below. In calculating the crystallite diameter D of the composite oxide film, “2θ” and “β” in the table are parameters of the above equation (1), and “b” and “b ₀ ” in the table are the above ( It becomes a parameter of the equation (2) or the above equation (3).

一例として、表１の試料（複合酸化物膜）Ａに関して、βを上記（３）式のコーシー型近似で求めると、
β（ｒａｄ）＝√｛（０．３６５８）^２−（０．０４７３８１）^２｝×π÷１８０＝０．００６３３の算出値となる。
また、λ（ｎｍ）＝０．１５４０５６として試料Ａの結晶子径Ｄを上記（１）式により求めると、
Ｄ（ｎｍ）＝０．９×０．１５４０５６／（０．００６３３×ｃｏｓ１５．３３４７）＝２２．７となる。

As an example, regarding the sample (composite oxide film) A in Table 1, β is obtained by Cauchy-type approximation of the above equation (3).
β (rad) = √ {(0.3658) ² − (0.0473811) ² } × π ÷ 180 = 0.00633.
Further, when λ (nm) = 0.154056 and the crystallite diameter D of the sample A is obtained by the above equation (1),
D (nm) = 0.9 × 0.154056 / (0.00633 × cos15.3347) = 22.7.

  In Table 1, the relationship between the crystallite sizes of the composite oxides A to D is A <B <C <D, and this relationship is consistent with the results confirmed in advance. Therefore, according to the present method, not only the crystallite diameter of the composite oxide film formed under a certain film formation condition but also the crystallite diameter of the composite oxide film formed under different film formation conditions. It was confirmed that it can be calculated and evaluated correctly.

(Comparative example)
Similar to the above example, X-ray diffraction measurement was performed on the composite oxide films A, B, C, and D having different film forming conditions. Next, after removing the intensity of the diffraction peak derived from the glass flat plate as the background intensity, waveform separation processing was performed using waveform separation software. Next, the half width of the diffraction peak derived from the complex oxide film obtained by waveform separation was determined, and the crystallite diameter of the complex oxide film was calculated by applying this half width.

  In this comparative example, 2θ = 30.6 deg. Derived from the composite oxide film without reflecting the shape of the diffraction peak due to the glass flat plate. Waveform separation processing was performed on nearby diffraction peaks, and crystallite diameters were determined for each of the complex oxide films A, B, C, and D. The calculation results of the crystallite diameters of the composite oxide films A, B, C, and D obtained by this method are shown in Table 2 below.

  In Table 2, the crystallite diameters of the composite oxide film A and the composite oxide film B are required to be approximately the same, and the size relationship between the crystallite diameters of the composite oxide film C and the composite oxide film D is as follows. It is reversed. Therefore, when the waveform separation process is performed without reflecting the shape of the diffraction peak due to the glass plate, it is not possible to calculate an accurate crystallite diameter for each of the composite oxide films A, B, C, and D. It was confirmed.

DESCRIPTION OF SYMBOLS 1 ... Test sample 2 ... Amorphous base material 3 ... Thin film

Claims (4)

A diffraction peak derived from the amorphous substrate and the thin film are obtained by performing X-ray diffraction measurement using a Bragg-Brentano concentrated optical system on a test sample having a thin film formed on the surface of the amorphous substrate. A measurement step for obtaining a diffraction pattern including a diffraction peak derived from
Of the diffraction pattern obtained in the measurement step, the diffraction pattern is derived from the amorphous substrate within a diffraction angle range including a diffraction peak derived from the amorphous substrate and a diffraction peak derived from the thin film. a diffraction peak and a diffraction peak including portions that were buried in the diffraction peak derived from the amorphous Shitsumoto member a diffraction peak derived from the thin film, only those as the diffraction pattern obtained by the measuring step Using a waveform separation step to separate the waveform,
Obtaining the half-value width of the diffraction peak derived from the thin film obtained in the waveform separation step, and calculating the crystallite diameter of the thin film based on the half-value width;
A crystallite diameter calculating method comprising: In the waveform separation step, the diffraction angle, diffraction intensity, half width, peak shape parameter, and asymmetric parameter of the diffraction peak derived from the amorphous base material are changed so that the difference between the actual data and the calculated data is minimized. And changing the diffraction angle, diffraction intensity, half width, peak shape parameter and asymmetric parameter of the diffraction peak derived from the thin film so that the difference between the actual data and the calculated data is minimized.
The crystallite diameter calculation method according to claim 1, wherein: The waveform separation step is performed using waveform separation software for separating the Kα1 line and the Kα2 line.
The crystallite diameter calculation method according to claim 1 or 2, characterized in that: The crystallite diameter according to any one of claims 1 to 3, wherein, in the measurement step, X-ray diffraction measurement is performed on a test sample having a thickness of the thin film of 10 nm or more and 500 nm or less. Calculation method.

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