JP5154334B2 - Crystal structure analysis method - Google Patents

Description

  The present invention relates to a structure analysis method for bulk crystals, semiconductor thin film crystals, and multiple quantum well structures, and particularly, heteroepitaxially grown thin film crystals having a large degree of lattice mismatch, epitaxial thin films including strain and strained superlattices. This is useful for examining the presence / absence, degree, and characteristics of structural deterioration.

  Conventionally, when structural evaluation of GaN-based materials or the like is performed by X-ray diffraction measurement, it is important to identify the factor of peak broadening due to the tilt distribution and twist distribution due to mosaic crystallinity, and its qualitative and quantitative evaluation. ing.

Here, the technical meaning of “tilt distribution” and “twist distribution” will be described first.
In the mosaic crystal state, it is not a single large crystal state but an aggregate of a large number of microcrystalline regions separated by defects, dislocations, and the like.
At this time, not all the microcrystalline regions are aligned with the same crystal orientation (as the crystal orientation of the substrate), but the crystal orientations are slightly different depending on the influence of the generation of surrounding defects, dislocations, etc. It is distributed to rotate.
For this reason, when this is measured by X-ray diffraction, the distribution of crystal orientations is observed as a broadening of diffraction peaks, and the type and degree of crystal orientation distribution can be evaluated.

As a typical example, a crystal orientation deviation in which the rotation axis of rotation representing the crystal orientation deviation is in the direction of the substrate surface (tangential method) is called tilt, and such a crystal orientation deviation angle. This distribution is called tilt distribution.
In addition, the crystal orientation deviation in which the rotation axis representing the crystal orientation deviation is in the direction perpendicular to the substrate surface (normal direction) is called twist. The distribution is called twist distribution.

  As described above, when performing structural evaluation, it is important to identify the peak broadening factor based on the tilt distribution and twist distribution due to mosaic crystallinity and quantitative evaluation thereof.

  However, conventionally, analysis using reciprocal lattice mapping measurement has been mainly used for such a demand. However, the reciprocal lattice mapping measurement is not necessarily applicable to all cases due to problems such as the time required for measurement and the difficulty in measuring and analyzing weak peaks. In this sense, the development of other analysis methods for the tilt distribution and twist distribution analysis is also important.

As another analysis method that meets this requirement, there is a peak spread factor analysis using the dependency on the reflection index hkl. This analysis method is based on a principle that is different from the reciprocal lattice mapping measurement method. In addition to the advantage of compensating for the disadvantages of the reciprocal lattice mapping measurement method described above, peak spreading factor analysis can be performed in combination with the reciprocal lattice mapping measurement method. It can also be expected to be able to perform more diversified.
In particular, in the structural evaluation of GaN-based samples that have been actively studied in recent years, the evaluation of the twist distribution is important, and a new analysis method as described above is required.

  As a report example using a GaN-based sample for peak broadening factor analysis using such dependence on the reflection index hkl, only a simple analysis using the peak half width (FWHM) of the main peak has been reported. (Non-patent document 1: V. Srikant, JS Speck & DR Clarke J. Appl. Phys. 82, 4286-4295 (1997)), a universal methodology that can directly analyze the peak shape itself in detail has not been known.

  Against this background, the present inventors have developed a method for identifying the peak broadening due to the twist distribution by analysis using the dependence of the peak shape itself on the reflection index hkl. (Japanese Patent Application No. 2007-211185, Non-Patent Document 2: K. Nakashima and T. Matsuoka, J. Appl, Crystallogr. 41, 191-197 (2008))

V. Srikant, J. S. Speck & D. R. Clarke J. Appl. Phys. 82, 4286-4295 (1997) K. Nakashima and T. Matsuoka, J. Appl, Crystallogr. 41, 191-197 (2008)

  The inventor of the present application examines the method of identifying the peak broadening caused by the twst distribution by the analysis using the dependency of the peak shape itself on the reflection index hkl, and selects the reflection index used for the analysis. (Japanese Patent Application No. 2008-039583), this was an improvement for avoiding the influence of the light receiving system during measurement. However, the method of directly identifying the part where the influence of the light receiving system in this measurement exists, the method of separating and identifying the part without the influence, and the method of directly analyzing the part where the influence of the light receiving system exists, etc. It was not considered at all.

The present invention uses the dependence on the reflection index hkl when evaluating the structure of an arbitrary bulk crystal or a single layer and a multilayer structure crystal made of an arbitrary material system formed by epitaxial growth on an arbitrary substrate by X-ray diffraction. This solves the problem in the analysis method for simply analyzing and identifying the cause of the peak spread of the peak spread shape.
That is, in the conventional analysis method, the invention is for solving the problem that the investigation and formulation regarding the peak broadening analysis due to the twist distribution, which is important in the GaN material system, etc., are insufficient, resulting from the twist distribution. A simple and universal analysis method using the reflection index dependence for peak broadening analysis is provided.

  In particular, the part where the influence of the light receiving system exists in the measurement, which has not been studied so far, is directly identified, and the part that is separated and identified without the influence, and the part where the influence of the light receiving system exists is directly A new analysis method is provided.

The configuration of the present invention for solving the above problems is as follows.
A crystal structure analysis method for structural evaluation by X-ray diffraction of an arbitrary bulk crystal or a single layer and a multilayer structure crystal made of an arbitrary material system produced by epitaxial growth on an arbitrary substrate,
By selecting two or more different reflection index hkl conditions and performing X-ray diffraction measurement in the vicinity of the plurality of selected reflection indices hkl under the measurement arrangement of the symmetrical reflection arrangement, the horizontal axis is the scan angle Δθ. Obtaining a hkl profile whose vertical axis represents X-ray intensity;
The factor sin θ _C is calculated when the angle between the reflection index hkl surface specified by the selected reflection index hkl and the surface of the bulk crystal, the surface of the multilayer crystal, or the surface of the substrate is the surface angle θ _C. A step of redrawing the horizontal axis Δθ of each hkl profile into a re-standardized hkl profile by renormalization processing to renormalize to Δθ / sin θ _C ;
By collecting the peak spread shapes of the peaks to be analyzed in each of the re-normalized hkl profiles and aligning and displaying the peak vertices, the re-normalized peak spread shapes are compared and re-standardized. Analyzing the dependence of the shape on the reflection index hkl;
By determining whether or not the re-standardized peak broadening shape is an invariant shape independent of the reflection exponent hkl by the dependency analysis on the reflection exponent hkl, the peak broadening shape of the analysis target peak is A series of analysis method steps comprising determining whether or not a peak spread shape is caused by a local twist distribution caused by the mosaic property (the whole series of analysis method steps are referred to as basic step 1) . Have
In addition, the measurement of each hkl reflection X-ray diffraction profile in the above-described series of analysis method steps (basic step 1) is performed by measuring the X-ray receiver aperture angle under two conditions, a wide aperture angle condition and a narrow aperture angle condition. By applying the above-described series of analysis method steps (basic step 1) for each aperture angle condition, and examining the dependence of the peak broadening shape in the renormalized profile on the reflection index hkl, the dependence due to the twist distribution can be obtained. Step of determining presence / absence of a portion to be shown (the step of applying and analyzing the basic step 1 to the measurement profile under the wide aperture angle condition is referred to as a basic step 1-A and is the basic for the measurement profile under the narrow aperture angle condition) the step of applying the step 1 analysis with basic process is referred to as 1-B), compares the peak spread shape in the case of using the different opening angle condition for each hkl profile, light Identifying portions that do not appear as part of the difference by opening angle condition appears, has a step of separating (referred to as step 2), by confirming that the invariant above all comparing step, i.e., basic steps 1-A In each of the basic steps 1-B, the re-standardized peak broadening shape is confirmed to be an invariant shape independent of the reflection index hkl, and the light receiving system aperture is also compared in the step 2. Confirm that the peak broadening shape does not depend on the angular condition, and extract the peak broadening part that shows invariance in all three comparisons as the common part of the parts obtained from each analysis. Accordingly, to identify the corresponding universal distribution peak broadening shape portion indicating the invariance in the case of the all is due to the twist distribution And butterflies.

  In the structure analysis method of the present invention, in the above-described crystal structure analysis method, an open slit condition (a light receiving system aperture angle of about 2 degrees) is not used as a wide aperture angle condition, and a normal light receiving system slit is used as a narrow aperture angle condition. A structure analysis method for a crystal, characterized by using a condition for inserting (a light receiving system aperture angle of about 0.1 to 0.5 degrees).

[Action]
In the present invention, when the structure is evaluated by X-ray diffraction by using the above-mentioned evaluation means, especially in the analysis method for analyzing and identifying the peak broadening factor of the peak broadening shape using the dependence on the reflection index hkl. Provide a simple and universal analysis method for peak broadening due to distribution.
In particular, it brings about the effect that it is possible to directly identify and separate a portion where the influence of the light receiving system exists in the measurement that has not been studied so far.

According to the present invention, when the structure is evaluated by X-ray diffraction, an analysis method for easily analyzing and identifying the peak expansion factor of the peak expansion shape using the dependence on the reflection index hkl, particularly the peak expansion analysis caused by the twist distribution. The effect of improving the simple and universal analysis method related to can be obtained.
In particular, it is possible to directly identify and separate a part where the influence of the light receiving system at the time of measurement, which has not been studied in the conventional analysis method so far, and this is caused by the twist distribution. The peak spread can be identified with the work of confirming that there is no influence of the light receiving system, and it is possible to analyze the peak spread due to the twist distribution, which is more accurate than the conventional one. Bring.

  The best mode for carrying out the present invention will be described below in detail based on examples.

  As a specific example of the present invention, an example in which a GaN epitaxial thin film sample fabricated on a (0001) sapphire substrate by MOVPE growth method is applied to the present invention for structural evaluation will be described below. It should be noted that this material system is a typical example in which the X-ray diffraction peak broadening due to the twist distribution is mainly observed.

As a first stage of the embodiment of the present invention, various hkl reflection profiles are measured with respect to the GaN sample in FIG. 1 in a symmetrical reflection arrangement, and the horizontal axis (scan angle) Δθ of each hkl profile is expressed as Δθ / sin θ _C. Shows a renormalized hkl profile redrawn by renormalization processing to renormalize. At this time, θc represents a surface angle described later.
Note that the measurement was performed under an open slit condition (a light receiving system opening angle of about 2 degrees) in which a normal light receiving system slit was not inserted in front of the X-ray detector as a wide opening angle condition.

The above-mentioned hkl profile is generated when an X-ray diffraction measurement is performed by irradiating a sample with X-rays under the condition of a symmetrical reflection arrangement as shown in FIG. 2 using an X-ray diffractometer. This is obtained by detecting the intensity of diffracted X-rays.
This hkl profile is obtained with the horizontal axis Δθ representing the scan angle and the vertical axis representing the intensity of the diffracted X-rays.

The “scan angle Δθ” is determined in advance from a slightly smaller angle than the X-ray incident angle specified by the selected reflection index hkl, and from the X-ray incident angle specified by the selected reflection index hkl. The angle when the X-ray incident angle with respect to the reflection index hkl plane is changed (scanned) to a slightly larger angle is shown.
Therefore, when the X-ray incident angle with respect to the reflection index hkl surface that is changed (scanned) in this way becomes the X-ray incident angle specified by the selected reflection index hkl, the scan angle Δθ is 0 °.

In the X-ray analysis method in this case, as shown in FIG. 2, the measurement arrangement is a symmetrical reflection arrangement, and the X-ray incident angle (θin in FIG. 2) with respect to the reflection index hkl plane (the surface shown by the oblique lines in FIG. 2). ) Is changed (scanned), the incident angle θin of the irradiated X-ray with respect to the reflection index hkl surface and the outgoing angle θout of the diffracted X-ray with respect to the reflection index hkl surface are always kept at the same angle. .
In FIG. 2, the angle formed by the reflection index hkl surface (the surface indicated by the oblique lines in FIG. 2) and the surface of the sample (or the substrate surface) is defined as a surface angle θc.

  From FIG. 1, it can be seen that the central portion of the peak broadening shape has an invariant peak broadening shape that does not depend on hkl. As shown in FIG. 3, this point can be confirmed more accurately by displaying and comparing each peak spread shape in FIG. From this result, it can be concluded that the portion showing an invariant peak broadening shape independent of the index hkl is a peak broadening shape reflecting the twist distribution.

However, in some hkl profiles, an unnatural portion is seen in a portion away from the central portion. An example of this is shown in FIG. FIG. 4 is an example of a part having an unusual profile shape, and this part does not show invariance to the exponent.
This cause is considered to be a singular shape that appears due to the aperture angle of the light receiving system in the measurement. However, in each hkl profile measurement, the ratio of the background noise level to the signal intensity (S / N ratio) at the time of measurement also changes. Since the influence of the cause is also considered, it is desirable to directly check what causes the non-invariance to be shown in order to analyze the hkl invariance of the measurement profile shape.

Therefore, as the second stage of the embodiment of the present invention, the hkl invariance analysis of the measurement profile shape is performed under the condition that the light receiving system aperture angle is changed. That is, for the same GaN sample, various hkl reflection profiles were measured in a symmetric reflection arrangement, and the horizontal axis Δθ of each hkl profile was re-normalized to re-normalize to Δθ / sin θ _C. The normalized hkl profile is shown in FIGS. 5 (a) and 5 (b).
In the measurement, the narrow aperture angle condition was measured by inserting a normal light receiving system slit (light receiving system aperture angle of about 0.25 degrees) in front of the X-ray detector.

5 (a) and 5 (b), it can be seen that the peak center portion has an invariant peak broadening shape that does not depend on hkl. As shown in FIG. 6, this point can be confirmed more accurately by displaying and comparing the peak spread shapes of FIGS. 5A and 5B with the peak vertices aligned and superimposed.
From this result, it can be concluded that the portion showing an invariant peak broadening shape independent of the index hkl is a peak broadening shape reflecting the twist distribution. That is, it can be easily confirmed that there is a mosaic crystal structure having a twist angle distribution that is continuously distributed in an almost symmetrical manner around an average state where there is no twist.

However, in FIGS. 5 (a) and 5 (b), in some hkl profiles, sub-peaks are seen at portions that are greatly separated from the peak center. This sub-peak portion is not observed in all hkl profiles, and even if observed, it is observed as an invariant shape that does not necessarily depend on the exponent hkl when compared with sub-peak shapes in other hkl profile measurements. No.
Such a peak reflects the twist distribution in the conventional analysis method (Japanese Patent Application No. 2007-211185, Non-Patent Document 2: K. Nakashima and T. Matsuoka, J. Appl, Crystallogr. 41, 191-197 (2008)). The peak spread shape is not determined.

Examining the characteristics of the index where such sub-peaks are observed, it can be seen that the reflection index hkl is observed such that the surface angle θ _C determined corresponding to the index hkl is 50 degrees or more. The influence of the aperture angle of the X-ray detector system at the time of measurement has been reported as a factor having such index dependence (Japanese Patent Application No. 2008-039583), and this factor also affects the observation of sub-peaks in this embodiment. It is thought to have given.
For this reason, even if the sub-peak is a sub-peak that appears due to a difference in twist distribution, the conventional method is also affected by the aperture angle of the X-ray detector system due to the measurement, so that the conventional analysis is twist. It is not determined that the peak spread shape reflects only the distribution.

  As a conclusion of the conventional analysis method, this conclusion itself is correct and has no problem, but apart from this conclusion, the influence of the aperture angle of the X-ray detector system can be separated and recognized from the exponential dependence as described above. Even so, this separation and recognition is only an indirect identification, more directly identifying the influence of the aperture angle of the X-ray detector system, and in conjunction with the exponential dependence analysis, the peak caused by the twist distribution The problem that the conventional analysis method does not answer to the request to identify the spread remains as a problem to be improved.

  It is the gist of the present invention to improve this part. Therefore, each hkl profile under the wide aperture angle condition in FIG. 1 and each hkl profile under the narrow aperture angle condition in FIGS. 5A and 5B are compared for each hkl and depends on the light receiving system aperture angle condition. The step of examining the profile shape portion not to be performed is performed together with the index dependency analysis.

  An example of this result is shown in FIGS. 7A and 7B as the third stage of the embodiment of the present invention. As can be seen from FIGS. 7A and 7B, the profile shape portion that does not depend on the light receiving system aperture angle condition is only the center portion of the peak, and this portion corresponds to a portion that does not exhibit hkl dependency. However, the singular shape portion and the sub-peak portion that showed exponential dependence in the analysis of FIGS. 1 and 3 to 6 change depending on the light receiving system aperture angle condition in the comparison of FIGS. 7 (a) and 7 (b). It can be directly confirmed that it corresponds to the part.

  From the above, in the comparison of the profile shapes in FIGS. 7A and 7B, the matching part is a part that can be measured without being influenced by the light receiving system opening angle condition without depending on the light receiving system opening angle condition. Thus, it was possible to identify and analyze the portion with a peak broadening shape reflecting the twist distribution with higher accuracy than before.

  As described above, according to the present invention, by directly identifying and separating the influence of the aperture angle of the light receiving system that has been insufficiently analyzed in the past, the peak spread shape caused by the twist distribution by the index dependence analysis can be obtained with higher accuracy than the conventional method. It became clear that the identification and analysis of this would be possible.

Various hkl reflection profiles were measured on a GaN sample with a symmetrical reflection arrangement. In this measurement, an open slit condition (light receiving system) in which a normal light receiving system slit was not inserted in front of the X-ray detector as a wide aperture angle condition. FIG. 6 is a characteristic diagram showing a re-normalized hkl profile measured by an re-normalization process in which the horizontal axis Δθ of each hkl profile is re-normalized to Δθ / sin θ _C measured at an opening angle of about 2 degrees. It is explanatory drawing which shows the measurement arrangement | positioning of the symmetrical arrangement | positioning in X-ray diffraction. It is a characteristic view which shows the typical example which displayed and compared each peak spreading shape of FIG. It is a characteristic view which shows the special example (the part which carried out the profile shape peculiar to the arrow part can be seen) which displayed and compared each peak spreading shape of FIG. Various hkl reflection profiles were measured with respect to the GaN sample in a symmetrical reflection arrangement. In this measurement, a normal light receiving system slit (light receiving system opening angle of 0.25 degrees) was placed in front of the X-ray detector as a narrow opening angle condition. FIG. 6 is a characteristic diagram showing a renormalized hkl profile that was measured by inserting a degree) and redrawn by renormalization processing in which the horizontal axis Δθ of each hkl profile is renormalized to Δθ / sin θ _C. FIG. 6 is a characteristic diagram showing the peak spread shapes of FIG. FIG. 6 is a characteristic diagram showing an example of a result of comparing each hkl profile under the wide aperture angle condition of FIG. 1 and each hkl profile under the narrow aperture angle condition of FIG. 5 for each hkl.

Explanation of symbols

θin Incident angle θout Output angle θc Surface angle Δθ Scan angle

Claims (2)

A crystal structure analysis method for structural evaluation by X-ray diffraction of an arbitrary bulk crystal or a single layer and a multilayer structure crystal made of an arbitrary material system produced by epitaxial growth on an arbitrary substrate,
By selecting two or more different reflection index hkl conditions and performing X-ray diffraction measurement in the vicinity of the plurality of selected reflection indices hkl under the measurement arrangement of the symmetrical reflection arrangement, the horizontal axis is the scan angle Δθ. Obtaining a hkl profile whose vertical axis represents X-ray intensity;
The factor sin θ _C is calculated when the angle between the reflection index hkl surface specified by the selected reflection index hkl and the surface of the bulk crystal, the surface of the multilayer crystal, or the surface of the substrate is the surface angle θ _C. A step of redrawing the horizontal axis Δθ of each hkl profile into a re-standardized hkl profile by renormalization processing to renormalize to Δθ / sin θ _C ;
By collecting the peak spread shapes of the peaks to be analyzed in each of the re-normalized hkl profiles and aligning and displaying the peak vertices, the re-normalized peak spread shapes are compared and re-standardized. Analyzing the dependence of the shape on the reflection index hkl;
By determining whether or not the re-standardized peak broadening shape is an invariant shape independent of the reflection exponent hkl by the dependency analysis on the reflection exponent hkl, the peak broadening shape of the analysis target peak is A series of analysis method steps comprising determining whether or not a peak spread shape is caused by a local twist distribution caused by the mosaic property (the whole series of analysis method steps are referred to as basic step 1) . Have
In addition, the measurement of each hkl reflection X-ray diffraction profile in the above-described series of analysis method steps (basic step 1) is performed by measuring the X-ray receiver aperture angle under two conditions, a wide aperture angle condition and a narrow aperture angle condition. By applying the above-described series of analysis method steps (basic step 1) for each aperture angle condition, and examining the dependence of the peak broadening shape in the renormalized profile on the reflection index hkl, the dependence due to the twist distribution can be obtained. Step of determining presence / absence of a portion to be shown (the step of applying and analyzing the basic step 1 to the measurement profile under the wide aperture angle condition is referred to as a basic step 1-A and is the basic for the measurement profile under the narrow aperture angle condition) the step of applying the step 1 analysis with basic process is referred to as 1-B), compares the peak spread shape in the case of using the different opening angle condition for each hkl profile, light Identifying portions that do not appear as part of the difference by opening angle condition appears, has a step of separating (referred to as step 2), by confirming that the invariant above all comparing step, i.e., basic steps 1-A In each of the basic steps 1-B, the re-standardized peak broadening shape is confirmed to be an invariant shape independent of the reflection index hkl, and the light receiving system aperture is also compared in the step 2. Confirm that the peak broadening shape does not depend on the angular condition, and extract the peak broadening part that shows invariance in all three comparisons as the common part of the parts obtained from each analysis. Accordingly, to identify the corresponding universal distribution peak broadening shape portion indicating the invariance in the case of the all is due to the twist distribution Structure analysis method of the crystal to the butterflies.   2. The crystal structure analysis method according to claim 1, wherein an open slit condition (a light receiving system aperture angle of about 2 degrees) is not used as a wide aperture angle condition, and a normal light receiving system slit is inserted as a narrow aperture angle condition ( A crystal structure analysis method using a light receiving system aperture angle of about 0.1 to 0.5 degrees).

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