JP5165498B2 - 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 at the time of 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 spread analysis due to the twist distribution which is important in the GaN material system and the like 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. A first step of obtaining an hkl profile in which the vertical axis represents the 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 second step of redrawing the hkl profile by re-standardizing the horizontal axis Δθ of each hkl profile by re-standardizing 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. A third step of 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 fourth step of determining whether or not the peak spread shape is caused by a local twist distribution caused by mosaicity, and
Further, as a result of applying the above-described series of steps, that is, the first step to the fourth step , in the fourth step, the central portion of the peak to be analyzed does not depend on the reflection index hkl and is invariant. but are seen, if the weak sub-peak structure is peak shape itself in dependence on the reflective indices hkl to distant parts changes from the center to appear, as the analysis for this sub-peak, attracting hkl profile the renormalization, collected As a result of mutual comparison analysis of the re-standardized hkl profile , that is, as a result of performing the third step and the fourth step on the sub-peak, the sub-peak appears even if the peak shape of the sub-peak does not match or the peak position of the horizontal axis ([Delta] [theta] / sin [theta _C axis) when is reflected in constant position apart regardless of the reflection index hkl from the main peak By examining whether, characterized in that the origin of the sub-peak is composed of a fifth step of determining whether a peak from large twist the peculiar portion in uneven twist distribution.

In the structure analysis method of the present invention, the reflection index hkl used for observing the sub-peak structure in the crystal structure analysis method described above is intentionally set so that the surface angle θ _C is 50 degrees or more. It is characterized by using.

[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 is possible to identify and separate parts that are not affected by the light receiving system by directly identifying and separating the parts that are affected by the light receiving system in the measurement that has not been studied so far. This brings about the effect that it becomes possible to directly analyze the portion where the influence of the light receiving system exists.

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, by directly identifying and separating the parts that are affected by the light receiving system during measurement, an item that has not been studied so far in the conventional analysis method, the parts that are not affected by the light receiving system are combined. In addition, it is possible to directly analyze the part where the influence of the light receiving system exists. More specifically, the present invention also relates to the origin of the weak sub-peak portion observed at a position away from the main peak, in which the influence of the twist distribution could not be essentially analyzed by the influence of the light receiving system in the conventional analysis method. This brings about the effect that analysis becomes possible.

  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 an embodiment of the present invention, various hkl reflection profiles are measured with respect to a GaN sample in FIGS. 1A and 1B in a symmetrical reflection arrangement, and the horizontal axis (scan angle) Δθ of each hkl profile is expressed as Δθ. A renormalized hkl profile redrawn by performing renormalization processing to renormalize to / sin θ _C is shown. At this time, θc represents a surface angle described later.
In the measurement, a normal light receiving system slit (light receiving system opening angle of about 0.25 degrees) was inserted in front of the X-ray detector.

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.

  1 (a) and 1 (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. 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. 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 FIG. 1, in some of the hkl profiles, sub-peaks can be seen at portions that are greatly separated from the peak center (which can be clearly separated from the main peak portion having the continuous distribution). 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 there is no problem, but separately from this conclusion, the effect of the aperture angle of the X-ray detector system is recognized as described above, and the observed sub-peak However, the problem that the conventional analysis method does not answer to the request to obtain information on whether or not the sub-peak appears due to the difference in twist distribution remains as a problem to be improved.

It is the gist of the present invention to improve this part. For this reason, the peak positions on the horizontal axis (Δθ / sin θ _C axis) when the sub-peak appears are constant from the main peak regardless of the index hkl, even though the peak shape itself does not match in FIGS. It is checked whether it is appearing at a position that is only a distance away. If the origin of the sub-peak is a peak from a highly twisted singular part in a non-uniform twist distribution, the sub-peak shape itself matches because it is affected by the aperture angle of the X-ray detector system in relation to the measurement. Even if not, it is predicted in principle that the invariance with respect to the index hkl is observed for the peak position where the sub-peak is observed.
In other words, it is predicted that the peak position on the horizontal axis (Δθ / sin θ _C axis) when the sub-peak appears will appear at a certain distance from the main peak regardless of the index hkl, and this is experimentally investigated. By confirming the trace of invariance, it can be determined whether or not the origin of the sub-peak is a peak from a specific part that is largely twisted in a non-uniform twist distribution.

The figure which performed this operation | work based on FIG. 1 is shown in FIG. In fact, in FIG. 4, it can be confirmed that the peak position on the horizontal axis (Δθ / sin θ _C axis) of the sub-peaks is observed so as to appear at a certain distance from the main peak regardless of the index hkl.

From the above, it can be concluded that the origin of the sub-peaks is a peak from a specific part that is largely twisted in a non-uniform twist distribution. This suggests that there is a small crystal part that is largely different from the main part of the twist distribution corresponding to the main peak and has a different twist angle independently of the main part. It can be said that this can be easily determined is a great advantage of the present invention.
Since the observed sub-peak intensity is weak on the log scale with respect to the main peak intensity, it is assumed that the observation is not performed in the reciprocal lattice mapping measurement. Therefore, it is a great advantage of the present invention that such a weak subpeak can be analyzed.

  As described above, it is understood that the present invention makes it possible to easily evaluate and analyze whether or not the cause is due to the twist distribution even for the sub-peak structure that has been insufficiently analyzed. It was.

Renormalized hkl redrawn by renormalizing the GaN sample by measuring various hkl reflection profiles in a symmetrical reflection arrangement and re-normalizing the horizontal axis Δθ of each hkl profile to Δθ / sin θ _C It is a characteristic view which shows a profile. 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 characteristic which displayed and compared each peak spreading shape of FIG. It is a characteristic view which shows the characteristic which compared the exponent dependence of the subpeak position in FIG.

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. A first step of obtaining an hkl profile in which the vertical axis represents the 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 second step of redrawing the hkl profile by re-standardizing the horizontal axis Δθ of each hkl profile by re-standardizing 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. A third step of 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 fourth step of determining whether or not the peak spread shape is caused by a local twist distribution caused by mosaicity, and
Further, as a result of applying the above-described series of steps, that is, the first step to the fourth step , in the fourth step, the central portion of the peak to be analyzed does not depend on the reflection index hkl and is invariant. but are seen, if the weak sub-peak structure is peak shape itself in dependence on the reflective indices hkl to distant parts changes from the center to appear, as the analysis for this sub-peak, attracting hkl profile the renormalization, collected As a result of mutual comparison analysis of the re-standardized hkl profile , that is, as a result of performing the third step and the fourth step on the sub-peak, the sub-peak appears even if the peak shape of the sub-peak does not match or the peak position of the horizontal axis ([Delta] [theta] / sin [theta _C axis) when is reflected in constant position apart regardless of the reflection index hkl from the main peak By examining whether, structural analysis of crystals, characterized in that the origin of the sub-peak is composed of a fifth step of determining whether a peak from large twist the peculiar portion in uneven twist distribution Method. The crystal structure analysis method according to claim 1, wherein the reflection index hkl used for observing the sub-peak structure is intentionally used so that the surface angle θ _C is 50 degrees or more. Of crystal structure analysis.

Images