JP2001147206A - Strain detecting microscopic image processing apparatus and method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and an apparatus for investigating the strain or flaw in the minute region of a crystal. SOLUTION: Scanning transmission type electronography is digitalized to be taken in a computer and subjected to digital two-dimensional Fourier transform to form a diffraction pattern and one or a plurality of diffraction spot positions in the diffraction pattern are calculated to be compared with the position of a diffraction point in the case of an ideal crystal structure to detect the strain of a crystal lattice. The interval between lattice surfaces or the direction of lattice surfaces or a deformation matrix due to strain is calculated from the spot positions to obtain strain data easy to understand or this operation is performed in a plurality of regions to search the relative change of strain due to a place or mapping is performed to perform the imaging of strain.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for evaluating crystals, and more particularly, to a measuring apparatus and a measuring method for evaluating crystals.

[0002]

2. Description of the Related Art As a conventional method for examining crystal distortion, an X-ray diffraction method has been established, and as a method for examining distortion of a minute portion of a crystal, a micro-Raman method has been known.

With recent advances in microfabrication technology, semiconductor devices using semiconductor crystals have been highly integrated and the device size has been reduced. As a result, stress acting on minute regions in semiconductor crystals and accompanying crystal defects have become problems. Become.

In the conventional method for examining crystal distortion using the micro-Raman method or the like, since the size of the integrated semiconductor element is smaller than the spatial resolution, the crystal distortion inside the semiconductor crystal of the integrated semiconductor element is directly measured. Measuring is
Impossible.

[0005]

Since the conventional X-ray diffraction method and Raman spectroscopy have insufficient spatial resolution, it is not possible to measure a material in nm (nanometer) as a sample, such as the internal structure of a semiconductor device. As an apparatus for evaluating the distortion of the crystal structure of a fine sample, for example, Japanese Patent Application Laid-Open No. 6-36729 discloses a device in which a convergent electron beam diffraction pattern obtained by an electron microscope main body is taken and the sample is subjected to crystal structure distortion. Is calculated approximately, and the Holtz (H) shown in the convergent electron beam diffraction pattern is calculated approximately.
OLZ) line and the calculated Holtz line,
A method and apparatus for displaying a lattice plane of a sample corresponding to non-matching Holtz lines have been proposed. JP-A-6-367
In Japanese Patent Publication No. 29, a transmission electron microscope having an imaging lens below a sample is used.

[0006] For example, Japanese Patent Application Laid-Open No. 7-6725 discloses a composition and lattice measurement for detecting a composition change and a three-dimensional lattice strain structure at the interface or in a thin film of a multilayer thin film sample at a resolution of an atomic order to enable quantitative analysis. As a scanning electron microscope, an accelerated electron beam is incident on a wedge-shaped cleaved specimen, detecting the equal-thickness interference fringes that appear on the transmission image, and using the phenomenon that the distance of the equal-thickness interference fringes changes due to the inclination of the lattice plane. There is disclosed a configuration in which a lattice plane inclination angle distribution is measured, a lattice distortion structure analysis is performed, and a quantitative analysis of the composition distribution is performed by processing so that the equal thickness interference fringes represent only a composition change. . However, this Japanese Patent Application Laid-Open No. 7-6725 also uses a transmission electron microscope having an imaging lens below the sample.

In a patent application prior to the present application, a method of performing Fourier analysis on a transmission electron microscope image (Japanese Patent Application No. Hei.
0-250354: Unpublished at the time of filing of the present application) and a method of irradiating a negative film of a transmission electron microscope image with a laser beam for analysis (Japanese Patent Application No. 10-238863: unpublished at the time of filing the application) has been proposed. ing.

In a method of performing Fourier analysis on a transmission electron microscope image or a method of irradiating a negative film of the transmission electron microscope image with a laser beam and analyzing the image, the transmission electron microscope image is used. Can be analyzed.

However, the transmission electron microscope described above has a problem that small distortion of an image due to aberration of the electron lens cannot be avoided because the electron lens is used for image formation.

[0010] Accordingly, the present invention has been made in view of the above problems, and an object of the present invention is to provide an apparatus and a method capable of examining distortion and defects in a minute region of a crystal. It is in. Other objects, features, advantages and the like of the present invention will be immediately apparent to those skilled in the art from the following description.

[0011]

SUMMARY OF THE INVENTION In order to achieve the above object, the present invention provides a two-dimensional Fourier transform of a partial area of a scanning transmission electron microscope image, calculates a diffraction pattern of the area, and calculates a diffraction pattern in the diffraction pattern. Local lattice distortion is detected from a difference between a spot position and a diffraction point position in an ideal crystal structure.

The present invention provides means for performing a two-dimensional Fourier transform on a partial area of a scanning transmission electron microscope image, and obtaining a diffraction pattern of the area from the result of the two-dimensional Fourier transform; Means for detecting local lattice distortion from the difference between the position of the diffraction spot in the medium and the position of the diffraction point in the ideal crystal structure.

According to the present invention, there is provided means for performing a two-dimensional Fourier transform on each of a plurality of regions of a scanning transmission electron microscope image, and obtaining a diffraction pattern of the plurality of regions from the two-dimensional Fourier transform result; Means for detecting local lattice distortion from the difference between the position of the diffraction spot in the pattern and the position of the diffraction point in the ideal crystal structure,
Detecting local lattice distortion for the plurality of regions;
It is possible to investigate the difference in relative distortion depending on the location.

According to the present invention, two-dimensional Fourier transform is performed on a plurality of regions in the entire region or a partial region of the scanning transmission electron microscope image, and the plurality of regions are obtained from the two-dimensional Fourier transform result. Means for acquiring a diffraction pattern of a region, means for detecting local lattice distortion from a difference between the position of a diffraction spot in the diffraction pattern and the position of a diffraction point in an ideal crystal structure, and Means for mapping the distribution of

According to the present invention, two-dimensional Fourier transform is performed on each of a plurality of regions in the entire region or a part of the scanning transmission electron microscope image, and
Means for obtaining the diffraction pattern of the region from the dimensional Fourier transform result, means for obtaining the position of the diffraction spot in the diffraction pattern, and means for calculating the crystal plane spacing from the positions of the diffraction spots in the plurality of regions, Means for mapping the distribution of the crystal plane spacing.

In the present invention, means for performing a two-dimensional Fourier transform on a partial area of a scanning transmission electron microscope image and obtaining a diffraction pattern of the area from the result of the two-dimensional Fourier transform; Means for detecting local lattice distortion from the difference between the position of the diffraction spot in the pattern and the position of the diffraction point in the ideal crystal structure, measurement by the means for acquiring the diffraction pattern and means for detecting the distortion Is performed for two diffraction spots that are not in the same or opposite directions from the origin of the diffraction space, and a deformation matrix is calculated from the positions of the two diffraction spots and the diffraction point positions in an ideal crystal structure. Means.

In the present invention, a means for performing a two-dimensional Fourier transform on a plurality of regions of a scanning transmission electron microscope image and acquiring a diffraction pattern of the plurality of regions from the two-dimensional Fourier transform result; Means for detecting local lattice distortion from the difference between the position of the diffraction spot in the diffraction pattern and the position of the diffraction point in the ideal crystal structure, and the means for acquiring the diffraction pattern and the means for detecting the distortion The measurement is performed for two diffraction spots that are not in the same or opposite directions from the origin of the diffraction space, and a deformation matrix for obtaining a deformation matrix from the positions of the two diffraction spots and the positions of the diffraction points in an ideal crystal structure. Calculating means;
It is possible to examine the difference in relative distortion depending on the location.

In the present invention, a two-dimensional Fourier transform is performed on a plurality of regions in the entire or partial region of the scanning transmission electron microscope image, and
Means for acquiring a diffraction pattern of the plurality of regions from a result of the dimensional Fourier transform, and local lattice distortion due to a difference between a position of a diffraction spot in the diffraction pattern and a position of a diffraction point in an ideal crystal structure. The means for detecting, the means for acquiring the pattern of the diffraction, and the means for detecting the distortion are measured for two diffraction spots that are not in the same or opposite directions from the origin of the diffraction space.
A deformation matrix calculating means for obtaining a deformation matrix from the position of a diffraction spot at a point and the position of a diffraction point in an ideal crystal structure, and means for mapping the distribution of strain are provided.

According to the present invention, there is provided means for extracting and displaying a part of an original scanning transmission microscope image for a selected region of the mapped distribution displayed on the display device.

[0020]

Embodiments of the present invention will be described. The present invention uses a scanning transmission electron microscope
A diffraction pattern is formed by performing a two-dimensional Fourier transform, the position of one or more diffraction spots in the diffraction pattern is determined, and the position of the diffraction spot is compared with the diffraction point position in an ideal crystal structure. Is detected.

From the results, the spacing between crystal planes,
The direction of the crystal plane can be determined. To calculate the plane distance d of the crystal plane, the relative coordinates from the diffraction point position corresponding to the wave number of zero at the position of the diffraction spot corresponding to the crystal plane are represented by digital pixel coordinates (k _x , k _y ), and It is calculated from equation (1).

[0022]

In the above equation (1), a is the actual distance between each pixel in the scanning transmission electron microscope digital image, and wx and wy are the respective digital two-dimensional Fourier transforms.
This is the number of data in the x and y directions. The direction of the crystal plane is k _x
If ≠ 0, the angle from the x axis is calculated using the 90-degree method, tan (k _y / k _x )
It can be calculated from ^-1 -90 and is parallel to the y-axis when k _x = 0.

Further, a deformation matrix due to distortion can be obtained from two different diffraction spot positions and an ideal crystal structure. This means that the relative coordinates from the diffraction point position corresponding to the zero wave number at the positions of the two diffraction spots are (k _1x , k _1y ) and (k _2x , k _2y ) in digital pixel coordinates, and in the case of an ideal crystal structure If the diffraction point coordinates corresponding to these diffraction points are (k ⁰ _1x , k ⁰ _1y ) and (k ⁰ _2x , k ⁰ _2y ), they can be calculated by the following equation (2).

[0025]

In the above equation (2), t on the left shoulder of the matrix represents a transposed matrix, and -1 on the right shoulder represents an inverse matrix.

These analyzes largely depend on the precision of the magnification of the image of the scanning transmission electron microscope. Therefore, in the same scanning transmission electron microscope field of view, these analyzes are performed for a plurality of regions, and the results are relatively compared. You can find out.

Further, in the embodiment of the present invention,
These operations are performed on a plurality of regions in the same scanning transmission electron microscope field of view, and the distortion detection result is mapped to each region, thereby imaging distortion information.

Further, the image information and the coordinates of a plurality of areas are recorded together, and a position to be checked is indicated on the display image of the display device, whereby the original electronic information corresponding to the area is obtained from the coordinate information of the area. It is configured to take out a part of the microscope image and display a lattice image of the place.

In the embodiment of the present invention, a scanning transmission electron microscope image is used, and the spatial resolution can be increased by narrowing the area for two-dimensional Fourier transform.

In a preferred embodiment of the measuring device according to the present invention, an image processing device for processing an image of a scanning electron microscope captures the microscope image as digital data by an image input unit and the image input unit. Two-dimensional Fourier transform means for performing two-dimensional Fourier transform (two-dimensional fast Fourier transform; FFT) on a region in the image;
Diffraction pattern array obtaining means for obtaining a diffraction pattern array from a two-dimensional Fourier coefficient, diffraction spot position detecting means for detecting a diffraction spot position, and detecting distortion from a comparison between the diffraction spot position and the diffraction point position of an ideal crystal structure. And a mapping means for mapping the distribution of the strain, if necessary.

According to another embodiment of the present invention, a crystal plane information calculation for obtaining a plane interval and a plane direction of a crystal plane corresponding to the diffraction spot from a diffraction spot position detected by the diffraction spot position detecting means is provided. It is good also as composition provided with a means.

In still another embodiment, the present invention is applied to two diffraction spots not in the same direction or in opposite directions from the origin of the diffraction space, and the positions of the two diffraction spots and the ideal crystal structure are determined. And a configuration provided with a deformation matrix calculation means for obtaining a deformation matrix from the diffraction point position in step (1).

Unlike the transmission electron microscope, the scanning transmission electron microscope does not use a lens for imaging below the sample, and thus has no effect of image distortion due to the aberration of the electron lens in principle.

[0035]

Embodiments of the present invention will be described in detail with reference to the drawings.

[First Embodiment] FIG. 1 is a diagram showing a processing flow of a first embodiment of the present invention. FIG. 2 shows a Si substrate (1
00) It is a figure which shows the outline | summary of the scanning transmission electron microscope cross-sectional observation image (also called "scanning transmission electron microscope image") of the sample which made Ge epitaxially grow on the surface. From the scanning transmission electron microscope image shown in FIG. 2, a square area of 256 dots vertically and 256 dots centered on a target portion is extracted, and a two-dimensional array aij (i And j each constitute an integer of 1 to 256) (step 101).

An array bij of a two-dimensional Gaussian distribution (i and j are each an integer of 1 to 256) is calculated by the following equation (3). Array b
ij may be stored in a storage device.

Bij = exp (−0.0004 ((i−129) ² + (j−129) ² )) (3)

The elements of the array bij and the image array two-dimensional array aij are multiplied to form an array cij (i and j are 1 to 2 respectively).
(An integer of 56) is calculated by the following equation (4). cij = aij × bij… (4)

The array cij is transformed into a two-dimensional fast Fourier transform (Fast
Fourier transform is performed using Fourier Transform (Step 102), and a complex number array dij that is a spatial frequency component subjected to Fourier transform is obtained.

Here, dij performs a Fourier transform such that a Fourier component (DC component) having zero wave number is arranged at (i, j) = (1,1).

The absolute value of each element of the array dij is calculated, and all the elements of the array dij are rearranged so that the element corresponding to the Fourier component having zero wave number is located at the center position of the array to obtain a diffraction pattern array eij. .

That is, for an element where i is in the range of 1 to 128 and j is in the range of 1 to 128, the following equation (5), eij = | d (i + 128) (j + 128) | 1 ≦ i ≦ 128,1 ≦ j ≦ 128)… (5)

For an element where i is in the range of 1 to 128 and j is in the range of 129 to 256, the following equation (6) is used: eij = | d (i + 128) (j-128) | (1 ≦ i ≤128,129≤j≤256)… (6)

For an element where i is in the range of 129 to 256 and j is in the range of 1 to 128, the following equation (7) is used: eij = | d (i−128) (j + 128) | (129 ≦ i ≦ 256,1 ≦ j ≦ 128)… (7)

For an element in which i is in the range of 129 to 256 and j is in the range of 129 to 256, the following equation (8) is used: eij = | d (i-128) (j-128) | ≤256,129≤j≤256)… (8)

The diffraction pattern array eij
Find all elements of.

FIG. 3 is a diagram showing an example of the diffraction pattern obtained in this way.

Next, the position coordinates of the diffraction point (diffraction spot) are obtained by searching for the coordinates of the maximum value in the diffraction pattern array eij (step 103).

From the difference between the coordinates of the diffraction point (diffraction spot) and the position of the diffraction point calculated from the ideal lattice constant of the crystal, the lattice distortion at the target location is examined (step 104).

Center coordinates of the coordinates of the obtained maximum value (diffraction point)
If the distance from (i, j) = (129,129) is larger than the value determined from the lattice constant of the ideal crystal, the lattice is smaller than the ideal crystal state. If the distance from the center coordinates (i, j) = (129,129) of the value coordinates is smaller than the value obtained from the lattice constant of the ideal crystal, the lattice is extended from the ideal crystal state. Is represented.

As a result of this analysis, in the portion where Ge was epitaxially grown in FIG. 2, the diffraction point was moved inward by about 4% from the position expected in the silicon crystal. Thus, the Ge portion indicates that the lattice is close to the original Ge lattice.

[Embodiment 2] A second embodiment of the present invention will be described. In the first embodiment, the magnification of the scanning transmission electron microscope must be accurately calibrated.
However, in practice, there is a limit to this calibration accuracy.

In order to investigate finer distortion,
Relative distortion can be measured by examining relative distortion due to comparison with a reference position in a photograph (image) of the same scanning transmission electron microscope.

Two areas in the scanning transmission electron microscope image shown in FIG.
A two-dimensional array aij (i and j are 1 to 2 respectively) taking out a square area of 256 dots and 256 dots and taking the brightness of each dot as a value
56 integers).

An array bij of a two-dimensional Gaussian distribution (i and j are each an integer of 1 to 256) is calculated from the above equation (3), and each element of this array bij and the image array aij is calculated according to the above equation (4). Multiply and multiply the array cij (i and j are each an integer from 1 to 256) by 2
Calculate for each of the two regions.

For each of the two regions, the sequence cij
Is subjected to two-dimensional Fourier transform using a two-dimensional fast Fourier transform to obtain a two-dimensional Fourier transformed complex array dij (two-dimensional Fourier coefficient). At this time, dij performs a two-dimensional Fourier transform such that a Fourier component with a wave number of zero comes at (i, j) = (1,1).

The absolute value of each element of the array dij is calculated for each region, and all the elements are rearranged so that the element corresponding to the Fourier component with zero wave number is located at the center position of the array to obtain the diffraction pattern array eij. . That is, the calculations of the above equations (5) to (8) were performed on the arrays of the respective regions, and all elements of the array eij were obtained. The diffraction patterns are shown in FIG. 4 and FIG. FIG. 4 is a diagram showing a diffraction pattern by a two-dimensional FFT of a part of the Si substrate part of FIG. 2 (about 10 nm below a Ge island). FIG. 5 is a diagram showing a diffraction pattern by two-dimensional FFT of a partial region of the Ge island in FIG.

Subsequently, the coordinates of the diffraction point are obtained by searching for the coordinates of the maximum value of the diffraction pattern array for each region.

From the difference in the coordinates of the diffraction points obtained for each area, the relative lattice distortion at each location is examined.

Here, the center coordinates of the coordinates of the obtained maximum value
When the distance from (i, j) = (129,129) is large, it indicates that one region has a smaller lattice than the other region.

When the Ge portion was examined and compared in a plurality of regions, it was found that the spot position changed depending on the location. This result means that there is a small local distortion in the Ge film.

Third Embodiment Next, a third embodiment of the present invention will be described. When distortion is compared in a plurality of regions in a scanning transmission electron microscope image as in the above-described second embodiment, the entire region or a target region of a scanning transmission electron microscope photograph (image) is further compared. If a plurality of regions are selected at intervals, distortion is obtained in each region, and the obtained result is visualized as image information, the understanding of the distortion is further deepened.

The image of the scanning transmission electron microscope shown in FIG. 2 is divided into square areas of 256 dots in width and 256 dots in each area, and in each area, a two-dimensional array ai having the brightness of each dot in the area as a value.
j (i and j are each an integer of 1 to 256).

The two-dimensional Gaussian distribution array bij (i and j are each an integer of 1 to 256) is calculated from the above equation (3), and each element of the array and the image array is multiplied by the above equation (4). Then, an array cij (i and j are each an integer of 1 to 256) is calculated for the array of each region. For each area,
This array cij is subjected to Fourier transform using a two-dimensional fast Fourier transform method, and a two-dimensional Fourier transformed complex array dij
Is calculated. At this time, dij performs a Fourier transform such that a Fourier component with a wave number of zero comes at (i, j) = (1,1).

The absolute value of each element of the array dij is calculated for each region, and the diffraction pattern array eij is obtained by rearranging all the elements so that the element corresponding to the Fourier component with zero wave number is located at the center of the array. . That is, the calculations of the above equations (5) to (8) are performed on the arrays of the respective areas, and all elements of the array eij are obtained.

For each region, the coordinates of the diffraction point are obtained by searching for the coordinates of the local maximum value of the diffraction pattern array.

FIGS. 6 and 7 show the results of mapping and mapping the x and y coordinates of the 111 diffraction points obtained for each region.

In the display shown in FIGS. 6 and 7, in the mapping, a bright portion indicates that the diffraction point is farther from the center, while a dark portion indicates that the diffraction point is closer to the center. From this result, the strain distribution in the Ge film can be understood.

FIG. 21 is a diagram showing a schematic configuration of a measuring apparatus for performing the methods described in the first to third embodiments of the present invention. Referring to FIG. 21, the measuring device includes a scanning transmission electron microscope 10 and an image processing device 20 including a computer (data processing device). The image processing device 20 includes an input device 30, a display device 40, and a storage device. Device 5
0 is connected, and the image processing apparatus 20 includes an image input unit 22 that captures an electron microscope image of the scanning transmission electron microscope 10 as digital image data, and 2 A two-dimensional Fourier transform unit 23 for performing a two-dimensional Fourier transform, a diffraction pattern acquisition unit 24 for obtaining a diffraction pattern array eij from a two-dimensional Fourier coefficient dij, a diffraction spot position detection unit 25 for detecting a diffraction spot position, Strain detector 2 for detecting distortion from comparison with the diffraction point position of the ideal crystal structure
6 and a control unit 21 for controlling the whole.
In the embodiment, a mapping unit 27 for mapping the distribution xy coordinates of the distortion is provided.

[Embodiment 4] Next, a fourth embodiment of the present invention will be described. It is easier to understand the state of the distortion by obtaining the plane spacing and the plane orientation of the crystal plane from the displacement of the spot position in the diffraction pattern. Therefore, in the fourth embodiment of the present invention, from the diffraction spot positions in a plurality of regions obtained in the third embodiment, the plane spacing and plane direction of the crystal plane corresponding to the diffraction spot are obtained and mapped.

A diffraction point in a diffraction pattern of an X-ray or an electron beam is generated by reflection and interference by a crystal plane. Even in the diffraction pattern calculated by Fourier transform, a pattern equivalent to a diffraction pattern by a wave such as an X-ray or an electron beam is obtained, so that information on a crystal plane can be obtained from the position of the diffraction point.

The spacing between crystal planes is inversely proportional to the distance from the origin of the diffraction pattern to the diffraction point corresponding to the crystal plane. Therefore, by calculating the reciprocal of the distance from the origin of the diffraction pattern to the diffraction point corresponding to the crystal plane, it is possible to relatively examine the change in the crystal plane spacing in a plurality of regions.

On the other hand, with respect to the crystal plane, the direction from the origin of the diffraction pattern to the diffraction point corresponding to the crystal plane has a relationship corresponding to the normal to the crystal plane. Therefore, when the coordinates of the diffraction point are expressed as (k _x , k _y ), if k _x ≠ 0, the inverse tangent function tan (k _y / k _x ) ^-1 -90 corresponds to the crystal corresponding to the diffraction point. X of face
When k _x = 0, the crystal plane corresponding to the diffraction point is parallel to the y-axis.

The above calculations were performed on the scanning transmission electron microscope image shown in FIG. 2, and the results of mapping the plane spacing of the 111 crystal plane and the direction of that plane are shown in FIGS. 8 and 9, respectively.
Shown in 8 and 9, the Si substrate shown in FIG.
The surface spacing changes at the interface portion of e, and the direction of the surface is Ge
You can see how it is changing inside the island.

FIG. 22 is a diagram showing the configuration of an apparatus for performing the method according to the fourth embodiment of the present invention. Referring to FIG. 22, in addition to the configuration shown in FIG. 21, the image processing apparatus 20 determines, based on the diffraction spot position detected by the diffraction spot position detection unit 25, the plane spacing and / or the crystal plane corresponding to the diffraction spot. Or crystal plane information calculation unit 2 for determining the direction of the plane
8, and the distribution of the crystal plane spacing or plane direction is output from the mapping unit 27.

[Embodiment 5] Next, a fifth embodiment of the present invention will be described. When the displacement of the spot position in the diffraction pattern is expressed as a deformation matrix element of the crystal, the state of the distortion is easier to understand than usual. In a fifth embodiment of the present invention,
From the displacement of the diffraction spot obtained in the first embodiment, the deformation in the horizontal and vertical directions with respect to the sample substrate surface (FIG. 1)
0) as a matrix expression. The transformation matrix is obtained by the following operation.

First, the diffraction point positions (k
_1x , k _1y ) and (k _2x , k _2y ), the lattice vector (r _1x ,
r _1y ) and (r _2x , r _2y ) are obtained by the following equation (9).

[0079]

From this lattice vector and the lattice vectors (r ⁰ _1x , r ⁰ _1y ) and (r ⁰ _2x , r ⁰ _2y ) of the ideal crystal structure, a deformation matrix is obtained by the following equation (10).

[0081]

The obtained transformation matrix is given by the following equation (11).

[0083]

The unit vector x in the horizontal direction and the unit vector y in the vertical direction with respect to the sample substrate surface are x and y, respectively.
This is a matrix indicating that the shape has been deformed by ε _xx , ε _xy , ε _yx , ε _{yy in the} direction.

Further, it is possible to easily perform this operation on a plurality of areas and compare the differences in deformation.

FIG. 23 is a diagram showing the configuration of an apparatus for carrying out the method according to the fifth embodiment of the present invention. Referring to FIG. 23, the image processing apparatus 20 further includes a deformation matrix calculation unit 29 that calculates a deformation matrix in addition to the configuration illustrated in FIG.

[Embodiment 6] Next, a sixth embodiment of the present invention will be described. In the sixth embodiment of the present invention, the entire region of the electron micrograph is divided and each region is divided into the fifth region.
The operation of the embodiment is performed to map and image the state of the deformation of the crystal. Gives very useful information that is imaged.

FIGS. 11 to 14 show the results of mapping the scanning transmission electron microscope image shown in FIG.

[0089] While the island of Ge for the portion of the Si is spreading grating, looking at the result of mapping epsilon _xx component and epsilon _yy component, manner of change is different in the x and y directions, epsilon _xy and The fact that the mapping result of the ε _yx component changes between left and right inside the island indicates that the lattice is curved inside the island.

[Embodiment 7] Next, a seventh embodiment of the present invention will be described. If a unique point is found in the mapping of the diffraction spot position, crystal plane spacing, plane direction, or deformation matrix element of the crystal lattice, only that part is taken out from the scanning transmission electron micrograph and the lattice image is taken. Investigation is useful for examining the cause of distortion.

In the seventh embodiment of the present invention, the position designated on the display screen on which the position of the diffraction spot, the spacing between crystal planes, the direction of the plane, or the deformation matrix element of the crystal lattice is mapped, is scanned by a scanning transmission electron microscope. It is taken out from the picture and displayed. Such processing is performed by using a computer (the image processing apparatus 20 in FIG. 21) to extract a part of a scanning transmission electron microscope photograph corresponding to an arbitrary point on the mapping result image.

According to the method described in the third embodiment,
The position of the diffraction spot is calculated by a computer (diffraction spot position detecting means 24 in FIG. 21), and the calculation result is recorded as a file in the storage device 50 together with the coordinates of the area in the scanning transmission electron microscope image.

From the recorded file, the displacement of the position of the diffraction spot is mapped and imaged by the mapping means 26 and displayed on the display device 40.

When the observer designates a place on the display screen by using a pointing device such as a mouse as an input device 30 provided in the image processing device (computer) 20, the displacement of the designated diffraction spot position is changed. The coordinates of the region in the scanning electron microscope image corresponding to the mapping data are extracted, and from the coordinates, only the image of the corresponding region can be extracted from the original scanning transmission electron microscope image.

FIG. 15 in which the diffraction spot positions are mapped.
16 shows the Si substrate portion adjacent to the outside of the Ge island indicated by the arrow and taken out and enlarged. FIG.
This portion has an abnormal spot position when viewed from an image obtained by mapping the diffraction spot position, but an abnormal portion such as a defect cannot be confirmed as long as the lattice image of this portion is taken out and viewed.

[Eighth Embodiment] An eighth embodiment of the present invention will be described. In the eighth embodiment of the present invention, the same operation can be performed by mapping the plane spacing and the plane direction of the crystal plane by the mapping unit 27 (see FIG. 22).
According to the eighth embodiment of the present invention, according to the method of the fourth embodiment, the plane spacing and the direction of the crystal planes are calculated by the crystal plane information calculating means 27 in FIG. The information is recorded in a file of the storage device 50 together with the coordinates of the area in the electron microscope image.

From the recorded file, the plane spacing and plane direction of the crystal planes are mapped by the mapping means 26 to be imaged and displayed on the display device 40. An observer designates a location using a pointing device such as a mouse provided in the computer 20 from the two types of display screens, and corresponds to data obtained by mapping the plane spacing or plane direction of the specified crystal plane. The coordinates of the area in the scanning transmission electron microscope image are extracted, and based on the extracted coordinates,
Only the image of the corresponding region is extracted from the original scanning transmission electron microscope image.

FIG. 18 is an enlarged view of a corner portion of a Ge island indicated by an arrow in FIG. 17 in which the crystal plane spacing is mapped. This portion has a markedly reduced surface spacing when viewed from an image on which the surface spacing is mapped, but an abnormal portion such as a defect cannot be confirmed as long as the lattice image of this portion is taken out and viewed.

[Embodiment 9] A ninth embodiment of the present invention will be described. In the ninth embodiment of the present invention, the transformation matrix element of the crystal lattice is mapped to the mapping unit 27 (see FIG. 23).
And perform the same operation. In the ninth embodiment of the present invention, the deformation matrix element of the crystal lattice is calculated by the deformation matrix calculation unit 29 shown in FIG. 23 in the same manner as in the sixth embodiment, and the calculation result is calculated for the region in the scanning transmission electron microscope image. It is recorded in a file of the storage device 50 together with the coordinates.

From the recorded file, the deformation matrix element of the crystal lattice is mapped to the mapping means 26 to be imaged and displayed on the display device 40. In the display screen, the observer specifies a location using a pointing device such as a mouse provided in the computer 20, and the scanning transmission electron microscope corresponding to the mapping data of the specified deformation matrix element of the crystal lattice. The coordinates of the region in the image are extracted, and only the image of the corresponding region is extracted from the original scanning transmission electron microscope image based on the coordinates.

FIG. 20 is an enlarged view of the interface portion between the island and the substrate indicated by the arrow in FIG. 19 in which the deformation matrix element ε _yy of the crystal lattice is mapped. This part shows a steep change in the upper and lower parts when viewed in an image in which the deformation matrix element ε _yy of the crystal lattice is mapped. Although the brightness of the image changes, the lattice is continuously connected from the substrate to the island, and no abnormal portion such as a defect can be confirmed.

From the above examination, in this case, in the scanning electron microscope image shown in FIG. 2, near the interface between Si and Ge,
There are no dislocations or point defects, and it can be determined that the lattice is elastically distorted.

[0103]

As described above, according to the present invention,
This has the effect that lattice distortion and crystallinity of a minute region in the crystal can be examined.

The reason is that, in the present invention, a scanning transmission electron microscope image is digitized and taken into a computer, a two-dimensional Fourier transform is performed to form a diffraction pattern, and a diffraction spot position in the diffraction pattern is obtained. Compared to the diffraction point position for an ideal crystal structure,
This is because, in a plurality of regions, the distance between the crystal planes calculated from the spot positions and the spot positions, the direction of the planes, and the deformation matrix of the crystal lattice can be calculated and relatively compared.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a process according to a first embodiment of the present invention.

FIG. 2 is a diagram showing a scanning transmission electron micrograph (cross-sectional observation) of a sample in which Ge is epitaxially grown on a Si (100) surface.

FIG. 3 is a diagram showing a two-dimensional digital Fourier transform pattern of a partial region (near the lower center) of FIG. 2;

FIG. 4 shows a portion (about 10 nm of a Ge island) of the Si substrate portion of FIG. 2;
It is a figure which shows the two-dimensional digital Fourier-transformation pattern of the area | region of the bottom).

5 is a diagram showing a two-dimensional digital Fourier transform pattern of a partial region of the Ge island in FIG. 2;

FIG. 6 is a diagram showing a mapping result of a spot position kx in a two-dimensional digital Fourier transform pattern.

FIG. 7 is a diagram showing a mapping result of a spot position ky in a two-dimensional digital Fourier transform pattern.

FIG. 8 shows 11 out of 2D digital Fourier transform patterns
FIG. 11 is a diagram showing a result of calculating and mapping one surface interval.

FIG. 9: 11 out of 2D digital Fourier transform patterns
FIG. 9 is a diagram showing a result of calculating and mapping the direction of one surface.

FIG. 10 is a diagram showing a change in an x-axis and a y-axis vector due to deformation of a crystal lattice.

FIG. 11 is a diagram showing a result of calculating a deformation matrix element from a two-dimensional digital Fourier transform pattern and mapping its ε _xx component.

FIG. 12 is a diagram showing a result of calculating a deformation matrix element from a two-dimensional digital Fourier transform pattern and mapping its ε _xy component.

FIG. 13 is a diagram showing a result of calculating a deformation matrix element from a two-dimensional digital Fourier transform pattern and mapping its ε _yx component.

FIG. 14 is a diagram showing a result of calculating a deformation matrix element from a two-dimensional digital Fourier transform pattern and mapping its ε _yy component.

FIG. 15 is a diagram showing an abnormal portion on the surface of the Si substrate by an arrow in the result of FIG. 6;

16 is a diagram showing a lattice image photograph of the portion shown in FIG. 15 by a scanning transmission electron microscope.

FIG. 17 is a diagram showing an abnormal portion of a surface interval of Ge islands by an arrow in the result of FIG. 8;

18 is a view showing a lattice image photograph of the portion shown in FIG. 17 with a scanning transmission electron microscope.

FIG. 19 is a diagram showing a portion where the deformation matrix element ε _yy of the lattice changes sharply in the result of FIG. 14 with an arrow.

FIG. 20 is a view showing a lattice image photograph of the portion shown in FIG. 19 with a scanning transmission electron microscope.

FIG. 21 is a diagram showing an embodiment of the device configuration of the present invention.

FIG. 22 is a diagram showing another embodiment of the device configuration of the present invention.

FIG. 23 is a view showing still another embodiment of the device configuration of the present invention.

[Explanation of symbols]

 Reference Signs List 10 scanning electron microscope 20 image processing device (computer) 21 control unit 22 image input unit 23 two-dimensional Fourier transform unit 24 diffraction pattern acquisition unit 25 diffraction spot position detection unit 26 distortion detection unit 27 mapping unit 28 crystal plane information detection unit 29 Deformation matrix calculation unit 30 Input device 40 Display device 50 Storage device

Claims (16)

[Claims] A step of performing a two-dimensional Fourier transform on a partial area of a scanning transmission electron microscope image to determine a diffraction pattern of the area; determining a position of a diffraction spot in the diffraction pattern; Detecting a local lattice distortion from a difference between the position of the spot and the position of the diffraction point calculated from the ideal crystal structure. 2. A step of performing a two-dimensional Fourier transform on each of a plurality of regions of a scanning transmission electron microscope image to determine a diffraction pattern of the plurality of regions, determining a position of a diffraction spot in the diffraction pattern, The step of detecting local lattice distortion from the difference between the position of the diffraction spot and the position of the diffraction point calculated from the ideal crystal structure; A measurement method characterized by examining the difference between the two. 3. A step of performing a two-dimensional Fourier transform on each of a plurality of regions in the entire or partial region of the scanning transmission electron microscope image to obtain a diffraction pattern of the region; Obtaining a position of a diffraction spot in the diffraction pattern, and performing a measurement for detecting a local lattice distortion from a difference between the position of the diffraction spot and a position of a diffraction point calculated from an ideal crystal structure. And a step of mapping the obtained distribution of the distortion. 4. A step of performing a two-dimensional Fourier transform on each of a plurality of regions in the entire or partial region of the scanning transmission electron microscope image to obtain diffraction patterns of the plurality of regions. And determining the position of the diffraction spot in each of the regions, calculating the plane spacing and / or plane direction of the crystal planes, and mapping the plane spacing and / or plane direction distribution of the crystal planes. A measuring method characterized by the following. 5. A step of performing a two-dimensional Fourier transform on a partial area of a scanning transmission electron microscope image to determine a diffraction pattern of the area, determining a position of a diffraction spot in the diffraction pattern, Detecting local lattice distortion from the difference between the position of the diffraction spot and the position of the diffraction point calculated from the ideal crystal structure, in the same or opposite direction from the origin of the diffraction space. The method is performed for two diffraction spots that are not the same, and a deformation matrix is obtained from the positions of the two diffraction spots and the diffraction point positions in an ideal crystal structure. 6. A step of performing a two-dimensional Fourier transform on each of a plurality of regions of a scanning transmission electron microscope image to obtain diffraction patterns of the plurality of regions, and determining a position of a diffraction spot in the diffraction pattern. Determining the local lattice distortion from the difference between the position of the diffraction spot and the position of the diffraction point calculated from the ideal crystal structure. It is performed on two diffraction spots that are not in the same or opposite directions. A deformation matrix is obtained from the positions of the two diffraction spots and the diffraction point positions in the ideal crystal structure, and the difference in relative distortion depending on the location is examined. , A measuring method characterized in that: 7. A step of performing a two-dimensional Fourier transform on each of a plurality of regions in the entire or partial region of the scanning transmission electron microscope image to obtain a diffraction pattern of the plurality of regions. Determining the position of the diffraction spot in the diffraction pattern, detecting the local lattice distortion from the difference between the position of the diffraction spot and the position of the diffraction point calculated from the ideal crystal structure; Is performed for two diffraction spots that are not in the same or opposite directions from the origin of the diffraction space, and a deformation matrix is calculated from the positions of the two diffraction spots and the diffraction point positions in the ideal crystal structure. And measuring the strain distribution. 8. The method according to claim 3, wherein a part of a scanning transmission microscope image is extracted and displayed for a characteristic region of the mapped distribution. Measuring method. 9. A means for performing a two-dimensional Fourier transform on a partial region of an image obtained by a scanning transmission electron microscope, and acquiring a diffraction pattern of the region from the two-dimensional Fourier transform result; Means for determining the position of the diffraction spot in the diffraction pattern, comparing the position of the diffraction spot with the position of the diffraction point in an ideal crystal structure, and detecting local lattice distortion from the difference between the two. An image processing apparatus, comprising: 10. A means for performing a two-dimensional Fourier transform on each of a plurality of regions of an image obtained by a scanning transmission electron microscope, and obtaining diffraction patterns of the plurality of regions from the two-dimensional Fourier transform result. Finding the position of the diffraction spot in the diffraction pattern, comparing the position of the diffraction spot with the position of the diffraction point in an ideal crystal structure, and detecting local lattice distortion from the difference between the two. An image processing apparatus, comprising: detecting local lattice distortions in the plurality of regions and investigating a difference in relative distortion depending on locations. 11. A two-dimensional Fourier transform is performed on each of a plurality of regions in an entire region or a partial region of an image obtained by a scanning transmission electron microscope.
Means for acquiring a diffraction pattern of the plurality of regions from a result of the two-dimensional Fourier transform, and determining a position of a diffraction spot in the diffraction pattern, and determining a position of the diffraction spot and a position of a diffraction point in an ideal crystal structure. An image processing apparatus comprising: means for comparing and detecting local lattice distortion based on a difference between the two; and means for mapping a distribution of the detected distortion. 12. A two-dimensional Fourier transform is performed on a plurality of regions in an entire region or a partial region of an image obtained by a scanning transmission electron microscope.
Means for deriving the diffraction pattern of the region from the result of the two-dimensional Fourier transform; means for detecting the position of the diffraction spot in the diffraction pattern; and An image processing apparatus, comprising: means for calculating the following: and means for mapping the distribution of the crystal planes in the plane interval or plane direction. 13. A two-dimensional Fourier transform is performed on a partial area of an image obtained by a scanning transmission electron microscope,
Means for acquiring a diffraction pattern of the region from the result of the two-dimensional Fourier transform, and determining the position of a diffraction spot in the diffraction pattern, and comparing the position of the diffraction spot with the position of a diffraction point in an ideal crystal structure. A means for detecting local grating distortion, wherein the measurement using the means for acquiring the diffraction pattern and the means for detecting the distortion is performed in the same direction or in the opposite direction from the origin of the diffraction space. An image processing apparatus, comprising: a transformation matrix calculation unit that performs a transformation on a diffraction spot at a point, and obtains a transformation matrix from a position of the diffraction spot and a position of a diffraction point in an ideal crystal structure. 14. A two-dimensional Fourier transform is performed on a plurality of regions of an image obtained by a scanning transmission electron microscope,
From the two-dimensional Fourier transform result, means for obtaining a diffraction pattern of the plurality of regions, determine the position of the diffraction spot in the diffraction pattern, the position of the diffraction spot, the position of the diffraction point in the ideal crystal structure and Means for detecting local lattice distortion from the difference, measurement by the means for acquiring the diffraction pattern and means for detecting the distortion, the two diffraction spots not in the same direction or in opposite directions from the origin of the diffraction space. And a deformation matrix calculation means for obtaining a deformation matrix from the position of the diffraction spot and the position of the diffraction point in an ideal crystal structure. An image processing apparatus characterized by the above-mentioned. 15. A two-dimensional Fourier transform is performed on a plurality of regions in an entire region or a partial region of an image obtained by a scanning transmission electron microscope, and from the result of the two-dimensional Fourier transform, Means for acquiring the diffraction pattern of the plurality of regions, determine the position of the diffraction spot in the diffraction pattern, the position of the diffraction spot, local from the difference between the position of the diffraction point in the ideal crystal structure Means for detecting lattice distortion, measurement by the means for acquiring the diffraction pattern and means for detecting the distortion are performed on two diffraction spots that are not in the same direction or in opposite directions from the origin of the diffraction space, and And a deformation matrix calculating means for calculating a deformation matrix from the positions of the diffraction points in the ideal crystal structure, and means for mapping the distribution of strain. An image processing apparatus characterized in that: 16. The apparatus according to claim 1, further comprising means for extracting and displaying a part of an original scanning transmission microscope image for a selected area of the mapped distribution displayed on a display device. Item 16. The image processing apparatus according to any one of Items 11, 12, and 15.