JP3134853B2 - Crystal distortion measuring method, crystal distortion measuring device and recording medium - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a crystal evaluation technique, and more particularly, to a crystal for obtaining information such as crystal distortion, crystal plane spacing, and distribution thereof in a sample based on a transmission electron microscope image of the sample. The present invention relates to a strain measurement method and apparatus.

[0002]

2. Description of the Related Art As the degree of integration of semiconductor devices has increased, the size of semiconductor devices has become smaller. As the element size decreases, stress acting on a minute region in the semiconductor crystal and a crystal defect accompanying the stress become a problem.

As a conventional method for examining distortion in a sample crystal, an X-ray diffraction method has been established. Also, as a technique for examining the distortion of a minute portion of a crystal, a micro-Raman method is known.

[0004]

However, in recent years, semiconductor elements have been highly integrated, and the size of the integrated semiconductor has become much smaller, and the spatial resolution of a conventional method for examining crystal distortion such as a micro-Raman method has been reduced. It is as follows. As a result, it is impossible with the conventional method to directly measure the crystal strain inside the semiconductor crystal of the integrated semiconductor device.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a crystal distortion detecting method and apparatus capable of detecting a distortion, a defect, and a plane spacing in a minute region of a crystal, or examining a distribution thereof.

[0006]

SUMMARY OF THE INVENTION A crystal distortion measuring method according to the present invention is a crystal distortion measuring method for acquiring information on a crystal in a sample from a transmission electron microscope image of the sample. Converting the image into an image; and performing a two-dimensional Fourier transform on at least a part of the area of the digital image to calculate a diffraction pattern of the area.

A crystal distortion measuring apparatus according to the present invention is a crystal distortion measuring apparatus for acquiring information on a crystal in a sample from a transmission electron microscope image of the sample. Means, two-dimensional Fourier transform for at least a part of the area of the digital image to calculate a diffraction pattern of the area, and calculation means for performing a calculation process on the diffraction pattern. .

That is, in the present invention, a diffraction image is obtained by converting a transmission electron microscope image into a digital image, taking it into a computer or the like, and executing a digital two-dimensional Fourier transform. Once the diffraction pattern is determined, one or more diffraction spot positions in the diffraction pattern are determined, and the distortion of the crystal lattice can be detected by comparing with the diffraction point position in an ideal crystal structure. it can. This distortion can be mapped as a distribution of the distortion by measuring each region in the sample.

Further, according to the present invention, it is possible to obtain the plane spacing and plane direction of the crystal plane from the measurement result of the diffraction spot position. The plane spacing d of the crystal plane is represented by (k _x , k _y ) in digital pixel coordinates, the relative coordinates of the position of the diffraction spot corresponding to the crystal plane from the diffraction point position corresponding to zero wave number,
It can be calculated from the following equation.

[0010]

(Equation 1) Where a is the actual distance between each pixel (pixel) in the digitized TEM image, w _x and w
_y is the number of data in the x and y directions in the digital two-dimensional Fourier transform, respectively. The direction of the crystal plane is
If k _x ≠ 0, the angle from the x-axis is tan in 90 degree
^-1 (k _y / k _x ) −90 °, and k _x = 0
Then it is parallel to the y-axis.

Further, a deformation matrix due to distortion can be obtained from two different diffraction spot positions and an ideal crystal structure. This transformation matrix shows the relative coordinates from the diffraction point position corresponding to the wave number zero of the positions of the two diffraction spots in digital pixel coordinates (k _1x , k _1y ) and
and (k _2y, k _2y) and ideal diffraction point coordinates corresponding to these diffraction point when the crystal structure, respectively ^{_{(k o 1x, k o 1y}} )
And ^{_{(k o 2x, k o 2y}} ) and that,

[0012]

(Equation 2) Can be calculated by the following equation. Here, t on the left shoulder of the matrix means a transposed matrix, and -1 on the right shoulder means an inverse matrix.

The above-described analysis by the crystal strain measuring method of the present invention is generally performed by a computer that has captured a transmission electron microscope image as a digital image (typically, 8-bit (256 gradation) black and white image data). Will be
The accuracy of these analyzes greatly depends on the accuracy of the magnification of a transmission electron microscope image captured as digital image data. Therefore, it is conceivable to perform these analyzes on a plurality of regions in the same transmission electron microscope field of view and relatively compare the results. By adopting such a method, the accuracy of the electron microscope image is reduced. A minute distortion can be examined as a relative change depending on a place.

Further, by performing these operations in a plurality of areas and mapping the results, it is possible to image distortion. Also, the image information and the coordinates of those areas are recorded together, and a position to be examined is designated from the image, so that a part of the original electron microscope image corresponding to the area is extracted from the coordinate information of the area. , A grid image of that location can also be displayed. Further, by obtaining the intensity of the diffraction spot in a plurality of regions and mapping the result, it is possible to image crystal information represented by crystallinity.

In the present invention, using a transmission electron microscope image,
On the other hand, since the two-dimensional Fourier transform is performed, the spatial resolution of the measurement can be increased by narrowing the region to be subjected to one-time two-dimensional Fourier transform.

[0016]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, a preferred embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing a configuration of a crystal distortion measuring apparatus according to a preferred embodiment of the present invention. This crystal distortion measuring apparatus captures a transmission electron microscope image (electron micrograph) of a sample and outputs it as a digital image, and accumulates and calculates the digital image acquired by the image reading unit 11. A storage unit 12 for temporarily storing diffraction patterns and the like, and for storing data such as diffraction point positions in an ideal crystal structure, and a partial area (for example, 256 dots horizontally × 2 dots vertically) in a digital image.
A two-dimensional Fourier transform processing unit 13 that performs a two-dimensional Fourier transform on a 56-dot area) to obtain a diffraction pattern, and a calculation processing unit 14 that performs various calculation processes based on the calculated diffraction pattern And the calculation processing unit 14
And a display unit 15 for performing display based on the calculation result in. The image reading unit 11 corresponds to an image input unit, and is typically configured by an image scanner. The two-dimensional Fourier transform processing unit 13 corresponds to a Fourier transform unit.

The calculation processing section 14 corresponds to a calculation means. For example, (i) calculates the position of a diffraction spot in the obtained diffraction pattern, and calculates the position of the diffraction spot and the diffraction point in an ideal crystal structure. From the difference with the position, to detect local lattice distortion in the sample, (ii) calculate the diffraction spot position from the diffraction pattern in multiple regions in the electron microscope image,
Detect relative crystal distortion by location in the sample,
(iii) calculating the diffraction spot intensity from the diffraction pattern,
(iv) Find the crystal information of the sample from the diffraction spot intensities in a plurality of regions in the electron microscope image. (v) Find the diffraction point positions from the diffraction patterns in the plurality of regions in the electron microscope image. (Vi) For two diffraction spots not in the same direction or in the opposite directions from the origin of the diffraction space, ideally the positions of the two diffraction spots in the calculated diffraction pattern Calculating the deformation matrix from the diffraction point positions in the various crystal structures, (vii) detecting the relative crystal distortion due to the location in the sample from the deformation matrix in a plurality of regions in the electron microscope image, (viii The calculation processing such as mapping the result obtained by each calculation processing described above as a distribution is executed.

The display unit 15 corresponds to a display means, and is constituted by, for example, a CRT. Further, the display unit 15 extracts a part of the digital image of the transmission electron microscope image stored in the storage unit 12 by a display method such as a superimposed display, and calculates a result of the calculation by the calculation processing unit 14 (mapping). And a function of displaying the result in association with the result).

The crystal strain measuring apparatus according to this embodiment is generally configured as a computer system.

Next, an example of a crystal strain evaluation procedure using the crystal strain measurement apparatus will be described with reference to the flowchart of FIG.

Assuming that a transmission electron microscope photograph of the sample is given, the photograph is first taken into a computer constituting a crystal distortion measuring apparatus (step 51) and stored in the storage unit 12 as digital image data. The capture of a photograph is specifically performed by the image reading unit 11. Next, an area having a number of pixels suitable for Fourier transform, which is an area to be evaluated, is extracted from the digital image and treated as a two-dimensional array (step 52). And
A two-dimensional Fourier transform is performed on the two-dimensional array by the two-dimensional Fourier transform processing unit 13 (step 5).
3) Obtain a diffraction pattern. In the two-dimensional Fourier transform,
It is assumed that a window function such as a two-dimensional Gaussian distribution function (two-dimensional Gaussian distribution function) is used.

The processing after obtaining the diffraction pattern is various as shown in the embodiment described later. For example, a Fourier transform pattern, that is, a spot position in the diffraction pattern is detected (step 54), and an ideal crystal is obtained. The distortion of the crystal in the sample is detected by comparing with the diffraction point position of the structure (step 55). The diffraction point position of an ideal crystal structure may be obtained in advance by actual measurement or by calculation from crystallographic parameters.

Next, the present invention will be described in more detail by way of examples. In each of the following examples, a sample obtained by epitaxially growing Ge in an island shape on the surface of a Si (100) substrate was used. FIG. 3 is a transmission electron micrograph showing a cross section of the sample.

(Example 1) A cross-sectional observation photograph of a sample shown in FIG.
cm × height 14.5 cm) using an image scanner device at 200 dpi (2 inches per inch (= 25.4 mm)).
(Dots) with a precision of (00 dots) into the computer, and from the image, take out a square area of 256 (horizontal) × 256 (vertical) dots centering on the target portion, and set the brightness of each dot (pixel) as a value. A two-dimensional array a _ij (i and j are each an integer of 1 to 256) was configured.

In addition, an array b of a two-dimensional Gaussian distribution
_ij (i and j are integers of 1 to 256, respectively) are given by b _ij = exp ｛−0.0004 ((i-129) ² + (j
-129) ² )｝, and multiply this array with each element of the image array to obtain an array c _ij (i and j are integers of 1 to 256, respectively): c _ij = a _ij × b _ij Calculated. This array c _ij was subjected to Fourier transform using a two-dimensional complex fast Fourier transform method, and the Fourier-transformed complex number array d _ij was calculated.

At the time of Fourier transform, (i, j) = (1, 1,
The arrangement d _ij was determined so that 1) was a Fourier component with zero wave number. After that, the absolute value of each element of the array d _ij was calculated, and all the elements were rearranged such that the element corresponding to the Fourier component with zero wave number was located at the center position of the array, thereby obtaining a diffraction pattern array e _ij . That is, for elements in which _i is in the range from 1 to 128 and j is in the range from 1 to 128, e _ij = | d _{(i + 128) (j + 128)} | Up to 128 and j is 129
For elements in the range from to 256, e _ij = | d _{(i + 128) (j-128)} | where i is in the range from 129 to 256 and j is 1
For elements in the range from to 128, e _ij = | d _{(i-128) (j + 128)} | where i is in the range from 129 to 256 and j is 1
For elements in the range from 29 to 256, e _ij = | d _{(i-128) (j-128)} | was calculated, and all elements of the array e _ij were obtained. FIG. 4 shows the diffraction pattern thus obtained.

The coordinates of the diffraction point were obtained by searching for the coordinates of the maximum value of the diffraction pattern array. The difference between the coordinates of the diffraction point and the position calculated from the ideal lattice constant of the crystal was examined for the lattice distortion at the target position. Here, if the distance from the obtained coordinates of the maximum value to the center coordinates (i, j) = (129,129) is larger than the value obtained from the lattice constant of the ideal crystal, the lattice is in the ideal crystal state. A smaller shrinkage, and conversely, a smaller size, indicates that the lattice is more elongated than the ideal crystalline state. As a result of this analysis, in the portion where Ge was epitaxially grown, the diffraction point moved inward by about 4% from the position expected in the silicon crystal. From this, it was found that the lattice of Ge was closer to the original Ge lattice.

(Embodiment 2) In order to perform the analysis as in Embodiment 1, it is necessary that the magnification of the electron microscope be accurately calibrated. However, there is a limit to this calibration accuracy. With respect to finer distortion, relative measurement can be performed by examining relative distortion by comparison with a reference position in the same electron micrograph.

FIG. 3 shows a cross-sectional observation photograph of a sample (transmission width 20.5 cm × height 1) at a magnification of 2.5 million times as shown in FIG.
4.5 cm) using an image scanner device for 200 d
The image is captured by a computer with the accuracy of pi, and the horizontal 2
Take out a square area of 56 dots × 256 dots vertically,
A two-dimensional array a _ij (i and j are integers of 1 to 256, respectively) having the brightness of each dot as a value was formed.

Using the same two-dimensional Gaussian distribution array b _ij as in the first embodiment, an array c _ij is calculated for each region array according to c _ij = a _ij × b _{ij in the same} manner as in the first embodiment. The array c _ij is Fourier-transformed for each region using a two-dimensional complex fast Fourier transform method, and a complex array d _ij
Was calculated. In the Fourier transform, (i, j) = (1,1,
The arrangement d _ij was determined so that 1) was a Fourier component with zero wave number. Thereafter, as in the first embodiment, the array d _ij
Were calculated, and all the elements were rearranged so that the element corresponding to the Fourier component with zero wave number was located at the center position of the array, thereby obtaining a diffraction pattern array e _ij .

FIGS. 5 and 6 show the diffraction patterns thus obtained. FIG. 5 is a diffraction pattern (two-dimensional digital Fourier transform pattern) obtained from a region about 10 nm below the island-like Ge in the Si substrate portion of the sample, and FIG. 6 is a graph showing the diffraction pattern of the island-like Ge of the sample. 3 is a diffraction pattern (two-dimensional digital Fourier transform pattern) obtained from a partial region of.

The coordinates of the diffraction point were obtained by searching for the coordinates of the local maximum value of the diffraction pattern array for each region.
From the difference in the coordinates of the diffraction points obtained for each region, the relative lattice distortion at each location was examined. Here, center coordinates (i, j) = (12
When the distance to (9,129) is large, it indicates that one region has a smaller lattice than the other region. Ge
When the portion was examined and compared in a plurality of regions, it was found that the spot position changed depending on the location. The result is
This means that there is a small local distortion in the Ge film.

(Embodiment 3) When comparing distortions in a plurality of regions as in the second embodiment, a plurality of regions are selected at equal intervals in the entire region of the electron micrograph or in the target region, and the distortion is selected in each region. Is obtained, and the result is imaged and visualized.
A better understanding of distortion.

FIG. 3 shows a cross-sectional observation photograph of a sample at a magnification of 2.5 million times with a transmission electron microscope (width 20.5 cm × height 1).
4.5 cm) using an image scanner device for 200 d
The image is taken into the computer with the accuracy of pi,
It is divided into a square area of 56 dots × 256 dots vertically, and in each area, the brightness of each dot in the area is set as a value.
A dimensional array a _ij (i and j are each an integer of 1 to 256) was formed.

Using the same two-dimensional Gaussian distribution array b _ij as in the first embodiment, an array c _ij is calculated for each array according to c _ij = a _ij × b _{ij in the same} manner as in the first embodiment. The array c _ij is Fourier-transformed for each region using a two-dimensional complex fast Fourier transform method, and a complex array d _ij
Was calculated. In the Fourier transform, (i, j) = (1,1,
The arrangement d _ij was determined so that 1) was a Fourier component with zero wave number. Thereafter, as in the first embodiment, the array d _ij
Were calculated, and all the elements were rearranged so that the element corresponding to the Fourier component with zero wave number was located at the center position of the array, thereby obtaining a diffraction pattern array e _ij .

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.
FIGS. 7 and 8 show the results of mapping and mapping the x- and y-coordinates of the (111) diffraction point obtained for each region. In this mapping, the bright part is farther from the center of the diffraction point, while the dark part indicates that the diffraction point is closer to the center. From this result, Ge
The strain distribution in the film was found.

(Example 4) Defects are often introduced in places where crystals are extremely distorted, and the crystallinity deteriorates only in those parts. When examining such crystallinity, it is sometimes easier to understand that the intensity is mapped than the spot position of the diffraction point.

FIG. 2 shows a photograph of a cross-sectional observation of a sample at a magnification of 2.5 million times with a transmission electron microscope (width 20.5 cm × height 1).
4.5 cm) using an image scanner device for 200 d
The image is taken into the computer with the accuracy of pi,
It is divided into a square area of 56 dots × 256 dots vertically, and in each area, the brightness of each dot in the area is set as a value.
A dimensional array a _ij was determined.

Using the same two-dimensional Gaussian distribution array b _ij as in the first embodiment, an array c _ij is calculated for each array according to c _ij = a _ij × b _{ij in the same} manner as in the first embodiment. The array c _ij is Fourier-transformed for each region using a two-dimensional complex fast Fourier transform method, and a complex array d _ij
Was calculated. In the Fourier transform, (i, j) = (1,1,
The arrangement d _ij was determined so that 1) was a Fourier component with zero wave number. Thereafter, as in the first embodiment, the array d _ij
Were calculated, and all the elements were rearranged so that the element corresponding to the Fourier component with zero wave number was located at the center position of the array, thereby obtaining a diffraction pattern array e _ij .

The coordinates of the diffraction point were determined by searching for the coordinates of the local maximum value of the diffraction pattern array for each region.
FIG. 9 shows the result of mapping and intensifying the intensity of the (111) diffraction point obtained for each region. In this mapping, a bright portion has a large diffraction point intensity, and a dark portion has a small diffraction point intensity.
From this result, the interface between the Si substrate and Ge in the sample is:
It is considered that defects such as dislocations and point defects have not been introduced.

(Embodiment 5) It is preferable to obtain the plane spacing and the plane orientation of the crystal plane from the displacement of the spot position in the diffraction pattern.
It is easier to understand the distortion. Here, from the diffraction spot positions of a plurality of regions obtained in Example 3, the plane spacing and the plane direction of the crystal plane corresponding to the diffraction spot are obtained,
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 the Fourier transform, a pattern equivalent to a diffraction pattern by a wave such as an X-ray or an electron beam can be obtained. Therefore, 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. For this reason, 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 spacing between the plurality of regions. On the other hand, with respect to the crystal plane, there is a relationship that the direction from the origin of the diffraction pattern to the diffraction point corresponding to the crystal plane corresponds 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, tan ⁻¹ (k _y / k _x ) −90 ° becomes x of the crystal plane corresponding to the diffraction point. If k _x = 0, the crystal plane corresponding to the diffraction point is parallel to the y-axis.

FIG. 10 and FIG. 11 show the results obtained by performing this calculation using the electron micrograph shown in FIG. 3 and mapping the plane spacing of the (111) crystal plane and the direction of the plane. S
The surface spacing changes at the portion of i and Ge, and the direction of the surface is
It can be seen that it is changing inside the Ge island.

(Embodiment 6) When the displacement of the spot position in the diffraction pattern is represented as a deformation matrix element of the crystal, the state of the distortion can be understood more easily than usual. Here, Example 1
The horizontal and vertical deformations on the surface of the sample substrate were obtained as a matrix expression from the diffraction spot displacement obtained in the above. FIG. 12 is a diagram illustrating changes in the x-axis direction vector and the y-axis direction vector due to the deformation of the crystal lattice.

The transformation matrix can be obtained by the following operation. First, the diffraction point positions of the two (111) spots
From (k _1x , k _1y ) and (k _2x , k _2y ), a lattice vector in the real space
(r _1x , r _1y ) and (r _2x , r _2y ) are obtained by the following equations.

[0047]

(Equation 3) This lattice vector and the lattice vector of the ideal crystal structure
Because ^{_{(r o 1x, r o 1y}} ) and ^{_{(r o 2x, r o 2y}} ) and deformation matrix is obtained by the following equation.

[0048]

(Equation 4) The transformation matrix found here is

[0049]

(Equation 5) And a unit vector in the horizontal direction with respect to the sample substrate surface.

[0050]

[Outside 1] And the vertical unit vector

[0051]

[Outside 2] Is each

[0052]

[Outside 3] It is a matrix representing 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.

(Embodiment 7) It is also possible to divide the entire region of an electron micrograph and perform the operation of Embodiment 6 in each region to map the state of the deformation of the crystal. Information.

FIGS. 13 to 16 show the results of mapping the electron micrograph shown in FIG. The lattice is wider on the Ge island than on the Si part, but the ε _xx component and ε
Looking at the mapping result of the _yy component, the way of change is x
The direction differs from the y direction. Further, the fact that the mapping result of the ε _xy and ε _yx components changes between left and right inside the island indicates that the lattice is curved inside the island.

(Embodiment 8) When a unique point is found in the mapping of the position of the diffraction spot, the spot intensity, the spacing between crystal planes, the direction of the plane, or the deformation matrix element of the crystal lattice, only that part is identified by an electron microscope. It is useful to take out of the photograph and examine the lattice image to examine the cause of the occurrence of distortion. Such processing can be performed by extracting a part of an electron micrograph corresponding to an arbitrary point on the image showing the mapping result.

The position of the diffraction spot was calculated by a computer in the same manner as in Example 3, and the calculation result was recorded in a file together with the coordinates of the area in the electron microscope image. From the file recorded in this way, the displacement of the position of the diffraction spot is mapped and imaged and displayed. When the observer specifies a location on the display screen using a pointing device such as a mouse provided in a computer, the area in the electron microscope image corresponding to the mapping data of the specified diffraction spot position From the original electron microscope image, and it is possible to extract only the image of the corresponding region from the original electron microscope image.

FIG. 17 shows abnormal portions in the mapping result of the diffraction spot positions shown in FIG. 7 by arrows. FIG. 18 shows a region obtained by extracting a region corresponding to the substrate portion adjacent to the outside of the island indicated by the arrow from the transmission electron microscope image and enlarging the extracted portion. 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.

(Embodiment 9) The same processing as in Embodiment 8 can be performed not only for the position of the diffraction spot but also for the intensity of the spot.

In the same manner as in Example 4, the intensity of the diffraction spot was calculated, and the calculation result was recorded in a file together with the coordinates of the area in the electron microscope image. From the file recorded in this way, the displacement of the intensity of the diffraction spot is mapped and imaged and displayed. When the observer specifies a location in the display image using a pointing device, the coordinates of the region in the electron microscope image corresponding to the mapping data of the specified diffraction spot intensity are extracted, and from the coordinates, Only the image of the corresponding region was extracted from the original electron microscope image.

FIG. 19 shows an abnormal portion by an arrow in the mapping result of the diffraction spot intensity shown in FIG. FIG. 20 is an enlarged view of a region corresponding to the substrate portion indicated by the arrow extracted from the transmission electron microscope image and the extracted portion enlarged. In this part, the difference in contrast between the upper part and the lower part is remarkable when viewed in the image in which the diffraction spot intensity is mapped, but as a result of taking out the lattice image of this part and observing it, this difference in contrast is It can be seen that the reason is that the appearance changed greatly in this part. This is probably because the sample thickness of the sliced electron microscope sample changed, and the appearance of the lattice image changed in this portion.

(Embodiment 10) It is possible to map the plane spacing and plane direction of crystal planes and display them in association with an electron microscope image as in Embodiments 8 and 9.

In the same manner as in Example 4, the plane spacing and plane direction of the crystal planes were calculated by a computer, and the calculation results were recorded in a file together with the coordinates of the area in the electron microscope image. From the file recorded in this manner, the plane spacing and plane direction of the crystal planes are mapped and imaged and displayed. When the observer specifies a location from these two types of display screens using the pointing device, the electron microscope image corresponding to the data mapping the plane spacing or plane direction of the specified crystal planes , The coordinates of the corresponding region were extracted, and from the coordinates, only the image of the corresponding region was extracted from the original electron microscope image.

FIG. 21 shows an abnormal portion of the interplanar spacing at the Ge portion by an arrow in the mapping result of the interplanar spacing of the crystal shown in FIG. A region corresponding to the corner portion of the island indicated by the arrow is extracted from the transmission electron microscope image, and FIG. 22 is an enlarged view of the extracted portion. In this part, it can be seen from the image mapped with the surface spacing that the surface spacing is significantly shorter, but as long as the lattice image of this portion is taken out and viewed, an abnormal portion such as a defect cannot be confirmed.

(Embodiment 11) The same processing as in Embodiments 8 to 10 can be performed on the deformation matrix element of the crystal lattice.

In the same manner as in Example 7, the deformation matrix element of the crystal lattice was calculated, and the calculation result was recorded in a file together with the coordinates of the area in the electron microscope image. From the file recorded in this way, the deformation matrix elements of the crystal lattice are mapped and imaged and displayed. When the observer specifies a location in the display image using a pointing device, the coordinates of the region in the electron microscope image corresponding to the mapping data of the deformation matrix element of the specified crystal lattice are extracted, and from the coordinates. Only the image of the corresponding region was extracted from the original electron microscope image.

FIG. 23 is a diagram in which, as a result of mapping the deformation matrix element ε _yy component of the crystal lattice shown in FIG. 16, a portion where the deformation matrix element ε _yy changes sharply is indicated by an arrow. FIG. 24 is an enlarged view of a region corresponding to the interface between the island and the substrate indicated by the arrow, taken from the transmission electron microscope image. In this part, a steep change in the vertical direction can be seen in the image mapping the transformation matrix element ε _yy of the crystal lattice,
As far as the lattice image of this part is taken out and seen, a change in the brightness of the image due to the difference between the elements of Si and Ge can be seen, but the lattice is continuously connected from the Si substrate part to the Ge island part. Abnormal parts such as defects and defects cannot be confirmed.

Examination of the results described in each of the above examples shows that the sample shown in the electron micrograph in FIG.
No dislocations or point defects exist near the interface with, and it can be determined that the lattice is elastically distorted.

The crystal strain measuring apparatus described above reads a computer program for realizing the same into a computer such as a super computer, a workstation (WS), or a personal computer (PC), and executes the program. Can also be realized. The program for performing crystal distortion measurement is magnetic tape or CD-R.
The data is read into a computer by a recording medium such as an OM.
FIG. 25 is a block diagram illustrating a configuration of a computer that performs the above-described crystal strain measurement.

This computer has a central processing unit (CPU) 2
1, a hard disk device 22 for storing programs and data, a main memory 23, an input device 24 such as a keyboard and a mouse, and a display device 25 such as a CRT.
A reading device 26 that reads a recording medium 27 such as a magnetic tape or a CD-ROM; and an image scanner 28 that reads a transmission electron micrograph and converts it into digital image data
And, it consists of. The hard disk device 22, main memory 23, input device 24, display device 25, reading device 26, and image scanner 28 are all connected to the central processing unit 21. In this computer, a recording medium 27 storing a program for performing crystal distortion measurement is mounted on a reading device 26, the program is read from the recording medium 27 and stored in the hard disk drive 22, and the program stored in the hard disk drive 22 is read. The central processing unit 21 executes the crystal distortion measurement.

In particular, since the calculation processing after obtaining the diffraction pattern is various as shown in the above-described first to eleventh embodiments, the program may be executed in accordance with a command input by a user to a computer. A process of calculating a diffraction spot from a diffraction pattern and detecting relative crystal distortion due to a location in the sample, (ii) calculating the intensity of the diffraction spot from the diffraction pattern, and calculating the intensity of the sample based on the calculation result of the intensity. A process of mapping crystal information as a distribution, (iii) obtaining a diffraction point position from a diffraction pattern, calculating a crystal plane spacing from the position of the diffraction point in each region, and mapping the distribution of the crystal plane spacing, and (iv) Deformation matrix is calculated based on the diffraction pattern of two diffraction spots that are not in the same or opposite directions from the origin of the diffraction space, and the relative crystal distortion depending on the location in the sample It is preferable to selectively execute a process such as a process of detecting the

[0072]

As described above, according to the present invention, a transmission electron microscope image is converted into a digital image, taken into a computer, subjected to a two-dimensional Fourier transform to form a diffraction pattern, and a diffraction spot position in the diffraction pattern. And the spot intensity, compare with the diffraction point position in the case of an ideal crystal structure, and calculate the crystal plane spacing, plane direction, and crystal lattice calculated from the spot position and intensity or the spot position in multiple areas. By calculating the deformation matrix and comparing relatively, it is possible to investigate the lattice distortion and crystallinity of a small region in the crystal, which could not be observed due to insufficient spatial resolution with the conventional method. effective.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a crystal distortion measuring device according to a preferred embodiment of the present invention.

FIG. 2 is a flowchart illustrating an example of a processing procedure according to a preferred embodiment of the present invention.

FIG. 3 is a transmission electron micrograph instead of a drawing, showing a cross section of a sample in which Ge is epitaxially grown on a Si (100) surface.

4 is a diagram showing a two-dimensional digital Fourier transform pattern obtained from a region near the lower center in FIG. 3;

5 is a diagram showing a two-dimensional digital Fourier transform pattern obtained from a region of about 10 nm below the island-like Ge in the Si substrate portion in FIG. 3;

FIG. 6 is a diagram illustrating a two-dimensional digital Fourier transform pattern obtained from a partial region of the island-shaped Ge in FIG. 3;

7 is a diagram showing a result of mapping the two-dimensional spot position k _x of the digital Fourier transform pattern.

8 is a diagram illustrating a mapping result of the spot position k _y of two-dimensional digital Fourier transform pattern.

FIG. 9 is a diagram showing a mapping result of a spot intensity in a two-dimensional digital Fourier transform pattern.

FIG. 10 is a diagram showing a result of calculating and mapping a (111) plane interval from a two-dimensional digital Fourier transform pattern.

FIG. 11 is a diagram illustrating a result of calculating and mapping the direction of the (111) plane from the two-dimensional digital Fourier transform pattern.

FIG. 12 is a diagram illustrating a change in a vector on an x-axis and a vector on a y-axis due to deformation of a crystal lattice.

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 _xx 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 _xy component.

FIG. 15 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. 16 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.

17 is a diagram in which an abnormal portion on the surface of the Si substrate is indicated by an arrow in the mapping result shown in FIG. 7;

FIG. 18 is a lattice image photograph of a portion indicated by an arrow in FIG. 17 as a substitute for a drawing, taken by a transmission electron microscope.

FIG. 19 is a diagram showing an abnormal portion of the Si substrate portion with an arrow in the mapping result shown in FIG. 9;

20 is a lattice image photograph of a portion indicated by an arrow in FIG. 19 as a substitute for a drawing, taken by a transmission electron microscope.

21 is a diagram in which an abnormal portion of a surface interval in an island-shaped Ge portion is indicated by an arrow in the mapping result shown in FIG. 10;

FIG. 22 is a lattice image photograph as a substitute for a drawing of a portion indicated by an arrow in FIG. 21 by a transmission electron microscope.

FIG. 23 is a diagram in which, in the mapping result shown in FIG. 16, a portion where the deformation matrix element ε _yy of the lattice changes sharply is indicated by an arrow.

24 is a lattice image photograph of a portion indicated by an arrow in FIG. 22 as a substitute for a drawing, taken by a transmission electron microscope.

FIG. 25 is a block diagram showing a configuration of a computer system used for carrying out the crystal distortion measuring method of the present invention.

[Explanation of symbols]

 Reference Signs List 11 image reading unit 12 storage unit 13 two-dimensional Fourier transform processing unit 14 calculation processing unit 15 display unit 21 central processing unit (CPU) 22 hard disk device 23 main memory 24 input device 25 display device 26 reading device 27 recording medium 28 image scanner 51 ~ 55 steps

Continuation of the front page (58) Fields investigated (Int. Cl. ⁷ , DB name) G01N 23/00-23/227 G06T 1/00 H01L 21/66 JICST file (JOIS)

Claims (21)

(57) [Claims] 1. A crystal distortion measuring method for acquiring information on a crystal in a sample from a transmission electron microscope image of a sample, the method comprising: converting the transmission electron microscope image into a digital image; Performing a two-dimensional Fourier transform on at least a part of the region to calculate a diffraction pattern of the region. 2. The method according to claim 1, further comprising a step of detecting a local lattice distortion in the sample from a difference between the calculated position of the diffraction spot in the diffraction pattern and a position of a diffraction point in an ideal crystal structure. The method for measuring crystal distortion according to claim 1. 3. The diffraction pattern is calculated for each of a plurality of regions in the transmission electron microscope image, a diffraction spot is calculated from the diffraction pattern, and a relative crystal distortion depending on a position in the sample is detected. The method for measuring crystal distortion according to claim 1, wherein 4. The diffraction pattern is calculated for each of a plurality of regions in the transmission electron microscope image, and the intensity of the diffraction spot is calculated from the diffraction pattern. The crystal distortion measurement method according to claim 1, wherein is mapped as a distribution. 5. The diffraction pattern position is calculated by calculating the diffraction pattern for each of a plurality of regions in the transmission electron microscope image, and the crystal plane spacing is calculated from the positions of the diffraction points in each region. 2. Map the distribution of
3. The method for measuring crystal distortion according to item 1. 6. A step of calculating the diffraction pattern for two diffraction spots that are not in the same direction or in the opposite directions from the origin of the diffraction space, and the positions of the two diffraction spots in the diffraction pattern correspond to the ideal positions of the diffraction spots. The crystal distortion measuring method according to claim 1, wherein a deformation matrix is calculated from a diffraction point position in a typical crystal structure. 7. The method according to claim 6, wherein the transformation matrix is calculated for each of a plurality of regions in the transmission electron microscope image, and a relative crystal distortion depending on a position in the sample is detected.
3. The method for measuring crystal distortion according to item 1. 8. The crystal distortion measuring method according to claim 3, wherein mapping of the distribution of the detected relative crystal strain is performed. 9. The crystal distortion according to claim 4, wherein a part of the transmission electron microscope image is extracted and displayed in association with a characteristic region in the mapped distribution. Measuring method. 10. A crystal distortion measuring apparatus for acquiring information on a crystal in a sample from a transmission electron microscope image of the sample, wherein: an image input unit for capturing the transmission electron microscope image as a digital image; A crystal distortion measuring apparatus, comprising: a Fourier transform unit that performs a two-dimensional Fourier transform on at least a part of the region to calculate a diffraction pattern of the region; and a calculation unit that performs a calculation process on the diffraction pattern. . 11. The calculation means calculates a position of a diffraction spot in the diffraction pattern, and calculates a local lattice position in the sample from a difference between the position and a diffraction point position in an ideal crystal structure. The crystal distortion measuring apparatus according to claim 10, wherein the apparatus detects a distortion. 12. The Fourier transform unit calculates the diffraction pattern for each of a plurality of regions in the transmission electron microscope image, and the calculation unit calculates a diffraction spot position in each of the diffraction patterns. Detecting relative crystal distortion by location in the sample.
0. The crystal strain measuring apparatus according to 0. 13. The Fourier transform unit calculates the diffraction pattern for each of a plurality of regions in the transmission electron microscope image, and the calculation unit calculates the intensity of a diffraction spot in each of the diffraction patterns. , Claim 10
3. The method for measuring crystal distortion according to item 1. 14. The Fourier transform unit calculates the diffraction pattern for each of a plurality of regions in the transmission electron microscope image, and the calculation unit obtains a diffraction point position from each of the diffraction patterns. The crystal distortion measuring apparatus according to claim 10, wherein a crystal plane interval is calculated from a position of a diffraction point in the region. 15. The Fourier transform means calculates the diffraction pattern for two diffraction spots that are not in the same direction or in the opposite directions from the origin of the diffraction space, and the calculation means calculates the two points in the diffraction pattern. The crystal distortion measurement apparatus according to claim 10, wherein a deformation matrix is calculated from a position of the diffraction spot and a position of a diffraction point in an ideal crystal structure. 16. A display unit for displaying a distribution obtained as a result of calculation by the calculation unit.
16. The crystal distortion measuring device according to any one of 1 to 15. 17. The crystal distortion measuring apparatus according to claim 16, wherein the display unit extracts and displays a part of the transmission electron microscope image in association with a characteristic region in the distribution. 18. A recording medium storing a program used by a computer for inputting a transmission electron microscope image of a sample as a digital image, wherein a two-dimensional Fourier transform is performed on at least a part of the area of the digital image. A computer-readable recording medium storing a program for causing the computer to execute the step of calculating the diffraction pattern of the region by performing the calculation. 19. A step of detecting local lattice distortion in the sample from a difference between a calculated position of a diffraction spot in the diffraction pattern and a position of a diffraction point in an ideal crystal structure. Is further executed by the computer.
The recording medium according to claim 18. 20. A recording medium storing a program used by a computer for inputting a transmission electron microscope image of a sample as a digital image, wherein a two-dimensional Fourier transform is performed on at least a part of the area of the digital image. Calculating a diffraction pattern for two diffraction spots that are not in the same direction or diametrically opposite directions from the origin of the diffraction space; and determining the positions of the two diffraction spots and the ideal crystal structure in the diffraction pattern. Calculating a deformation matrix from the diffraction point positions in step (a), and a computer-readable recording medium storing a program for causing the computer to execute the steps. 21. A recording medium storing a program used by a computer for inputting a transmission electron microscope image of a sample as a digital image, wherein a two-dimensional Fourier transform is performed on at least a part of the area of the digital image. By applying, while causing the computer to perform the step of calculating the diffraction pattern in each of a plurality of regions in the transmission electron microscope image, (i) calculate a diffraction spot from the diffraction pattern, in the sample Detecting relative crystal strain by location in the, (ii) calculating the intensity of the diffraction spot from the diffraction pattern, mapping the crystal information of the sample as a distribution based on the calculation result of the intensity, (iii) calculating a diffraction point position from the diffraction pattern, calculating a crystal plane interval from the position of the diffraction point in each region, Mapping a cloth; and A computer-readable recording medium storing a program for causing the computer to execute at least one of the steps of detecting a crystal distortion.