JP3226314B2 - Scanning probe microscope data processor - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data processing apparatus for a scanning probe microscope such as a scanning tunnel microscope, and more particularly to an improvement in analysis accuracy.

[0002]

2. Description of the Related Art In recent years, a scanning tunneling microscope (STM) has been developed.
Is increasingly used as a microscope with atomic scale resolution. In addition, an atomic force microscope (AFM) is a similar kind of microscope having a resolution similar to or close to that of STM.
And a magnetic force microscope (MFM) are known. These microscopes are collectively referred to as a scanning probe microscope (SXM)
It is being put to practical use in various fields.

In the above STM, the distance between the conductive sample and the probe is brought close to 1 nm or less, a voltage is applied between the two, and a change in distance due to unevenness of the sample surface is detected by a tunnel current.
While the feedback control is performed so that the distance is constant by the actuator in the direction, the probe is raster-scanned in the x, y direction over a range of several nm to several tens μm by the actuator that drives the metal probe in the x, y, z directions. Drive
This feedback signal is synchronized with x, y scanning to achieve three-dimensional imaging of the sample surface.

In the above AFM and MFM, the local relationship between the probe and the sample is elastically displaced to a cantilever or the like by a force depending on the distance between the probe and the sample, and this displacement is detected. Similarly, a three-dimensional image of the surface characteristics of the sample is formed in the same manner as in the above-described STM by using the feedback control signal.

As described above, the scanning probe microscope (SX)
By using M), the atomic arrangement, charge density distribution, magnetization distribution, and the like on the sample surface can be observed in real space. In a scanning tunneling microscope (STM) and an atomic force microscope (AFM), an array of superconducting vortices, including a 7 × 7 silicon surface, a surface atomic array such as graphite,
The structure of a charge density wave observed in a low-dimensional electric conductor, the state of molecular arrangement of an organic substance such as a liquid crystal or an LB film, and the structure of DNA have been observed. Magnetic force microscope (MFM)
In this study, the surface distribution of magnetic material, the state of magnetic domains and domain walls, or the recording state of a magnetic recording medium are observed.

[0006] By the way, as a method of analyzing the atomic size such as the crystal structure and the charge density distribution of the sample surface, conventionally,
High-resolution electron microscopes and diffraction methods (electron diffraction, x-ray diffraction) are known and widely used for structural analysis and the like. However, in order to use these techniques, the experimental environment must be set to a high vacuum, which makes preparation for the experiment difficult, and the obtained result is an inverse aerial image, which makes analysis difficult.

[0007] When examining the vortex of a superconductor or the magnetization distribution of a magnetic material, a bitter method in which a fine powder is spread on a sample surface and directly observed with an optical microscope is used. And information other than a microscope image cannot be obtained.

[0008] Compared to the above method, the scanning probe microscope (SXM) can be measured even in the atmosphere, and the obtained image is a real space image, so that the interpretation is easy. further,
The image includes various surface physical information as well as the surface structure.

[0009]

As described above, observing the structure and state of the sample surface, such as the arrangement of atoms and the distribution of charge density, using a scanning probe microscope (SXM) is a structural analysis method for other atomic sizes. (Differential methods such as a high-resolution electron microscope and electron beam diffraction and x-ray diffraction) are experimentally easier and more direct. In addition, compared with other direct structure observation means, there is a feature that the resolution is higher and information other than the structure can be observed.

However, to perform a quantitative analysis,
It is often insufficient to use the obtained image as it is. For example, assume that the atomic arrangement on the graphite surface is observed using STM or AFM. In these scanning probe microscopes, since the structure in the real space can be directly observed, an image as shown in FIG. 2A is obtained. In FIG. 2A, the atoms are arranged in a honeycomb pattern to form a hexagonal lattice as shown in FIG. 3B, and the state of the six-fold symmetric atomic arrangement can be clearly understood. By the way, in FIG.
When trying to determine the spacing between atoms (lattices), FIG.
As shown in the figure, the peak position of each lattice must be determined with a mushroom, and the distance between the positions must be determined.
This method cannot improve quantitative accuracy.
For example, comparing the intervals l and m shown in FIG. 2A, it can be seen that a large difference is included.

The present invention has been made in view of the above points, and provides a scanning probe microscope data processing apparatus capable of quantitatively and accurately obtaining the periodic interval and direction of a periodic structure, the symmetry of the structure, and the like. The purpose is to provide.

[0012]

To achieve the above object, a scanning probe microscope data processing apparatus of the present invention comprises:
A scanning unit that relatively scans a probe and a sample to accumulate sample data obtained from the sample as array-like digital data; and performs two-dimensional Fourier transform on the array-like digital data accumulated by the accumulation unit. And a data processing means for obtaining a power spectrum by using the power spectrum and rearranging the power spectrum such that the zero frequency is at the center of the frequency space.

[0013]

That is, in the scanning probe microscope data processing apparatus according to the present invention, the power spectrum is obtained by performing two-dimensional Fourier transform on the array-like digital data by the data processing means. They are arranged so that they are centered.

That is, in order to increase the analysis accuracy, it is effective to convert an image into a frequency space and perform analysis there. For this purpose, a power spectrum is calculated by performing a two-dimensional Fourier transform of the image. FIG. 2B shows an image obtained by performing a Fourier transform on the image shown in FIG.
The six spectral positions appearing in FIG. 2B correspond to the period of the atomic arrangement in FIG. 2A, and the distance from the origin position in the frequency space of this spectrum is the period of the atomic arrangement. Can be said to be the wavelength, that is, the lattice spacing. further,
It can also be seen from the arrangement of the peak positions of the spectrum (the arrangement of six) that the atomic arrangement on the graphite surface has six times symmetry. As described above, performing the analysis in the frequency space by performing the Fourier transform on the image can improve the quantitative accuracy more than performing the analysis from the image in the real space.

[0015]

Embodiments of the present invention will be described below with reference to the drawings. (First Embodiment) FIG. 1 is a block diagram of a scanning probe microscope data processing apparatus according to a first embodiment of the present invention. In the scanning probe microscope (SXM) 10,
The probe 11 faces the sample 12, and is scanned in the x and y directions by the movement of the sample stage 14 by the xy scanning drive circuit 13. The displacement r of the distance d between the probe 11 and the sample 12 moving on the sample surface by the movement of the sample table 14
Is detected by the displacement detector 15 engaged with the probe 11, and the detection output is input to a servo circuit 17 that controls the z driver 16 so as to keep the distance d constant.

In general, the analog output of the servo circuit 17 is converted into a digital signal through an analog / digital (A / D) converter 18 to determine the scanning range.
In the line buffer 19 controlled by the counter 20,
The data is taken in synchronization with the output of the xy counter 20. That is, the detection signal from the displacement detector 15 is stored in the line buffer 19 as a digital signal d (i) [where i = 1,
2,..., I] in synchronization with the output timing i of the xy counter 20, and treated as a bit string.
When the scanning is completed and the entirety of one line is stored in the buffer 19, the digital signal train fetched into the line buffer 19 in this manner is synchronized with the output timing j of the xy counter 20 so that the digital signal train f The image data is transferred to the image buffer 21 as (i, j). For example, the signal f
(100, 3) indicates that it is the 100th digital amplitude value in the third scanning line. This bit string has a length representing, for example, 256 scanning points.

The SXM data is data in which J scan lines and data of I scan points are arranged in a grid pattern for each scan line to form an image. The data array f (i, j) placed in the image buffer 21 can be displayed on the CRT 22, stored as a file 23, or transferred to the data processing circuit 24 for analysis processing by selection.

The data processing circuit 24 includes a selection switching circuit 25 for selecting processing contents and an adder 2 for adding data.
6 and an arithmetic circuit 2 for performing peak search and filtering
7, an FFT operation circuit 28 for performing a fast Fourier transform (FFT), and a reordering circuit 29 for reordering data
And a conversion circuit 30 having a table of trigonometric functions and logarithm, and outputting sine, cosine and logarithm of input data, and performing a structural analysis and a filtering process by combining these.

The procedure for transferring the measured data from the image buffer 21 to the data processing circuit 24, calculating the power spectrum, and displaying the measured power spectrum on the CRT 22 will be described below. In order to execute such a process, the following procedure may be executed while being sequentially selected by the sequential selection switching circuit 25, or the procedure of the process may be programmed in advance and automatically executed. The processing flow is as shown in FIG. 4A, and the data flow in this processing is as shown in FIG. 4B. 4A and 4B are denoted by the same reference numerals in order to clarify the relationship therebetween.

First, it is determined whether or not there is data in the image buffer 21 (step ST1).
The data is measured or read from the file 23 (step ST2). That is, the measurement data or the data stored in the file 23 is temporarily stored in the image buffer 21 as described above in the digital signal train f (i, j).
Captured as Then, when the data is taken into the image buffer 21, the data flag (dat) indicating the presence or absence of the data is set to "1" indicating the presence of the data, and the selection flag for designating the conversion process of the FFT operation circuit 28 is further set. (Fflg) is set to “0” designating not to execute the FFT operation (step ST3).

Thereafter, the process waits for the selection of the FFT operation circuit 28 by the selection switching circuit 25 (step ST4). If the FFT operation circuit 28 is selected, the selection flag (ff) is set.
lg) is set to "1" designating execution of the FFT operation (step ST5). Then, the data is transferred from the image buffer 21 to the FFT operation circuit 28, and the image is subjected to a two-dimensional Fourier transform (step ST6).

That is, in the FFT operation circuit 28, the two-dimensional Fourier transform (F) of the image function f (i, j) {f (i, j)} = F (u, v) = {f (i, j) exp {-2πj (ui + vj)} or inverse transform (F ^-1 ) {F (u, v)} = f (i, j) = {F (u, v) exp {2πj (ui + vj)} Performed by a conversion algorithm. In these equations, i and j represent the spatial coordinates of the x and y axes, respectively, and u and v represent the coordinates of the frequency space in the x and y directions.

As described above, the FFT operation circuit 28 can execute the Fourier transform and the inverse transform at high speed. Therefore, before the processing, it is necessary to specify in advance which conversion is to be performed, and the conversion is written in the selection flag (fflg). The contents of the flag are determined as: fflg = 0: No operation is performed, 1: FFT operation is performed, -1: Inverse FFT operation is performed, and the FFT operation circuit 28 executes the operation while referring to the value of this flag. .

By the way, as shown on the left side of FIG. 5A, the result of the Fourier transform by the fast Fourier transform algorithm is that the frequency components in each of the x and y directions start from the zero frequency and the number of pixels (here, , I, J), and increases to the Nyquist frequency defined by で of this, and returns to the low frequency again at this Nyquist frequency. Looking at the one-dimensional case, it is as shown on the left side of FIG. 5B.
Therefore, it is necessary to perform rearrangement so that the zero frequency becomes the center of the frequency space as shown on the right side of each of FIGS. This rearrangement is executed by the rearrangement circuit 29. Therefore, the calculation result of the FFT operation is not immediately returned to the image buffer 21 but is transferred to the rearrangement circuit 29 for the time being, and the above rearrangement is executed. That is, after "0" is written in the selection flag (fflg) (step ST7), the data is transferred to the rearrangement circuit 29, and the rearrangement is executed (step ST8).

After the rearrangement operation, the FFT operation circuit 2
8 (the FFT is not executed at this time, the selection flag (fflg) must be set to “0” in the step ST7), and then transferred to the conversion circuit 30 and displayed. Therefore, logarithmic conversion of the power spectrum resulting from the FFT operation is performed. In the conversion circuit 30,
A table containing logarithmic values is created, and when data is input, the logarithmic value is output.

The table storing the logarithmic value is, for example,
Assuming that the power spectrum is a 2-byte digital signal sequence, 32k data values can be represented. If a logarithmic value corresponding to each of the 32k data values is prepared in advance as a table (a table of 64 kbytes), a logarithmic value can be obtained without having to calculate the power spectrum as a result of the FFT operation. .

As described above, the data after the logarithmic conversion is returned to the image buffer 21 again (step ST).
9), upon selection (step ST10), CRT 22
Is displayed (step ST11).

As described above, the position of the peak of the power spectrum reflects the periodicity and symmetry of the structure in the image. In other words, the peak positions of the six spectra in FIG. 2B represent the irregularities of the graphite atoms in FIG.

(Second Embodiment) The power spectrum obtained by the operation performed in the first embodiment has a structure in which the original image f (i, j) has a periodicity.
A peak that reflects this appears. The interval (wavelength) of the periodic structure is obtained from the relationship between the peak position and the scanning range in this frequency space, and the azimuth (angle) of the period of the structure is obtained from the angle between the peak position and the coordinate axis. Further, the symmetry of the periodic structure and the relative positional relationship of the structure can be understood from the number of peaks and the relative positional relationship.

The relationship between the peak position and the period interval is as follows. Considering the spectrum as shown in FIG. 3A, the spectra of S1 and S4 have the same structure (that is, L × exp (−ikx) and L × exp (−ikx)).
exp (ikx), which correspond to two waves having the same period and amplitude but opposite directions). Similarly, S2 and S
5, S3 and S6 represent the same structure. S1, S
4 shows that the scanning range of the original image is L
If the distance (wavelength) of the structure is L × lx / Lx
Periodic structure. Further, since the spectrum S1 is inclined by θ with respect to the x-axis in the frequency space, it is understood that the above-described periodic structure is rotated by θ with respect to the x-axis in the real space. In addition, there are six spectra, all of which represent the same frequency, and are arranged at equal intervals in angle, indicating that they are symmetric six times.

As described above, it can be understood that various information can be obtained by executing the FFT of the image and examining the frequency space. In particular, accurately examining the peak position requires quantitatively analyzing the image. This is important for analysis. The automatic search of the peak position may be executed in the following procedure. The processing procedure is as shown in FIG. 6A, and the data flow in this processing is as shown in FIG. 6B. (A) and (B) of FIG.
Are given the same reference numerals in order to clarify their relationship.

The calculation of the power spectrum may be performed in the same manner as in the first embodiment. When the power spectrum is obtained (step ST21), the selection switching circuit 25
Selects the arithmetic circuit 27 (step ST22), and executes a peak search (step ST23). This operation is
In order to determine whether or not the spectrum F (u, v) is a peak, an intensity comparison is performed within a specified neighboring area centered on F (u, v). At this time, if F (u, v) has the highest intensity, F (u, v) is regarded as a peak. The calculation method is as follows.

That is, the spectrum F (u, v) (where,
u and v are coordinates in the frequency space corresponding to i and j, respectively. In the case of a digital image, both u and v are positive integers.
u = 1, 2,..., I / 2; v = 1, 2,..., J / 2). F (u, v) and F (ud, vd), F (u, v)
v) and F (ud + 1, vd),... are executed in synchronization with the timing of the arithmetic circuit 27. On the way, F
If (u, v) is smaller, the operation is stopped; otherwise, the operation is continued. F (u + d, v + d)
If F (u, v) has the highest intensity, F (u, v)
v) is regarded as a peak, and coordinates (u, v) in the frequency space
Is stored in a buffer (not shown) for storing the peak position. In this manner, the comparison operation is performed for all the spectra, and the peak can be searched.

The frequency at the position (u, v) is lx = (u
^Two + V ² ) ^1/2 , The angle with the x coordinate in the frequency space is θ =
cos ^-1 (u / v). That is, the interval and angle of the periodic structure are obtained from these values.

The data after the calculation is returned to the image buffer 21 again (step ST24), and the power spectrum and its peak position are displayed on the CRT 22 by selection (step ST25). If necessary, the frequency space of the peak position is displayed. Also, the coordinates (wavelength) and angle of the obtained structure are displayed (step ST26).

(Third Embodiment) In the first and second embodiments, when the peak position of the power spectrum is not clear, an image is further added to reduce a random noise component. By reducing and enhancing the structure itself, the peak of the spectrum can be sharpened. That is, the images may be added while repeatedly measuring the same area, or the images of the same area may be repeatedly read and added as a file. The procedure of this processing is as shown in FIG. 7A, and the data flow in this processing is as shown in FIG. 7B. 7A and 7B are given the same reference numerals in order to clarify the relationship therebetween.

First, it is determined whether or not there is data in the image buffer 21 (step ST31). If there is no data, the data is measured or read from the file 23 is performed (step ST32). That is, the measurement data or the data stored in the file 23 is temporarily stored in the image buffer 21 as described above.
(I, j). Then, when the data is taken into the image buffer 21, the data flag (dat) indicating the presence / absence of data is set to “1” indicating the presence of data.
Is set (step ST33).

Thereafter, the adder 2 is selected by the selection switching circuit 25.
6 (step ST34), and add the data to the adder 1
Transfer to 6. In this way, the data is sequentially transferred and the data is added (step ST35). When the required number of images have been added, the addition operation is stopped, and the added data is again stored in the image buffer 21 as f (i, j).
(Step ST36).

As described above, the data f for which addition has been completed
(I, j) is F as described in the first and second embodiments.
An FT operation is performed (step ST37), and necessary processing is added. Alternatively, when performing display (step ST
38), image data is displayed on the CRT 22 (step ST39).

[0040]

As described in detail above, according to the present invention,
It is possible to provide a scanning probe microscope data processing apparatus capable of quantitatively and accurately obtaining the periodic interval and direction of the periodic structure, the symmetry of the structure, and the like.

That is, by performing a two-dimensional Fourier transform of an image, its Fourier transform spectrum is calculated, and furthermore, by automatically retrieving the peak position of the spectrum from the power spectrum, the periodic interval of the periodic structure, It is possible to quantitatively determine the direction, the symmetry of the structure, and the like, and it becomes easy to perform a structural analysis in an atomic level region on the crystal surface.

[Brief description of the drawings]

FIG. 1 is a block configuration diagram of a scanning probe microscope data processing apparatus according to an embodiment.

2A is a diagram showing an image obtained when observing an atomic arrangement on a graphite surface, and FIG. 2B is a diagram showing a peak position of a spectrum obtained by performing Fourier transform on the image of FIG. It is.

3A is a diagram showing a spectrum obtained by Fourier transforming the image of FIG. 2A, and FIG. 3B is a diagram schematically showing an atomic arrangement on a graphite surface.

FIG. 4A is a flowchart for explaining the operation of the first embodiment, and FIG. 4B is a diagram showing a data flow.

5A is a diagram illustrating a result of Fourier transform and a result of rearrangement thereof, and FIG. 5B is a diagram illustrating a result of Fourier transform and a result of rearrangement thereof when viewed in a one-dimensional case; It is.

FIG. 6A is a flowchart for explaining the operation of the second embodiment, and FIG. 6B is a diagram showing a data flow.

FIG. 7A is a flowchart for explaining the operation of the third embodiment, and FIG. 7B is a diagram showing a data flow.

[Explanation of symbols]

10 Scanning Probe Microscope (SXM), 21 Image Buffer, 22 CRT, 23 File, 24 Data Processing Circuit, 25 Selection Switching Circuit, 26 Adder, 27
Arithmetic circuit, 28: Fast Fourier transform (FFT) arithmetic circuit, 29: Rearrangement circuit, 30: Conversion circuit.

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int. Cl. ⁷ , DB name) G01B ^7/ 00-7/34 G01B 21/00-21/32 G01N 13/10

Claims (1)

(57) [Claims] An accumulating means for accumulating sample data obtained from said sample as array-like digital data by relatively scanning a probe and a sample; and storing said array-like digital data accumulated by said accumulating means. Data processing means for obtaining a power spectrum by performing two-dimensional Fourier transform and rearranging the power spectrum so that the zero frequency becomes the center of the frequency space.