Methods, systems, and media for measuring single crystal crystallographic orientation

Abstract

The application provides a method, system and medium for measuring a single crystal orientation, relates to the fields of crystallography condensed state physics and particle diffraction, and comprises the following steps: S1, scanning a single crystal sample, recording a part of a diffraction pattern, calculating a standard diffraction pattern according to Bragg diffraction conditions, and registering the two types of diffraction patterns to obtain a crystal orientation angle and a pattern center coordinate value corresponding to each experimental diffraction pattern; S2, performing fitting calculation on the pattern center coordinate value according to a geometric relationship to obtain a position of a sample surface relative to a diffraction detector; and S3, applying the obtained position of the sample surface to calculate an actual crystal orientation angle of the single crystal sample. The application can correct experimental operation errors and accurately measure a single crystal orientation.

Description

Technical Field

[0001] This invention relates to the fields of crystallography (condensed matter physics) and particle diffraction technology, and more specifically, to a method, system, and medium for measuring the crystal orientation of a single crystal. Background Technology

[0002] Due to the absence of defects such as grain boundaries, single-crystal materials exhibit unique mechanical, optical, and electrical properties, leading to their widespread application in fields such as engine blades, solar cells, and integrated circuits. The properties of single-crystal materials are typically anisotropic; therefore, accurately understanding the crystal orientation of single-crystal samples is of great scientific and engineering significance. For example, nickel-based single-crystal superalloys exhibit excellent creep resistance in the (100) direction, thus requiring precise control of the crystal orientation of single-crystal blades during their production and installation.

[0003] There are various methods for measuring crystal orientation. The anisotropy of the corrosion resistance of single-crystal materials can be used to calibrate silicon single crystals with the (111) crystal orientation, but corrosion and etching operations are destructive to the sample. The growth rate of single crystals is also different on each crystal plane, so the crystal orientation of the sample can be inferred from the edges of the single crystal, but this method cannot detect processed semiconductor single-crystal wafers. The invention patent with publication number CN103913417B discloses a single-crystal silicon rod crystal orientation detection device and its crystal orientation detection method, and introduces a method for detecting the crystal orientation of single-crystal samples. It requires multiple specialized devices, such as brackets, support arms, crystal orientation detection sensors and their brackets, cylinders, fixed protective covers, lifting protective covers, etc., and the equipment is relatively complex. A non-destructive and widely applicable method for crystal orientation determination is particle diffraction technology, including X-ray diffraction, electron backscatter diffraction (EBSD), transmission electron diffraction, neutron diffraction, etc. EBSD technology relies on a scanning electron microscope (SEM), a compact instrument. The electron beam is accelerated and directed onto the sample surface. Some particles are backscattered from the sample surface, and the angle of backscattering and the interplanar spacing of the sample conform to the Bragg diffraction equation, thus forming a characteristic diffraction pattern on the screen—the Kikuchi pattern. Analyzing the Kikuchi pattern can quickly provide information such as crystal type, orientation, grain size, and degree of deformation. However, accurately measuring the orientation angle of a single crystal (error <1°) is difficult, especially affected by inaccurate sample placement and unclear EBSD probe position during the measurement operation. Figure 1 As shown, such experimental errors are usually much higher than the industry-required single-crystal orientation angle accuracy, which limits the ability of particle diffraction technology to measure single-crystal orientation angles. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method, system, and medium for measuring the crystal orientation of a single crystal.

[0005] According to the present invention, a method, system, and medium for measuring the crystal orientation of a single crystal are provided, the solution of which is as follows:

[0006] In a first aspect, a method for measuring the crystal orientation of a single crystal is provided, the method comprising:

[0007] Step S1: Scan the single crystal sample and record a portion of the diffraction pattern. Calculate the standard diffraction pattern based on the Bragg diffraction condition. Register the two types of diffraction patterns to obtain the crystal orientation angle and pattern center coordinates corresponding to each experimental diffraction pattern.

[0008] Step S2: Fit the coordinates of the pattern center based on the geometric relationship to obtain the position of the sample surface relative to the diffraction detector;

[0009] Step S3: Use the fitted sample surface position to calculate the actual crystal orientation angle of the single crystal sample.

[0010] Preferably, the particle diffraction device for scanning the single crystal sample in step S1 includes an electron microscope, a Laue diffraction device, or a neutron diffractometer.

[0011] Preferably, the position of the sample surface relative to the diffraction detector obtained in step S2 includes: the sample surface normal vector and the distance from the detector.

[0012] Preferably, the particle diffraction technique used in the method is electron backscatter diffraction (EBSD), with the sample tilted 70° towards the EBSD detector.

[0013] Secondly, a system for measuring the crystal orientation of a single crystal is provided, the system comprising:

[0014] Module M1: Scans the single crystal sample, records a portion of the diffraction pattern, calculates the standard diffraction pattern based on the Bragg diffraction condition, and registers the two types of diffraction patterns to obtain the crystal orientation angle and pattern center coordinates corresponding to each experimental diffraction pattern.

[0015] Module M2: Fits the coordinates of the pattern center based on geometric relationships to obtain the position of the sample surface relative to the diffraction detector;

[0016] Module M3: Uses the fitted position of the sample surface to calculate the actual crystal orientation angle of the single crystal sample.

[0017] Preferably, the particle diffraction device for scanning single-crystal samples in module M1 includes: an electron microscope, a Laue diffraction device, or a neutron diffractometer.

[0018] Preferably, the position of the sample surface relative to the diffraction detector obtained in module M2 includes: the sample surface normal vector and the distance from the detector.

[0019] Preferably, the particle diffraction technique used in the system is electron backscatter diffraction (EBSD), with the sample tilted 70° towards the EBSD detector.

[0020] Thirdly, a computer-readable storage medium is provided that stores a computer program, which, when executed by a processor, implements the steps of the method.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. This invention relates to the characterization of the crystal orientation of single-crystal samples, accurately obtaining the sample's placement position and crystal orientation angle during measurement, and is applicable to all single-crystal samples;

[0023] 2. This invention is based on a spherical standard diffraction pattern and uses globally integrated digital image coherence technology to register the standard pattern with the experimental particle diffraction pattern to obtain the geometric parameters of the particle diffraction experiment, which belongs to non-destructive testing;

[0024] 3. The code for this invention is simple to write, has a fast convergence speed, and high accuracy. Attached Figure Description

[0025] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0026] Figure 1 Ideal and non-ideal sample placement postures when measuring the crystal orientation of single-crystal silicon wafers using EBSD;

[0027] Figure 2 The geometric relationship between the EBSD pattern center (PC) and the sample;

[0028] Figure 3 This is a PC point cloud image obtained from a single EBSD scan;

[0029] Figure 4 The electron backscattering diffraction images of (100) crystal plane silicon wafer samples at tilt angles of 70°, 60° and 50°, including cases with and without background gray values;

[0030] Figure 5 (100) Silicon wafer pattern center coordinate distribution diagram;

[0031] Figure 6 The distribution of pattern center coordinates obtained by crystal orientation calibration when a single-crystal silicon wafer is placed at different tilt angles;

[0032] Figure 7 Electron backscattering diffraction images of single-crystal silicon wafers with (100)(110)(111) crystal planes;

[0033] Figure 8 The plane fitting error of the center point cloud of the pattern for single crystal silicon wafers with different crystal planes is given in pixels (corresponding to 20μm, 40μm, and 40μm respectively).

[0034] Figure 9 The distribution of crystal orientation angle error (°) for monocrystalline silicon wafers. Detailed Implementation

[0035] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0036] This invention provides a method for measuring the crystal orientation of a single crystal, referring to... Figure 1 As shown, the method specifically includes:

[0037] Step S1: This method has no special requirements for the sample fixation method and position. Using particle diffraction devices such as electron microscope, Laue diffraction device, and neutron diffractometer, the single crystal sample is scanned in a large space to record a series of diffraction patterns. The standard diffraction pattern is calculated according to the Bragg diffraction conditions. The two types of diffraction patterns are registered to obtain the crystal orientation angle and pattern center coordinate values ​​corresponding to each experimental diffraction pattern.

[0038] Step S2: Fit the coordinates of the pattern center based on geometric relationships, such as plane fitting or polynomial fitting, to obtain the position of the sample surface relative to the diffraction detector, including the sample surface normal vector and the distance from the detector, overcoming the difficulty in accurately detecting the sample position. Fitting results obtained from scanning data with a larger spatial range are more accurate.

[0039] Step S3: Use the position of the sample surface obtained by fitting to calculate the actual crystal orientation angle of the single crystal sample, thereby effectively correcting the errors introduced in the measurement experiment, such as sample placement posture and detector tilt.

[0040] This method can be applied to fields such as X-ray diffraction, electron backscatter diffraction, Laue diffraction, and transmission electron diffraction to measure the crystal orientation angles of single-crystal samples at multiple scales.

[0041] The present invention will now be described in more detail.

[0042] This invention, based on the particle diffraction image integrated registration and correction method previously proposed by the inventors (Invention Patent Application No. 202011064748.X, Authorization No. CN112213339B), provides a method for accurately measuring the crystal orientation of a single-crystal sample. This invention can employ various particle diffraction techniques for measurement; the following description uses EBSD technology as an example to introduce a method for measuring the crystal orientation of a single-crystal sample within a scanning electron microscope.

[0043] Reference Figure 2 and Figure 3 As shown, the sample is typically tilted 70° towards the EBSD detector. Existing crystal orientation measurement techniques assume that the sample placement is known. Inaccurate sample placement will lead to tilting and rotation of the PC point cloud, which is common with large or irregularly shaped samples. Within the EBSD probe reference frame, the coordinates of the EBSD electron beam interaction volume are x... * =(x * ,y * ,z * The sample crystal orientation uses Euler angles. The corresponding 3×3 rotation matrix Q is:

[0044]

[0045] The single-crystal orientation measurement technology solution is as follows:

[0046] (1) Using EBSD correction methods such as integrated registration, the crystal orientation angles of all Kikuchi images relative to the EBSD probe were corrected. and the center coordinates of the pattern [x * ,y * ,z * Each Kikuchi image corresponds to 6 parameters.

[0047] (2) Perform a shape fit (least squares method) on the coordinates of the pattern center to accurately obtain the placement position of the sample surface relative to the EBSD probe, including the unit normal vector N of the sample surface. s The more scanning points, the larger the area covered, and the more accurate the sample placement obtained from the fitting. If the sample surface is planar, then minimize the following formula:

[0048] T(N s ,d)=(N s ·x * (x)+d) 2

[0049] In the formula x * (x) summarizes the coordinates of the pattern center obtained from the previous calculations, where d is a constant.

[0050] If the sample surface has other shapes, only the surface fitting formula needs to be modified.

[0051] (3) Combining rotation matrix Q and N s The true crystal orientation of the sample was calculated.

[0052] For example, if a single-crystal silicon wafer is labeled as (100) silicon wafer, then the unit normal vector of the sample's crystal plane is S = [1, 0, 0]. T It is important to note the crystal symmetry; that is, in specific calculations, S can take values ​​of [±1, 0, 0].T [0, ±1, 0] T [0,0,±1] T The six vectors are crystallographically equivalent. Applying the rotation matrix Q to S:

[0053] S r =QS

[0054] The surface normal vector S of the single-crystal silicon wafer in the EBSD probe coordinate system can be obtained. r And the two normal vectors N s S r The included angle, arccos(S) r ·N s The minimum included angle obtained from six S values ​​is the error between the actual and nominal crystal orientations of the silicon wafer. This invention can obtain the crystal orientation error corresponding to each Kikuchi diagram, which is the distribution map of the crystal orientation error.

[0055] Application Example 1: Sample posture detection.

[0056] To test the effectiveness of this invention in detecting sample placement, this embodiment used a (100) crystal plane single-crystal silicon wafer to capture Kikuchi images with a large step size (50 μm) and full resolution (1200 × 1600). Each scan saved 30 × 40 Kikuchi images. The corresponding Kikuchi patterns are as follows: Figure 4 As shown, the pattern quality varies depending on whether there is a background grayscale value or not. The pattern quality is highest at a 70° tilt angle and lowest at a 50° tilt angle. This is because when the sample is tilted at a higher angle, more backscattered electrons are emitted, resulting in lower noise in the generated image. Figure 5 This shows the pattern center coordinate distribution diagram of a (100) silicon wafer at a 70° tilt angle, from y * and z * A noticeable tilt is visible. This is due to the large size of the circular silicon wafer sample and the lack of markings on its uniform surface, making it difficult to align with the detector in a scanning electron microscope. Figure 4 The asymmetric distribution of background grayscale values ​​in the sample is due to the difficulty in accurately positioning the sample, which is a major challenge in measuring the crystal orientation of single-crystal samples.

[0057] Figure 6 The point cloud distribution diagrams of the pattern center coordinates of a (100) crystal plane single-crystal silicon wafer tilted at 70°, 60° and 50° in a scanning electron microscope are plotted. It can be seen that the different point cloud planes have an angle of about 10°. This method can calculate the normal vector of the point cloud plane. Figure 6 The distribution of pattern center coordinates obtained by crystal orientation calibration when a single-crystal silicon wafer is placed at different tilt angles shows that this method can detect the placement posture of the sample.

[0058] Table 1 lists the sample surface normal vectors and their included angles at different tilt angles, from which the following conclusions can be drawn:

[0059] 1. The x-component of the normal vector is significant and cannot be ignored, which violates the default assumption in EBSD scanning experiments that the sample is tilted along the x-axis. This indicates that the method is necessary to detect the orientation of single-crystal samples; otherwise, the error introduced by experimental operation would be too large.

[0060] 2. The pairwise angles between the three normal vectors are close to the theoretical values ​​of 10° and 20°. In particular, the normal vector angles corresponding to the two sets of images with higher quality (60°-70°) are 10.09°, and the angle between them and the true value is only 0.09°. This shows that the point cloud plane fitting results of this method have good angular resolution.

[0061] Table 1. Surface normal vectors and their included angles of single-crystal silicon wafers obtained by this method at different tilt angles.

[0062]

[0063]

[0064] The excellent accuracy of this invention in detecting the orientation of samples will help to accurately measure the crystal orientation of single-crystal samples.

[0065] Application Example 2: Monitoring crystal orientation error of single-crystal silicon wafer samples.

[0066] To test the effectiveness of this invention in measuring single-crystal orientation, this embodiment used a commonly used single-crystal silicon wafer with three crystal planes (100), (110), and (111). Kikuchi images with a relatively large step size (50 μm) and high resolution (1140×1600, 600×800, 600×800) were captured, and 30×40 Kikuchi images were saved for each scan. The corresponding Kikuchi patterns are as follows: Figure 7 As shown. The pattern quality varies. The (100) silicon wafer has higher pattern quality and lower noise because the electron beam current is large during EBSD scanning and the storage resolution is high. Figure 8 The remaining residuals of the plane fitting method used in this invention are also shown. It can be seen that the residuals are randomly distributed, and the plane fitting does not have significant systematic errors. Furthermore, for high-quality Kikuchi flower patterns, the correction results are more accurate, and the fitting residuals are smaller, typically less than 1 pixel. The EBSD calibration error for crystal orientation angles can reach 0.03°. Combined with the aforementioned 0.1° error when calibrating sample tilt angles, this invention can measure the crystal orientation angles of single-crystal samples within an error range of 0.15°. Figure 9The method also demonstrates the error between the measured crystal orientation angles and the markings on the single-crystal samples. The average crystal orientation angle errors for the three silicon wafers were 0.22°, 0.45°, and 1.61°, respectively. The errors of the first two are within the 0.5° range claimed by single-crystal silicon wafer manufacturers, but the crystal orientation error of the (111) silicon wafer is significantly higher, which is consistent with the fact that the (111) crystal surface is the most difficult to polish. As can be seen from this application example, the present invention can conveniently correct errors in the experimental operation of single-crystal crystal orientation measurement and can be used as a reliable quality control method for single-crystal manufacturing manufacturers.

[0067] This invention provides a method, system, and medium for measuring the crystal orientation of single crystals. The invention is simple to implement and can be used to measure the crystal orientation angles of single crystal samples of different shapes, such as rods and thin sheets. It is the first to propose using particle diffraction to detect the sample placement posture, achieving sub-pixel accuracy in sample surface fitting. Combined with Euler angle measurement with an accuracy of 0.03°, the crystal orientation of single crystal samples can be accurately measured. When processing single-crystal silicon wafers, it can clearly distinguish whether the crystal surface error exceeds the manufacturer's specified 0.5°.

[0068] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0069] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for measuring the orientation error distribution of a single crystal, characterized in that, include: Step S1: Scan the single crystal sample and record a portion of the diffraction pattern. Calculate the standard diffraction pattern based on the Bragg diffraction condition. Register the two types of diffraction patterns to obtain the crystal orientation angle and pattern center coordinates corresponding to each experimental diffraction pattern. Step S2: Fit the coordinates of the pattern center based on the geometric relationship to obtain the position of the sample surface relative to the diffraction detector; Step S3: Use the fitted sample surface positions to calculate the crystal orientation error distribution of the single crystal sample; The position of the sample surface relative to the diffraction detector obtained in step S2 includes: the unit normal vector of the sample surface. and the distance from the detector; Steps S1-S3 include: Within the EBSD probe reference frame, the coordinates of the EBSD electron beam interaction volume are: The sample crystal orientation uses Euler angles The expression corresponds to the 3×3 rotation matrix. for: The integrated registration method was used to correct the crystal orientation angles of all Kikuchi images relative to the EBSD probe. and the center coordinates of the pattern Each Kikuchi image corresponds to 6 parameters; Shape fitting is performed on the coordinates of the pattern center to accurately determine the placement of the sample surface relative to the EBSD probe, including the unit normal vector of the sample surface. ; Combined with rotation matrix and The true crystal orientation of the sample is calculated. Apply rotation matrix Normal vector of the nominal crystal plane on the sample surface : The surface normal vector of the single-crystal silicon wafer in the EBSD probe coordinate system can be obtained. And the two normal vectors , The included angle, Six equivalents need to be selected. The smallest included angle obtained is the error between the actual crystal orientation and the nominal crystal orientation of the silicon wafer.

2. The method for measuring the orientation error distribution of a single crystal according to claim 1, characterized in that, The particle diffraction device used to scan the single crystal sample in step S1 includes an electron microscope, a Laue diffraction device, or a neutron diffractometer.

3. The method for measuring the orientation error distribution of a single crystal according to claim 1, characterized in that, The method employs electron backscatter diffraction (EBSD) as the particle diffraction technique, with the sample tilted 70° towards the EBSD detector.

4. A system for measuring the orientation error distribution of a single crystal, characterized in that, include: Module M1: Scans single crystal samples, records a portion of the diffraction patterns, calculates the standard diffraction pattern based on the Bragg diffraction conditions, and registers the two types of diffraction patterns to obtain the crystal orientation angles and pattern center coordinates corresponding to each experimental diffraction pattern. Module M2: Fits the coordinates of the pattern center based on geometric relationships to obtain the position of the sample surface relative to the diffraction detector; Module M3: Calculates the actual crystal orientation angle of the single crystal sample by applying the fitted position of the sample surface; The position of the sample surface relative to the diffraction detector obtained in module M2 includes: the unit normal vector of the sample surface. and the distance from the detector; The modules M1-M3 include: Within the EBSD probe reference frame, the coordinates of the EBSD electron beam interaction volume are: The sample crystal orientation uses Euler angles The expression corresponds to the 3×3 rotation matrix. for: The integrated registration method was used to correct the crystal orientation angles of all Kikuchi images relative to the EBSD probe. and the center coordinates of the pattern Each Kikuchi image corresponds to 6 parameters; Shape fitting is performed on the coordinates of the pattern center to accurately determine the placement of the sample surface relative to the EBSD probe, including the unit normal vector of the sample surface. ; Combined with rotation matrix and The true crystal orientation of the sample is calculated. Apply rotation matrix Normal vector of the nominal crystal plane on the sample surface : The surface normal vector of the single-crystal silicon wafer in the EBSD probe coordinate system can be obtained. And the two normal vectors , The included angle, Six equivalents need to be selected. The smallest included angle obtained is the error between the actual crystal orientation and the nominal crystal orientation of the silicon wafer.

5. The system for measuring the orientation error distribution of a single crystal according to claim 4, characterized in that, The particle diffraction device for scanning single-crystal samples in module M1 includes: an electron microscope, a Laue diffraction device, or a neutron diffractometer.

6. The system for measuring the orientation error distribution of a single crystal according to claim 4, characterized in that, The system employs electron backscatter diffraction (EBSD) as the particle diffraction technique, with the sample tilted 70° towards the EBSD detector.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 3.

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