TY - JOUR
AU1 - Kim, Seung, Jae
AU2 - Joo,, Wonjong
AU3 - Kim, Dong, Hwan
AB - Abstract Electron microscopy is used to determine the form and size of samples from images. Consequently, distortion or error in the images produces incorrect data. This study developed an algorithm to enhance the scanner signal in order to improve the orthogonality of the image. The results of images with poor orthogonality, when observed from the central axis standard, are analogous to those of rotationally transformed images. Therefore, we believe that transmitting enhanced signals with rotationally transformed images will improve the quality of the data. orthogonality, scan skew, raster scan, scan coil, scan line, scanning electron microscope Introduction Scanning electron microscopy (SEM) is used to determine the shape, form and dimensions of specimens [1–3]. Any distortion of the specimen image produces incorrect data. SEM works by focusing electrons from an electron gun with a lens into a beam and transmitting a signal as a voltage current to investigate a uniform facet of a specimen. Horizontal and vertical scan coils positioned at 90° phase differences are used to move the electron beam vertically and horizontally. The scanner can be a magnetic deflector, which has a coil structure, or a static deflector, which has a plate structure. Magnetic deflector scan systems are comparably easy to manufacture, but it is difficult to enlarge the scanning range [4,5]. By contrast, static deflectors have a wide scanning range, but are difficult to manufacture. This study examined methods to compensate for the orthogonality of the image resulting from errors in the scan coil assembly in the x- and y-directions when a magnetic deflector scanner was used to acquire large- to small-scale images. It is difficult to minimize the errors in the mechanical assembly phase. However, this problem can be overcome by adjusting the waveform to compensate for the errors. Recent research has examined ways to compensate for errors in the horizontal length resulting from z-axis rotation [6,7]. This study focused on image distortion around the z-axis, which produces oblique images on both the x- and y-axes. In SEM, it is relatively straightforward to compensate for oblique images on both the x- and y-axes by adjusting the align coil. In addition, one can compensate for a distorted image or length change around the boundary by adjusting the scan wave modification [8] or by decreasing the deflector response time [9]. Other types of image distortion can be compensated for by using image-processing techniques, although these are limited to a certain level of distortion [10,11] and do not deal with the fundamental source of distortion. This study examined coordinate transformation to compensate for x, y orthogonality, independent of any z-axis rotation, which means that the image is oblique only at the x-axis due to a mechanical assembly problem, making it difficult to fix. This is a directional problem that occurs when a magnetic field is formed due to a structural error in the scanner resulting from stage rotation, unlike a change in scanning range. The resulting image distortion can make a rectangular sample look like a parallelogram or a circle look like an ellipse. Several reports have introduced ways to improve image orthogonality [12,13]. However, the main methods used to compensate for image orthogonality involve the pattern generation by controlling a stage, by shifting the x- and y-axes using software, or by multiplying the DAC (Digital Analogue Converter). These methods are limited in their ability to increase the resolution and to handle multichannel input data for various transformation computations, such as coordinate transformation and skew compensation, because they have constraints limiting accurate scan signal generation and involve only the x- and y-axes input channels. Here, we propose a new scheme for modifying the scan waves by measuring the amount of skew in an image due to mechanical misalignment in the assembly process. With reference to the horizontal axis, the skew angle is first measured from the image, and new scan data for the horizontal axis are computed using the original horizontal and vertical axis data with digitally multiplied data. A digital multiplier was used to generate the scan signal and to handle the skew and rotation transformation by supplying eight input channels. Next, a circuit with operational amplifiers (Op-Amps) with different weighting factors was proposed to increase the resolution of the wave signal. Our method enables adjustment by measuring the skew direction and creating a scan signal modified in appropriate different directions. Our research is presented in the following order. First, we analyze the cause of the scan skew in the magnetic field scanner structure. Second, we propose and apply an algorithm that compensates for the skew. Third, we verify the procedure by comparing the images obtained. Our method should improve distorted images, specifically skewed images caused by structural problems in the scan coil, with the help of compensation methods. Raster scan system Scanner structure Figure 1 shows a schematic of a SEM, with the scanner placed inside condenser lens 2. The rectangular scanner uses a magnetic deflector and is assembled in a holder by winding the coil. The scanner (coil) has four electromagnetic structures (Fig. 2) and the current direction is indicated. The scanning range affects the magnification power, and the deflection angles are controlled by setting the coils with a two-stage structure, in order to make measurements from low magnification to high magnification. The impedance ratio for each stage is 1:2. The upper coil (single scan) is used for low magnification and the upper and lower coils (dual scan) are used for high magnification. Fig. 1. Open in new tabDownload slide A schematic of a thermionic scanning electron microscope. Fig. 1. Open in new tabDownload slide A schematic of a thermionic scanning electron microscope. Fig. 2. Open in new tabDownload slide A magnetic deflector scanner (left is horizontal, right is vertical). Fig. 2. Open in new tabDownload slide A magnetic deflector scanner (left is horizontal, right is vertical). Scanner and frequency definition An ordinary raster scan [6] tries to obtain scan coordinates that are of square form, as shown in Fig. 3b, but magnetic scan skew occurs due to the error in the scan coil assembly, as shown in Fig. 3a and c. Even if the scan coil is assembled correctly, it is often misaligned with respect to the center of the electron beam emission line, causing a skewed image at some angle. The procedure involved in scanning the display from left to right is called a horizontal scan. Scanning from top to bottom is a vertical scan, and the display formed by the scan lines is called a raster scan [6]. The line formed from one scan line to another line is called a feedback line. Figure 4 outlines the method by which electron beams scan the surface of a specimen. On a raster scan, the frequency is determined by multiplying the time taken to acquire the data from one point by the vertical and horizontal resolution of the image. Here, fx and fy are the scan frequencies in the horizontal and vertical directions, respectively. First, the sampling frequency is set to S. Then, the total number pixels in the horizontal and vertical directions are computed; these are represented by Px and Py, respectively. In reality, the image shown in a monitor sometimes does not cover all of the pixels, cutting out boundary portions to give a clear image. The cut pixels, the so-called margin, are represented by Cx. In addition, an oversampling technique is introduced to acquire clear image data. The oversampling carries out multiple data acquisition between each sampling, where z is the number of additional samples. The vertical scan frequency is similar to the horizontal scan frequency, but this scan should cover one complete frame. Consequently, the scan time is much smaller than the horizontal scan frequency. As a result, the scan frequencies for the x- (horizontal) and y- (vertical) axes are determined by the following: (1) (2) Fig. 3. Open in new tabDownload slide Scan coordinates according to the scan coil assembly. Fig. 3. Open in new tabDownload slide Scan coordinates according to the scan coil assembly. Fig. 4. Open in new tabDownload slide Raster scan definition. Fig. 4. Open in new tabDownload slide Raster scan definition. The amplitude of the scan waveform is the voltage, as shown in Fig. 5. The magnitude rate based on time is indicated by a, and the input voltage V (t) of the coil is determined by multiplying the rate and time in one cycle. As observed from the frequencies, the change in the magnitude of the waveforms with time differs in the horizontal and vertical directions. Equations (3) and (4) denote the scan waves generated in one frame scanning in the horizontal and vertical directions. (3) (4) where n and m are the numbers of pixels in the horizontal and vertical axes, respectively, T is the period required to scan the horizontal axis once, 1(·) is a unit function and u(·) is a unit step function, where each function takes a value only for a positive domain and is zero for the other domains. and show the offset values used to make the voltage signal vary between negative and positive values, respectively. a is the slope of horizontal signal and b is the magnitude of vertical signal for one line scan; these values are determined by the image magnitude set by the user. Fig. 5. Open in new tabDownload slide Raster scan coordinate alteration to form one frame. Fig. 5. Open in new tabDownload slide Raster scan coordinate alteration to form one frame. Cause and measures to counter scan skew Cause of skewed images SEM creates images by collecting the secondary electrons emitted from the sample surface after it is struck by high-energy electron beams. The horizontal and vertical scanners are assembled at 90° to each other. Error can occur during the process of mounting the coils in the holder. If the angle between the two coils is greater or smaller than 90° due to an assembly error, a directional mismatch problem occurs during the raster scan due to non-uniform magnetic field formation. In comparison, in a static deflector, which uses an electric pad rather than magnetic coil, the mechanical assembly is not a concern due to its simple structure. The scanning of the sample surface by the electron beam is determined by the combination of magnetic fields in the horizontal and vertical directions. The two must be perpendicular to each other, in order to form a perfectly square scan area. Figure 6 shows skewed scan area coordinates resulting from a coil assembly error. Depending on whether the scanners are oriented at right angles, the resulting changes in the coordinates can be as great as the skew angle of the scanner. In order to explain this further, Fig. 6 shows cases with extreme 45° skew angles in two directions. Figure 6a shows a −45° declination of the vertical coil, with the horizontal direction as the base, while (b) shows the normal coordinates and (c) shows +45° inclination. In actuality, the change in the angle is usually less than 10°. Figure 7 shows secondary electron images with a loss in orthogonality due to scan skew, which is attributed to image distortion. Fig. 6. Open in new tabDownload slide Rectangular raster scan coordinates due to scan skew. Fig. 6. Open in new tabDownload slide Rectangular raster scan coordinates due to scan skew. Fig. 7. Open in new tabDownload slide Secondary electron image due to scan skew for different skew angles (left, negative; center, normal; right, positive skew angle). Fig. 7. Open in new tabDownload slide Secondary electron image due to scan skew for different skew angles (left, negative; center, normal; right, positive skew angle). Solution methods A rectangular raster scan forms an image by assuming that the scan surface is perfectly square. However, skewed images are produced when the magnetic deflector directions of the two coils not orthogonal. The following method is proposed to overcome this problem. The scan waveforms are a function of time, and the horizontal and vertical scan signals are synchronized and changed. Setting up a reference axis and rotating the other axis can compensate for the scan skew. This means that horizontal scan skew produces images that look as if rotational transformation of a horizontal scan occurred with a fixed vertical scan. We attempted to resolve this problem by producing signals that were not perfectly square to compensate for the scan skew. This can be done by increasing or decreasing the input signals in the direction opposing the skewed direction through coordinate transformation in the scan lines [12,13]. We anticipate that this will restore the scan coordinates by applying rotational transformation only to the horizontal axis. Modification algorithm design Hardware design Figure 8 shows a system block diagram outlining raster scan waveform generation. Only the DAC and adjustable parts used to produce the raster scan waveforms are indicated. The system has data storage, adjustment (controlling the offset and size of the waveforms) and arithmetic (signal calculation for the skew data) components. The waveform data are produced along with an image size that is obtained from the raster scan system. The previously observed scan waveform is a sawtooth waveform that changes with time. With the initial image acquisition signal, the CPLD (Complex Programmable Logic Device) produces an address to deliver the SRAM (Static Random Access Memory) data to the DAC, to create the final waveform for the raster scan. To generate the waveform, the DSP produces digital data representing the waveform, along with the image size produced from a personal computer (PC). The data produced by the DSP are written to the SRAM via a data bus. Figure 9 shows a circuit that generates sawtooth waves and controls the shift and zoom of the waveforms. This circuit is composed of a 16-bit DAC and a high bandwidth Op-Amp. Detailed signal control is possible through the variable resistance within the circuit. Figure 10 shows the circuit board in the arithmetic component. It was designed to compute the scan rotation using an 8-bit base digital multiplier. It compensates for any rotation and orthogonality by multiplying the sawtooth wave signal produced from the DAC by a trigonometric function value. At this point, a digital multiplier was used to multiply the trigonometric value for digital data ranging from −128 to 128; the trigonometric value can be expressed as −1 to +1. However, in order to increase the resolution of the output signal while improving the orthogonality, which is the main purpose of this work, Op-Amps were installed in the multiplier output. The digital multiplier is connected to the DSP in series. As a result, the output is produced by multiplying the value delivered from the PC. The final waveform output from the multiplier is produced through the Op-Amp. At this point, it is proposed that the Op-Amp circuit in Fig. 10 increases the resolution of the multiplier arithmetic element, overcoming the resolution limit in the 8-bit data structure. The derivation of the digital multiplier and Op-Amp will be described in more detail below. Fig. 8. Open in new tabDownload slide Block Diagram of raster scan waveform occurrence and secondary electron signal transformation system. Fig. 8. Open in new tabDownload slide Block Diagram of raster scan waveform occurrence and secondary electron signal transformation system. Fig. 9. Open in new tabDownload slide Control of production, offset and size of the waveform. Fig. 9. Open in new tabDownload slide Control of production, offset and size of the waveform. Fig. 10. Open in new tabDownload slide Rotation and skew control circuit. Fig. 10. Open in new tabDownload slide Rotation and skew control circuit. Algorithm design The skew is improved in the following sequence. The base axis (vertical) is set upright via stage rotation after obtaining a secondary electron image using samples with excellent orthogonality. The operating program calculates the skew angle of the obtained images (as shown in Fig. 11). The calculated angles are delivered to the DSP and transformed into data that will be delivered to the digital multiplier for calculating the rotational transformation. Equation (5) gives the general rotational transformation. However, the improvement in the orthogonality of the scan skew in SEM applies the transformation only to the horizontal scan, with the vertical scan as a fixed axis (see Eq. 6). Consequently, this is not completely a combined vertical and horizontal rotation that corresponds to simple image rotation. Fig. 11. Open in new tabDownload slide Measuring and improving the angle on the image. Fig. 11. Open in new tabDownload slide Measuring and improving the angle on the image. X,Y rotation matrix: (5) X,Y skew matrix: (6) Here, X and Y represent the original image densities before rotational transformation and θ is the angle to be rotated as a result of normal or skew rotation. Equation (7) transforms the skew angle measured from the image in Fig. 11 into digital data. In Eq. (6), the values of cos θ and sin θ range from −1 to +1. In order to convert the digital data, which can be used for digital multiplier input, into an 8-bit (256 in decimal) number format, the values of cos θ and sin θ must be calculated and converted into an 8-bit decimal number format as ⁠. Table 1 shows the range of θ and the data conversion. (7) Table 1. Digital converted values and original skew angle values . Radian value . Digital value (8 bit) . cos θ: 0–360° −1 to +1 0–256 Sin θ: 0–360° −1 to +1 0–256 . Radian value . Digital value (8 bit) . cos θ: 0–360° −1 to +1 0–256 Sin θ: 0–360° −1 to +1 0–256 Open in new tab Table 1. Digital converted values and original skew angle values . Radian value . Digital value (8 bit) . cos θ: 0–360° −1 to +1 0–256 Sin θ: 0–360° −1 to +1 0–256 . Radian value . Digital value (8 bit) . cos θ: 0–360° −1 to +1 0–256 Sin θ: 0–360° −1 to +1 0–256 Open in new tab For precise orthogonality compensation, the digital multiplier should have high resolution. However, it is difficult to obtain a digital multiplier that can handle rapidly changing signals, such as scan waveforms. When expressing the digitally converted values of θdc and θds using the 8-bit digital multiplier, in order to express the entire 360° range, it is valuable to consider the 180° range, excluding the overlapping size. This means that the minimum possible digital value is 180°/256 = 0.7°. The digital multipliers that are not used for decimal calculation must be expressed as 1 or 2 for the minimum digital value, which restricts their application for the orthogonality improvement calculation. Therefore, there is a limitation to precise compensation and to increasing the resolution. To overcome this limit, we introduced a scale compensation circuit that consists of Op-Amps with different resistors that enable more accurate value adjustment. For precise control, the circuit design shown in Fig. 10 produces an output by calculating two channels of the x-direction signal (XIN) produced from the digital multiplier. The resulting signal passes through a reverse amplifier, reflecting the weighted value, to produce the final output signal (⁠⁠). In Eq. (8), the ratio of R to R1 or R3 is 1:1, and the ratio of R to R2 or R4 is 0.1:1. For instance, if the measured skew angle is 4°, then θd is between 5 and 6 because 4° is between 3.515° and 4.218° (⁠⁠). Consequently, the digital multiplier is 5. However, this 5 represents 3.515°. Therefore, more accurate data are needed. By introducing the weighting factor R/R2 = 0.1 and R/R4 = 0.1, as shown in the proposed circuit, 0.3515° can be added to the original 3.515°, ultimately yielding 3.515° + 0.3515° = 3.866°, which is closer to the skew angle of 4°. With a ratio of 0.1:1 for R2 and R4, the resolution changes from 0.7° to 0.7°/10 = 0.07°. The final x-axis scan signal reflecting the skew rotation and precise compensation using the Op-Amps is given in Eq. (8), while the y-axis scan signal keeps the original value of the y-axis signal. We need to remember that the final x-axis scan signal combines the original x-axis and y-axis signals, which differs from general scan signal generation, as shown in Eqs. (3) and (4). Considering the digital multiplier and weighting factors using OP-Amps and given the original scan input signals XIN and ⁠, the final scan signals to the x- and y-axes and are obtained with Eq. (8). (8) Experimental results with compensation Waveform comparison analysis The formation of a rectangular scan area from the raster scan is determined by the signals from both scan directions. To improve the scan skew, when applying current to the scan coil that forms the magnetic field, weight factors are applied to the input signals to compensate for the skew angle, which form new magnetic fields around the coils. Figure 12 shows the results of skew rotational transformation on the horizontal scan after applying the weight factors to the input signals, as suggested in Eq. (8). It was possible to improve the orthogonality by applying skew rotational transformation to the input signals as much as the skewed angle. The original wave is formed by Eqs. (3) and (4), and the improved waveforms are implemented as Eq. (8). Image comparison analysis Images from before and after the compensation algorithm were compared. Figures 13–15 show before (left figures) and after images (right figures) of the scans of a rectangular nickel mesh, circular piece of tin on a carbon structure and rectangular gold mesh, respectively. From the measured results, we confirmed that the scan skew of the image (due to the loss of orthogonality before compensation) was eliminated after the compensation. We hope to increase the precision of the measuring sample form and length in this manner. Fig. 12. Open in new tabDownload slide Raster scan waveforms for the scans (left, original scan; right, compensated scan). Fig. 12. Open in new tabDownload slide Raster scan waveforms for the scans (left, original scan; right, compensated scan). Fig. 13. Open in new tabDownload slide Measurement results for the nickel mesh (pitch 25 μm). Fig. 13. Open in new tabDownload slide Measurement results for the nickel mesh (pitch 25 μm). Fig. 14. Open in new tabDownload slide Measurement results for the tin on carbon (particle size 1–10 μm). Fig. 14. Open in new tabDownload slide Measurement results for the tin on carbon (particle size 1–10 μm). Fig. 15. Open in new tabDownload slide Measurement results for the gold mesh (pitch 100 μm). Fig. 15. Open in new tabDownload slide Measurement results for the gold mesh (pitch 100 μm). Conclusions This work considered how to improve the skewed images that are inevitably formed by electromagnetic scanning systems and proposed a solution to eliminate scan skew problems due to error in the assembly of magnetic deflector scanners. The process using the proposed method can be summarized as follows. Obtain samples with excellent orthogonality and observe the image in the chamber. Measure the skew angle and convert it into digital data for compensation. Using the angle, produce the output signal based on the digital input signal of an 8-bit digital multiplier, to which skew rotational transformation is applied. Confirm the results by observing real-time images of the proposed scan waveforms. Measuring rectangular and circular samples, we overcame the skew error and obtained enhanced images. By using an 8-bit digital multiplier and Op-Amps with a different set of resistors, the resolution of skewed images was compensated for up to 0.07°. Although the manufacture of scanners with mechanical assembly errors causing skewed images in SEM cannot be avoided completely, it is possible to minimize the error by applying our proposed method. References 1 Hawkes P W , Spense J C H . , Science of Microscopy , 2007 New York Springer Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC 2 A Guide to Scanning Microsope Observation 2nd ed JEOL LTD., Peabody, MA, USA Available at http://www.jeol.com Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC 3 Watt I M . , The Principles and Practice of Electron Microscopy , 1997 2nd ed. Cambridge Cambridge University Press Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC 4 Kim D H , Park K , Park M J , Jung H W , Jang D Y . 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TI - Raster scan waveform compensation control for enhancing the orthogonality of images in SEM
JF - Microscopy
DO - 10.1093/jmicro/dft024
DA - 2013-08-01
UR - https://www.deepdyve.com/lp/oxford-university-press/raster-scan-waveform-compensation-control-for-enhancing-the-7fS1eSzNg0
SP - 475
EP - 484
VL - 62
IS - 4
DP - DeepDyve
ER -