Microsc. Microanal. 20, 1625–1637, 2014 doi:10.1017/S1431927614013282
© MICROSCOPY SOCIETY OF AMERICA 2014
A New Methodology to Analyze Instabilities in SEM Imaging Catalina Mansilla,* Václav Ocelík, and Jeff T. M. De Hosson Department of Applied Physics, Materials innovation institute M2i, University of Groningen, Nijenborgh 4, Groningen, 9474 AG, The Netherlands
Abstract: This paper presents a statistical method to analyze instabilities that can be introduced during imaging in scanning electron microscopy (SEM). The method is based on the correlation of digital images and it can be used at different length scales. It consists of the evaluation of three different approaches with four parameters in total. The methodology is exemplified with a specific case of internal stress measurements where ion milling and SEM imaging are combined with digital image correlation. It is concluded that before these measurements it is important to test the SEM column to ensure the minimization and randomization of the imaging instabilities. The method has been applied onto three different field emission gun SEMs (Philips XL30, Tescan Lyra, FEI Helios 650) that represent three successive generations of SEMs. Important to note that the imaging instability can be quantified and its source can be identified. Key words: scanning electron microscopy, digital image correlation, self-correlation image, residual stress, focused ion beam
I NTRODUCTION The development of new tools for in situ measurements in scanning electron microscope (SEM), e.g. of displacements and residual stress, demands a high degree of precision for a reliable subsequent digital analysis. In the case of residual stress, local measurements can be performed in a dual beam microscope [combined SEM and focused ion beam (FIB)] combining image milling and digital image correlation (DIC). The residual stress state can be derived from the local changes in the image (Kahn-Jetter & Chu, 1990; Sutton et al., 2009). Residual stresses can be defined as stresses that remain after the external loading (external forces, heat gradients, etc.) has been removed (Withers & Bhadeshia, 2001). They are present in almost all materials, and arise when inelastic processes occur, like plastic deformation or thermal treatments. These stresses influence the lifetime of products in service and as a consequence, precise knowledge and control of residual stresses are of high practical value. The traditional methods available for measuring internal stresses are grouped into destructive and nondestructive. The most prominent nondestructive method is X-ray diffraction (Prummer & Pfeiffervollmar, 1983). However, it requires a crystalline lattice using the distance between lattice plane as strain gauge. Common destructive methods are curvature measurement (Shull & Spaepen, 1996), nanoindentation (Bouzakis et al., 2004), and hole drilling (Nelson, 2010). Most of them determine the mean stress in large volumes or areas.
Received June 19, 2014; accepted September 10, 2014 *Corresponding author. [email protected]; [email protected]; j.t.m.de.hosson @rug.nl
The so-called slit milling method combines the ion milling and imaging capabilities provided by a dual beam microscope with DIC software to measure the residual stress (Kahn-Jetter & Chu, 1990; Sutton et al., 2009). It is based on a relaxation method, in which the residual stresses released in the vicinity of a slit are inferred from the local relaxation displacements measured by DIC. A scheme of the procedure followed in the measurement is shown in Figure 1. The procedure starts with the acquisition of the first SEM image of the area to be analyzed. After capturing the first image, a slit is milled. It is worth mentioning that generally the electron and the ion columns inside a dual beam system have different orientations, which implies that the sample under investigation has to be repositioned for milling. Afterwards, the sample is tilted backwards and a second image of the same area is taken. From the comparison of these two SEM images recorded by DIC before and after stress release the displacements field is obtained. These experimentally observed displacements are compared with the values of displacements obtained by the analytical solution for an isotropic elastic material, and the magnitude of the residual stress is obtained from the slope of such fitting (Tada et al., 2000; Winiarski et al., 2010). DIC is an image-based method that consists of dividing the digital images in smaller sub-regions, called “facets.” Each facet must contain enough features that unambiguously correlate with the same sub-region in the next image. Then, these facets are compared by matching and when the highest correlation is found, the displacement of the center of these sub-regions is obtained. The two-dimensional cross correlation allows separating the horizontal X from the vertical Y components of the in-plane displacement vector generated
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Figure 1. Steps involved in the measurement of residual stress using a combination of scanning electron microscopy, focused ion beam machining, and digital image correlation.
by the stress release. For instance, Figure 1 shows the displacements corresponding to the X component, which are perpendicular to the plane of the slit. It is worth mentioning that DIC displacements are presented as color images. The scale bar of the images is in the range of tens of nanometers. Each color means that a group of pixels (facet) is displaced over the respective number of nanometers. When studying the displacements in the X direction, the displacement is to the right (red) or to the left (blue). When studying displacements in the Y direction, the displacement happens up or down. As the method is not based on diffraction, it can be applied to almost any solid state material, including amorphous layers, thin coatings, and polymers. In addition, owing to the small size of the slit, it may also provide local information. Several authors have previously used SEM image correlation to measure stresses on the top of a coating by relaxation displacement measurement after FIB slit milling (Kang et al., 2003; Sabaté et al., 2007; Winiarski et al., 2010). Different relaxation geometries have been proposed (Korsunsky et al., 2010; Song et al., 2012; Krottenthaler et al., 2013). The observed displacements are often in the sub-pixel size, but they can be accurately determined by DIC. However, the shifts due to instabilities of the SEM could be in the same range as the displacements caused by the stress release. Typically, problems appear during the analysis of magnetic materials or because of the presence of stray magnetic fields
(Pawley, 1985, 1987). To quantify displacements in the range of nanometers, the precision of measurements at reduced length scales at high magnifications is critical. Therefore, an evaluation of the SEM stability is crucial for this type of measurement. It is worth mentioning that the DIC algorithm provides a precision of about 1 × 10−5 under favorable conditions (imaging by high quality digital optical cameras) (Shen & Paulino, 2011). Thermal noise of the SEM beam scanning system is listed as the main reason for the presence of “artificial” displacements observed between two consecutive SEM scans under the same conditions analyzed by digital speckle correlation (Wang et al., 2006). The images obtained from the SEM were not fully repeatable. A confidence interval around the average “artificial” displacement assuming a normal distribution N(µ, σ) is proposed to characterize the size of noise introduced by SEM imaging. Sub-pixel resolution is according to a study by Sabaté et al. (2006), a principal requirement for achieving appropriate resolution for strain measurements. The advantage of this quantity lies in its direct comparison with the sub-pixel resolution of the DIC algorithm (0.01) (Nelson et al., 2006). In Sabaté’s paper, the precision of the displacement is characterized by relating the pixel size in X and Y direction Nx,y and sub-pixel precision k: δux;y ¼ Nx;y k:
(1)
A New Methodology to Analyze Instabilities in SEM
The study also shows that sub-pixel accuracy generally decreases with increasing SEM magnification, resulting in a breaking of unlimited downscaling capability of the method, in the case of constant k. It was demonstrated that SEM images taken at a magnification 40k and pixel dimension of 2.8 nm result in a standard deviation on the level of 0.1 pixel, giving the accuracy of every measured point of the displacement field about 0.3 nm. In general, different origins of the drift are mentioned, e.g., drift in electron beam positioning during scanning, sample stage drift, reposition error after stage tilting for ion milling, and object surface charging. Lagattu et al. (2006) studied the stability of SEM imaging for DIC calculation of strain during in situ SEM tensile testing. The same approach with a correlation of two successive images on the same area without any deformation was used to study this stability. A wide longitudinal band parallel to the SEM line scanning direction was detected with erratic transverse strain of − 5.2 × 10−3. A spatial resolution of 1 µm was reported in this work. However, very high image resolution (2,400 × 2,000 pixels) was used with an unknown type of SEM and imaging conditions. Sutton et al. (2007) studied more systematically the imaging instability of three SEM systems, over a wide range of magnifications from 200 to 10k. Their qualitative study shows that for each of these microscopes an image shift occurred at random positions during the SEM imaging, demonstrating that image errors are a generic feature of this process. These shifts are often organized in multiple vertical and/or horizontal bands for both horizontal and vertical displacements. An image integration procedure was suggested as a method for reduction of SEM image shifts induced by SEM imaging instability. A displacement accuracy of 0.02 pixels (1 nm at magnification of 10 k) could be achieved. Winiarski et al. (2012) used this approach in their submicron-scale depth profiling study of residual stress in an amorphous material by incremental FIB slotting. Uncertainty in strain on a level of 3.7 × 10−4 was reported in a study using a resolution of 1,024 × 884 pixels, image integration over eight scans, and overall dwell time of 24 µs. An integration of 128 frames with extremely small (50 ns) dwell time was done in a residual stress analysis of thin coatings (Sebastiani et al., 2011). A better accuracy in the fast electron beam scanning direction (horizontal) was also reported in a study of residual stresses at micrometer scales (Korsunsky et al., 2010), where decreasing the scanning dwell time down to 1 µs is mentioned as an important factor to achieve acceptable reliability of digital image acquisition. The aim of this work is to introduce an appropriate statistical method to characterize the randomness and intensity of instabilities observed during SEM operation. Moreover, the stability of three different field emission gun SEMs (Philips XL30, Tescan Lyra, FEI Helios 650) that represent three subsequent generations of SEMs are evaluated. This work provides a protocol to validate imaging conditions using SEM for measurements of stress release and for any type of study based on a combination of SEM imaging and DIC.
MATERIALS
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Mechanism of SEM Image Acquisition: Introduction of Imaging Parameters A concise description of the imaging process and the parameters involved is appropriate. The volume affected by incident electrons is called the “interaction volume.” From the signals emitted during this interaction volume, the secondary electron (SE) emission is of particular interest in our work. Because small variations of topography will modify the intensity of the SEs, the information obtained with the SE detector is mainly correlated to the topography of the specimen. For optimum scanning, different parameters can be used depending on the specimen character or the quality of the desired image. Some of these parameters are depicted in Figure 2, which shows the schematics of image formation in an SEM. Each pixel in the SEM image corresponds to each position of the electron beam on the sample. The distances between the spots in horizontal and vertical directions are the same, as well as the size of the pixels in both of these directions. The ratio between the image pixel size and the distance between two spots on the sample defines the magnification of the image. Currently, the field of view is preferred to provide information about the magnification. Nevertheless, there are other options that influence the final acquisition of an image. For instance, an additional delay time could be required before starting the line scan in order to synchronize the scanning process with the frequency of the power line. This option is called synchronization and it can be switched on or off depending on the microscope and the dwell time (line synchronization). When an image is obtained after the first scan (i.e., single scan), it is formed by just one frame. New generation SEMs offer the possibility of collecting images by increasing the number of frames (number of scans), where the final image is formed by an integration of signal intensities at each pixel collected in individual frames. This option is called integration. In addition, the latest generation of SEMs can execute the option of synchronization between frames.
Figure 2. Schematic of the formation of an image in a scanning electron microscope.
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Assuming that W is the width of the image and H the height of the image in pixels, the total time (ttotal) required to collect an SEM image can be estimated as: ttotal ¼ ½td W H + tlbs ðH - 1Þ NF + tFbs ðNF - 1Þ;
(2)
where td is the dwell time, tlbs the time required for return and synchronization at the beginning of each line, NF the number of integrated frames, and finally tFbs the time for moving the beam from the last image pixel to the first one plus time for the frame synchronization. Often the dwell time of integrated scans tdi is given as the total time that beam spent for one pixel: tdi ¼ NF td :
(3)
Typical values used in above equations are: H, W ~ 1,000 pixels, td ~ 50 µs, tlbs ~ 0.5 to 4 ms without and 11−20 ms with synchronization at the beginning of each line. It could be deduced that a typical time to collect an SEM image with resolution of 106 pixels requires 50 − 60 s.
Experimental Details The stability of SEM images is evaluated using DIC by measuring the local displacement between two images taken at the same place under the same imaging conditions, with a certain delay time. In an ideal situation, the local displacement between these two images would be nil, and therefore values separating from 0 are caused owing to instabilities during the measurement. Thus, the study starts with the acquisition of a first image of the area to be analyzed. Afterwards, the sample holder is moved away and returned back, and then a second image of the same area is collected. A time delay of 2−3 min between consecutive images was used. In some cases, more than two images were acquired to study longer-term stability. It is worth mentioning that instability patterns are not necessarily repeatable in multiple image collection (Sutton et al., 2007; Mansilla et al., 2013). This procedure was applied at different imaging conditions in order to study the influence on the stability of the microscope images. DIC analysis of the images was carried out with Aramis 5.3 DIC software (GOM mbH, 2004) using a facet size of Table 1. Condition P1 P2 P3 P4 P5 P6 P7 P8 P9 a
21 × 21 pixels or 43 × 43 pixels, with a step between the center of neighbor facets of 11 or 21 pixels, respectively. The facet size was chosen considering the contrast of each image and to avoid discontinuities in the DIC calculations. Images from each microscope were evaluated using the same facet size and with a constant spacing between them. The DIC calculation provides the vector of displacement between two tested images for the center of each facet i: Δi ¼ ðΔix ; Δiy Þ:
(4)
DIC software also possesses a rigid motion correction that is able to eliminate the sample holder motion between collection of two images before and after the movement in such a way that the average displacement is close to 0, i.e.: 1X i Δ ~ 0; (5) N i where N is the number of all facets analyzed. As DIC is an image-based method, high contrast on the surface is required in order to get optimum results. Different surface decoration techniques depend on the studied surface area and the homogeneity of the decoration (pattern) (Winiarski et al., 2012). Deposition of yttria-stabilized zirconia (YSZ) nanoparticles is a good method because it can be applied rapidly on large surface areas (Sabaté et al., 2007). Therefore, YSZ nanoparticles were deposited on the surface from a 40% aqueous ethanol suspension (~30 mg/cm3) and dried at room temperature before the measurements. An ultrasonic bath was used for 30 min to break up the large YSZ particle agglomerates in the suspension before deposition.
Equipment and Parameters Under Study In order to study the influence of imaging conditions on stability during SEM operation, different parameters were varied during the acquisition of images in three field emission SEMs: XL30 ESEM (Philips, Netherlands), Lyra (Tescan, Czech Republic), and Helios 650 (FEI, Netherlands). Table 1 shows the different imaging parameters studied for the Philips XL30 (conditions labeled with P). In this study,
Imaging Conditions Studied For Philips ESEM XL30. Beam Energy (kV)
Spot Size (Microscope Units)a
WD (mm)
Resolution (Pixels)
Pixel Size (nm)
Dwell Time (μs)
10 10 10 10 10 10 10 5 3
5 5 5 5 5 5 3 5 5
10 10 10 10 10 5 10 10 10
1,296 × 968 1,296 × 968 1,296 × 968 1,936 × 1,452 1,296 × 968 1,296 × 968 1,296 × 968 1,296 × 968 1,296 × 968
230.0 23.3 11.65 23.3 23.3 23.3 23.3 23.3 23.3
41 41 41 28 62 41 41 41 41
Spot size corresponds to a beam current range of 1 pA–25 nA for microscope units from 1 to 6. Typically, spot size 5 matches a beam current of 2 nA. WD, working distance. Imaging condition set P2 is considered as a reference, and the modified parameters in the other condition sets with respect to P2 are highlighted in bold.
A New Methodology to Analyze Instabilities in SEM
the parameters evaluated are: electron beam energy, spot size, working distance, image resolution, dwell time, and pixel size. It is worth mentioning that this microscope works in single scan regime. Imaging condition set P2 is considered as a reference, and the modified parameters in the other condition sets with respect to P2 are highlighted in bold. As this microscope is the oldest one in the study, an inferior level of imaging stability is expected. Table 2 summarizes the different imaging parameters used for the Tescan Lyra (conditions labeled with L). Here, the typical parameters (electron beam energy, spot size, working distance, resolution, and field of view) were kept constant. In this case, the selected parameters under study were the dwell time and the number of frames (i.e., the effect of integration), in order to get a lower level of instabilities. We have also studied the effect of the synchronization per line. An advantage with respect to the Philips XL30 is that this option can be disconnected. All images were acquired at an electron beam energy of 10 kV, fixed spot size, 8.984 mm working distance, and resolution of 768 × 768 pixels, with a field of view of 21.6 µm, resulting in a pixel size of 28.12 nm. Table 3 presents the different imaging conditions studied for the Helios 650 (conditions labeled with F). At this point, all images were acquired at constant electron beam energy, spot size, and working distance. The conditions studied were image resolution, dwell time, number of frames, synchronization per line, and synchronization per frame. Table 2.
Imaging Conditions Studied for Tescan Lyra.
Dwell Condition Time (μs) L1 L2 L3 L4 L5 L6 L7
48.6 5.4 1.8 0.6 16.2 5.4 1.8
Number of Frames Synchronization Integration 1 10 30 100 1 3 10
Off Off Off Off On On On
Off On On On Off On On
All images were acquired at 10 kV, constant beam current of 1 nA, 8.984 mm of working distance, and resolution 768 × 768 pixels with a pixel size of 28.12 nm.
Table 3. Condition F1 F2 F3 F4 F5 F6 F7
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DISCUSSION
Description of the Statistical Method Performed to Analyze the Imaging Instability Introduced During SEM Operation Figure 3 shows eight representative images of the different types of displacements owing to instabilities that can be observed by the DIC technique under different imaging conditions. In these images, a black and white SEM image is overlaid by a color image that characterizes local displacements [in X (horizontal) or Y (vertical) direction] with the corresponding scale. Two of them (Figs. 3a, 3b) show a random displacement distribution; whereas a certain degree of order is present in the others (i.e., they show different types of nonrandom instabilities). Three different criteria were applied to evaluate and quantify the imaging instability of the three SEM columns. The first criterion evaluates the overall degree of instability introduced during the measurement (i.e., the “intensity” of instability). The second and third identify if order is present and characterize its direction if it exists. Thus, the second is designed to find patterns in rows and columns, as expected from the way an SEM image is formed (see Fig. 2). In the third, any type of ordered distribution is identified. In the following subsections, we will describe the statistical parameters used to distinguish among all situations demonstrated in Figure 3. Criterion 1: Standard Deviation of the Displacements The general instability of the SEM images can be expressed as a value of standard deviation (SDDIC) of displacements of the centers of all facets between subsequently recorded images, calculated for both X (horizontal) and Y (vertical) directions by DIC (SDDIC and SDDIC x y , respectively): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X i 2 SDDIC (6a) ¼ Δx ; x N i SDDIC y
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X i 2 ¼ Δy : N i
(6b)
It is worth mentioning that the average displacement of the DIC images is not a valid measurement of the imaging instability, and just indicates the net drift of the whole image. In contrast, SDDIC can be interpreted as the “intensity of
Imaging Conditions Studied for FEI Helios 650. Resolution (Pixels)
Pixel Size (nm)
Dwell Time (μs)
Number of Frames
Mains
Drift
768 × 512 768 × 512 768 × 512 768 × 512 768 × 512 1,024 × 884 1,024 × 884
38.80 38.80 38.80 38.80 38.80 29.00 29.00
50 50 3 3 12 12 50
1 1 16 16 4 4 1
Off On On On On On Off
Off Off Off On On On Off
All images were acquired at 30 kV, with a beam current of 0.80 nA and 4 mm of working distance.
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Figure 3. Examples of different patterns observed in the images of displacements after digital image correlation. Random images (a, b), periodic features in vertical direction (c, d), periodic features in horizontal direction (e, f), periodic features in both directions (g), ordered in diagonal direction (h). Together with the label of each image (see Tables 1–3), the direction and range of displacement are indicated: (a) F4 horizontal (6 nm); (b) F6 horizontal (16 nm); (c) P8 horizontal (16 nm); (d) P3 horizontal (10 nm); (e) F7 horizontal (18 nm); (f) P3 vertical (18 nm); (g) P2 vertical (6 nm); (h) F1 horizontal (24 nm).
imaging instability,” and it can be used to discriminate between good or bad imaging conditions. The values of SDDIC for these images are summarized in Table 4. Moreover, the relative SDDIC, calculated after normalization of SDDIC with the image size, is also included. This parameter allows a better comparison between different microscopes and pixel sizes. In most cases, this parameter has been found to be around 10−5. Images included in Figures 3a and 3g show smaller relative SDDIC ( 1, a smaller correlation in columns than in rows exists. ∙ If R ~ 1, the meaning is not that decisive. Table 4 summarizes the values of R for the images included in Figure 3. It is shown that both images without ordering (Figs. 3a, 3b) have values of R close to unity, as expected. In contrast, images with order in vertical and horizontal directions (Figs. 3c–3f) show values of R clearly smaller or bigger than 1. However, the cases depicted in Figures 3g and 3h present values of R close to 1, but they show a certain order. In Figure 3g, a double patterning (in rows and columns at the same time) is observed. In Figure 3h, a diagonal ordering is detected. Thus, for values of R ~ 1 the criterion fails to provide a unique interpretation about the type of distribution of the imaging instabilities. Therefore, a new parameter is needed. Criterion 3: Self-Correlation (SC) of Displacement Images To evaluate the presence of ordered patterns in any direction, we calculate the SC image of the displacement images obtained by DIC. An SC image is defined by Orfanidis (1996) as: X Gð k 1 ; k 2 Þ ¼ f ðx; yÞf ðx + k1 ; y + k2 Þ; (9) x;y
where f (x, y) is the displacement matrix. This equation convolutes the image and the same image shifted over a distance k1 and k2 in the x and y axis, with respect to the center of the image. The result is a new image G (k1, k2), which is a measure of how different the two images are (original versus shifted). The more similar the image and the shifted image are, the higher the value of the SC is. In fact, the SC has a maximum for a displacement vector (k1, k2) = (0, 0), i.e., comparison of two identical images without relative displacement. Considering an image with size of n × m points, an SC image with (2n − 1) × (2m − 1) points is obtained, as a consequence of the displacement of the shifted image over the original.
The periodicity in the original image is highlighted as a periodic pattern in the SC image (Mansilla et al., 2013). To evaluate the SC image, the SC parameter (g) is calculated for each point (k1, k2) in the SC image. The SC parameter for an exact shifting during the comparison of these two images (original and shifted image matrixes) is defined by Orfanidis (1996) as: P aij bij i;j
g ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2P 2; aij bij i;j
(10)
i;j
where aij and bij are the values of the displacements for the overlapping region between the two image matrixes (original and shifted, respectively). This parameter makes it possible to distinguish between positive and negative correlation, or the absence of it. By definition, the g parameter is normalized between +1 and −1, and its meaning bears an easy interpretation. Thus:
∙ If g ~ 1, a positive correlation exists, ∙ If g ~ − 1, a negative correlation (anti-correlation) exists, ∙ If g ~ 0, an absence of correlation exists. Figure 4 shows the SC images calculated from displacement images depicted in Figure 3. It can be seen that the periodicity from the original image is clearly revealed in the SC images. Thus, Figures 4a and 4b show (with an exception of a sharp black point in their centers) a homogenous gray color (g ~ 0), indicating their random nature. In contrast, in Figures 4c and 4d vertical ordering is highlighted, similar to Figures 4e and 4f, where horizontal ordering is observed. Finally, Figure 4g reproduces the double periodicity in rows and columns from Figure 3g, and Figure 4h shows a diagonal patterning, in agreement with what was observed in Figure 3h. It is worth mentioning that SC images distinguish among cases with R ~ 1 (i.e., Figs. 3a, 3b versus Figs. 3g, 3h). Nevertheless, the SC images help to distinguish between two
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Figure 5. Histograms of the self-correlation images included in Figure 4. Random images (a, b), ordered in vertical direction (c, d), ordered in horizontal direction (e, f), ordered in both directions (g), ordered in diagonal direction (h). The x and y axes and the bin size have been kept constant in all cases to facilitate comparison between them.
types of ordered situations, which are depicted in the top and bottom rows in Figure 4 (i.e., Figs. 4c, 4e, 4g versus Figs. 4d, 4f, 4h). Thus, images in the bottom row show a unique black band (vertical, horizontal, and diagonal) surrounded by two white regions. This is a consequence of the gradient of displacements observed in the corresponding DIC images in Figure 3. In contrast, each SC image in the top row shows several black and white bands (in vertical, horizontal, or both directions). This is a consequence of the correlation of the displacements of the corresponding DIC images in Figure 3 in columns and rows, by alternating the sign of displacement from one band to the next. Thus, the origin of these DIC images cannot be attributed to an effect of bad recovery of the stage position, and it can only be explained by artificial displacements caused by the electron beam while scanning (cf. Fig. 2). In these cases, the vertical and horizontal bands are associated with short- and long-term imaging instabilities in time, respectively. Regarding the DIC images in the bottom row of Figure 3 (those showing a gradient of displacement), the most likely reason for the observed patterns is a bad recovery of the stage position, although an explanation based on scanning effects cannot be totally discarded.
Further information from the SC images can be extracted by studying their respective intensity histograms, which are plotted in Figure 5. It can be seen that SC images calculated from DIC images with a random displacement distribution show a narrow histogram centered around 0 (Figs. 5a, 5b). In the other cases, much wider distributions are observed. Cases depicted in Figures 5d and 5f are particularly extreme, as most of the points are located in the regions of maximum correlation and anti-correlation (i.e., g values around 1 or −1). To quantify the SC images, the standard deviation (SDSC) and the average (AvSC) of these histograms is done for each SC image obtained from a DIC image. The values of these parameters for all images shown in Figure 4 are included in Table 4. Thus, two additional parameters are used to distinguish between a good and a bad imaging condition. Figure 6 depicts a plot where SDSC is plotted against AvSC. Each point in this plot represents one SC image obtained from a X or Y displacement field observed at particular imaging conditions for all three microscopes under study. This plot represents a condensed map, where the characteristics of each SC image can be interpreted at the same time. It can be seen that most of the points lay in a
A New Methodology to Analyze Instabilities in SEM
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Figure 6. Plot of SDSC versus AvSC from the intensity histograms of the self-correlation images. Each point in this plot represents an analysis of all X or Y displacement distribution at conditions specified in Tables 1–3. Two different groups are indicated by dashed lines. Representative examples of the self-correlated images and corresponding profiles belonging to each group are included on the sides.
unique region whose limits are indicated by a dashed box. This region is characterized by a linear relation between SDSC and AvSC, being AvSC negative. Few points are out of this zone (indicated by a dashed ellipse) and show higher AvSC than the points with similar values of SDSC (i.e., these points are displaced to the right of the linear trend). To explain the reason for these two regions, selected SC images of samples belonging to each group are included on the right and left sides of the map. Moreover, profiles from these SC images are also depicted, whose directions are indicated by a red line in the corresponding SC image. It is noteworthy that these profiles do not correspond to any particular line, but all the possible vertical or horizontal profiles from the image are plotted together in the same plot. The difference is that both profiles from the SC images belonging to the ellipse region show a wavy aspect, finishing in both sides with zones with positive correlations, i.e., darker colors (shape of “w” in the top case and “multiple w” in the bottom). In contrast, the profiles from images belonging to the linear region show the opposite behavior, i.e., they finish on both sides with regions with negative correlation coefficients i.e. lighter colors (shape of “ ∧ ” in the top case and a combination of “w” and “ ∧ ” in the bottom). Thus, the average values depend on the “wavelength” of the “wave” of the profile of image under study. Nevertheless, for practical applications, both SDSC and AvSC should be small or close to 0, respectively, in order to consider the displacements negligible and random. Finally, it is noted that the SC images need to be calculated from the DIC images after subtraction of the average displacement, i.e., the net drift of the whole image has to be 0; otherwise the values of SDSC and AvSC are affected; the AvSC separates from 0, and the SDSC decreases.
diagram summarizing the whole procedure is displayed in Figure 7, where subsequent decisions depending on the values of the four parameters defined before (SDSC, AvSC, R, and SDDIC or relative SDDIC) have to be made. To do that, acceptable ranges for these parameters have been defined after analyses of many sets of images recorded with different microscopes and considering the acceptance of instability in case of residual stress measurements (see Table 5). Thus, the region of acceptance for SDSC and AvSC is included in Figure 6 as a green box (dashed line), which is located around the origin as can be expected. The use of the flow diagram in Figure 7 is illustrated with the DIC images enclosed in Figure 3, whose statistical parameters are summarized in Table 4. Thus, the first step is evaluation of the parameters from the SC images. These parameters are very restrictive, and only two of the eight images from our example are accepted (these are the images showing random distributions). To identify the type of ordering in the rest of the images (images with nonrandom distribution), the remaining six images can be analyzed by using the R parameter. Then, they are divided into three groups: vertical, horizontal, and those with a R value close to 1, which are those with a similar degree of ordering in horizontal and vertical directions, or in a different direction than these. The random images identified by the SC criterion show values of R that are close to 1 and are in the acceptable range. Nevertheless, they can be further separated by analysis of the SDDIC. Thus, one of the images shows a value higher than the threshold, whereas the other shows a value that is below. Therefore, just one image condition is selected at the end, without any type of patterning and the lowest amount of random imaging instability.
Combined Criterion: Algorithm for Image Instability Evaluation After analysis of all the images, a complete criterion for examination of the different DIC images is described. A flow
Application of the Method In this section, the method described above is applied to the microscopes and conditions indicated previously.
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Figure 7. Flow diagram for stability classification of images. The images depicted in Figure 3 are used as an example of the application of the method (see also Tables 4 and 5). The best condition is highlighted with a green square.
Philips ESEM XL30 The statistical parameters obtained for the measurement conditions described in Table 1 are listed in Table 6. None of the conditions show SDSC values within the range of acceptance, which indicates a certain degree of order present in all cases. In fact, the majority of the statistical parameters are out of the limits defined in Table 5. Therefore, we can conclude that this microscope is an unstable instrument and not appropriate for the tasks defined in Figure 1. The influence of pixel size can be observed, with P2 being the best condition in the group P1–P4, in agreement with a study by Mansilla et al. (2013). However, in the rest of the conditions, finding a correlation between imaging conditions and statistical
Table 5. Ranges of Acceptance for the Different Statistical Parameters in Case of Stress Measurement. Parameter Limits
Relative SDDIC
R
SDSC
AvSC
Bottom Top
0.0 5 × 10−5
0.9 1.1
0.0 0.2
− 0.025 0.025
parameters is not possible, probably because of the great influence of errors in the re-positioning of the stage (see examples in Figs. 3d, 3f, 3h). For this microscope, we have found examples of all of the nonrandom behavior included in Figure 3. For those that can be attributed only to effects of the electron beam (i.e., showing patterns like those in Figs. 3c, 3e, 3g), an additional analysis was carried out to find the reason for these results. Thus, horizontal profiles were taken and further analyzed by Fourier transform. A consistent peak located at a frequency of ∼150 Hz was found, which is three times the frequency of the power input. This indicates that such bands are related to the synchronization of the beam with the power input. Tescan Lyra Statistical parameters obtained for the measurement conditions described in Table 2 are summarized in Table 7. This microscope is more stable than the previous one, and therefore more statistical parameters are found within the ranges of acceptance. Figure 8 shows the influence of the number of integrated frames (conditions L1–L4) in the four statistical parameters under study. SDDIC is shown in nanometers because, for this microscope, the field of view
A New Methodology to Analyze Instabilities in SEM Table 6.
Statistical Parameters Obtained for Philips ESEM XL30. Image X
Condition
SDSC
AvSC
R
P1 P2 P3 P4 P5 P6 P7 P8 P9
0.730 0.338 0.714 0.351 0.348 0.281 0.396 0.405 0.237
− 0.222 − 0.098 − 0.235 0.032 − 0.108 − 0.113 − 0.159 − 0.007 − 0.060
0.178 0.990 0.178 1.596 1.206 1.263 0.675 0.593 1.257
Image Y
SDDIC (nm) Relative SDDIC (×105) SDSC 67.504 1.394 7.298 2.113 1.311 1.720 1.847 2.923 1.126
22.6 4.6 48.3 4.7 4.3 5.7 6.1 9.7 3.7
was equal for all the conditions analyzed. In general, images of the displacements in the X direction (Fig. 8a) show less instability than the corresponding images for displacements in the Y direction (Fig. 8b). In fact, two of the experimental conditions (L2 and L3) fulfill all of the criteria in the X displacements, but not in Y. It is worth mentioning that L4 in X is also close to the good ranges, but fails owing to a value of AvSC slightly out of range. This is one of the few examples that fulfills the SDSC criterion, but fails in AvSC. Therefore, although L2 and L3 are the best conditions tested for this microscope, they are not perfectly stable. Between them, L3 (30 integration frames) would probably be the best, as the parameters in the Y image are better than those for L2 (10 integration frames). In general, the influence of the number of integration frames is very similar for all of the parameters, and tends to randomize and minimize the imaging instabilities. This outcome is in good agreement with the qualitative results found by Sutton et al. (2007). However, it looks like too many frames (see the case of 100 frames in X) leads to slight worsening of the parameters under study. When synchronization is on (L5 − L7, see Table 2), the improvement after using more frames is again observed (see Table 7), although the parameters are worse than in the previous cases. FEI Helios 650 The statistical parameters obtained for the measurement conditions described in Table 3 are summarized in Table 8. This is clearly the microscope with the most stable imaging
Table 7.
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0.532 0.263 0.705 0.477 0.704 0.495 0.689 0.663 0.570
AvSC
R
− 0.153 − 0.087 − 0.217 − 0.217 − 0.196 − 0.187 − 0.228 − 0.230 − 0.253
0.776 1.179 5.349 1.650 5.096 1.673 4.058 2.771 3.712
SDDIC (nm) Relative SDDIC (×105) 11.674 0.984 7.348 2.088 5.018 2.401 4.889 6.287 2.831
5.2 4.4 65.2 6.2 22.2 10.6 21.7 27.9 12.6
for DIC. Three conditions (F3, F4, and F5) fulfill all criteria, in both the X and Y directions. These are the best results obtained for all three microscopes, where all values are depicted in the cloud around the point (0, 0.1) in Figure 6. Among them, the best condition would probably be F4, as it is random like the others, but it shows the lowest values of relative SDDIC (i.e., lowest intensity of imaging instability). In this microscope, the importance of using the integration option for imaging instability reduction is again observed (F3 and F4 versus F1 and F2). Condition F5 is still good, but the reduction in pixel size (F6) worsens the parameters. Finally, when the integration is deactivated (F7), all of the parameters again become out of range. Figure 6 provides a solid base for a wide discussion concerning SEM imaging stability for DIC purposes. A general conclusion is that the stability strongly depends on imaging conditions for all three microscopes. Although it is almost impossible to achieve very stable conditions for the Philips XL30 SEM, stability of the Tescan Lyra and FEI Helios 650 SEMs covers a wide range of our characterization parameters. Nevertheless, at some imaging conditions stability is also poor. In general, the stability of imaging in the X direction is never worse than stability in the Y direction. Therefore, in applications where only measurements in one direction are required, it is suggested to select X as the measurement direction. Another general rule to increase imaging stability is to decrease time for image collection. In addition,
Statistical Parameters Obtained for Tescan Lyra. Image X
Condition
SDSC
AvSC
R
L1 L2 L3 L4 L5 L6 L7
0.301 0.168 0.164 0.182 0.308 0.201 0.229
− 0.030 − 0.012 − 0.023 − 0.048 − 0.138 − 0.014 0.003
1.682 1.003 1.004 1.062 1.224 1.102 1.045
Image Y
SDDIC (nm) Relative SDDIC (×105) SDSC 1.201 0.775 0.681 0.716 1.398 1.297 1.166
5.5 3.6 3.1 3.3 6.5 6.0 5.4
0.534 0.316 0.242 0.239 0.649 0.276 0.328
AvSC
R
− 0.179 − 0.150 − 0.104 − 0.087 − 0.218 − 0.102 − 0.153
2.214 1.194 1.124 1.110 2.190 1.131 1.261
SDDIC (nm) Relative SDDIC (×105) 2.111 0.723 0.635 0.635 2.826 1.183 1.103
9.8 3.3 2.9 2.9 13.1 5.5 5.1
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Figure 8. Variation of the proposed statistical parameters with the number of integrated frames for the Tescan Lyra for displacements in X (a) and Y directions (b). The dashed horizontal lines represent the acceptance limits for each parameter defined in Table 5.
instabilities can be reduced by introducing an integration regime, in which the time for collection of one frame is decreased 10−100 times, keeping the same overall dwell time. The increase in image resolution always results in an increase in time for image collection and thus leads to a decrease in imaging stability. Therefore, very high SEM image resolutions (exceeding ∼106 pixels) are not recommended for DIC applications. Collection of SEM images with electron beam synchronization at the beginning of each line with power net is also not suggested, owing to frequently observed vertical features in displacement images, originating from external interference. On the other hand, horizontal bands observed in displacement images occur because of long-term instabilities (~5 to 10 s). Collection of the SEM images in an integration regime effectively suppresses the influence of both of these effects. Usually it collects one frame in a time faster than 5 s, and in many microscopes it also automatically disables the synchronization option.
Table 8.
CONCLUSIONS The paper presents a quantitative analysis of SEM imaging instabilities by DIC. Three different approaches and four parameters were used to characterize the presence of nonrandom instabilities and their intensity. A flow diagram designed to decide which conditions are best can be implemented as a computer algorithm, avoiding the use of human eye. Our approach discriminates between good and bad conditions and also allows distinguishing between good and better. Moreover, the origin of the problems (bad reproducibility of the stage movement or electron beam scanning) can be inferred when good stability is not obtained. This method has been applied for three microscopes and different operating conditions. Newer generation microscopes show better results (FEI Helios 650 performs better than the Tescan Lyra, which performs better than the Philips ESEM XL30). In general, the use of an integration option led to better stability, and the use of a synchronization option is not recommended for this purpose.
Statistical Parameters Obtained for FEI Helios 650. Image X
Condition
SDSC
AvSC
R
F1 F2 F3 F4 F5 F6 F7
0.481 0.693 0.094 0.110 0.095 0.092 0.431
− 0.145 − 0.324 0.000 − 0.018 0.001 − 0.014 − 0.059
0.924 6.426 0.978 1.024 0.998 1.038 2.717
Image Y
SDDIC (nm) Relative SDDIC (×105) SDSC 4.691 3.221 0.661 0.485 0.822 2.121 1.714
15.7 10.8 2.2 1.6 2.8 7.1 5.8
0.293 0.602 0.096 0.110 0.107 0.170 0.437
AvSC
R
− 0.133 − 0.176 − 0.007 − 0.024 0.002 − 0.085 − 0.177
0.937 0.707 1.003 1.005 1.025 1.111 2.482
SDDIC (nm) Relative SDDIC (×105) 2.951 2.404 0.709 0.654 0.780 2.239 2.030
14.9 12.1 3.6 3.3 3.9 8.7 7.9
A New Methodology to Analyze Instabilities in SEM
ACKNOWLEDGMENTS This research was carried out under project number M61.7.10415 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl). Dr. H. Mulders from FEI, The Netherlands and Dr. T. Hrnčíř from Tescan, Czech Republic are acknowledged for their discussion, data, and technical support.
REFERENCES ARAMIS V5.3.0 USER MANUAL, GOM mbH, D-38106 Braunschweig, Germany, Rev A, 20.8.2004. BOUZAKIS, K.-D., SKORDARIS, G., HADJIYIANNIS, S., ASIMAKOPOULOS, A., MIRISIDIS, J., MICHAILIDIS, N., ERKENS, G., CREMER, R., KLOCKE, F. & KLEINJANS, M. (2004). A nanoindentation based determination of internal stress alterations in PVD films and their cemented carbides substrates induced by recoating procedures and their effect on the cutting performance. Thin Solid Films 447–448, 264–271. KAHN-JETTER, Z.L. & CHU, T.C. (1990). Three-dimensional displacement measurements using digital image correlation and photogrammic analysis. Exp Mech 30, 10–16. KANG, K.J., YAO, N., HE, M.Y. & EVANS, A. G. (2003). A method for in situ measurement of the residual stress in thin films by using the focused ion beam. Thin Solid Films 443, 71–77. KORSUNSKY, A.M., SEBASTIANI, M. & BEMPORAD, E. (2010). Residual stress evaluation at the micrometer scale: Analysis of thin coatings by FIB milling and digital image correlation. Surf Coat Technol 205, 2393–2403. KROTTENTHALER, M., SCHMID, C., SCHAUFLER, J., DURST, K. & GÖKEN, M. (2013). A simple method for residual stress measurements in thin films by means of focused ion beam milling and digital image correlation. Surf Coat Technol 215, 247–252. LAGATTU, F., BRIDIER, F., VILLECHAISE, P. & BRILLAUD, J. (2006). Inplane strain measurements on a microscopic scale by coupling digital image correlation and an in situ SEM technique. Mater Charact 56, 10–18. MANSILLA, C., OCELIK, O. & DE HOSSON, J.Th.M. (2013). Statistical analysis of SEM image noise. In: 11th International Conference on Surface Effects and Contact Mechanics: Computational Methods and Experiments, J.Th.M. De Hosson & C.A. Brebbia (Eds), pp. 13–24. vol. 78, 2013. WIT Transactions on Engineering Sciences. Siena, Italy: WIT Press. NELSON, D.V. (2010). Residual stress determination by hole drilling combined with optical methods. Expl Mech 50, 145–158. NELSON, D.V., MAKINO, A. & SCHMIDT, T. (2006). Residual stress determination using hole drilling and 3D image correlation. Expl Mech 46, 31–38. ORFANIDIS, S.J. (1996). Optimum Signal Processing. An Introduction, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall. PAWLEY, J. (1985). Strategy for locating and eliminating sources of mains frequency stray magnetic-fileds. Scanning 7, 43–46.
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PAWLEY, J.B. (1987). Use of pseudo-stereo techniques to detect magnetic stray field in the SEM. Scanning 9, 134–136. PRUMMER, R. & PFEIFFERVOLLMAR, H. (1983). A method for X-ray stress-analysis of thermochemically treated materials. Adv X-Ray Anal 26, 225–231. SABATÉ, N., VOGEL, D., GOLLHARDT, A., KELLER, J., CANÉ, C., GRÀCIA, I., MORANTE, J.R. & MICHEL, B. (2007). Residual stress measurement on a MEMS structure with high-spatial resolution. J Microelectromech Syst 16, 365–372. SABATÉ, N., VOGEL, D., GOLLHARDT, A., MARCOS, J., GRÀCIA, I., CANÉ, C. & MICHEL, B. (2006). Digital image correlation of nanoscale deformation fields for local stress measurement in thin films. Nanotechnology 17, 5264–5270. SEBASTIANI, M., EBERL, C., BEMPORAD, E. & PHARR, G.M. (2011). Depth-resolved residual stress analysis of thin coatings by a new FIB-DIC method. Mat Sci Eng A 528, 7901–7908. SHEN, B. & PAULINO, G.H. (2011). Direct extraction of cohesive fracture properties from digital image correlation: A hybrid inverse technique. Exp Mech 53, 143–163. SHULL, A.L. & SPAEPEN, F. (1996). Measurements of stress during vapor deposition of copper and silver thin films and multilayers. J Appl Phys 80, 6243–6256. SONG, X., YEAP, K.B., ZHU, J., BELNOUE, J., SEBASTIANI, M., BEMPORAD, E., ZENG, K. & KORSUNSKY, A.M. (2012). Residual stress measurement in thin films at sub-micron scale using focused ion beam milling and imaging. Thin Solid Films 520, 2073–2076. SUTTON, M.A., LI, N., JOY, D.C., REYNOLDS, A.P. & LI, X. (2007). Scanning electron microscopy for quantitative small and large deformation measurements part I: SEM imaging at magnifications from 200 to 10,000. Exp Mech 47, 775–787. SUTTON, M.A., ORTEU, J.J. & SCHREIER, H.W. (2009). Image Correlation for Shape, Motion and Deformation Measurements—Basic Concepts, Theory and Applications. New York, NY: Springer. TADA, H., PARIS, P. & IRWIN, G. (2000). The Stress Analysis of Cracks Handbook. 3rd edition, ASME Press, New York. WANG, H., XIE, H., JU, Y. & DUAN, Q. (2006). Error analysis of digital speckle correlation method under scanning electron microscope. Exp Tech 30, 42–45. WINIARSKI, B., GHOLINIA, A., TIAN, J., YOKOYAMA, Y., LIAW, P.K. & WITHERS, P.J. (2012). Submicron-scale depth profiling of residual stress in amorphous materials by incremental focused ion beam slotting. Acta Mater 60, 2337–2349. WINIARSKI, B., LANGFORD, R.M., TIAN, J., YOKOYAMA, Y., LIAW, P.K. & WITHERS, P.J. (2010). Mapping residual stress distributions at the micron scale in amorphous materials. Metall Mater Trans A 41, 1743–1751. WINIARSKI, B., SCHAJER, G.S. & WITHERS, P.J. (2012). Surface decoration for improving the accuracy of displacement measurements by digital image correlation in SEM. Exp Mech 52, 793–804. WITHERS, P.J. & BHADESHIA, H.K.D.H. (2001). Residual stress part 2—Nature and origins. Mater Sci Technol 17, 366–375.
© MICROSCOPY SOCIETY OF AMERICA 2014
A New Methodology to Analyze Instabilities in SEM Imaging Catalina Mansilla,* Václav Ocelík, and Jeff T. M. De Hosson Department of Applied Physics, Materials innovation institute M2i, University of Groningen, Nijenborgh 4, Groningen, 9474 AG, The Netherlands
Abstract: This paper presents a statistical method to analyze instabilities that can be introduced during imaging in scanning electron microscopy (SEM). The method is based on the correlation of digital images and it can be used at different length scales. It consists of the evaluation of three different approaches with four parameters in total. The methodology is exemplified with a specific case of internal stress measurements where ion milling and SEM imaging are combined with digital image correlation. It is concluded that before these measurements it is important to test the SEM column to ensure the minimization and randomization of the imaging instabilities. The method has been applied onto three different field emission gun SEMs (Philips XL30, Tescan Lyra, FEI Helios 650) that represent three successive generations of SEMs. Important to note that the imaging instability can be quantified and its source can be identified. Key words: scanning electron microscopy, digital image correlation, self-correlation image, residual stress, focused ion beam
I NTRODUCTION The development of new tools for in situ measurements in scanning electron microscope (SEM), e.g. of displacements and residual stress, demands a high degree of precision for a reliable subsequent digital analysis. In the case of residual stress, local measurements can be performed in a dual beam microscope [combined SEM and focused ion beam (FIB)] combining image milling and digital image correlation (DIC). The residual stress state can be derived from the local changes in the image (Kahn-Jetter & Chu, 1990; Sutton et al., 2009). Residual stresses can be defined as stresses that remain after the external loading (external forces, heat gradients, etc.) has been removed (Withers & Bhadeshia, 2001). They are present in almost all materials, and arise when inelastic processes occur, like plastic deformation or thermal treatments. These stresses influence the lifetime of products in service and as a consequence, precise knowledge and control of residual stresses are of high practical value. The traditional methods available for measuring internal stresses are grouped into destructive and nondestructive. The most prominent nondestructive method is X-ray diffraction (Prummer & Pfeiffervollmar, 1983). However, it requires a crystalline lattice using the distance between lattice plane as strain gauge. Common destructive methods are curvature measurement (Shull & Spaepen, 1996), nanoindentation (Bouzakis et al., 2004), and hole drilling (Nelson, 2010). Most of them determine the mean stress in large volumes or areas.
Received June 19, 2014; accepted September 10, 2014 *Corresponding author. [email protected]; [email protected]; j.t.m.de.hosson @rug.nl
The so-called slit milling method combines the ion milling and imaging capabilities provided by a dual beam microscope with DIC software to measure the residual stress (Kahn-Jetter & Chu, 1990; Sutton et al., 2009). It is based on a relaxation method, in which the residual stresses released in the vicinity of a slit are inferred from the local relaxation displacements measured by DIC. A scheme of the procedure followed in the measurement is shown in Figure 1. The procedure starts with the acquisition of the first SEM image of the area to be analyzed. After capturing the first image, a slit is milled. It is worth mentioning that generally the electron and the ion columns inside a dual beam system have different orientations, which implies that the sample under investigation has to be repositioned for milling. Afterwards, the sample is tilted backwards and a second image of the same area is taken. From the comparison of these two SEM images recorded by DIC before and after stress release the displacements field is obtained. These experimentally observed displacements are compared with the values of displacements obtained by the analytical solution for an isotropic elastic material, and the magnitude of the residual stress is obtained from the slope of such fitting (Tada et al., 2000; Winiarski et al., 2010). DIC is an image-based method that consists of dividing the digital images in smaller sub-regions, called “facets.” Each facet must contain enough features that unambiguously correlate with the same sub-region in the next image. Then, these facets are compared by matching and when the highest correlation is found, the displacement of the center of these sub-regions is obtained. The two-dimensional cross correlation allows separating the horizontal X from the vertical Y components of the in-plane displacement vector generated
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Figure 1. Steps involved in the measurement of residual stress using a combination of scanning electron microscopy, focused ion beam machining, and digital image correlation.
by the stress release. For instance, Figure 1 shows the displacements corresponding to the X component, which are perpendicular to the plane of the slit. It is worth mentioning that DIC displacements are presented as color images. The scale bar of the images is in the range of tens of nanometers. Each color means that a group of pixels (facet) is displaced over the respective number of nanometers. When studying the displacements in the X direction, the displacement is to the right (red) or to the left (blue). When studying displacements in the Y direction, the displacement happens up or down. As the method is not based on diffraction, it can be applied to almost any solid state material, including amorphous layers, thin coatings, and polymers. In addition, owing to the small size of the slit, it may also provide local information. Several authors have previously used SEM image correlation to measure stresses on the top of a coating by relaxation displacement measurement after FIB slit milling (Kang et al., 2003; Sabaté et al., 2007; Winiarski et al., 2010). Different relaxation geometries have been proposed (Korsunsky et al., 2010; Song et al., 2012; Krottenthaler et al., 2013). The observed displacements are often in the sub-pixel size, but they can be accurately determined by DIC. However, the shifts due to instabilities of the SEM could be in the same range as the displacements caused by the stress release. Typically, problems appear during the analysis of magnetic materials or because of the presence of stray magnetic fields
(Pawley, 1985, 1987). To quantify displacements in the range of nanometers, the precision of measurements at reduced length scales at high magnifications is critical. Therefore, an evaluation of the SEM stability is crucial for this type of measurement. It is worth mentioning that the DIC algorithm provides a precision of about 1 × 10−5 under favorable conditions (imaging by high quality digital optical cameras) (Shen & Paulino, 2011). Thermal noise of the SEM beam scanning system is listed as the main reason for the presence of “artificial” displacements observed between two consecutive SEM scans under the same conditions analyzed by digital speckle correlation (Wang et al., 2006). The images obtained from the SEM were not fully repeatable. A confidence interval around the average “artificial” displacement assuming a normal distribution N(µ, σ) is proposed to characterize the size of noise introduced by SEM imaging. Sub-pixel resolution is according to a study by Sabaté et al. (2006), a principal requirement for achieving appropriate resolution for strain measurements. The advantage of this quantity lies in its direct comparison with the sub-pixel resolution of the DIC algorithm (0.01) (Nelson et al., 2006). In Sabaté’s paper, the precision of the displacement is characterized by relating the pixel size in X and Y direction Nx,y and sub-pixel precision k: δux;y ¼ Nx;y k:
(1)
A New Methodology to Analyze Instabilities in SEM
The study also shows that sub-pixel accuracy generally decreases with increasing SEM magnification, resulting in a breaking of unlimited downscaling capability of the method, in the case of constant k. It was demonstrated that SEM images taken at a magnification 40k and pixel dimension of 2.8 nm result in a standard deviation on the level of 0.1 pixel, giving the accuracy of every measured point of the displacement field about 0.3 nm. In general, different origins of the drift are mentioned, e.g., drift in electron beam positioning during scanning, sample stage drift, reposition error after stage tilting for ion milling, and object surface charging. Lagattu et al. (2006) studied the stability of SEM imaging for DIC calculation of strain during in situ SEM tensile testing. The same approach with a correlation of two successive images on the same area without any deformation was used to study this stability. A wide longitudinal band parallel to the SEM line scanning direction was detected with erratic transverse strain of − 5.2 × 10−3. A spatial resolution of 1 µm was reported in this work. However, very high image resolution (2,400 × 2,000 pixels) was used with an unknown type of SEM and imaging conditions. Sutton et al. (2007) studied more systematically the imaging instability of three SEM systems, over a wide range of magnifications from 200 to 10k. Their qualitative study shows that for each of these microscopes an image shift occurred at random positions during the SEM imaging, demonstrating that image errors are a generic feature of this process. These shifts are often organized in multiple vertical and/or horizontal bands for both horizontal and vertical displacements. An image integration procedure was suggested as a method for reduction of SEM image shifts induced by SEM imaging instability. A displacement accuracy of 0.02 pixels (1 nm at magnification of 10 k) could be achieved. Winiarski et al. (2012) used this approach in their submicron-scale depth profiling study of residual stress in an amorphous material by incremental FIB slotting. Uncertainty in strain on a level of 3.7 × 10−4 was reported in a study using a resolution of 1,024 × 884 pixels, image integration over eight scans, and overall dwell time of 24 µs. An integration of 128 frames with extremely small (50 ns) dwell time was done in a residual stress analysis of thin coatings (Sebastiani et al., 2011). A better accuracy in the fast electron beam scanning direction (horizontal) was also reported in a study of residual stresses at micrometer scales (Korsunsky et al., 2010), where decreasing the scanning dwell time down to 1 µs is mentioned as an important factor to achieve acceptable reliability of digital image acquisition. The aim of this work is to introduce an appropriate statistical method to characterize the randomness and intensity of instabilities observed during SEM operation. Moreover, the stability of three different field emission gun SEMs (Philips XL30, Tescan Lyra, FEI Helios 650) that represent three subsequent generations of SEMs are evaluated. This work provides a protocol to validate imaging conditions using SEM for measurements of stress release and for any type of study based on a combination of SEM imaging and DIC.
MATERIALS
AND
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METHODS
Mechanism of SEM Image Acquisition: Introduction of Imaging Parameters A concise description of the imaging process and the parameters involved is appropriate. The volume affected by incident electrons is called the “interaction volume.” From the signals emitted during this interaction volume, the secondary electron (SE) emission is of particular interest in our work. Because small variations of topography will modify the intensity of the SEs, the information obtained with the SE detector is mainly correlated to the topography of the specimen. For optimum scanning, different parameters can be used depending on the specimen character or the quality of the desired image. Some of these parameters are depicted in Figure 2, which shows the schematics of image formation in an SEM. Each pixel in the SEM image corresponds to each position of the electron beam on the sample. The distances between the spots in horizontal and vertical directions are the same, as well as the size of the pixels in both of these directions. The ratio between the image pixel size and the distance between two spots on the sample defines the magnification of the image. Currently, the field of view is preferred to provide information about the magnification. Nevertheless, there are other options that influence the final acquisition of an image. For instance, an additional delay time could be required before starting the line scan in order to synchronize the scanning process with the frequency of the power line. This option is called synchronization and it can be switched on or off depending on the microscope and the dwell time (line synchronization). When an image is obtained after the first scan (i.e., single scan), it is formed by just one frame. New generation SEMs offer the possibility of collecting images by increasing the number of frames (number of scans), where the final image is formed by an integration of signal intensities at each pixel collected in individual frames. This option is called integration. In addition, the latest generation of SEMs can execute the option of synchronization between frames.
Figure 2. Schematic of the formation of an image in a scanning electron microscope.
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Assuming that W is the width of the image and H the height of the image in pixels, the total time (ttotal) required to collect an SEM image can be estimated as: ttotal ¼ ½td W H + tlbs ðH - 1Þ NF + tFbs ðNF - 1Þ;
(2)
where td is the dwell time, tlbs the time required for return and synchronization at the beginning of each line, NF the number of integrated frames, and finally tFbs the time for moving the beam from the last image pixel to the first one plus time for the frame synchronization. Often the dwell time of integrated scans tdi is given as the total time that beam spent for one pixel: tdi ¼ NF td :
(3)
Typical values used in above equations are: H, W ~ 1,000 pixels, td ~ 50 µs, tlbs ~ 0.5 to 4 ms without and 11−20 ms with synchronization at the beginning of each line. It could be deduced that a typical time to collect an SEM image with resolution of 106 pixels requires 50 − 60 s.
Experimental Details The stability of SEM images is evaluated using DIC by measuring the local displacement between two images taken at the same place under the same imaging conditions, with a certain delay time. In an ideal situation, the local displacement between these two images would be nil, and therefore values separating from 0 are caused owing to instabilities during the measurement. Thus, the study starts with the acquisition of a first image of the area to be analyzed. Afterwards, the sample holder is moved away and returned back, and then a second image of the same area is collected. A time delay of 2−3 min between consecutive images was used. In some cases, more than two images were acquired to study longer-term stability. It is worth mentioning that instability patterns are not necessarily repeatable in multiple image collection (Sutton et al., 2007; Mansilla et al., 2013). This procedure was applied at different imaging conditions in order to study the influence on the stability of the microscope images. DIC analysis of the images was carried out with Aramis 5.3 DIC software (GOM mbH, 2004) using a facet size of Table 1. Condition P1 P2 P3 P4 P5 P6 P7 P8 P9 a
21 × 21 pixels or 43 × 43 pixels, with a step between the center of neighbor facets of 11 or 21 pixels, respectively. The facet size was chosen considering the contrast of each image and to avoid discontinuities in the DIC calculations. Images from each microscope were evaluated using the same facet size and with a constant spacing between them. The DIC calculation provides the vector of displacement between two tested images for the center of each facet i: Δi ¼ ðΔix ; Δiy Þ:
(4)
DIC software also possesses a rigid motion correction that is able to eliminate the sample holder motion between collection of two images before and after the movement in such a way that the average displacement is close to 0, i.e.: 1X i Δ ~ 0; (5) N i where N is the number of all facets analyzed. As DIC is an image-based method, high contrast on the surface is required in order to get optimum results. Different surface decoration techniques depend on the studied surface area and the homogeneity of the decoration (pattern) (Winiarski et al., 2012). Deposition of yttria-stabilized zirconia (YSZ) nanoparticles is a good method because it can be applied rapidly on large surface areas (Sabaté et al., 2007). Therefore, YSZ nanoparticles were deposited on the surface from a 40% aqueous ethanol suspension (~30 mg/cm3) and dried at room temperature before the measurements. An ultrasonic bath was used for 30 min to break up the large YSZ particle agglomerates in the suspension before deposition.
Equipment and Parameters Under Study In order to study the influence of imaging conditions on stability during SEM operation, different parameters were varied during the acquisition of images in three field emission SEMs: XL30 ESEM (Philips, Netherlands), Lyra (Tescan, Czech Republic), and Helios 650 (FEI, Netherlands). Table 1 shows the different imaging parameters studied for the Philips XL30 (conditions labeled with P). In this study,
Imaging Conditions Studied For Philips ESEM XL30. Beam Energy (kV)
Spot Size (Microscope Units)a
WD (mm)
Resolution (Pixels)
Pixel Size (nm)
Dwell Time (μs)
10 10 10 10 10 10 10 5 3
5 5 5 5 5 5 3 5 5
10 10 10 10 10 5 10 10 10
1,296 × 968 1,296 × 968 1,296 × 968 1,936 × 1,452 1,296 × 968 1,296 × 968 1,296 × 968 1,296 × 968 1,296 × 968
230.0 23.3 11.65 23.3 23.3 23.3 23.3 23.3 23.3
41 41 41 28 62 41 41 41 41
Spot size corresponds to a beam current range of 1 pA–25 nA for microscope units from 1 to 6. Typically, spot size 5 matches a beam current of 2 nA. WD, working distance. Imaging condition set P2 is considered as a reference, and the modified parameters in the other condition sets with respect to P2 are highlighted in bold.
A New Methodology to Analyze Instabilities in SEM
the parameters evaluated are: electron beam energy, spot size, working distance, image resolution, dwell time, and pixel size. It is worth mentioning that this microscope works in single scan regime. Imaging condition set P2 is considered as a reference, and the modified parameters in the other condition sets with respect to P2 are highlighted in bold. As this microscope is the oldest one in the study, an inferior level of imaging stability is expected. Table 2 summarizes the different imaging parameters used for the Tescan Lyra (conditions labeled with L). Here, the typical parameters (electron beam energy, spot size, working distance, resolution, and field of view) were kept constant. In this case, the selected parameters under study were the dwell time and the number of frames (i.e., the effect of integration), in order to get a lower level of instabilities. We have also studied the effect of the synchronization per line. An advantage with respect to the Philips XL30 is that this option can be disconnected. All images were acquired at an electron beam energy of 10 kV, fixed spot size, 8.984 mm working distance, and resolution of 768 × 768 pixels, with a field of view of 21.6 µm, resulting in a pixel size of 28.12 nm. Table 3 presents the different imaging conditions studied for the Helios 650 (conditions labeled with F). At this point, all images were acquired at constant electron beam energy, spot size, and working distance. The conditions studied were image resolution, dwell time, number of frames, synchronization per line, and synchronization per frame. Table 2.
Imaging Conditions Studied for Tescan Lyra.
Dwell Condition Time (μs) L1 L2 L3 L4 L5 L6 L7
48.6 5.4 1.8 0.6 16.2 5.4 1.8
Number of Frames Synchronization Integration 1 10 30 100 1 3 10
Off Off Off Off On On On
Off On On On Off On On
All images were acquired at 10 kV, constant beam current of 1 nA, 8.984 mm of working distance, and resolution 768 × 768 pixels with a pixel size of 28.12 nm.
Table 3. Condition F1 F2 F3 F4 F5 F6 F7
RESULTS
AND
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DISCUSSION
Description of the Statistical Method Performed to Analyze the Imaging Instability Introduced During SEM Operation Figure 3 shows eight representative images of the different types of displacements owing to instabilities that can be observed by the DIC technique under different imaging conditions. In these images, a black and white SEM image is overlaid by a color image that characterizes local displacements [in X (horizontal) or Y (vertical) direction] with the corresponding scale. Two of them (Figs. 3a, 3b) show a random displacement distribution; whereas a certain degree of order is present in the others (i.e., they show different types of nonrandom instabilities). Three different criteria were applied to evaluate and quantify the imaging instability of the three SEM columns. The first criterion evaluates the overall degree of instability introduced during the measurement (i.e., the “intensity” of instability). The second and third identify if order is present and characterize its direction if it exists. Thus, the second is designed to find patterns in rows and columns, as expected from the way an SEM image is formed (see Fig. 2). In the third, any type of ordered distribution is identified. In the following subsections, we will describe the statistical parameters used to distinguish among all situations demonstrated in Figure 3. Criterion 1: Standard Deviation of the Displacements The general instability of the SEM images can be expressed as a value of standard deviation (SDDIC) of displacements of the centers of all facets between subsequently recorded images, calculated for both X (horizontal) and Y (vertical) directions by DIC (SDDIC and SDDIC x y , respectively): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X i 2 SDDIC (6a) ¼ Δx ; x N i SDDIC y
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X i 2 ¼ Δy : N i
(6b)
It is worth mentioning that the average displacement of the DIC images is not a valid measurement of the imaging instability, and just indicates the net drift of the whole image. In contrast, SDDIC can be interpreted as the “intensity of
Imaging Conditions Studied for FEI Helios 650. Resolution (Pixels)
Pixel Size (nm)
Dwell Time (μs)
Number of Frames
Mains
Drift
768 × 512 768 × 512 768 × 512 768 × 512 768 × 512 1,024 × 884 1,024 × 884
38.80 38.80 38.80 38.80 38.80 29.00 29.00
50 50 3 3 12 12 50
1 1 16 16 4 4 1
Off On On On On On Off
Off Off Off On On On Off
All images were acquired at 30 kV, with a beam current of 0.80 nA and 4 mm of working distance.
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Figure 3. Examples of different patterns observed in the images of displacements after digital image correlation. Random images (a, b), periodic features in vertical direction (c, d), periodic features in horizontal direction (e, f), periodic features in both directions (g), ordered in diagonal direction (h). Together with the label of each image (see Tables 1–3), the direction and range of displacement are indicated: (a) F4 horizontal (6 nm); (b) F6 horizontal (16 nm); (c) P8 horizontal (16 nm); (d) P3 horizontal (10 nm); (e) F7 horizontal (18 nm); (f) P3 vertical (18 nm); (g) P2 vertical (6 nm); (h) F1 horizontal (24 nm).
imaging instability,” and it can be used to discriminate between good or bad imaging conditions. The values of SDDIC for these images are summarized in Table 4. Moreover, the relative SDDIC, calculated after normalization of SDDIC with the image size, is also included. This parameter allows a better comparison between different microscopes and pixel sizes. In most cases, this parameter has been found to be around 10−5. Images included in Figures 3a and 3g show smaller relative SDDIC ( 1, a smaller correlation in columns than in rows exists. ∙ If R ~ 1, the meaning is not that decisive. Table 4 summarizes the values of R for the images included in Figure 3. It is shown that both images without ordering (Figs. 3a, 3b) have values of R close to unity, as expected. In contrast, images with order in vertical and horizontal directions (Figs. 3c–3f) show values of R clearly smaller or bigger than 1. However, the cases depicted in Figures 3g and 3h present values of R close to 1, but they show a certain order. In Figure 3g, a double patterning (in rows and columns at the same time) is observed. In Figure 3h, a diagonal ordering is detected. Thus, for values of R ~ 1 the criterion fails to provide a unique interpretation about the type of distribution of the imaging instabilities. Therefore, a new parameter is needed. Criterion 3: Self-Correlation (SC) of Displacement Images To evaluate the presence of ordered patterns in any direction, we calculate the SC image of the displacement images obtained by DIC. An SC image is defined by Orfanidis (1996) as: X Gð k 1 ; k 2 Þ ¼ f ðx; yÞf ðx + k1 ; y + k2 Þ; (9) x;y
where f (x, y) is the displacement matrix. This equation convolutes the image and the same image shifted over a distance k1 and k2 in the x and y axis, with respect to the center of the image. The result is a new image G (k1, k2), which is a measure of how different the two images are (original versus shifted). The more similar the image and the shifted image are, the higher the value of the SC is. In fact, the SC has a maximum for a displacement vector (k1, k2) = (0, 0), i.e., comparison of two identical images without relative displacement. Considering an image with size of n × m points, an SC image with (2n − 1) × (2m − 1) points is obtained, as a consequence of the displacement of the shifted image over the original.
The periodicity in the original image is highlighted as a periodic pattern in the SC image (Mansilla et al., 2013). To evaluate the SC image, the SC parameter (g) is calculated for each point (k1, k2) in the SC image. The SC parameter for an exact shifting during the comparison of these two images (original and shifted image matrixes) is defined by Orfanidis (1996) as: P aij bij i;j
g ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2P 2; aij bij i;j
(10)
i;j
where aij and bij are the values of the displacements for the overlapping region between the two image matrixes (original and shifted, respectively). This parameter makes it possible to distinguish between positive and negative correlation, or the absence of it. By definition, the g parameter is normalized between +1 and −1, and its meaning bears an easy interpretation. Thus:
∙ If g ~ 1, a positive correlation exists, ∙ If g ~ − 1, a negative correlation (anti-correlation) exists, ∙ If g ~ 0, an absence of correlation exists. Figure 4 shows the SC images calculated from displacement images depicted in Figure 3. It can be seen that the periodicity from the original image is clearly revealed in the SC images. Thus, Figures 4a and 4b show (with an exception of a sharp black point in their centers) a homogenous gray color (g ~ 0), indicating their random nature. In contrast, in Figures 4c and 4d vertical ordering is highlighted, similar to Figures 4e and 4f, where horizontal ordering is observed. Finally, Figure 4g reproduces the double periodicity in rows and columns from Figure 3g, and Figure 4h shows a diagonal patterning, in agreement with what was observed in Figure 3h. It is worth mentioning that SC images distinguish among cases with R ~ 1 (i.e., Figs. 3a, 3b versus Figs. 3g, 3h). Nevertheless, the SC images help to distinguish between two
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Figure 5. Histograms of the self-correlation images included in Figure 4. Random images (a, b), ordered in vertical direction (c, d), ordered in horizontal direction (e, f), ordered in both directions (g), ordered in diagonal direction (h). The x and y axes and the bin size have been kept constant in all cases to facilitate comparison between them.
types of ordered situations, which are depicted in the top and bottom rows in Figure 4 (i.e., Figs. 4c, 4e, 4g versus Figs. 4d, 4f, 4h). Thus, images in the bottom row show a unique black band (vertical, horizontal, and diagonal) surrounded by two white regions. This is a consequence of the gradient of displacements observed in the corresponding DIC images in Figure 3. In contrast, each SC image in the top row shows several black and white bands (in vertical, horizontal, or both directions). This is a consequence of the correlation of the displacements of the corresponding DIC images in Figure 3 in columns and rows, by alternating the sign of displacement from one band to the next. Thus, the origin of these DIC images cannot be attributed to an effect of bad recovery of the stage position, and it can only be explained by artificial displacements caused by the electron beam while scanning (cf. Fig. 2). In these cases, the vertical and horizontal bands are associated with short- and long-term imaging instabilities in time, respectively. Regarding the DIC images in the bottom row of Figure 3 (those showing a gradient of displacement), the most likely reason for the observed patterns is a bad recovery of the stage position, although an explanation based on scanning effects cannot be totally discarded.
Further information from the SC images can be extracted by studying their respective intensity histograms, which are plotted in Figure 5. It can be seen that SC images calculated from DIC images with a random displacement distribution show a narrow histogram centered around 0 (Figs. 5a, 5b). In the other cases, much wider distributions are observed. Cases depicted in Figures 5d and 5f are particularly extreme, as most of the points are located in the regions of maximum correlation and anti-correlation (i.e., g values around 1 or −1). To quantify the SC images, the standard deviation (SDSC) and the average (AvSC) of these histograms is done for each SC image obtained from a DIC image. The values of these parameters for all images shown in Figure 4 are included in Table 4. Thus, two additional parameters are used to distinguish between a good and a bad imaging condition. Figure 6 depicts a plot where SDSC is plotted against AvSC. Each point in this plot represents one SC image obtained from a X or Y displacement field observed at particular imaging conditions for all three microscopes under study. This plot represents a condensed map, where the characteristics of each SC image can be interpreted at the same time. It can be seen that most of the points lay in a
A New Methodology to Analyze Instabilities in SEM
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Figure 6. Plot of SDSC versus AvSC from the intensity histograms of the self-correlation images. Each point in this plot represents an analysis of all X or Y displacement distribution at conditions specified in Tables 1–3. Two different groups are indicated by dashed lines. Representative examples of the self-correlated images and corresponding profiles belonging to each group are included on the sides.
unique region whose limits are indicated by a dashed box. This region is characterized by a linear relation between SDSC and AvSC, being AvSC negative. Few points are out of this zone (indicated by a dashed ellipse) and show higher AvSC than the points with similar values of SDSC (i.e., these points are displaced to the right of the linear trend). To explain the reason for these two regions, selected SC images of samples belonging to each group are included on the right and left sides of the map. Moreover, profiles from these SC images are also depicted, whose directions are indicated by a red line in the corresponding SC image. It is noteworthy that these profiles do not correspond to any particular line, but all the possible vertical or horizontal profiles from the image are plotted together in the same plot. The difference is that both profiles from the SC images belonging to the ellipse region show a wavy aspect, finishing in both sides with zones with positive correlations, i.e., darker colors (shape of “w” in the top case and “multiple w” in the bottom). In contrast, the profiles from images belonging to the linear region show the opposite behavior, i.e., they finish on both sides with regions with negative correlation coefficients i.e. lighter colors (shape of “ ∧ ” in the top case and a combination of “w” and “ ∧ ” in the bottom). Thus, the average values depend on the “wavelength” of the “wave” of the profile of image under study. Nevertheless, for practical applications, both SDSC and AvSC should be small or close to 0, respectively, in order to consider the displacements negligible and random. Finally, it is noted that the SC images need to be calculated from the DIC images after subtraction of the average displacement, i.e., the net drift of the whole image has to be 0; otherwise the values of SDSC and AvSC are affected; the AvSC separates from 0, and the SDSC decreases.
diagram summarizing the whole procedure is displayed in Figure 7, where subsequent decisions depending on the values of the four parameters defined before (SDSC, AvSC, R, and SDDIC or relative SDDIC) have to be made. To do that, acceptable ranges for these parameters have been defined after analyses of many sets of images recorded with different microscopes and considering the acceptance of instability in case of residual stress measurements (see Table 5). Thus, the region of acceptance for SDSC and AvSC is included in Figure 6 as a green box (dashed line), which is located around the origin as can be expected. The use of the flow diagram in Figure 7 is illustrated with the DIC images enclosed in Figure 3, whose statistical parameters are summarized in Table 4. Thus, the first step is evaluation of the parameters from the SC images. These parameters are very restrictive, and only two of the eight images from our example are accepted (these are the images showing random distributions). To identify the type of ordering in the rest of the images (images with nonrandom distribution), the remaining six images can be analyzed by using the R parameter. Then, they are divided into three groups: vertical, horizontal, and those with a R value close to 1, which are those with a similar degree of ordering in horizontal and vertical directions, or in a different direction than these. The random images identified by the SC criterion show values of R that are close to 1 and are in the acceptable range. Nevertheless, they can be further separated by analysis of the SDDIC. Thus, one of the images shows a value higher than the threshold, whereas the other shows a value that is below. Therefore, just one image condition is selected at the end, without any type of patterning and the lowest amount of random imaging instability.
Combined Criterion: Algorithm for Image Instability Evaluation After analysis of all the images, a complete criterion for examination of the different DIC images is described. A flow
Application of the Method In this section, the method described above is applied to the microscopes and conditions indicated previously.
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Figure 7. Flow diagram for stability classification of images. The images depicted in Figure 3 are used as an example of the application of the method (see also Tables 4 and 5). The best condition is highlighted with a green square.
Philips ESEM XL30 The statistical parameters obtained for the measurement conditions described in Table 1 are listed in Table 6. None of the conditions show SDSC values within the range of acceptance, which indicates a certain degree of order present in all cases. In fact, the majority of the statistical parameters are out of the limits defined in Table 5. Therefore, we can conclude that this microscope is an unstable instrument and not appropriate for the tasks defined in Figure 1. The influence of pixel size can be observed, with P2 being the best condition in the group P1–P4, in agreement with a study by Mansilla et al. (2013). However, in the rest of the conditions, finding a correlation between imaging conditions and statistical
Table 5. Ranges of Acceptance for the Different Statistical Parameters in Case of Stress Measurement. Parameter Limits
Relative SDDIC
R
SDSC
AvSC
Bottom Top
0.0 5 × 10−5
0.9 1.1
0.0 0.2
− 0.025 0.025
parameters is not possible, probably because of the great influence of errors in the re-positioning of the stage (see examples in Figs. 3d, 3f, 3h). For this microscope, we have found examples of all of the nonrandom behavior included in Figure 3. For those that can be attributed only to effects of the electron beam (i.e., showing patterns like those in Figs. 3c, 3e, 3g), an additional analysis was carried out to find the reason for these results. Thus, horizontal profiles were taken and further analyzed by Fourier transform. A consistent peak located at a frequency of ∼150 Hz was found, which is three times the frequency of the power input. This indicates that such bands are related to the synchronization of the beam with the power input. Tescan Lyra Statistical parameters obtained for the measurement conditions described in Table 2 are summarized in Table 7. This microscope is more stable than the previous one, and therefore more statistical parameters are found within the ranges of acceptance. Figure 8 shows the influence of the number of integrated frames (conditions L1–L4) in the four statistical parameters under study. SDDIC is shown in nanometers because, for this microscope, the field of view
A New Methodology to Analyze Instabilities in SEM Table 6.
Statistical Parameters Obtained for Philips ESEM XL30. Image X
Condition
SDSC
AvSC
R
P1 P2 P3 P4 P5 P6 P7 P8 P9
0.730 0.338 0.714 0.351 0.348 0.281 0.396 0.405 0.237
− 0.222 − 0.098 − 0.235 0.032 − 0.108 − 0.113 − 0.159 − 0.007 − 0.060
0.178 0.990 0.178 1.596 1.206 1.263 0.675 0.593 1.257
Image Y
SDDIC (nm) Relative SDDIC (×105) SDSC 67.504 1.394 7.298 2.113 1.311 1.720 1.847 2.923 1.126
22.6 4.6 48.3 4.7 4.3 5.7 6.1 9.7 3.7
was equal for all the conditions analyzed. In general, images of the displacements in the X direction (Fig. 8a) show less instability than the corresponding images for displacements in the Y direction (Fig. 8b). In fact, two of the experimental conditions (L2 and L3) fulfill all of the criteria in the X displacements, but not in Y. It is worth mentioning that L4 in X is also close to the good ranges, but fails owing to a value of AvSC slightly out of range. This is one of the few examples that fulfills the SDSC criterion, but fails in AvSC. Therefore, although L2 and L3 are the best conditions tested for this microscope, they are not perfectly stable. Between them, L3 (30 integration frames) would probably be the best, as the parameters in the Y image are better than those for L2 (10 integration frames). In general, the influence of the number of integration frames is very similar for all of the parameters, and tends to randomize and minimize the imaging instabilities. This outcome is in good agreement with the qualitative results found by Sutton et al. (2007). However, it looks like too many frames (see the case of 100 frames in X) leads to slight worsening of the parameters under study. When synchronization is on (L5 − L7, see Table 2), the improvement after using more frames is again observed (see Table 7), although the parameters are worse than in the previous cases. FEI Helios 650 The statistical parameters obtained for the measurement conditions described in Table 3 are summarized in Table 8. This is clearly the microscope with the most stable imaging
Table 7.
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0.532 0.263 0.705 0.477 0.704 0.495 0.689 0.663 0.570
AvSC
R
− 0.153 − 0.087 − 0.217 − 0.217 − 0.196 − 0.187 − 0.228 − 0.230 − 0.253
0.776 1.179 5.349 1.650 5.096 1.673 4.058 2.771 3.712
SDDIC (nm) Relative SDDIC (×105) 11.674 0.984 7.348 2.088 5.018 2.401 4.889 6.287 2.831
5.2 4.4 65.2 6.2 22.2 10.6 21.7 27.9 12.6
for DIC. Three conditions (F3, F4, and F5) fulfill all criteria, in both the X and Y directions. These are the best results obtained for all three microscopes, where all values are depicted in the cloud around the point (0, 0.1) in Figure 6. Among them, the best condition would probably be F4, as it is random like the others, but it shows the lowest values of relative SDDIC (i.e., lowest intensity of imaging instability). In this microscope, the importance of using the integration option for imaging instability reduction is again observed (F3 and F4 versus F1 and F2). Condition F5 is still good, but the reduction in pixel size (F6) worsens the parameters. Finally, when the integration is deactivated (F7), all of the parameters again become out of range. Figure 6 provides a solid base for a wide discussion concerning SEM imaging stability for DIC purposes. A general conclusion is that the stability strongly depends on imaging conditions for all three microscopes. Although it is almost impossible to achieve very stable conditions for the Philips XL30 SEM, stability of the Tescan Lyra and FEI Helios 650 SEMs covers a wide range of our characterization parameters. Nevertheless, at some imaging conditions stability is also poor. In general, the stability of imaging in the X direction is never worse than stability in the Y direction. Therefore, in applications where only measurements in one direction are required, it is suggested to select X as the measurement direction. Another general rule to increase imaging stability is to decrease time for image collection. In addition,
Statistical Parameters Obtained for Tescan Lyra. Image X
Condition
SDSC
AvSC
R
L1 L2 L3 L4 L5 L6 L7
0.301 0.168 0.164 0.182 0.308 0.201 0.229
− 0.030 − 0.012 − 0.023 − 0.048 − 0.138 − 0.014 0.003
1.682 1.003 1.004 1.062 1.224 1.102 1.045
Image Y
SDDIC (nm) Relative SDDIC (×105) SDSC 1.201 0.775 0.681 0.716 1.398 1.297 1.166
5.5 3.6 3.1 3.3 6.5 6.0 5.4
0.534 0.316 0.242 0.239 0.649 0.276 0.328
AvSC
R
− 0.179 − 0.150 − 0.104 − 0.087 − 0.218 − 0.102 − 0.153
2.214 1.194 1.124 1.110 2.190 1.131 1.261
SDDIC (nm) Relative SDDIC (×105) 2.111 0.723 0.635 0.635 2.826 1.183 1.103
9.8 3.3 2.9 2.9 13.1 5.5 5.1
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Figure 8. Variation of the proposed statistical parameters with the number of integrated frames for the Tescan Lyra for displacements in X (a) and Y directions (b). The dashed horizontal lines represent the acceptance limits for each parameter defined in Table 5.
instabilities can be reduced by introducing an integration regime, in which the time for collection of one frame is decreased 10−100 times, keeping the same overall dwell time. The increase in image resolution always results in an increase in time for image collection and thus leads to a decrease in imaging stability. Therefore, very high SEM image resolutions (exceeding ∼106 pixels) are not recommended for DIC applications. Collection of SEM images with electron beam synchronization at the beginning of each line with power net is also not suggested, owing to frequently observed vertical features in displacement images, originating from external interference. On the other hand, horizontal bands observed in displacement images occur because of long-term instabilities (~5 to 10 s). Collection of the SEM images in an integration regime effectively suppresses the influence of both of these effects. Usually it collects one frame in a time faster than 5 s, and in many microscopes it also automatically disables the synchronization option.
Table 8.
CONCLUSIONS The paper presents a quantitative analysis of SEM imaging instabilities by DIC. Three different approaches and four parameters were used to characterize the presence of nonrandom instabilities and their intensity. A flow diagram designed to decide which conditions are best can be implemented as a computer algorithm, avoiding the use of human eye. Our approach discriminates between good and bad conditions and also allows distinguishing between good and better. Moreover, the origin of the problems (bad reproducibility of the stage movement or electron beam scanning) can be inferred when good stability is not obtained. This method has been applied for three microscopes and different operating conditions. Newer generation microscopes show better results (FEI Helios 650 performs better than the Tescan Lyra, which performs better than the Philips ESEM XL30). In general, the use of an integration option led to better stability, and the use of a synchronization option is not recommended for this purpose.
Statistical Parameters Obtained for FEI Helios 650. Image X
Condition
SDSC
AvSC
R
F1 F2 F3 F4 F5 F6 F7
0.481 0.693 0.094 0.110 0.095 0.092 0.431
− 0.145 − 0.324 0.000 − 0.018 0.001 − 0.014 − 0.059
0.924 6.426 0.978 1.024 0.998 1.038 2.717
Image Y
SDDIC (nm) Relative SDDIC (×105) SDSC 4.691 3.221 0.661 0.485 0.822 2.121 1.714
15.7 10.8 2.2 1.6 2.8 7.1 5.8
0.293 0.602 0.096 0.110 0.107 0.170 0.437
AvSC
R
− 0.133 − 0.176 − 0.007 − 0.024 0.002 − 0.085 − 0.177
0.937 0.707 1.003 1.005 1.025 1.111 2.482
SDDIC (nm) Relative SDDIC (×105) 2.951 2.404 0.709 0.654 0.780 2.239 2.030
14.9 12.1 3.6 3.3 3.9 8.7 7.9
A New Methodology to Analyze Instabilities in SEM
ACKNOWLEDGMENTS This research was carried out under project number M61.7.10415 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl). Dr. H. Mulders from FEI, The Netherlands and Dr. T. Hrnčíř from Tescan, Czech Republic are acknowledged for their discussion, data, and technical support.
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