Scanning Electron Microscopy
Figure 5 : A four-quadrant overhead backscatter detector for an SEM. (a) Each detector pair represents one orthogonal direction (i.e., North-South pair and West-East pair). The four detectors produce four different images of the same object. (b) through (e) show a detail on a euro coin in images acquired from the N (b) and S (c) detectors and the W (d) and E (e) detectors. The local slopes at each pixel, z/y and z/x, can be calculated from the N-S image pair and the W-E image pair, respectively. These calculations are the fi rst step toward producing a height map.
distorted 3D mesh out of this topography model, (3) pasting the original leſt SEM image onto it, and (4) colorizing it with a brown false color from the map height and shading. Figure 4c shows a profi le through the 3D representation corresponding to a cross section of the 3D reconstruction. T is example demonstrates the ability of the method to accurately add a third dimension to a pair SEM stereo images, provided there is enough local texture [ 4 ]. T e Ra value determined by soſt ware here matched the known value for the calibration specimen (Ra = 3.00 µm). Four-quadrant BSE detectors . A simpler method for performing reconstruction to reveal the third dimension requires a segmented overhead BSE detector [ 5 , 6 ]. Most such detectors employ four separate sectors symmetrically arranged around a hole for the primary electron beam, but some systems use other arrangements. While MountainsMap SEM can manage various confi gurations, we will only discuss the four-quadrant case since it is the easiest to understand. A discussion of how this contrast is formed is given in [ 2 ]. A major advantage of this method is that it only requires taking one “shot” of the sample, since all four images are acquired simultaneously by the four detectors ( Figure 5 ). Each detector pair represents one
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orthogonal direction (that is, North-South pair and West-East pair). Figures 5 b and 5 c show images of a euro-coin detail that correspond to the North and South channels of a four-quadrant detector. Holes are diffi cult to distinguish from black inclusions on the original four images. Shape from shading . T e shape-from-shading method employs several mathematical steps. First, the slope in the direction of each pair of detectors is calculated (that is, North-South pair and West-East pair). A major advantage of using a pair of detectors symmetrically arranged over the specimen is that the diff erential signal obtained from the pair neutralizes refl ectance and allows the local slope to be calculated. If both signals decrease, we achieve a black dot. Conversely if one signal is high while the other is low, we will obtain a local slope. Each pair of detectors gives, for each pixel, the local slope of the surface z in the pair direction, for example, ∂z/∂x and ∂z/∂y (see Figure 5). T is results in two separate scalar fi elds (that is, two intermediate images of orthogonal derivatives or slopes). T en, the height map z(x,y) is processed by integration of these two local slopes ∂z/∂x and ∂z/∂y. Once the height map is obtained, the height value of each pixel is known, and creation of a 3D representation is just a question of applying 3D rendering algorithms. Relative heights on a surface may be calculated from the diff erences between the images of each detector pair. Figure 6 shows images resulting from the following steps. Image (a) is a height map obtained by the integration of slopes. T e height is false-color-coded using a lookup table. T e rainbow color scale applied here is traditionally used to express height on a physical map, where the lowest points are blue (the sea), the plains are green, the mountains are red, and the highest points are white (snow-capped peaks). Image (b) is the height map used to produce a 3D mesh. At this stage, topography is still shown alone in false color without using the original SEM image for the rendering. Image (c) shows the fi nal 3D rendering. T e original SEM image is now pasted onto the previous 3D form to render texture (note that the black inclusions are back, whereas the previous image just shows the pits). Having four diff erent channels allows a diff erent color to be associated with each image pair, resulting in a much clearer perception of surface features. Here purple has been allocated to one pair, and blue to the other, creating a lighting eff ect on the 3D shape (purple refl ections highlight the cliff at the leſt bottom corner). Image (d) shows the same image, but with yellow and red assigned to the two detector pairs. Of course, in this type of reconstruction, it is only possible to reconstruct the visible part of the sample (that facing the electron detector). “Cliff s” and overhangs are not taken into account. T is method can only be metrologically accurate if all the slopes of the object are visible. Note that unlike conven- tional stereo imaging ( Figure 4 ), it was not necessary to take two successive scans or to tilt the sample.
Can we get 3D shape from a single SEM image? It is commonly accepted that one image alone is not suffi cient for producing correct height ( Z axis) information. Putting the accuracy of height values aside, however, image reconstruction can provide a useful 3D eff ect. Under specifi c conditions, MountainsMap SEM algorithms can produce a credible 3D color model from a single SEM image. While the heights cannot be extracted because the Z axis is not calibrated, the 3D rendering is worth a look ( Figure 7 ). T e calculation of this rendering required several steps. First, the image in Figure 7a was subtracted
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