Depth resolution in on-axis TKD 1099
tion, according to the definition above, was determined experimentally in a straightforward way, with limited hypotheses. The process consisted of recording diffraction patterns in the area of the twin boundary and then analyzing patterns along a straight line crossing the twin (see Figs. 3, 4). The key principle is that, while the twin boundary moves closer to the top surface (i.e., the surface of incidence of the beam) and further from the bottom surface, the depth reso- lution becomes equal to the distance between the twin boundary and the back surface at the point where the pattern stops containing Kikuchi diffraction information associated to the top crystal. In order to determine the depth resolution, it only requires at that point to determine the corresponding in-depth position of the twin boundary. This determination can be done because a twin boundary forms a straight plane, and is thus predictable; all we need to know is the position of the intersection of the twin boundary with the back surface and the angle that the twin boundary forms with the surface. The angle that the twin boundary forms with the surface was determined in two ways: (1) in the beginning steps of the FIB preparation of the lamella, the angle is chosen (hence known, see Fig. 2). During the following steps of FIB preparation, until the final thinning and low-keV cleaning, special care was taken to ensure that this angle was maintained. (2) Alternatively, this angle was also calculated from the orientation of the two twinned crystals in the final lamella. Typical diffraction patterns of each crystal were recorded by on-axis TKD and indexed. Once their orientation was known, the angle could be determined because we know that the twin boundary is a (111) plane. With this secondmethod, the angle was found to be 9.2°. A difference of 1° between the
present study by the naked eye. By this definition, the depth resolution is also the minimal thickness of material at the bottom of the sample contributing alone to the Kikuchi dif- fraction pattern. This definition presents the depth resolu- tion as a finite length, although it results from a continuous absorption process as discussed in the next sections. The depth resolution only becomes a finite length when the limitations of the hardware and software are introduced. Thus, it can be expected that the depth resolution deter- mined experimentally will depend on the hardware used (S/N ratio, sensitivity, dynamic range), the acquisition parameters (integration time and image averaging in particular, and maybe even pattern resolution), and the software (ability to extract the signal from the noise with the dynamic background correction and detection threshold). The consequence is that a depth resolution value is not an intrinsic property. With this limitation in mind, this study mostly intends to produce depth resolution values that are relevant to the production of orientation maps with current technology (see On-Axis TKD Set-Up section for details on the experimental set-up). Most importantly, the results will allow us to draw general conclusions in terms of dependence with sample thickness and incident energy, i.e. independent on hardware, software, and acquisition parameters. With the twinned cubic Si bi-crystal, the depth resolu-
two values is reasonable and can very well be explained by the geometric tolerances of the systems. An intermediate value of 8.5° was selected and kept constant for all calcula- tions in the remainder of the study. The second unknown is the position of the intersection of the twin boundary with the back surface. This determination was done by analysis of the diffraction patterns. We determined this intersection as the point where the very first emerging diffraction spots associated to the bottom crystal were observed in diffraction patterns (point 2 in Fig. 4). We base this determination on the fact that very little material is required to produce diffraction spots (Germer, 1939) and propose that it should produce a very limited error. The thickness of the lamella at the exact location of
measurement of the depth resolution is also useful to know. This way, the dependence of the depth resolution with sample thickness can be studied. The determination of the total lamella thickness could be performed, but unlike for the determination of the depth resolution, the position of the intersection of the twin boundary with the top surface needs to be known. We also assumed that the very first appearance of diffraction spots, here associated to the top crystal, marked the position of this intersection (point 8 in Fig. 4). Finally, a difficult methodology question concerned the
evaluation of the disappearing of the Kikuchi diffraction associated to the top crystal. Quantitative analysis of the fading of the band contrast with a software was unsuccessful, both with the patterns and the Hough transform, because of the difficulty to isolate information (i.e., the bands specifi- cally associated to the top crystal), in particular when the contrast becomes low. The fading of a given Kikuchi band tends to blend with other intensity variations, like the one of nearby spots and more importantly with the generation of new nearby bands associated to the bottom crystal. Hence, it was done with the naked eye.What is gained here in terms of critical analysis of the patterns and ability to isolate infor- mation, is lost in terms of quantified threshold and reproducibility.
RESULTS AND DISCUSSION
Diffraction Pattern Evolution Along a Straight Line Crossing the Twin Boundary
Before we present the actual values of the depth resolution by on-axis TKD on cubic silicon and the dependence with incident energy and sample thickness, this subsection pre- sents the evolution of the diffraction pattern along a straight line scan crossing the twin boundary. This line scan is such that the in-depth position of the twin boundary under the incident beam varies with the lateral position of the beamon the surface, as displayed in Figure 4. The full sequence of diffraction patterns is presented, for an incident energy of 30 keV. Some features discussed below might not be well visible in the patterns displayed in Figure 4. However, even the tiniest and most subtle changes become very well visible to the naked eye when the patterns are scrolled inside a fixed
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