## 2 Preliminaries
### RBS/C Measurement Procedure  
During the RBS measurement, the backscattered ions were detected by a silicon detector with an energy resolution of 13 keV situated at a fixed position and at a scattering angle of 170\({}^{\circ}\)[8]. Insulation of the sample holder against the main body of the goniometer allows in-situ measurement of the actual ion beam current which measured 8-10 nA. Secondary electron emission was suppressed by positively biasing the sample holder to 280 V. The crystal sample was mounted on 4-axis goniometer (Figure 5), which enabled rotation around all three axes (see ARGUS and MATLAB notations in Table 1):  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Axis of Rotation** & **Notation in Argus** & **Notation in MATLAB** \\ \hline X-Rotation (tilt-horizontal) & tiltPos = X-Tilt & Tilt \\ Y-Rotation (azimuthal) & thetaPos = theta & Theta \\ Z-Rotation (incoming beam) & PhiPos = phi & Phi \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations.  
Figure 4: Stereographic projection of the (100)-oriented Si crystal.  
During the stepwise rotation of the goniometer around one of the axes, RBS energy spectra were recorded simultaneously. Then, after summing counts (yield) within an appropriately selected region of interest (ROI) of each measured RBS spectrum (as it is shown in Figure 13), we constructed the dependency of Yield\({}_{\text{ROI}}\) vs. the angle of tilting (e.g., Figures 14 and 15). In this way, the channeling spectrum was created. The channeling spectrum represents the dependency of Yield\({}_{\text{ROI}}\) on the angle of rotation, and the position of dips represent intersections with one of the crystal axes or planes.  
At the earliest, channeling dip measurements were typically carried out around the Z-axis (the direction of the incident ion beam), commonly used to align the target crystal. However, if channeling measurements are carried out along azimuthal and tilt angles, the scanning range can be significantly reduced. A more detailed procedure of crystal alignment for RBS/C measurement can be found, e.g., in [1].  
Our solution described below uses rotation around axis-X and axis-Y. It generated an angular distribution of the Yield\({}_{\text{ROI}}\) which is fitted, and positions of the minima of dips were determined. By connecting the minima of corresponding dips, the projections of crystal planes were generated (e.g., Figures 14 and 15). The intersection of planes represents the angular position which is an offset of the major crystal axis (Figure 16). After entering this offset to the goniometer control, the alignment of the crystal was done. The accuracy of the alignment can be enhanced by repeating this procedure.  
Such RBS/C measurement for crystal alignment represented typically about 160 angular displacements (step of 0.2\({}^{\circ}\)) of the goniometer, and the RBS spectra recorded with a dose of 0.2 \(\mu\)C, respectively. We call this the \"coarse\" channeling measurement.  
This was followed by the RBS/C angular measurement through a selected axis or plane, which we call the \"fine\" channeling measurement. In this case, the usual tilting increments were 0.05\({}^{\circ}\) or less at the dose of 0.5 \(\mu\)C. The goniometer was driven by stepping motors and the minimum step was 0.01\({}^{\circ}\). After normalization of the channeling Yield\({}_{\text{ROI}}\), the minimum value of the dip, denoted as \(\chi_{\text{min}}\), and the angular width, were the two main parameters of the channeling spectrum that are determined (e.g., Figure 17).  
The previous situation was such that the operator had to write down parameters for every measured step manually into ARGUS to control the measurements. The control system of the Tandetron allows the users to load a set of parameters from a batch file even for multiple experiments, but each single step and parameter had to be written manually. The control parameters were stored in an XML structure.