Simulation of Rutherford backscattering spectrometry from arbitrary atom structures

Rutherford backscattering spectrometry in a channeling direction (RBS/C) is a powerful tool for analysis of the fraction of atoms displaced from their lattice positions. However, it is in many cases not straightforward to analyze what is the actual defect structure underlying the RBS/C signal. To reveal insights of RBS/C signals from arbitrarily complex defective atomic structures, we develop here a method for simulating the RBS/C spectrum from a set of arbitrary read-in atom coordinates (obtained, e.g., from molecular dynamics simulations). We apply the developed method to simulate the RBS/C signals from Ni crystal structures containing randomly displaced atoms, Frenkel point defects, and extended defects, respectively. The RBS/C simulations show that, even for the same number of atoms in defects, the RBS/C signal is much stronger for the extended defects. Comparison with experimental results shows that the disorder profile obtained from RBS/C signals in ion-irradiated Ni is due to a small fraction of extended defects rather than a large number of individual random atoms.

Figure 1

The schematic diagram of the RBS/C simulation. The solid line shows the path of a real ion, while the dashed lines show the paths of virtual ions used to speed up the RBS data collections (see text).

Figure 2

Illustration of how a collision partner is found in rbsadec.

Figure 3

The depth profiles of 20-keV Si ions in c-Si with different incident angles simulated by the present rbsadec code and the mdrange code.

Figure 4

The depth profiles of He ions in amorphous silicon with different energies simulated by rbsadec and trim.

Figure 5

The atomic structures with (a) 0.3 at.% randomly displaced atoms from the $\langle 001\rangle$ view, (b) 0.3 at.% interstitials plus vacancies from the $\langle 001\rangle$ view, with the inset showing the close view of $\langle 100\rangle$ dumbbell, (c) 0.3 at.% interstitials forming extrinsic SF from the $\langle 111\rangle$ view, and (d) 0.3 at.% vacancies forming a stacking fault tetrahedron from the $\langle 111\rangle$ view.

Figure 6

Stacking sequence of (a) perfect fcc structure and (b) extrinsic stacking faults (before relaxation).

Figure 7

Simulated RBS/C spectra from the crystal structure, from the structure with randomly displaced atoms, from the structure with Frenkel point defects, from the structure with extended defects, and from an amorphous structure. For each kind of defect, 0.24 at.% defective atoms are uniformly distributed in the middle region which is indicated by the shadowed area.

Figure 8

Simulated RBS/C spectra from the crystal, the structure with randomly displaced atoms, and the structure with point defects. The signal is for 0.5 at.% RDAs or point defects uniformly distributed in middle region.

Figure 9

(a) The RBS/C spectra (red line) from the structure with 20 at.% randomly displaced atoms. (b) RBS/C spectra (red line) from the structure with 0.24 at.% extended defects. In both (a) and (b), the RBS/C yield ($Y$ axis) was normalized by the nonchanneling RBS yields; ${\chi }_R\left(z\right)$ (black line) denotes the fraction of dechanneled ions, and the blue line indicates the RBS/C signals from perfect crystalline structure.

Figure 10

(a) The comparison of the experimental (black, green, and cyan markers) and simulated (orange, red, blue, and purple lines) RBS/C spectra of Ni samples. The cyan (orange) and black (purple) show the spectra of pristine crystal and fully amorphous reference structures obtained by experiment (simulations). The green markers show the experimental result for a Ni sample irradiated by ${\mathrm{Mn}}^{+}$ ions ($E_0=1.5$ MeV, $\mathrm{\Phi }=6.4\times {10}^{13}{\mathrm{cm}}^{-2}$). The blue and red lines are the fitted RBS/C spectra from the structure with RDAs and the structure with extended defects, respectively. (b) The depth profile of defects. The blue line is the depth profile (left $y$ axis) of RDAs corresponding to the fitted RBS/C spectrum in (a), while the red line is the fitted depth profile (left $y$ axis) of extended defects multiplied by 50. The green dashed line denotes the depth profiles (right $y$ axis) of disorder extracted by the iterative procedure [5].

Figure 11

(a) A high-resolution high angle annular dark field (HAADF) STEM image of irradiated Ni. Reproduced from Ref. [25]. (b) $\langle 110\rangle$ view of a structure with 10 at.% RDAs. (c) $\langle 110\rangle$ view of a structure with 0.2 at.% extended defects.