Binary Collision Approximation

The binary-collision approximation (BCA) is a set of assumptions that tremendously reduce the computational complexity of simulating ion-material interactions compared to a full n-body simulation (e.g., Molecular Dynamics). Ions interact with materials through nuclear and electronic stopping. These assumptions can be summarized as:

• Particles in the code are "superparticles," and represent many ions or atoms each
• Energetic particles interact with material atoms through a series of discrete, binary collisions
• Nuclear collisions occur at mean-free-path distances, or at exponentially distributed distances for a gas-type target
• Between collisions, particles travel in straight line, asymptotic-trajectory paths along which nonlocal electronic stopping can be applied
• Local electronic stopping (i.e., Oen-Robinson) can be applied on a per-collision basis and may be combined with nonlocal stopping using Lindhard's equipartition strategy
• Binary collisions are calculated by solving the classical scattering integral for a chosen interatomic potential
• Material atoms are allowed to transfer momentum to tracked collision partners following any collision, but only collisions that transfer an energy greater than the displacement energy are considered removed from their original locations
• Particles are stopped when their kinetic energy drops below a cutoff energy in the material, or when they leave the simulation boundary outside of the material
• Particles leaving the material experience a locally planar or isotropic surface binding potential

For an overview of the BCA, see Eckstein[1] or Robinson[2].

Scattering of two atoms/ions in the CoM frame. Theta is the scattering angle, p the impact parameter, and r0 the distance of closest approach (which is a function of the CoM energy and impact parameter).

Scattering of two atoms/ions in the lab frame. The impacting atom is deflected by Psi, and the atom at rest is set into motion at an angle Psi_recoil away from the incident atom/ion direction.

BCA for Plasma-Material Interactions

Plasma-Material Interactions in the PIC-BCA method. Phenomena modelled include: (a) sputtering, (b) ion-driven mixing, (c) vacancy production, (d) implantation, (e) layered composition, (f) ionization and redeposition, (g) reflection as neutrals. Regions of the plasma, including (i) the plasma presheath, (ii) the magnetic presheath, and (iii) the debye or electrostatic sheath are marked along the 1D PIC field axis.

Electronic Stopping

Various formulations of electronic stopping for protons on silicon. Medvedev-Volkov[3] PSTAR[4] Biersack-Varelas[5] Lindhard-Scharff[6] Bethe[7]. rustbca includes Biersack-Varelas, Lindhard-Scharff, and (not shown) Oen-Robinson electronic stopping. At energies below ~25 keV/nucleon, Lindhard-Scharff or Oen Robinson are the preferred formulations of electronic stopping. At intermediate and higher energies, Biersack-Varelas implements a semi-empirical interpolation between Lindhard-Scharff and Bethe stopping, allowing for rustbca simulations to adequately model incident ion energies up to ~ 1 GeV/nucleon.

References

[1] W. Eckstein, Computer Simulation of Ion-Solid Interactions (1991)

[2] M. T. Robinson, The binary collision approximation: Background and introduction, Rad. Eff. and Def. in Solids (1994)

[3] N. Medvedev & A. E. Volkov, Analytically solvable model of scattering of relativistic charged particles in solids, J. Phys. D: Appl. Phys., vol 52, 23 (2020)

[4] PSTAR

[5] J.P. Biersack & L.G. Haggmark, A Monte Carlo Computer Program for the Transport of Energetic Ions in Amorphous Targets, Nuc. Inst. & Meth. 174 (1980) Eqs. 27-33

[6] J. Lindhard & Scharff, Energy Dissipation by Ions in the keV Region, Phys Rev., 124, 128 (1961)

[7] H. A. Bethe, Ann. Phys. (Leipzig) 5, 325 (1930)