Binary Collision Approximation
The binary-collision approximation (BCA) is a set of assumptions that tremendously reduce the computational complexity of simulating ion-material interactions. 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
- Between collisions, particles travel in straight lines along which nonlocal electronic stopping is applied
- Binary collisions are calculated by solving the classical scattering integral for a chosen interatomic potential; local electronic stopping is applied following each collision
- 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 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 surface binding potential
For an overview of the BCA, see Eckstein[1] or Robinson[2].
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.
Various formulations of electronic stopping for protons on silicon. Medvedev-Volkov[3] PSTAR[4] Biersack-Varelas[5] Lindhard-Scharff[6] Bethe[7].
Coordinate system in the BCA as implemented in rustbca. Alpha, beta, and gamma correspond to the directional cosine angles in the x-, y-, and z-directions respectively.
[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)