Binary collision approximation
The binary collision approximation (BCA) signifies a method used in ion irradiation physics to enable efficient computer simulation of the penetration depth and damage production by energetic (with energies in the kilo-electronvolt (keV) range or higher) ions in solids. In the method, the ion is approximated to travel through a material by experiencing a sequence of independent binary collisions with sample atoms (nuclei). Between the collisions, the ion is assumed to travel in a straight path, experiencing electronic stopping power, but losing no energy in collisions with nuclei. [1] [2] [3].
Simulation approaches
In the BCA approach, a single collision between the incoming ion and a target atom (nucleus) is treated by solving the classical scattering integral between two colliding particles for the impact parameter of the incoming ion. Solution of the integral gives the scattering angle of the ion as well as its energy loss to the sample atoms, and hence what the energy is after the collision compared to before it. [1].
It is also possible to solve the time integral of the collision to know what time has elapsed during the collision.
The energy loss to electrons , i.e. electronic stopping power, can be treated either with impact-parameter dependent electronic stopping models [4], by subtracting a stopping power dependent on the ion velocity only between the collisions [5], or a combination of the two approaches.
The selection method for the impact parameter divided BCA codes into two main variaties: "Monte Carlo" BCA and crystal-BCA codes.
In the so called Monte Carlo BCA
approach the distance to and impact parameter of the next colliding atom is chosen randomly for a probability distribution which depends only on the atomic density of the material. This approach essentially simulates ion passage in a fully amorphous material. (Note that some sources call this variety of BCA just Monte Carlo, which is misleading since the name can then be confused with other completely different Monte Carlo simulation varieties).
It is also possible (although more difficult to implement) BCA methods for
crystalline materials, such that the moving ion has a defined position in a crystal, and the distance and impact parameter to the next colliding atom is determined to correspond to an atom in the crystal. In this approach BCA can be used to simulate also atom motion during channeling.
At low ion energies
the approximation of independent collisions between atoms starts to break down. This issue can be to some extent augmented by solving the collision integral for multiple simultaneous collisions [3]. However, at very low energies (below ~ 1 keV, for a more accurate estimate see [6]) the BCA approximation always breaks down, and one should use molecular dynamics ion irradiation simulation approaches since these can per design handle many-body collisions of arbitrarily many atoms. The MD simulations can either follow only the incoming ion ("recoil interaction approximation (RIA)" [7]) or simulate all atoms involved in a collision cascade [8].
BCA collision cascade simulations
The BCA simulations can be further subdivided by type depending on whether they
only follow the incoming ion, or also follow the recoils produced by the ion ("full cascade mode" e.g. in the popular BCA code SRIM).
If the initial recoil/ion mass is low, and the material where the cascade occurs has a low density (i.e. the recoil-material combination has a low stopping power), the collisions between the initial recoil and sample atoms occur rarely, and can be understood well as a sequence of independent binary collisions between atoms. This kind of a cascade can be theoretically well treated using BCA.
Damage production estimates
The BCA simulations give naturally the ion penetration depth, lateral spread and
nuclear and electronic deposition energy distributions in space. They can also be used to estimate the damage produced in materials, by using the assumption that any recoil which receives an energy higher than the threshold displacement energy of the material will produce a stable defect.
However, this equation should be used with great caution for several reasons. For instance, it does not account for any thermally activated recombination of damage, nor the well known fact that in metals the damage production is for high energies only something like 20% of the Kinchin-Pease prediction.[9]. BCA codes can, however, be extended with damage recombination models that improve on their reliability in this respect . [10] [11].
References
- ^ a b R. Smith (ed.), Atomic & ion collisions in solids and at surfaces: theory, simulation and applications, Cambridge University Press, Cambridge, UK, 1997.
- ^ M. T. Robinson, Computer simulation studies of high-energy collision cascades, Nucl. Instr. Meth. Phys. Res. B 67, 396 (1992).
- ^ a b M. T. Robinson and I. M. Torrens, Computer Simulation of atomic-displacement cascades in solids in the binary-collision approximation, Phys. Rev. B 9, 5008 (1974).
- ^ L. M. Kishinevskii, Cross sections for inelastic atomic collisions, Bull. Acad. Sci. USSR, Phys. Ser. 26, 1433 (1962)
- ^ J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions in Matter, 1985, and references therein.
- ^ G. Hobler and G. Betz, On the useful range of application of molecular dynamics simulations in the recoil interaction approximation, Nucl. Instr. Meth. Phys. Res. B 180, 203 (2001)
- ^ K. Nordlund, Molecular dynamics simulation of ion ranges in the 1 -- 100 keV energy range, Comput. Mater. Sci. 3, 448 (1995)
- ^ T. Diaz de la Rubia, R. S. Averback, R. Benedek, and W. E. King, Role of Thermal Spikes in Energetic Collision Cascades, Phys. Rev. Lett. 59, 1930 (1987), See also erratum: Phys. Rev. Lett. 60 (1988) 76.
- ^ Cite error: The named reference
Ave98was invoked but never defined (see the help page). - ^ H. L. Heinisch, Computer simulation of high energy displacement cascades, Rad. Eff. & Def. in Sol 113, 53 (1990)
- ^ T. S. Pugacheva, F. G. Djurabekova, and S. K. Valiev, Effects of cascade mixing, sputtering and diffusion by high dose light ion irradiation of boron nitride, Nucl. Instr. Meth. Phys. Res. B 141, 99 (1998)