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 defect production by energetic (with kinetic 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.

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. The scattering integral is defined in the centre-of-mass coordinate system (two particles reduced to one single particle with one interatomic potential) and relates the angle of scatter with the interatomic potential.

It is also possible to solve the time integral of the collision to know what time has elapsed during the collision. This is necessary at least when BCA is used in the "full cascade" mode, see below.

The energy loss to electrons, i.e. electronic stopping power, can be treated either with impact-parameter dependent electronic stopping models , by subtracting a stopping power dependent on the ion velocity only between the collisions, or a combination of the two approaches.

The selection method for the impact parameter divided BCA codes into two main varieties: "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). SRIM and SDTrimSP are Monte-Carlo BCA codes.

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