Binary collision approximation
Encyclopedia
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 atom
s (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.
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.
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).
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 channelling
.
The binary collision approximation can also be extended to simulate
dynamic composition changes of a material due to prolonged
ion irradiation, i.e. due to ion implantation
and sputtering
.
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.
However, at very low energies (below ~1 keV, for a more accurate estimate see )
the BCA approximation always breaks down, and one should use molecular dynamics
ion irradiation simulation approaches because 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 or RIA )
or simulate all atoms involved in a collision cascade
.
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.
of the material will produce a stable defect.
However, this approach 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. Moreover, this approach only predicts the damage production as if all defects were isolated
Frenkel pairs
, while in reality in many cases collision cascade
s produce defect clusters or even dislocations as the initial damage state.
BCA codes can, however, be extended with damage clustering and recombination models that improve on their reliability in this respect.
Finally, the average threshold displacement energy
is not very accurately known in most materials.
Particle radiation
Particle radiation is the radiation of energy by means of fast-moving subatomic particles. Particle radiation is referred to as a particle beam if the particles are all moving in the same direction, similar to a light beam....
physics to enable efficient computer simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
of the penetration depth and
defect
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
production by energetic (with kinetic energies in the kilo-electronvolt (keV
Electronvolt
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...
) 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 atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s (nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
). Between the collisions, the ion is assumed to travel in a straight path, experiencing electronic stopping power
Stopping power (particle radiation)
In passing through matter, fast charged particles ionize the atoms or molecules which they encounter. Thus, the fast particles gradually lose energy in many small steps. Stopping power is defined as the average energy loss of the particle per unit path length, measured for example in MeV/cm...
, but losing no energy in collisions with nuclei.
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 theimpact parameter
Impact parameter
The impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of the field U created by an object that the projectile is approaching...
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.
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
Stopping power (particle radiation)
In passing through matter, fast charged particles ionize the atoms or molecules which they encounter. Thus, the fast particles gradually lose energy in many small steps. Stopping power is defined as the average energy loss of the particle per unit path length, measured for example in MeV/cm...
,
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
Impact parameter
The impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of the field U created by an object that the projectile is approaching...
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 channelling
Channelling (physics)
Channelling is the process that constrains the path of a charged particle in a crystalline solid.Many physical phenomena can occur when a charged particle is incident upon a solid target, e.g., elastic scattering, inelastic energy-loss processes, secondary-electron emission, electromagnetic...
.
The binary collision approximation can also be extended to simulate
dynamic composition changes of a material due to prolonged
ion irradiation, i.e. due to ion implantation
Ion implantation
Ion implantation is a materials engineering process by which ions of a material are accelerated in an electrical field and impacted into another solid. This process is used to change the physical, chemical, or electrical properties of the solid...
and sputtering
Sputtering
Sputtering is a process whereby atoms are ejected from a solid target material due to bombardment of the target by energetic particles. It is commonly used for thin-film deposition, etching and analytical techniques .-Physics of sputtering:...
.
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.
However, at very low energies (below ~1 keV, for a more accurate estimate see )
the BCA approximation always breaks down, and one should use molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
ion irradiation simulation approaches because 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 or RIA )
or simulate all atoms involved in a collision cascade
Collision cascade
A collision cascade is a set of nearby adjacent energetic collisions of atoms induced by an energetic particle in a solid or liquid....
.
BCA collision cascade simulations
The BCA simulations can be further subdivided by type depending on whether theyonly follow the incoming ion, or also follow the recoils produced by the ion (full cascade mode, e.g., in the popular BCA code SRIM
Stopping and Range of Ions in Matter
Stopping and Range of Ions in Matter is a group of computer programs which calculate interaction of ions with matter; the core of SRIM is a program Transport of ions in matter . The programs were developed by James F. Ziegler and Jochen P. Biersack around 1983 and are being continuously upgraded...
).
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
Stopping power (particle radiation)
In passing through matter, fast charged particles ionize the atoms or molecules which they encounter. Thus, the fast particles gradually lose energy in many small steps. Stopping power is defined as the average energy loss of the particle per unit path length, measured for example in MeV/cm...
), 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 energyThreshold displacement energy
The threshold displacement energy T_d is the minimum kinetic energythat an atom in a solid needs to be permanentlydisplaced from its lattice site to adefect position.It is also known as "displacement threshold energy" or just "displacement energy"....
of the material will produce a stable defect.
However, this approach 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. Moreover, this approach only predicts the damage production as if all defects were isolated
Frenkel pairs
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
, while in reality in many cases collision cascade
Collision cascade
A collision cascade is a set of nearby adjacent energetic collisions of atoms induced by an energetic particle in a solid or liquid....
s produce defect clusters or even dislocations as the initial damage state.
BCA codes can, however, be extended with damage clustering and recombination models that improve on their reliability in this respect.
Finally, the average threshold displacement energy
Threshold displacement energy
The threshold displacement energy T_d is the minimum kinetic energythat an atom in a solid needs to be permanentlydisplaced from its lattice site to adefect position.It is also known as "displacement threshold energy" or just "displacement energy"....
is not very accurately known in most materials.
BCA codes
- SRIMStopping and Range of Ions in MatterStopping and Range of Ions in Matter is a group of computer programs which calculate interaction of ions with matter; the core of SRIM is a program Transport of ions in matter . The programs were developed by James F. Ziegler and Jochen P. Biersack around 1983 and are being continuously upgraded...
is likely the most used BCA code now. It can be used to simulate linear collision cascades in amorphous materials for all ion in all materials up to ion energies of 1 GeVGEVGEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
. Note, however, that SRIM does not treat effects such as channellingChannelling (physics)Channelling is the process that constrains the path of a charged particle in a crystalline solid.Many physical phenomena can occur when a charged particle is incident upon a solid target, e.g., elastic scattering, inelastic energy-loss processes, secondary-electron emission, electromagnetic...
, damage due to electronic energy deposition (necessary, e.g., to describe swift heavy ionSwift heavy ionSwift heavy ions are a special form of particle radiation for which electronic stopping dominates over nuclear stopping.They are accelerated in particle accelerators to very high energies, typically in the MeV or GeV range and have sufficient energy and mass to penetrate solids on a straight line...
damage in materials) or damage produced by excited electrons. - MARLOWE is a very long developed code that can handle crystalline materials and supports numerous different physics models.
- TRIDYN, newer versions known as SDTrimSP, is a BCA code capably of handling dynamic composition changes.