Collision cascade
Encyclopedia
A collision cascade is a set of nearby adjacent energetic (much higher than ordinary thermal energies) collisions of atom
s induced by an energetic particle in a solid or liquid.
If the maximum atom or ion energies in a collision cascade are higher than the threshold displacement energy
of the material (tens of eV
s or more), the collisions can permanently displace atoms from their lattice sites and produce defect
s. The initial energetic atom can be, e.g., an ion
from a particle accelerator
, an atomic recoil produced by a passing high-energy neutron
, electron
or photon
, or be produced when a radioactive nucleus decays and gives the atom a recoil energy.
The nature of collision cascades can vary strongly depending on the energy and mass of the recoil/incoming ion and density of the material (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 the binary collision approximation
(BCA) simulation approach. For instance, H and He ions with energies below 10 keV can be expected to lead to purely linear cascades in all materials.
The most commonly used BCA code SRIM
can be used to simulate linear collision cascades in disordered materials for all ion in all materials up to ion energies of 1 GeV
. Note, however, that SRIM does not treat effects such as damage due to electronic energy deposition or damage produced by excited electrons. The nuclear and electronic stopping power
s used are averaging fits to experiments, and are thus not perfectly accurate either.
In linear cascades the set of recoils produced in the sample can be described as a sequence of recoil generations depending on how many collision steps have passed since the original collision: primary knock-on atoms
(PKA), secondary knock-on atoms (SKA), tertiary knock-on atoms (TKA), etc. Since it is extremely unlikely that all energy would be transferred to a knock-on atom, each generation of recoil atoms has on average less energy than the previous, and eventually the knock-on atom energies go below the threshold displacement energy
for damage production, at which point no more damage can be produced.
methods.
Computer simulation-based animations of collision cascades in the heat spike regime are available on YouTube.
Typically, a heat spike is characterized by the formation of a transient underdense region in the center of the cascade, and an overdense region around it. After the cascade, the overdense region becomes interstitial defect
s, and the underdense region typically becomes a region of vacancies
.
If the kinetic energy of the atoms in the region of dense collisions is recalculated into temperature (using the basic equation E = 3/2·N·kBT), one finds that the kinetic energy in units of temperature is initially of the order of 10,000 K. Because of this, the region can be considered to be very hot, and is therefore called a heat spike or thermal spike (the two terms are usually considered to be equivalent). The heat spikes cools down to the ambient temperature in 1–100 ps, so the "temperature" here does not correspond to thermodynamic equilibrium temperature. However, it has been shown that after about 3 lattice vibrations, the kinetic energy distribution of the atoms in a heat spike has the Maxwell-Boltzmann distribution, making the use of the concept of temperature somewhat justified. Moreover, experiments have shown that a heat spike can induce a phase transition which is known to require a very high temperature, showing that the concept of a (non-equilibrium) temperature is indeed useful in describing collision cascades.
In many cases, the same irradiation condition is a combination of linear cascades and heat spikes. For example, 10 MeV Cu
ions bombarding Cu would initially move in the lattice in a linear cascade regime, since the nuclear stopping power
is low. But once the Cu ion would slow down enough, the nuclear stopping power would increase and a heat spike would be produced. Moreover, many of the primary and secondary recoils of the incoming ions would likely have energies in the keV range and thus produce a heat spike.
For instance, for copper irradiation of copper, recoil energies of around 5–20 keV are almost guaranteed to produce heat spikes. At lower energies, the cascade energy is too low to produce a liquid-like zone. At much higher energies, the Cu ions would most likely lead initially to a linear cascade, but the recoils could lead to heat spikes, as would the initial ion once it has slowed down enough. The concept subcascade breakdown threshold energy signifies the energy above which a recoil in a material is likely to produce several isolated heat spikes rather than a single dense one.
s, i.e. MeV and GeV heavy ions which produce damage by a very strong electronic stopping
, can also be considered to produce thermal spikes in the sense that they lead to strong lattice heating and a transient disordered atom zone. However, at least the initial stage of the damage might be better understood in terms of a Coulomb explosion
mechanism. Regardless of what the heating mechanism is, it is well established that swift heavy ions in insulators typically produce ion tracks forming long cylindrical damage zones of reduced density.
, typically lasts 0.1– 0.5 ps. If a heat spike is formed, it can live for some 1–100 ps until the spike temperature has cooled down essentially to the ambient temperature. The cooling down of the cascade occurs via lattice heat conductivity and by electronic heat conductivity after the hot ionic subsystem has heated up the electronic one via electron-phonon coupling. Unfortunately the rate of electron-phonon coupling from the hot and disordered ionic system is not well known, as it can not be treated equally to the fairly well known process of transfer of heat from hot electrons to an intact crystal structure. Finally, the relaxation phase of the cascade, when the defects formed possible recombine and migrate, can last from a few ps to infinite times, depending on the material, its defect
migration and recombination properties, and the ambient temperature.
production. The defects can be, e.g., point defects
such as
Frenkel pairs
, ordered or disordered dislocation
loops, stacking faults, or amorphous zones. Prolonged irradiation of many materials can lead to their full amorphization, an effect which occurs regularly during the ion implantation
doping of silicon chip
s.
The defects production can be harmful, such as in nuclear fission and fusion reactors where the neutrons slowly degrade the mechanical properties of the materials, or a useful and desired materials modification effect, e.g., when ions are introduced into semiconductor
quantum well
structures to speed up the operation of a laser. or to strengthen carbon nanotubes.
A curious feature of collision cascades is that the final amount of damage produced may be much less than the number of atoms initially affected by the heat spikes. Especially in pure metals, the final damage production after the heat spike phase can be orders of magnitude smaller than the number of atoms displaced in the spike. On the other hand, in semiconductors and other covalently bonded materials the damage production is usually similar to the number of displaced atoms. Ionic materials can behave like either metals or semiconductors with respect to the fraction of damage recombined.
, both in the linear spike and heat spike regimes. Heat spikes near surfaces also frequently lead to crater formation. This cratering is caused by liquid flow of atoms, but if the projectile size above roughly 100,000 atoms, the crater production mechanism switches to the same mechanism as that of macroscopic craters produced by bullets or asteroids.
The fact that lots of atoms are displaced by a cascade means that ions can be used to deliberately mix materials, even for materials that are normally thermodynamically immiscible. This effect is known as ion beam mixing
.
The non-equilibrium nature of irradiation can also be used to drive materials out of thermodynamic equilibrium, and thus form new kinds of alloys.
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 induced by an energetic particle in a solid or liquid.
If the maximum atom or ion energies in a collision cascade are higher than the 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"....
of the material (tens of eV
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...
s or more), the collisions can permanently displace atoms from their lattice sites and produce 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...
s. The initial energetic atom can be, e.g., an ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
from a particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
, an atomic recoil produced by a passing high-energy neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
, electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
or photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
, or be produced when a radioactive nucleus decays and gives the atom a recoil energy.
The nature of collision cascades can vary strongly depending on the energy and mass of the recoil/incoming ion and density of the material (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...
).
Linear cascades
When 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 powerStopping power
Stopping power is a colloquial term used to describe the ability of a firearm or other weapon to cause a penetrating ballistic injury to a target, human or animal, sufficient to incapacitate the target where it stands....
), 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 the binary collision approximation
Binary collision approximation
The binary collision approximation signifies a method used in ion irradiation physics to enable efficient computer simulation of the penetration depth and...
(BCA) simulation approach. For instance, H and He ions with energies below 10 keV can be expected to lead to purely linear cascades in all materials.
The most commonly used 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...
can be used to simulate linear collision cascades in disordered materials for all ion in all materials up to ion energies of 1 GeV
GEV
GEV 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 damage due to electronic energy deposition or damage produced by excited electrons. The nuclear and 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...
s used are averaging fits to experiments, and are thus not perfectly accurate either.
In linear cascades the set of recoils produced in the sample can be described as a sequence of recoil generations depending on how many collision steps have passed since the original collision: primary knock-on atoms
PKA (irradiation)
A Primary Knock-on Atom or PKA is an atom, which is displaced from its lattice site by irradiation; it is, by definition, the first atom that an incident particle encounters in the target...
(PKA), secondary knock-on atoms (SKA), tertiary knock-on atoms (TKA), etc. Since it is extremely unlikely that all energy would be transferred to a knock-on atom, each generation of recoil atoms has on average less energy than the previous, and eventually the knock-on atom energies go below the 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"....
for damage production, at which point no more damage can be produced.
Heat spikes (thermal spikes)
When the ion is heavy and energetic enough, and the material is dense, the collisions between the ions may occur so near to each other that they can not be considered independent of each other. In this case the process becomes a complicated process of many-body interactions between hundreds and tens of thousands of atoms, which can not be treated with the BCA, but can be modelled using molecular dynamicsMolecular 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...
methods.
Computer simulation-based animations of collision cascades in the heat spike regime are available on YouTube.
Typically, a heat spike is characterized by the formation of a transient underdense region in the center of the cascade, and an overdense region around it. After the cascade, the overdense region becomes interstitial defect
Interstitial defect
Interstitials are a variety of crystallographic defects, i.e. atoms which occupy a site in the crystal structure at which there is usually not an atom, or two or more atoms sharing one or more lattice sites such that the number of atoms is larger than the number of lattice sites.They are generally...
s, and the underdense region typically becomes a region of vacancies
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...
.
If the kinetic energy of the atoms in the region of dense collisions is recalculated into temperature (using the basic equation E = 3/2·N·kBT), one finds that the kinetic energy in units of temperature is initially of the order of 10,000 K. Because of this, the region can be considered to be very hot, and is therefore called a heat spike or thermal spike (the two terms are usually considered to be equivalent). The heat spikes cools down to the ambient temperature in 1–100 ps, so the "temperature" here does not correspond to thermodynamic equilibrium temperature. However, it has been shown that after about 3 lattice vibrations, the kinetic energy distribution of the atoms in a heat spike has the Maxwell-Boltzmann distribution, making the use of the concept of temperature somewhat justified. Moreover, experiments have shown that a heat spike can induce a phase transition which is known to require a very high temperature, showing that the concept of a (non-equilibrium) temperature is indeed useful in describing collision cascades.
In many cases, the same irradiation condition is a combination of linear cascades and heat spikes. For example, 10 MeV Cu
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
ions bombarding Cu would initially move in the lattice in a linear cascade regime, since the nuclear 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...
is low. But once the Cu ion would slow down enough, the nuclear stopping power would increase and a heat spike would be produced. Moreover, many of the primary and secondary recoils of the incoming ions would likely have energies in the keV range and thus produce a heat spike.
For instance, for copper irradiation of copper, recoil energies of around 5–20 keV are almost guaranteed to produce heat spikes. At lower energies, the cascade energy is too low to produce a liquid-like zone. At much higher energies, the Cu ions would most likely lead initially to a linear cascade, but the recoils could lead to heat spikes, as would the initial ion once it has slowed down enough. The concept subcascade breakdown threshold energy signifies the energy above which a recoil in a material is likely to produce several isolated heat spikes rather than a single dense one.
Swift heavy ion thermal spikes
Swift heavy ionSwift heavy ion
Swift 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...
s, i.e. MeV and GeV heavy ions which produce damage by a very strong electronic stopping
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 also be considered to produce thermal spikes in the sense that they lead to strong lattice heating and a transient disordered atom zone. However, at least the initial stage of the damage might be better understood in terms of a Coulomb explosion
Coulomb explosion
A Coulomb explosion is a mechanism for coupling electronic excitation energy from intense electromagnetic fields into atomic motion. The atomic motion can break the bonds that hold solids together...
mechanism. Regardless of what the heating mechanism is, it is well established that swift heavy ions in insulators typically produce ion tracks forming long cylindrical damage zones of reduced density.
Time scale
To understand the nature of collision cascade, it is very important to know the associated time scale. The ballistic phase of the cascade, when the initial ion/recoil and its primary and lower-order recoils have energies well above 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"....
, typically lasts 0.1– 0.5 ps. If a heat spike is formed, it can live for some 1–100 ps until the spike temperature has cooled down essentially to the ambient temperature. The cooling down of the cascade occurs via lattice heat conductivity and by electronic heat conductivity after the hot ionic subsystem has heated up the electronic one via electron-phonon coupling. Unfortunately the rate of electron-phonon coupling from the hot and disordered ionic system is not well known, as it can not be treated equally to the fairly well known process of transfer of heat from hot electrons to an intact crystal structure. Finally, the relaxation phase of the cascade, when the defects formed possible recombine and migrate, can last from a few ps to infinite times, depending on the material, its 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...
migration and recombination properties, and the ambient temperature.
Effects of collision cascades
Damage production by collision cascades
Since the kinetic energies in a cascade can be very high, it can drive the material locally far outside thermodynamic equilibrium. Typically this results in defectCrystallographic 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. The defects can be, e.g., point defects
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...
such as
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...
, ordered or disordered dislocation
Dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...
loops, stacking faults, or amorphous zones. Prolonged irradiation of many materials can lead to their full amorphization, an effect which occurs regularly during the 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...
doping of silicon chip
Silicon Chip
Silicon Chip is an Australian electronics magazine. It was started in November, 1987 by Leo Simpson. Following the demise of Electronics Australia, it is the only hobbyist-related electronics magazine remaining in Australia.- Magazine :...
s.
The defects production can be harmful, such as in nuclear fission and fusion reactors where the neutrons slowly degrade the mechanical properties of the materials, or a useful and desired materials modification effect, e.g., when ions are introduced into semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
quantum well
Quantum well
A quantum well is a potential well with only discrete energy values.One technology to create quantization is to confine particles, which were originally free to move in three dimensions, to two dimensions, forcing them to occupy a planar region...
structures to speed up the operation of a laser. or to strengthen carbon nanotubes.
A curious feature of collision cascades is that the final amount of damage produced may be much less than the number of atoms initially affected by the heat spikes. Especially in pure metals, the final damage production after the heat spike phase can be orders of magnitude smaller than the number of atoms displaced in the spike. On the other hand, in semiconductors and other covalently bonded materials the damage production is usually similar to the number of displaced atoms. Ionic materials can behave like either metals or semiconductors with respect to the fraction of damage recombined.
Other consequences of collision cascades
Collision cascades in the vicinity of a surface often lead to sputteringSputtering
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:...
, both in the linear spike and heat spike regimes. Heat spikes near surfaces also frequently lead to crater formation. This cratering is caused by liquid flow of atoms, but if the projectile size above roughly 100,000 atoms, the crater production mechanism switches to the same mechanism as that of macroscopic craters produced by bullets or asteroids.
The fact that lots of atoms are displaced by a cascade means that ions can be used to deliberately mix materials, even for materials that are normally thermodynamically immiscible. This effect is known as ion beam mixing
Ion Beam Mixing
Ion Beam Mixing is a process for adhering two multilayers, especially a substrate and deposited surface layer. The process involves bombarding layered samples with doses of ion radiation in order to promote mixing at the interface, and generally serves as a means of preparing electrical junctions,...
.
The non-equilibrium nature of irradiation can also be used to drive materials out of thermodynamic equilibrium, and thus form new kinds of alloys.