Theory of Displacement Damage

The effect of atoms being displaced during irradiation with high energy ions is perhaps the most important process taking place. The displacement of an atom from its regular lattice site depends on a value Ed which is the minimum energy that is required to displace the atom from its site. If the atom receives energy in excess of Ed

it is possible that further displacements may result from the movement of the primary displaced atom. If a hard-sphere approximation and classical non-relativistic mechanics is used, the maximum energy transferred to a stationary atom by a particle with mass M1 and energy E is given by equation 3.7,

Thus the minimum incident energy required to displace an atom is given by,

d

m E

M M

M E M

2 1

2 2 1

4

)

( 

 (3.17)

To determine the number of displacements produced by an incoming ion N_d it is important to understand the amount of energy transferred to the atom through collisions in the process of slowing down.

As stated previously hard-sphere collisions at the lower end of the energy range dominate as the process for atomic displacements. This occurs since the kinetic energy of the ion is not sufficient to penetrate the electron cloud of the stationary atom. If the kinetic energy is sufficient to penetrate the electron cloud collisions of the Rutherford type dominate. To approximate the transition from hard-sphere scattering to Rutherford scattering a theory developed by Kinchin and Pease (1955) is type. If the kinetic energy is greater than the Coulomb potential then the collisions are of the Rutherford type. A kinetic energy LA at which this transition occurs is defined and given by, Koehler (1956) also showed that the assumption of Rutherford scattering is only valid for scattering angles of the order b/a, where b is the distance of closest approach.

Thus at smaller angles the effect of screening electrons is still felt. Therefore collisions only occur for impact parameters less than r0, at which the minimum energy which can be transferred is,

)

Thus if E^*>Ed all Rutherford collisions displace atoms, but an energy LB exist above which only some of the Rutherford collisions do so. LB is given by,

)

Thus to summarize at higher energies the ion undergoes Rutherford collisions and in some cases atoms are displaced. If the energy falls below LB all Rutherford collisions displace atoms. The reason why only some Rutherford collisions displace atoms at energies E>>L_B is since half the energy lost to atoms which receive energy less than E_d and are thus not displaced. This energy loss is dissipated through lattice vibrations termed thermal spikes.

As the energy of the ion decreases further the importance of energy loss due to hard-sphere collisions become more important than that of electronic energy loss and for this reason Kinchin and Pease (1955) defined a transition energy L_C. It is a defined as the energy above which all energy loss is due to electronic excitation and below which is due to hard-sphere collisions. The value of LC is difficult to obtain in general but is approximated for insulators as,

G

For metals the relation is,

f

where A is the atomic weight. Thus in general it is found that the number of atoms displaced by an incoming ion Nd depends firstly on its energy. If its energy is less than LC the number of displaced atoms is determined as follows. Consider an atom with initial energy T < LC moving in a solid. The first collision then results in a sharing of the energy T with the struck atom which on average is half that of T. Both atoms will then continue with energy 1/2T and collide with one atom each sharing their energy with the struck atom with a factor of an half on average. This process will continue until the average energy of the struck atoms falls below 2E_d and if this occurs after q groups of collisions the total amount of displaced atoms will be given by,

) atom is displaced and below E_d obviously no atom is displaced. If T is bigger than L_C the expression becomes L_C/2E_d.

If the energy of the atom is bigger than LC and LB Kinchin and Pease showed that the moving atom will displace ΔN atoms in losing energy ΔE, where

Ed ion is light the expression may be simplified to,



where b = 0.5 if LB > LC and b = 0.25 of LB << LC. E0 is the ion initial energy. This simplification can be done since for light ions (Zeffective/Z) and I are practically independent of energy.

3.3.3 Defects

3.3.3.1 Defects Created During Irradiation

The defects created during ion implantation are predominantly point defects. As discussed in the above section the ion may impart upon colliding with an atom to it enough energy for it to be displaced from its regular lattice site and also displace further atoms. The number of point defects generated depends on the implantation species and the implantation energy as well as the displacement energy of the target atoms. A heavier atom, such as Si, will displace more atoms than a lighter atom (e.g.

hydrogen) since the heavier atom transfers more energy to the struck atom. Also it is evident from equation 3.16 that the higher the incoming energy the larger the transferred energy and the greater the number of displacements. These defects are formed over and above the thermodynamically stable concentration of point defects.

3.3.3.2 Aggregation of Point Defects and Growth of Defect Clusters During Heat Treatment

The number of vacancies and interstitials created during the irradiation process is approximately equal. During annealing, the defects will attempt to diffuse in the crystal as discussed in Section 2.3.3. This process will not be the same for vacancies and interstitials since they have different mobilities.

Furthermore, the point defects will during migration form clusters of point defects such as di-interstitial, di-vacancy, tri-interstitial and tri-vacancy etc. These compound defects may agglomerate to form large clusters which produce lattice strain. For interstitial clustering the atoms will agglomerate in the form of a platelet, lying between close-packed layers. Upon further growth, the cluster will form a ring of edge dislocation termed a dislocation loop. In the case of vacancy clustering a similar situation occurs except that the disc of vacancies may be prevented from collapsing to

a vacancy dislocation loop if the cluster growth takes place in the presence of a gas.

Instead gas bubbles or voids may form, if the gas eventually diffuses out of the bubble.