Ion Implantation and Synthesis of Materials - Studium

7.3 Displacements Produced by a Primary Knock-on 81Number of Displaced Atoms10 E d2E dE cPKA Energy, EFig. 7.2. A graphical representation of the number of displaced atoms in the cascade as afunction of PKA energy according to the model of Kinchen and Pease, (7.3)The second and fourth Kinchin–Pease assumptions, which treat the collidingparticles as hard-spheres (Assumption 2) and ignore electronic stopping(Assumption 4) result in an overestimate of 〈N d (E)〉 by (7.3). By correctlyaccounting for electronic stopping and using a realistic interatomic potential todescribe the atomic interactions, the Kinchin–Pease damage function is modifiedto〈 N ( E)〉 =dξν ( E)2Ed(7.4)where ξ < 1 and depends on atomic interactions (i.e., the interaction potential),and ν (E) is the amount of PKA energy not lost to electronic excitation, commonlyreferred to as the damage energy. The damage energy will be discussed in detail inSect. 7.4. Both analytical theory and computer simulations suggest a value nearξ = 0.8. The total modified Kinchin–Pease displacement damage function is givenby⎧⎪0 (for E < Ed)⎪〈 Nd( E) 〉 = ⎨ 1 (forEd < E < 2 Ed/ ξ )⎪ξν( E)⎪ (for 2 Ed/ ξ ≤ E