Ion Implantation and Synthesis of Materials - Studium

5.3 Nuclear Stopping 51MeV mg −1 cm −2 . In addition to the energy-loss rate, it is also customary to speakof the stopping cross-section, S, which is defined asd E/d xS ≡ ,N(5.3)where N is the atomic density. The stopping cross-section can be thought of as theenergy-loss rate per scattering center. The stopping cross-section has typical unitsof⎛−1 2)=− 3⎞⎞d E/ d x (eVcm eVcm⎜units: ⎜ ⎟⎟.N (atoms cm ) atom⎝The nomenclature of stopping cross-section comes from the unit of area in thenumerator.A proper understanding of the mechanisms of energy-loss is important not onlyin controlling the depth profile of implanted dopant atoms, but also in determiningthe nature of the lattice disorder produced during ion implantation or ion irradiationof the solid. In the process of slowing down in the substrate, the implantedions undergo violent collisions with some of the lattice atoms, thereby displacingthem from lattice sites.This problem of lattice disorder is a vital one in most ion beam modificationwork, and we will return to it again in Chap. 7. The basic principles are, however,treated in the present chapter, since ranges and lattice disorder both involve thesame energy-loss mechanisms. Other secondary effects accompanying ion implantationand ion irradiation of solids, such as sputtering of target-atoms, also dependstrongly on the relative importance of nuclear and electronic stopping.⎛⎝⎠⎠5.3 Nuclear StoppingIn nuclear stopping we are concerned with the average energy-loss that resultsfrom elastic collisions with target-atoms. The nuclear stopping power or nuclearenergy-loss rate is the energy lost by a moving particle due to elastic collisions perunit length traveled in the target. In Chap. 4 we defined the probability of a particlewith energy E undergoing a collision while traveling a distance dx, which resultsin an energy-loss between T and T + dT. From (4.11) we haved PE ( ) d σ ( E)dT = Ndx d T,dTdT