Ion Implantation and Synthesis of Materials - Studium

5.5 Electronic Stopping 575.5.1 High-Energy Electronic Energy-LossIn this section we will consider the case where the ion velocity is greater than2/3v0Z1. At higher velocities, the charge state of the ion increases and ulti-2/3mately becomes fully stripped of all its electrons at v≥v0Z1. At this point, theion can be viewed as a positive point charge Z 1 , moving with a velocity greaterthan the mean orbital velocity of the atomic electrons in the shells or subshells ofthe target-atoms. When the projectile velocity v is much greater than that of an orbitalelectron (fast-collision case), the influence of the incident particle on an atommay be regarded as a sudden, small external perturbation. This picture leads toBohr’s theory of stopping power. The collision produces a sudden transfer of energyfrom the projectile to the target electron. The energy-loss from a fast particleto a stationary nucleus or electron can be calculated from scattering in a centralforce field. The stopping cross-section decreases with increasing velocity becausethe particle spends less time in the vicinity of the atom. For this condition, the ionis a bare nuclei, and its interactions with target electrons can be accurately describedby a pure Coulomb interaction potential.In 1913, Bohr derived an expression for the rate of energy-loss of a chargedparticle on the basis of classical considerations. He considered a heavy particle,such as an α particle or a proton, of charge Z 1 e, mass M, and velocity v passing atarget-atom electron of mass m e at a distance b. As the heavy particle passes, theCoulomb force acting on the electron changes direction continuously. If the electronmoves negligibly during the passage of the heavy particle, then the impulseparallel to the path, the integral of F dt, is zero by symmetry, since, for each positionof the incident particle in the −x direction, there is a corresponding position inthe +x direction, which makes an equal and opposite contribution to the x componentof the momentum. However, throughout the passage, there is a force in the ydirection, and momentum ∆p is transferred to the electron. The energy-loss isgiven in Nastasi et al. (1996) ase2 41M1NZ2⎜edE2πZ e2mve− =⎟ln ,dx E m I⎛⎝⎞⎠2(5.15)with N given by the atomic density in the stopping medium.The average excitation energy, I, in electron-volts, for most elements is roughlyI ≅ 10 Z ,2(5.16)where Z 2 is the atomic number of the stopping atoms. The description of stoppingpower so far ignores the shell structure of the atoms and variations in electronbinding. Experimentally, these effects show up as small derivations (except for thevery light elements) from the approximation given by (5.16).