Ion Implantation and Synthesis of Materials - Studium

64 6 Ion Range and Range DistributionIncident IonαSurface PlanezR, Range(Path Length)R sSpreadR r , Radial RangeR pProjectedRangeyx sDepth(Penetration)(x s , y s , z s )tR pTransverseProjectedRangexFig. 6.2. Schematic drawing for the definition of depth, spread, radial range, longitudinalprojected range, transverse projected range, and path length (Eckstein 1991)In Fig. 6.2, a more general three-dimensional presentation of the penetration ofa projectile into a solid is shown. In this schematic, an energetic projectile entersthe sample surface at the point (0, 0, 0), at a angle α to the surface normal. Theprojectile is stopped at the point (x s , y s , z s ). For this presentation of an ion’s penetrationinto a solid, we define the range, R, and the projected range, R p , consistentwith the definitions used in Fig. 6.1. However, since the incident ion is not parallelto the surface normal, the depth of penetration, x s , which is defined as the perpendiculardistance below the surface of which the projectile comes to rest, is notequal to the projected range. If α = 0, these two quantities would be equal. Theradial range, R r , is the distance from the surface at the point of entrance, (0, 0, 0),to the point where the projectile comes to rest, (x s , y s , z s ). The spreading range, R s ,is the distance between the point where the projectile enters the surface and theprojection of the projectile’s final resting place onto the surface plane. The trans-tpverse projected range, R , is the vector connecting the radial range and the projectedrange. For a single projectile coming to rest at the point (x s , y s , z s ), we havethe following mathematical descriptions for the quantities defined in Fig. 6.2:1. the range spread2 2( ) 1/2R y zs=s+s,(6.1)