Ion Implantation and Synthesis of Materials - Studium

6.3 Calculations 69where B is a slowly varying function of E and R. In the energy region where nuclearstopping dominates and M 1 > M 2 , B = 1/3. Increased electronic stopping athigher energies leads to smaller values of B. For the case of M 1 < M 2 , large-anglescattering makes the correction between R p and R somewhat larger than the valuegiven by the above rule-of-thumb expression. On the other hand, electronic stoppingis usually appreciable in such cases, and this partially offsets the increase inthe correction term. Thus, B = 1/3 is a reasonable approximation for a wide rangeof implant conditions, allowing us to writeRp≅R.1 + ( M /3 M )2 1(6.13)For 50 keV As in Si, (6.13) gives R p = 33.4 nm, which is within 14% of the valuecalculated by SRIM, 38.8 nm.A more exact relation between range and projected range was calculated usingpower law-based LSS theory by Winterbon, Sigmund, and Sanders (WSS; 1970).Plots of R p /R as a function of M 2 /M 1 for the power law conditions of m = 1/3 and1/2, are presented in Fig. 6.4.0.0Range1.0R pR0.5∆R2 pxR p22∆R pyR p20.00.1 1.0M 2 /M 110.0Fig. 6.4. Relationship between range, R, projected range, R p , and range straggling, ∆R p , asfunctions of mass ratio, M 2 /M 1 . The range straggling, ∆R px , is in the direction of the incidention, and ∆R py is perpendicular to the incident ion. Dashed lines, m = 1/3; solid lines,m = 1/2 (Winterbon et al. 1970)