Ion Implantation and Synthesis of Materials - Studium

2.7 Screening Length 191χ(x) = 0.1818e -3.2x +0.5099e -0.9423x +0.2802e -0.4029x +0.02817e -0.2016x10 −1a U = 0.8854 x 0.529/(Z 10.23 + Z 2 0.23 )χ(x)−210Thomas-FermiMoliere−310BohrLenz-Jensen10 −40 1020 30Reduced Radius, x=r/aFig. 2.2. The reduced screening functions of (2.15). This screening function is identified asχ U , a universal screening function, with its argument, x, being defined as x ≡ r/a U , where a Uis the universal screening length given in (2.17) (Ziegler et al. 1985).a0.8853a0B=1/22/3 2/3( Z1 + Z2),(2.20)where a 0 is the Bohr radius, 0.0529 nm, and Z 1 and Z 2 are the atomic numbers ofthe two atoms. Firsov suggested that the interatomic potential would be best describedusing a reduced distance defined by a screening length of the forma0.8853a0F=2/31/2 1/2( Z1 + Z2),(2.21)with the constant 0.8853 being derived from the Thomas–Fermi atom. FollowingBohr, Lindhard also suggested using the atomic Thomas–Fermi screening functionfor the interatomic screening function, but with