Ion Implantation and Synthesis of Materials - Studium

5.3 Nuclear Stopping 531−m1−2mC ⎡ 4 ⎤mEMM1 2Sn ( E) = ⎢.2 ⎥1 − m ⎣( M1 + M2)⎦(5.7)Equation (5.7) provides a means for calculating stopping cross-sections based onthe Thomas-Fermi atom with an accuracy of ∼20%. The ranges of validity for valuesof m arem = 1/ 3 for ε ≤ 0.2,m = 1/ 2 for 0.08 ≤ε≤ 2,(5.8)where ε is the reduced energy introduced in (3.30):ε =Ma2 TF21+2 1 2M M Z Z eE.(5.9)Equation (5.9) gives the reduced energy in terms of the laboratory ion energy, E,where a TF is the Thomas-Fermi screening radius. For the condition m = 1/2 thecombination of (5.3) and (5.7)–(5.9) givesdEM1.308 ,dx M M2 1= π aTFNZ1Z2en 1+2dENZ Z M0.28(eVnm ) ,dx M M2 1 2 1=2/3n 1+21/2 1/2( Z1 + Z2)(5.10)where N is in atoms nm −3 . This result shows that the stopping power is energyindependentin the regime of m = 1/2.Equation (5.10) is a reasonable approximation through most of the keV energyregion. For example, for Ar (Z 1 = 18, M 1 = 40) on Si (Z 2 = 14, M 2 = 28, N = 50atoms nm−3 )dEdxn= 520 eVnm−1and for Ar on Cu (Z 2 = 29, M 2 = 64, N = 85 atoms nm −3 )dEdxn= 1, 060 eV nm−1.