Ion Implantation and Synthesis of Materials - Studium

7.6 Damage Production Rate and DPA 857.6 Damage Production Rate and DPAA commonly used measure of irradiation damage is displacements per atom (dpa).A unit of 1 dpa means that, on average, every atom in the irradiated volume hasbeen displaced once from its equilibrium lattice site.A simple approximation for dpa(x) per unit dose can be made by assuming thatN d (x), the number of displacements per unit volume at a depth x, can be expressedby a modified Kinchin–Pease expression of the formN ( x)d=0.8 FD( x)φ2Ed(7.8)where F D (x) has units of energy per unit length. The dependence of dpa versusdepth for a given dose, φ, can then be estimated bydpa( x)Nd( x) 0.4 FD( x)= ≈ φN NEd(7.9)In many instances it is useful to calculate the total number of dpa producedover the range of the ion. The exact calculation requires integrating (7.9) over theion’s energy as it comes to rest (E 0 to E d ). An estimate of the total dpa can bemade for ε < 1 and Z 1 > 5 and calculating N d (ν p (ε)), assuming ν p (ε) ≅ 0.8ε. For anion dose φ (ions cm −2 ) and an ion range R, the approximated dpa in the implantedregion is given bydpa≅Nd( ν p ( ε)) 0.4 ν (0.8 ε)φ ≅ φNR NREd(7.10)where N d (ν p (ε)) is the modified Kinchin–Pease damage function given by (7.4)and calculated for a damage energy given by 0.8ε.Consider, for example, 50 keV As on Si. We find E d = 16 eV for Si,N = 5.0 × 10 22 Si atoms cm −3 , and R = 37 nm. From (7.7) we have ν p (E) ≅ 0.8E,which gives a damage energy of ν p (E) ≈ 40 keV. The mean number ofdisplacements is 〈N d (E)〉 = 0.8 × 40 × 10 3 /(2 × 16) = 1 × 10 3 . The dpa per unitdose, dpa/φ, is equal to 10 3 /(5 × 10 22 × 37 × 10 −7 ) = 5.4 × 10 −15 dpa ion −1 cm −2 .Thus, for an ion dose of 1 × 10 14 As cm −2 , the Si target will experience a dpa of0.54.