A Survey of the Analytical Methods of Proton-NIEL Calculations in Silicon and Germanium

The nonionizing energy loss (NIEL) concept has been used for many years for qualitative estimation of the damage induced by radiation (particles and gamma rays). Different approaches, based on the physics of radiation interaction with the nuclear and electronic subsystems of the target atoms, are used for calculating NIEL values. The simplest model used is the binary collision approximation (BCA), which is applicable for energies larger than the threshold energy for Frenkel pair creation. In this article, we analyze the dependence of the calculated NIEL values (in silicon and germanium) on the basic interaction characteristics: the differential cross section (DCS) of energy transferred to the recoiling atoms and the partition factor between ionization and ion displacement. We estimate the differences between existing approaches and the possible scatter of the NIEL data for Coulomb, elastic, and inelastic nuclear scatterings. We also present new partition factors based on fits to experimental data. The contribution of low-energy cascade zones of displaced atoms (pockets) to the total damage is estimated using results of molecular dynamics (MD) calculation. We find for silicon a total increase of NIEL by 30%-40% relative to the original (BCA) NIEL value. The role of phonon excitations in the subthreshold cascades on the damage value is discussed.