cs. NIEL is that part of the energy introduced via both Coulomb (elastic), nuclear elastic, and nuclear inelastic interactions, which produces the initial vacancy-interstitial pairs and phonons (e.g., vibrational energy). NIEL can be calculated using the following analytic expression that sums the elastic and inelastic contributions as: NIEL=(N/A)[oeTe+oiTi]. The o's are total cross sections, the T's are effective average recoil energies corrected for ionization loss using the Lindhard theory [Lind63], N is Avogadro's number, and A is the gram atomic weight of the target material. In the case of compounds, the total NIEL is derived as a superposition (weighted by mole fraction) of the contributions for each atomic component [Zeig84]. Notice that the units of NIEL, (keVcm2/g), are the same as IV-59 those for stopping power (or LET) describing energy transfer by ionization and excitation per unit length. Burke has calculated NIEL in silicon for protons and other ions over a broad energy range [Burk86]. More recent calculations by Burke have incorporated improvements in the treatment of the nuclear elastic and inelastic reactions, and the Lindhard correction has been applied to the differential recoil spectrum instead of to the average recoil energy of the target atoms. The more accurate calculation is given by where do/dO is the differential cross section for a recoil in direction O, T(O) is the recoil energy, and L[T(O)] is the fraction of the recoil energy that goes into displacements [Lind63]. In the case of Si, the maximum amount of displacement damage energy is about 300 keV, regardless of the energy of the recoiling atom. The maximum damage energy increases with atomic number, and is about 2 MeV for GaAs. Figure 5 shows both the LET and NIEL for Si as a function of incident proton energy. Burke has calculated the proton NIEL for a variety of other materials. The most recent published NIEL calculations can be found in the December IEEE Transactions of Nuclear Science cited as follows: InGaAs [Mars92], GaAs and