Radiation-induced generation of Frenkel defects in silicon and germanium

Modification of properties of crystals under the action of defect-generating radiation is determined to a considerable extent by the Frenkel defect generation function, i.e. by the distribution of defects in terms of the distance between a knocked-out atom I and corresponding vacancy V that are genetically close (related to one and the same site). There are various definitions of the generation function. The distance R between an atom reaching its 'halting' energy Tf (at which any further nonthermal jumps are impossible) and the initial lattice site is an argument of the generation function. Let us define the partial generation function hT(R) as a probability density of the fact that as a result of the N = N(T) random jumps (atom-atom collisions) an atom with an energy of T will stop at a distance between the limits R and R+dR from its genetically close vacancy. If the distance R is expressed in terms of mean jump length l, then hT(R) will coincide (within the accuracy of notation) with the random walk probability wN(P) of the fact that as a result of N random jumps an atom will be at a distance between the limits P and P+1 from the starting point of walks, i.e. hT(R) = wN(T)(P) where P, as is known from the theory of random walks, is equal to R/l. Since the distribution of atoms of a crystal in the energy values T attained by them during collisions with electrons of energy E is determined by the differential cross-section of the energy transfer ∂σ(E,T)/ ∂T, it is also possible to consider an integrated defect generation function fE(P) that describes the distribution of defects in P within slices whose thickness is substantially smaller than the distance covered by attacking electrons in an irradiated sample, i.e. when secondary electrons may be neglected. Finally, it is possible to introduce the most general generation function gr,e0 describing the distribution of defects in their P within samples whose thicknesses are comparable to or in excess of path lengths of attacking electrons of energy E0. The present paper is designed to develop a theory that is able to determine generation functions. (author)