p. G. KLEMENS 



The energy loss by electronic excitation will far outweigh the loss by 

 collision with the crystal atoms if the moving particle or atom has a velocity 

 which is comparable or higher than electronic velocities. At lower energies, 

 collision processes will predominate. As a rough approximation, electronic 

 excitation ceases below a limiting energy E^ given by: 



E, = M, Ej8m (7) 



where Mj is the mass of the moving particle or atom, m the electronic mass, 

 and Eq an electronic energy: in insulators Eq is the first ionization energy 

 (band gap), in metals it is the upper energy of the conduction electrons 

 (Fermi energy). In both cases Eq is typically of the order of, say, 5 eV, so 

 that Ef is several keV, except for incident electrons. 



While electronic excitations may be neglected below Ef, collisions occur 

 also above E^, though relatively rarely, and must be considered. The 

 maximum energy transferred at a single collision is : 



where E is the energy of the moving particle and Mq the mass of the crystal 

 atom. 



It is possible to calculate the total number of displaced atoms, using the 

 known cross-sections for electron excitation and collision processes, and 

 following the degradation of energy of the incident fast particle, and of each 

 atom knocked from its lattice site. Such calculations were published by 

 Seitz^, and subsequently refined — see, for example, the reviews of Kinchin 

 and Pease^ and Seitz and Koehler^. 



The total number of displaced atoms may exceed considerably the 

 number of those displaced directly by the incident particle. Each primary 

 displaced atom, starting off with a lower energy, will lose relatively less 

 energy by electronic excitation, and since its mass equals the mass of a 

 crystal atom, it will more readily transfer energy in excess of E^^ to crystal 

 atoms and thus cause further displacements. These displaced atoms will in 

 turn displace others, and so on. The total number of displacements in such 

 a cascade arising from a primary displacement is typically of the order of 

 Ef/3E^. With A/q~ lO^m, typical numbers may range from 50 to 100. 



The neutron is particularly efficient in creating displacements, as it does 

 not lose energy by electronic excitation, but only by collision. The energy 

 transfer to a knocked-on atom is of the order of 10* to 10^ eV, and each 

 primary displacement produces a cascade as discussed above. 



On the other hand, a fast electron would lose most of its energy by 

 electionic excitation, since Ef is low, and in one of the rare collisions with 

 crystal atoms only a small fraction of its energy is transferred (2), so that 

 only some of these collisions will give rise to displacements, and fewer still 

 to secondary displacements. Indeed it is possible to adjust the bombardment 

 voltage so that only primary displacements can be created. 



Electromagnetic radiation primarily produces ionization effects (electronic 

 excitation). However, if the radiation is sufficiently hard (gamma rays) it 

 can produce Compton electrons which, in turn, may be sufficiently energetic 

 to cause occasional displacements. 



273 



