On Anomalous Diffusion of Fast Electrons through the Silicon Crystal

Abstract

Anomalous diffusion is a random process in which the root-mean-square displacement of a particle from the starting point depends nonlinearly on time. The possibility of such behavior for high-energy particles moving through the crystal under conditions close to axial channeling was found earlier. In this case, the rapid displacement of particles in a plane transverse to atomic strings (Lévi flights) is due to the temporary capture of the particles in planar channels. In this work, the anomalous diffusion exponent has been found by numerical simulation for different values of the energy of electron transverse motion in the (100) plane of a silicon crystal. It has been shown that, in the case of electrons with an energy exceeding by 1 eV the height of the saddle point of the potential of a system of atomic chains [100], the results are consistent with those obtained earlier. It has been confirmed that the anomalous nature of diffusion is due to the possibility of short-term capture of particles in planar channels. With increasing transverse energy, this possibility disappears and the diffusion becomes normal (Brownian).