On anomalous diffusion of fast electrons through the silicon crystal

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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, by means of numerical simulation, the anomalous diffusion exponent was found for different values of the energy of electron transverse motion in the (100) plane of a silicon crystal. It has been established 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 diffusion becomes normal (Brownian).

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About the authors

V. V. Syshchenko

Belgorod State University

Author for correspondence.
Email: syshch@yandex.ru
Russian Federation, Belgorod, 308015

A. I. Tarnovsky

Belgorod State University

Email: syshch@yandex.ru
Russian Federation, Belgorod, 308015

V. I. Dronik

Belgorod State University

Email: syshch@yandex.ru
Belgorod, 308015

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Supplementary files

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2. Fig. 1. Potential energy (7) of an electron moving near the [100] direction of a silicon crystal.

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3. Fig. 2. Typical trajectory of an electron in the plane transverse to the [100] direction of a silicon crystal. The energy of the transverse motion of an electron is 0.5 eV.

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4. Fig. 3. Numerically found time dependences in logarithmic scale for electrons with transverse motion energy of 0.5 (thin solid line), 1 (thin dashed line), 1.5 (thin dash-dotted line), 2 (thick solid line), 2.5 (thick dotted line) and 3 eV (thick dashed line) for variants (a) and (b) of initial conditions. In the case of the second variant, the values ​​of t0 used in Fig. 4 are marked with a circle and a dot on the curve for electrons with eV.

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5. Fig. 4. Graphs in the case of eV, obtained by formula (12) for mm (dotted line) and mm (dashed line), and also as a derivative of the function approximating the logarithmic curve in Fig. 4 by a polynomial of the 25th degree (solid line). The points correspond to the numerically found values ​​of the slope of the tangents to the logarithmic curve in Fig. 3b.

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6. Fig. 5. Dependencies for all studied values, calculated using formula (12) for mm for options (a) and (b) of choosing initial conditions; line types correspond to Fig. 3. Short horizontal lines in the figures on the right correspond to the values ​​of µend from Table 1.

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