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А. С. Долгов, Ю. Л. Жабчик
«Миграция примесных атомов в структуре графена»
PACS numbers: 61.48.Gh, 61.72.Bb, 61.72.J-, 61.72.Yx, 66.30.jp, 66.30.Pa, 68.35.Fx
The dependence of the graphene outstanding features (conductivity, etc.) either on the total defectiveness level or on the impurity distribution predetermines the importance of an analysis of the impurity-atoms’ transfers’ microkinetics over the graphene surface. The task of impurity-atoms’ transfer in the two-dimensional hexagonal structure, which models the single-atom carbon plane, is considered. As suggested, the impurity atoms occupy the positions in the vicinity of a certain atom of the host structure. The unlimited set of equations of the occupation-numbers’ kinetics for all the graphene sites by the including of the corresponding-type generating function is reduced to the finite set of the non-linear integrodifferential equations. The general properties and particular cases of obtained equations are examined. The moments of function of the particles’ distribution over the sites are defined. As shown, when the external influence setting the orientational irregularity of the jump probabilities is absent, then the equations for generating function may be linearized. Due to linearized equations, the general regularities of migration become like the behaviour of non-interacting particles or single vacancies. The respective parameters define some class of the migration processes, where the loss of the kinematic-interaction influence on the migration conformity is a general property. Interplay of the diffusion and drift components in a movement is revealed, when the external influence is sufficiently strong. The migration pattern is asymptotically isotropic. The features of the impurity-atoms’ redistribution between the both sides of graphene, which models the carbon structure with added hydrogen atoms (‘graphan’), are examined. For the spatial homogeneity conditions, the kinetics equations are reduced to the relationships for the average probabilities of filling of the positions on both graphene sides. As revealed, the impurity-atoms’ distribution relaxes to the equilibrium state, which can differ from the separation of a total amount of impurity atoms пополам, independently on the initial-filling. The relaxation parameter depends on both diffusion characteristics and the impurity-component density. The tendency to slowdown of the relaxation processes under the average level of filling of the structure is revealed. As also determined, the equilibrium state is less sensitive to the temperature than the probabilities of jumps.