Theoretical study of the diffusion of lithium in crystalline and amorphous silicon

The effect of the lattice deformation on potential barriers for the motion of a lithium atom in crystalline silicon has been studied through ab initio density functional calculations. A new universal method of calculating the diffusion coefficient of an admixture in amorphous solid media through the activation mechanism has been proposed on the basis of these data. The method is based on the calculation of the statistical distribution of potential barriers for the motion of an admixture atom between minima depending on the position of neighboring atoms. First, the amorphous structure, which is generated by annealing from the crystalline structure with vacancies, has been simulated. Then, the statistical distribution of the potential barriers in the amorphous structure for various local environments of the admixture atoms has been calculated by means of linear regression with the parameters determined for barriers in crystalline silicon subjected to different deformations. The diffusion coefficient of the admixture has been calculated from this distribution by using the Arrhenius formula. This method has been tested by the example of crystalline and amorphous silicon with admixture of lithium atoms. The method demonstrates that the diffusion of lithium in amorphous silicon is much faster than that in crystalline silicon; this relation is confirmed experimentally.