Vibrational Properties of the 〈001〉 Split Interstitial in Silicon

Abstract

AbstractA theoretical investigation is made of the vibrational behaviour of the 〈001〉 split interstitial in silicon using the Green's function formalism. In particular, the cases of the Si‐Si, C–C, and C–Si dumbbell are discussed. For the numerical calculation of the vibrational frequencies a modified Keating force model is used, in which the coupling of the dumbbell stoms each with another and to the four nearest‐neighbour atoms as well as the changes in the force constants between these four neighbours are described in terms of the ratio d/x (2d separation of the dumbbell atoms,4a lattice constant). The calculations are performed with d/a as parameter using a perfect crystal Green's function determined from neutron scattering data. The results show for reasonable values of d/a (0.5 ≦ d/a ≦ 1) in the case of the equiatomic dumbbell (D2d symmetry) the existence of two high‐frequency localized vibrations (an A1 ‐ and a B2 ‐ mode) and of two doubly degenerate (E ‐ type) resonance modes or localized modes near the maximum lattice frequency. In the case of the mixed dumbbell (C2v symmetry) also two high‐frequency localized modes (both of A1 ‐ type) and four resonance or low‐frequency localized modes (two of B1 and two of B2 ‐ type) are obtained. On the basis of the above calculations, an interpretation of the C(I) infrared absorption bands observed in carbon‐doped electron‐irradiated silicon crystals as the two A1 ‐ modes of the C–Si〈001〉 dumbbell can be made on the basis of the absolute values of the frequencies and the relative line intensities but becomes difficult when considering also the separation of the two modes and its isotopic shift with respect to carbon.