Atomic structure and energy of grain boundaries in silicon, germanium and diamond

Abstract

Abstract We have used Stillinger-Weber and Tersoffpotentials to calculate and simulate the atomic structures of ⟨011⟩ tilt boundaries with Σ = 1+2n2 (n = 1,2,3,4) in silicon, germanium and diamond lying in (111), (122), (133) and (144) planes with corresponding angles of 70.53°, 38.94°, 26.53° and 20.05° respectively. Both Stillinger-Weber and Tersoff potentials gave consistent values of grain boundary energies for silicon. The energies for diamond were considerably higher (about a factor of 6–7) than the corresponding values for silicon and germanium. The calculated values of the grain boundary period are in good agreement with coincidence site lattice periods. The boundaries with tilt angles θ< 20.05° can be represented by arrays of (a/2)⟨110⟩{001} dislocations with no dangling bonds. High-resolution electron microscopy results on the atomie structures of Σ=3, fivefold twins, and Σ = 9 are discussed. The high energy Σ = 9 boundary (second order twin) has been shown to split into two Iow energy Σ = 3 (first-order or primary twin) boundaries.