Lattice dynamics of diamond-like crystals from a tight-binding calculation of valence bands

We report on the results of calculations of the TA(X) phonon energy in the series of C, Si, Ge, Sn homopolar crystals. The starting point is the tight-binding model for the electronic Hamiltonian where Esand Epare taken to be the free atomic energies while the interatomic matrix elements are described by a universal d‒2Harrison's scaling law. The change of the total energy with the atomic distortion is given in terms of changes in the valence band energy and changes in the overlap energy. The numerical calculations for Si gives U1= ‒21.77eV and U2= 60.44eV, close to the values predicted by Harrison U1= ‒17.76eV and U2= 53.28eV. The calculations of the TA(X) phonon energy gives (in the case the interatomic distances are held constant): 26.09 THz (C), 6.46 THz (Si), 3.37THz (Ge) and 1.91 THz (Sn), in reasonably good agreement with the experimental results 24.1 THz (C), 4.49 THz (Si), 2.39 THz (Ge) and 1.26 THz (Sn). © 1988 IOP Publishing Ltd.