Tight binding model and interactions scaling laws for Silicon and Germanium

We provide a set of parameters for second-neighbor tight-binding model Hamiltonians, including spin-orbit interaction, in silicon and germanium. Our attempt is the construction of a simple Hamiltonian, useful as a stepping stone for the description of more complex systems. We introduce a criterion for establishing transferable scaling laws of the parameters. The results obtained, checked versus determination of deformation potentials under hydrostatic and uniaxial [001] stress, indicate a clear deviation from the d-2 Harrison scaling law.