The temperature dependence of the Grüneisen parameters of MgSiN2, AlN and (beta)-Si3N4

In this work, we present a method of improving the transferability of the Slater-Koster Tight-Binding (SK-TB) parameters given in [Handbook of the Band Structure of Elemental Solids, Plenum Press, New York, 1986] to describe the electronic properties at other lattice constants and structures. First of all, we express the Hamiltonian and onsite atom parameters as a function of distance. We validate our method by calculating the electronic structure for various lattice constants for Nb and Mo (bcc) and for Cu and Au (fcc) and we find good agreement with the APW results. Furthermore, we transfer successfully the SK-TB parameters of the bcc to the fcc structure of Nb and Mo and vice versa for Cu and Au. Moreover, we apply a uniform shift Vo, which equates the sum of SK-TB eigenvalues to the APW total energy for the available volumes. We find that Vo presents a smooth volume dependence. Finally, using the volume dependence of Vo and the SK-TB theory we calculate the total energy for every lattice constant.