First-principles study on structural, dielectric, and dynamical properties for three BN polytypes

We report the results of first-principles calculations on the structural properties (lattice constants and internal parameters), dielectric properties (macroscopic and static dielectric constants, and Born effective charge tensors), and dynamical properties $(\ensuremath{\Gamma}$-phonon frequencies) for the three polytypes of BN: the cubic zinc-blende structure $(c$-BN), the wurtzite structure $(w$-BN), and the hexagonal structure $(h$-BN). Our calculations were performed with the ultrasoft pseudopotential method and the linear response approach based on density-functional perturbation theory. By comparing the cohesive energies, we found that the c-BN structure is the most stable among the three polytypes at zero temperature. The computed equilibrium structural parameters, bulk moduli, and dielectric properties are in good agreement with the experimental data except for the lattice constant c of h-BN and the macroscopic dielectric constant along the c axis of h-BN. The $\ensuremath{\Gamma}$-phonon frequencies of c-BN and w-BN are close to each other. In order to distinguish c-BN and w-BN by Raman spectroscopy, it turns out that we should investigate the two Raman active ${E}_{2}$ modes that exist only in w-BN.