Theory of phonon dispersions and piezoelectricity in multilayers of hexagonal boron-nitride

Taking into account covalent, Coulomb and van der Waals interactions, we construct the dynamical matrix and calculate the phonon dispersion relations for multilayer crystals of hexagonal boron-nitride. Coulomb interactions account for a strong overbending of optical phonons. Applying and extending Born's long-wave theory to the case of multilayer crystals, we calculate the piezoelectric stress constant e(1),(11)(N) as a function of the number of layers N. In agreement with group theory, we find that e(1,11)(N-g) = 0 for N-g even; for an uneven number N-u of layers we obtain e(1,11)(N-u) = 7.31 x 10(-5) C cm(-2)/N-u, i.e. the piezoelectric constant decreases as 1/N-u. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim