  Fundamental properties of spontaneous and piezo polarization are reformulated
and critically reviewed. It was demonstrated that Landau definition of
polarization as a dipole density could be used to the infinite systems. The
difference between the bulk polarization and surface polarity are distinguished
thus creating clear identification of both components. The local model of
spontaneous polarization was created and used to calculate spontaneous
polarization as the electric dipole density. It was shown that the proposed
local model correctly predicts c-axis spontaneous polarization values of the
nitride wurtzite semiconductors. It was also shown that the proposed model
predicts zero polarization in the plane perpendicular to the c-axis, in
accordance with symmetry requirements. In addition, the model results are in
accordance with polarization equal to zero for zinc blende lattice. These data
confirm the basic correctness of the proposed model. The spontaneous
polarization values obtained for all wurtzite III nitrides (BN, AlN, GaN and
InN) are in basic agreement with the earlier calculations using Berry phase and
slab models of Bernardini et al. {Bernardini et al. Phys Rev B 56 (2001) R10024
& 63 (2001) 193201} but not with Dreyer et al. {Dreyer et al. Phys. Rev X 6
(2016) 021038}. Wurtzite nitride superlattices ab initio calculations were
performed to derive polarization-induced fields in the coherently strained
lattices showing good agreement with the polarization values. The strained
superlattice data were used to determine the piezoelectric parameters of
wurtzite nitrides obtaining the values that were in basic agreement with the
earlier data. Zinc blende superlattices were also modeled using ab initio
calculations showing results that are in agreement with the absence of
polarization of all nitrides in zinc blende symmetry.
