  We derive first- and second-order piezoelectric coefficients for the
zinc-blende III-V semiconductors, {Al,Ga,In}-{N,P,As,Sb}. The results are
obtained within the Heyd-Scuseria-Ernzerhof hybrid-functional approach in the
framework of density functional theory and the Berry-phase theory of electric
polarization. To achieve a meaningful interpretation of the results, we build
an intuitive phenomenological model based on the description of internal strain
and the dynamics of the electronic charge centers. We discuss in detail first-
and second-order internal strain effects, together with strain-induced changes
in ionicity. This analysis reveals that the relatively large importance in the
III-Vs of non-linear piezoelectric effects compared to the linear ones arises
because of a delicate balance between the ionic polarization contribution due
to internal strain relaxation effects, and the contribution due to the
electronic charge redistribution induced by macroscopic and internal strain.
