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

Origin of non-linear piezoelectricity in III-V semiconductors: Internal strain and bond ionicity from hybrid-functional density functional theory