We show that the piezoelectric effect that describes the emergence of an electric field in response to a crystal deformation in III-V semiconductors such as GaAs and InAs has strong contributions from second-order effects that have been neglected so far. We calculate the second-order piezoelectric tensors using density functional theory and obtain the piezoelectric field for [111]-oriented In$_x$Ga$_{1-x}$As quantum wells of realistic dimensions and concentration $x$. We find that the linear and the quadratic piezoelectric coefficients have the opposite effect on the field, and for large strains the quadratic terms even dominate. Thus, the piezoelectric field turns out to be a rare example of a physical quantity for which the first- and second-order contributions are of comparable magnitude.
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