  We report direct first-principles density-functional calculations of the
piezoelectric tensor $\tensor{d}$ relating polarization to applied stress for
the binary compounds AlN, GaN, and InN. The values of $\tensor{d}$ are rather
sensitive to the choice of the exchange-correlation functional, and results are
presented for both the local-density and gradient approximations. A comparison
with experiment and with values predicted indirectly from the elastic and
e-piezoconstant tensors is also presented.
