First-principles calculation of the piezoelectric tensor d of III-V   nitrides
  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. 
F. Bernardini, V. Fiorentini (Cagliari)