  The deformation potentials of cubic semiconductors are re-examined from the
point of view of the extended-basis $sp^3d^5s^*$ tight-binding model. Previous
parametrizations had failed to account properly for trigonal deformations, even
leading to incorrect sign of the acoustic component of the shear deformation
potential {\it d}. The strain-induced shifts and splittings of the on-site
energies of the p- and d-orbitals are shown to play a prominent role in
obtaining satisfactory values of deformation potentials both at the zone center
and zone extrema. The present approach results in excellent agreement with
available experimental data and ab-initio calculations.
