Surface-induced charge disturbances and piezoelectricity in insulating crystals

The charge disturbance induced by a surface in a three-dimensional insulating crystal is studied in the self-consistent-field approximation, when the surface is parallel to one of the lowest-index crystal planes. The disturbance is shown to decay exponentially into the interior of the crystal with a decay rate which depends only on the band structure of the infinite crystal and the position of the Fermi level relative to any surface states that may be formed. We then show that the macroscopic piezoelectric response of a semiconducting crystal does not depend on the way in which the crystal is terminated, thus resolving a previous controversy.