Electric Dipoles due to Trapped Electrons

The state of an electron trapped at a vacancy or impurity is described by a linear combination of atomic orbitals centred on the nearest neighbours. It is shown that when there are three mutually equidistant nearest neighbours or four, tetrahedrally disposed, the trapped electron may give rise to an electric dipole with directional degeneracy. The condition under which the electron ground state presents an electric dipole is obtained. To first order in deformation, the coupling of the dipole with the lattice does not destroy the directional degeneracy. Such a dipole leads to a Debye type of dielectric loss and piezoelectricity and also permits a resonance experiment with an alternating electric field.