Acoustic resonance, polarization moment and surface layer in dielectric plates

The fourth-order differential equations for the transverse displacement of a dielectric inhomogeneous plate in an electric field are solved analytically and the acoustic response is expressed in terms of an equivalent electrical circuit. Its components are determined experimentally from the flexure resonance characteristics and the polarization moment is deduced from the data. Polarization moments are reported for KH2PO4, KD 2PO4, KH2AsO4 SrTiO3 and BaTiO3. These moments are analysed in terms of the space-charge model involving drift and diffusion and a mismatch of electron affinity at the interface. For narrow depletion layers, the moments are proportional to the plate thickness. For deep depletion of carrier exhaustion throughout the sample, a third-power dependence of the moment on plate thickness is predicted.