4 - Effects

Piezoelectric effect means the production of electricity by pressure; more exactly, a polarization change vias mechanical strain or stress variation. Practically, it can be measured as a generated voltage between two electrodes. Piezoelectricity occurs only in insulating materials and is manifested by the appearance of charges on the surfaces of a piece of material that is being mechanically deformed. It is easy to see the nature of the basic molecular mechanism involved. The application of stress has the effect of separating the center of gravity of the positive charges from the center of gravity of the negative charges, producing a dipole moment. Clearly, whether or not the effect occurs depends upon the symmetry of the distributions of the positive and negative charges. This restricts the effect so that it can occur only in those material structures that are not having a center of symmetry. For a centro-symmetric crystal, no combination of uniform stresses will produce the necessary separation of the centers of gravity of the charges. It is clear that the converse effect also exists. When an electric field is applied to a piezoelectric crystal, it will strain mechanically. There is a one-to-one correspondence between the piezoelectric effect and its converse. The electric polarization, P, is related to the mechanical stress, T, or, conversely, the development of a mechanical strain, S, is related to an applied field, E. One can define a piezoelectric coefficient, d, respectively and similarly d^* to the converse effect, by: , where the subscript E indicates that the field is held constant and the subscript T that the stress is held constant. Because the polarization and electric field are vector quantities and mechanical stress and strain are second rank tensors, d must be a third rank tensor. It will consist of 27 elements, but based on the symmetry, only of 15 independent ones. An alternative piezoelectric coefficient, g, may also be defined as . Quartz is a classical example for piezoelectric crystals. Polycrystalline and amorphous materials in which the axes of the dipole moments are randomly oriented show no piezoelectricity. If the axes can be suitably aligned, piezoelectric polycrystalline ceramic materials [e.g., lead-zirconate-titanate (PZT), and BaTiO₃] or polymers [polyvinylidene-fluoride (PVDF)] can be produced.

It has been well known for several decades that metal films, semiconductor, and CERMET film resistors are characterized by a resistance variation when mechanical stress and/or strain is applied. This is due to the superposition of two effects: one is the resistivity change versus stress, called piezoresistivity, and the other is a pure geometrical effect caused by the deformation (called "geometrical piezoresistivity"). More recently, it has been pointed out that polymer thick film (PTF) resistors screened and cured on epoxy-glass or polyimide substrates also present a notable sensitivity to deformation. If a mechanical stress, T, is induced on a resistor, the resistivity (r) change can be expressed as: , where is the piezoresistivity coefficient. The behavior of single crystals with anisotropy (like silicon) can be described with a fourth rank tensor. In the practice, p-type resistors are used in the [110] crystal direction and the tensor equation can be simplified, thus ( is the stress). The deformation sensitivity of a resistor can be described with the gauge factor: , where L is the resistor length. If the current is parallel to the strain, the longitudinal G_L , and if the current is perpendicular to the strain, the transverse G_T gauge factors can be defined. For isotropic film type resistors their difference is determined by the Poisson ratio : . In metal film resistors, the change in resistivity is negligible. The basis of operation of a strain gage that consists of a metal alloy deposited onto flexible polymer substrates relies basically on a geometrical effect.

An electret is a piece of dielectric material, which has permanent polarization. If the internal leakage current through the dielectric is small the polarization remains constant for a long time. Preventing the charge neutralization effect caused by the surrounding gas molecules, for instance keeping the electret in vacuum, the polarization acts as a built-in voltage between two electrodes. If one electrode of the capacitor is deformed by pressure, the capacitance variation with the built-in voltage induces a measurable voltage variation when connected into a circuit. This is the operation principle of condenser microphones which would need a high voltage source without the application of electrets.