Thick-Film Piezoelectrics

Most of the early types of thick-film sensor were based on the principle that the properties of commercially available pastes could be exploited in some way. Thick-film strain gauge being the classic example. Thick-film piezoelectric sensors, on the other hand, have evolved from the need to develop special-purpose pastes with enhanced sensing characteristics.

Some of the fundamental linear relationships between the electrical and mechanical quantities of a piezoelectric material are given below:

D = dT + e ^TE	(1)
S = s^ET + dE	(2)

where D is the dielectric displacement, T the stress, e the dielectric constant, S the strain, E the applied electric field, s the compliance (inverse of modulus) and d (C/N) is a piezoelectric coefficient. The superscripts denote the quantity being kept constant at the boundary conditions. For example s^E is the compliance at a constant electric field (electrodes short circuited).

Equation (1) describes the direct piezoelectric effect. Any linear dielectric will posses the e ^TE term so, for a piezoelectric material, the equation relates the dielectric displacement to the applied stress. Equation (2) describes the reverse piezoelectric effect, relating the strain produced in response to an applied stress and electric field. For vibration or motion applications such as sounders high d coefficients are desirable. A further quantity is the voltage coefficient g, given by

(3)

This represents the open circuit voltage generated by an applied stress and is expressed in Vm/N.

In general the d and g coefficients have different values depending upon the orientation used. Numerical subscripts are used to specify the directional properties. Direction 3 is considered to be the direction along which the sample has been polarised and directions 1 and 2 are the other perpendicular dimensions. The d and g coefficients normally have two subscripts, the first of which refers to the electrical quantity, and the second represents the mechanical quantity. As an example, d₃₃ is a coefficient of the material measured when the applied force is along the same direction as the poling axis. For a disc, this would be the equivalent of a tensile or compressive force being applied across the thickness of the piezoelectric material.

The original discovery of piezoelectricity was in 1880 by Jacques and Pierre Curie who found that certain crystals produced a charge when stressed mechanically. The family of ferroelectric ceramic materials such as barium titanate and lead zirconate titanate (PZT) were developed in the 1940s. PZT is a ferroelectric material and hence the films must be polarised prior to use. This is achieved by placing a high electric field (around 3 MV/m) across the sample and elevating the temperature. Before polarisation the dipoles within the piezoelectric material are aligned in a random manner. The poling process causes the dipoles to align along the direction of the applied electric field. When the field is removed the material is left in a state of remnant polarisation. A plot of polarisation versus applied field yields the classic hysteresis curve, the analogy of a ferromagnetic material. The amount of remnant polarisation within the material depends on the poling conditions and therefore varies with the magnitude of the applied field and also the time and temperature. Other piezoelectric coefficients are affected similarly.