Introduction

Some crystal structures are naturally polarized and thus contain electric fields in the crystals. The ability of a crystal to generate temporary voltage, when heated or cooled, is a property of certain naturally polarized crystal structures, called pyroelectricity. When the temperature is changed, the position of atoms in the crystal structure is slightly changed, resulting in a change in polarization, which further results in the generation of voltage. The pyroelectric effect can be defined as the change of polarization as a function of temperature^[1].

There are two ways to determine the pyroelectric coefficient of a material. The pyroelectric charge and pyroelectric current can be measured and used to determine the coefficient^[1].

Pyroelectric current

One method to measure the pyroelectric charge is the direct method^[2].

In this method, the sample is held at a uniform constant rate of heating (e.g., dT/dt = 1 – 2 ^◦C min^-1) and the pyroelectric current is measured.  The pyroelectric coefficient is determined from: 

Where I is the current and A is the sample area.^[2]. Figure 1 shows an illustration of the set up for this method.

Figure 1. Illustration of the direct method. (Figure: Lauri Manner)

Pyroelectric charge

Technique for measuring the pyroelectric charge called the static method was introduced in 1915^[3]. The charge is determined as a function of temperature. Glass showed an improved version of this method in his 1969 paper^[4]. The pyroelectric coefficient with this method is obtained by graphical differentiation of the charge developed on the crystal faces when temperature is raised. Figure 2 shows the schematic of this method.

Figure 2. Schematic of the static method. (Figure: Lauri Manner)

If the polarization of the material being measured is reversible (Ferroelectricity), the pyroelectric coefficient can also be determined with a Sawyer-Tower loop (Figure 3)^[5]. With this method, the temperature dependence of the remanent polarization is measured.

Figure 3. Schematic of the Sawyer-Tower Circuit. (Figure: Lauri Manner)

Thin Films

The methods discussed above are mainly used for bulk samples. In case of thin films, estimating the parameters required for pyroelectric measurements can be challenging due to complex behavior, like stresses from growth or substrate clamping, and properties differing from bulk samples. 

There are, however, approaches to measure the pyroelectric coefficient from thin films. For example by heating the substrate and ignoring the presence of the thin film. Due to the heat capacity of the substrate being higher than the films, the heating of the film is guaranteed to be homogeneous. With this approach, any bulk material technique is also applicable. ^[6]For self supported, edge-clamped thin films, which pose unique opportunities for detector applications, there are two major measurement geometries. One way is to illuminate a small area in the center of the membrane, which generates pyroelectric current. Another way is by illuminating the membrane uniformly, which again produces pyroelectric current. 

When small area of the membrane is illuminated, the radiative resistance can be calculated simply with the area of the blackened area and the Stefan-Boltzmann radiation law. The pyroelectric coefficient can then be determined from the amount of absorbed radiation. With the uniform illumination, the total current is calculated from the derivative of the temperature with time in each point of the film and then summed over the whole area of the film.^[6]

Examples

In a study by Iljima et al. the direct method was utilized to measure the pyroelectric coefficient of PbTiO₃ thin films. These c-axis oriented thin films showed significiant pyroelectric currents in all grown specimen. One of the films had a large pyroelectric coefficient γ of 2.5 * 10^-8 C/cm² K. These films were suggested for applications to pyroelectric infrared detectors.^[7]

A very good example of the utilization of pyroelectric charge comes from the study by Glass, where he improved the static method and measured the change of polarization of Sr_1-xBa_xNb₂O₆. When x was 0.27, highest value for the pyroelectric coefficient was measured of 28 μC/m²K^[4].

Usual values for the pyroelectric coefficient depends on the ferroelectricity of the material. Some of the crystal that are pyroelectric are also ferroelectric, meaning that the electric field caused by the change in polarization can be altered with an external electric field. Table 1 shows pyroelectric coefficients for some pyroelectric materials.

Table 1. Pyroelectric coefficients for ferroelectric and nonferroelectric materials (units are μC/m²K). Values from^[8].

The primary coefficient comes from the electric displacement caused by the change in temperature. The secondary coefficient is due to the crystal deformation from thermal expansion, which causes electric displacement in the piezoelectric crystals^[8]. As Table 1 shows, ferroelectric materials show higher pyroelectric coefficients, which is the reason that these materials are usually more interesting in the applications of pyroelecric materials.

References