Secondary effects in wide frequency range measurements of the pyroelectric coefficient of ${\mathrm{Ba}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{TiO}}_3$ and ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ epitaxial layers

We describe measurements of the pyroelectric coefficient of epitaxial layers of ${\mathrm{Ba}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{TiO}}_3$ (BST) and ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ (PZT) using a modulated laser as the heat source in the frequency range 1 Hz to 10 MHz. The pyroelectric coefficient is also measured as a function of applied static electric field and for films grown on ${\mathrm{SrTiO}}_3$, ${\mathrm{DyScO}}_3$, and ${\mathrm{GdScO}}_3$ substrates. The heat diffusion equation is solved in cylindrical coordinates for the temperature field in a multilayer sample heated by a Gaussian-shaped laser beam. The secondary contribution to the pyroelectric effect caused by piezoelectric effects and in-plane thermal expansion is revealed by the difference between the pyroelectric coefficients at high and low frequencies. The secondary pyroelectric effect has the same dependence on applied field as the pyroelectric coefficient. The magnitude of the secondary effect changes with heating frequency because of changing mechanical conditions, but the pyroelectric coefficient has no other frequency dependence between 1 Hz and 10 MHz. The secondary effect is approximately 15% and 20% of the total pyroelectric response for PZT and BST films, respectively.

Figure 1

(a) Schematic description of the pyroelectric measurement. (b) Relative phases of the oscillating heat flux, $F$, temperature oscillations created by the heat flux, $T$($f$), and the measured ac current, $I$($f$). When nonpyroelectric currents are negligible in comparison with the pyroelectric current, the measured current leads the temperature change by 90°. The temperature change lags the heat flux by a phase angle, $\phi \left(T\right)$, that depends on frequency. The phase angle of the current, $\phi \left(I\right)$, is measured by the lock-in amplifier.

Figure 2

Heat transport model for the pyroelectric measurement. A Gaussian-shaped laser beam with a power $P_0$ and 1/$e$² radius $w_0$ is absorbed at the V top layer. The temperature oscillation within the pyroelectric film is $T(f,r,z)$. $\left(\begin{array}{cc}A& B\\ C& D\end{array}\right)$ is the heat transport matrix for the entire sample, and $\left(\begin{array}{cc}{A}_z& B_z\\ C_z& D_z\end{array}\right)$ is the heat transport matrix for a part of the sample at a distance $z$ from the top layer.

Figure 3

(a) Frequency dependence of the amplitude of the pyroelectric current. Measured data are shown as open circles, and the solid line is the model calculations for a fixed value of the pyroelectric coefficient. (b) The measured phase angle of the current (open circles), $\phi \left(I\right)$, and the phase angle of the pyroelectric current (solid line) calculated from the phase angle of the temperature, ${90}^{\circ }+\phi \left(T\right)$ for the BST/STO sample at zero bias voltage. The good match between the measured and calculated phase supports our assertion that nonpyroelectric currents are negligible in these experiments.

Figure 4

Sensitivity of the calculated amplitude of the temperature oscillations, see Eq. (11), as a function of selected parameters in the thermal model as a function of heater frequency for a PZT film on a DSO substrate. The radius of the top contact is 50 μm. Sensitivity to the laser power is unity.

Figure 5

Frequency dependence of the pyroelectric coefficient of the ${\mathrm{Ba}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{TiO}}_3$ layer grown on a ${\mathrm{SrTiO}}_3$ substrate. The radius of the top contact of the devices is (a) 50 μm and (b) 100 μm.

Figure 6

Hysteresis of the pyroelectric coefficient of PZT and BST films measured at 20 Hz and 20 kHz at room temperature. The $x$ axis of each plot is the dc bias voltage that is applied to the capacitors. The time between changes in the bias voltage is ∼30 s, and the increment between values of the bias voltate is 0.2 V.

Figure 7

Secondary pyroelectric coefficient of PZT and BST films due to the thermal expansion mismatch between the film and substrate as a function of the bias voltage. The right-hand axis of each plot is the corresponding converse piezoelectric coefficient $d_{31}$, calculated based on Eq. (12).