Piezoelectric Coefficient Characterization Using Combined Electrical and Light-Based Methodology

The extraction of
$\mathrm {d}_{33}$
piezoelectric charge constant versus applied voltage profiles play an important role in the design of tunable RF devices and circuits. Lead zirconate titanate (PZT) piezoelectric materials exhibit high piezoelectric constants and lightweight properties, which makes them promising candidates for high-performance smart RF-based tunable structures. Therefore, there is a need for characterizing piezoelectric materials relevant to their applications to predict their response during such operations. In this work, a combined electrical and light-based methodology to characterize the voltage dependency profile of
$\mathrm {d}_{33}$
is developed. A set of equations are extracted based on the electrical capacitance and light profilometer analysis. These equations are then used to compute the effective
$\mathrm {d}_{33}$
numerical values. PZT thin film of
$1~\mu \text{m}$
has been sandwiched between two electrodes and poled with the application of 20 volts/
$\mu \text{m}$
to demonstrate the power of the current approach. The voltage-based capacitance and change in area of the sample were collected at different DC biases. The numerical values obtained by the existing conventional methods lie in the computed range obtained by the current technique. It is worth adding that it is quite difficult to absolutely decide which method produces the most representative numerical values due to the substrate clamping effect, probing, resolutions, and accuracy.