Towards a three-dimensional analysis of polarization profiles in electret materials with thermal methods

Thermal pulse or thermal wave methods (such as the Laser Intensity Modulation Method, LIMM) are widely used to measure the distribution of space charge and/or electrical polarization in polymers and ceramics. Recent advances in data acquisition and processing made it possible obtain three dimensional polarization maps by scanning a focused laser beam across the sample. While extracting a polarization depth profile from the measured short-circuit current is a mathematically ill-posed problem, there are a number of proven techniques that allow the reconstruction of the polarization function p(z). However, these approaches generally assume a one-dimensional model for the spatial temperature distribution T(z) (where z is the depth coordinate), based on an analytical solution of Fick\´s second law. As was shown experimentally, this model neglects the fast lateral thermal diffusion in the (usually metallic) top electrode, resulting in a loss of lateral resolution. Since typical thermal diffusivities of metals are of the order of 10"4 m2/s (some three orders of magnitude higher than in polymers), the effects can be quite significant. For example, consider a material with a laterally structured polarization, as shown in Fig. 1. Even though the laser beam is focused on an area with zero polarization, the thermal pulse probes part of the poled region, leading to a non-zero pyroelectric current. When the data is then analyzed using the traditional one-dimensional model, one would mistakenly obtain a polarization under the spot of the focused beam. Hence, the lateral resolution can be significantly less than the laser spot size. In this work, we use a coupled equations approach together with a numerically calculated temperature distribution for a bi-layer system (metal electrode + polymer sample) to reconstruct the polarization profile of a two-dimensional model system. The results can be easily adapted to a real-world three-dimensional case.