Uncertainties of the Pulsed Electroacoustic Method: Peak Positions of Embedded Charge Distributions

The pulsed electroacoustic (PEA) method allows for nondestructive measurements of internal charge distributions in dielectric materials. These measurements have been paramount in understanding and mitigating charge accumulation, aging, and electrostatic discharge in materials for various applications. This study aims to examine more closely the uncertainties of pulsed electroacoustic measurements. The first few moments of a charge distribution are directly related to the magnitude, peak position, full-width-at-half-maximum, and skewness. The uncertainty in the magnitude of the charge distribution is often quite large, but the peak position can be determined with a precision of $\lt 1 {\mu} \text{m}$. This has been demonstrated in our lab with repeated PEA measurements of polyether-etherketone (PEEK) with internal charge present. This precision is further validated with measurements of PEEK irradiated with differing doses of 50 keV incident electrons, resulting in peak positions that differ by only a few ${\mu} \text{m}$. A final test is given by measurements monitoring the slow migration of the charge distributions in these irradiated samples over several months. The measured shifts in the peak position of the charge distributions are $\leq 1 {\mu} \text{m}$. Though the spatial resolutions of PEA measurements are typically $\sim 10 {\mu} \text{m}$, as defined by the fullwidth-at-half-maximum of the leading interfacial peak, the precision of the peak position can be more than an order of magnitude greater. The statistical analysis of the repeated measurements to determine uncertainties, as well as the validation measurements, demonstrate the high precision determination of the peak position of embedded charge distributions.