Contents lists available at ScienceDirect Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat Comparison of vibrating and fixed Kelvin Probe for non-destructive evaluation Michael Reznikov a,* , Maciej Noras b,** , Matthew Salazar a a Physical Optics Corporation, 1845 W. 205th Street, Torrance, CA, 90501, USA b University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC, 28223, USA ARTICLE INFO Keywords: Electrostatic induction Electrostatic measurements Space charge Surface corrosion Voltage measurement ABSTRACT This paper presents a comparative study of surface electrical potential measurement carried out with the classic vibrating Kelvin probe and with the newly designed swing capacitor transducer. Mathematical modeling and experimentation demonstrated that the non-vibrating swing capacitor probe is notably more sensitive (in some instances more than six times) than the vibrating Kelvin probe in cases where space charge is buried under dielectric layers with slow polarization. This provides an advantage in multi-layer structures, for example, to detect and localize corrosion under paint. 1. Introduction Excluding recent developments in the Kelvin Probe (KP) technique [1], which was stimulated by the availability of atomic force micro- scopy equipment, classic KP [2] is considered mature and established. The present work is the more detailed presentation of concept and re- search reported at the 2017 Annual Meeting of the Electrostatics So- ciety of America [3]. Originally, the capacitive probe measurement of surface (Volta) potential was proposed by Lord Kelvin (W. Thomson) [4] as a switching capacitive quadrant electrometer (CQE) utilizing the sampling capa- citor and the ground (discharge), as illustrated in Fig. 1. The CQE consists of a fixed and grounded electrode, which is split on four segments (“quadrants”), and a symmetric (for balance) elec- trode, which is suspended over the grounded electrode or between two grounded electrodes. While connected in series, the sampling capacitor and the CQE have the same charge. The ponderomotive force rotates the suspended CQE electrodes to minimize the capacitance between them and the fixed electrodes. The rotation stops when the reaction of twisted suspension compensates the torque from the electrostatic force. The established rotation angle is indicated as the angular displacement of the reflected light beam by the mirror, which is attached to the suspension. Thus, the CQE actually works as a capacitor as well as a meter of the charge induced in the capacitive sample holder. To dis- charge the CQE, it is periodically manually switched to the Earth's ground. Use of the potentiometer permits implementation of the “zero signal” approach to overcome the non-linearity of measurement, where the electrostatic rotating moment in the varied capacitor is compen- sated by the mechanical reaction of twisted suspension. Specifically, the biasing voltage of the potentiometer varies until the electrometer shows the “zero” signal. The corresponding biasing voltage is the exact po- tential difference induced between the sample of material and the re- ference electrode. Thus, the original KP actually measured the potential difference caused by the static, steady-state induced charge. To eliminate the time-consuming adjustment of biasing voltage, the vibrating electrode method [5], which is widely used in contemporary vibrating KP (shown in Fig. 2), was invented by W. A. Zisman 34 years later. In this KP, the distance between the probe and the sample ma- terial is adjusted to achieve a capacitance, C p , significantly larger than the capacitance of the probe to the ground, C G . In fact, the variation of C p and thus the aggregated capacitance, (C p -1 +C G -1 ) -1 , leads to the redistribution of electric charge between these two capacitors (C p and C G ), which generates the measured signal. The magnitude of the al- ternating current (AC) signal, created due to the vibration, is propor- tional to the variation of charge induced in the probe. The compen- sating biasing voltage is generated by the probe electronics, and it is applied either directly to the probe, as illustrated in Fig. 2, or/and to the electrostatic shield in proximity to the sensing electrode, which then cancels the electric field sensed by the probe (a field-zeroing method [6]). Such a compensating feedback loop is needed because C p (t) depends https://doi.org/10.1016/j.elstat.2018.09.008 Received 6 August 2018; Received in revised form 24 September 2018; Accepted 27 September 2018 * Corresponding author. ** Corresponding author. E-mail addresses: mreznikov@poc.com (M. Reznikov), mnoras@uncc.edu (M. Noras). Journal of Electrostatics 96 (2018) 57–63 0304-3886/ © 2018 Elsevier B.V. All rights reserved. T