Samples (A61 or A64) along with the error terms are determined. The actual impedance is then extracted for the PZT and PMN-PT samples applying the same error terms. Nonetheless, the determination of the relative dielectric continual of the investigated samples demands an added modelling of their capacitive structures. This -Irofulven Purity & Documentation implies a traceable metrological characterization of their structural dimensions (layer thickness and gold electrode region) to be employed for the capacitances’ calculations. The workflow of our protocol is schematically depicted in Figure two. Within this work, we describe the unique solutions adopted to this end Nanomaterials 2021, 11, x FOR PEER Review propose novel approaches to overcome intrinsic difficulties associated to complicated five of 19 and we structures and considerably rough surfaces.Figure 2. Schematic diagram describing the workflow measures of our measurement and simulation Figure 2. Schematic diagram describing the workflow methods of our measurement and simulation protocol for the determination of the dielectric continual of your high- samples. d and C denote the protocol for the determination from the dielectric continuous from the high- samples. d and C denote the measured thickness and capacitance with the PZT and PMN-PT dielectric layers, respectively. measured thickness and capacitance with the PZT and PMN-PT dielectric layers, respectively.three. Final results three.1. Capacitance Model three.1.1. Theory Inside a very first approximation, the capacitance of the micro-capacitors around the SiO2 standards along with the investigated high- samples are estimated working with the well-known parallel-plate capacitance CP with the disk capacitor calculated in the uniform field model:Nanomaterials 2021, 11,5 of3. Final results 3.1. Capacitance Model three.1.1. Theory Within a 1st approximation, the capacitance of the micro-capacitors around the SiO2 requirements plus the investigated high- samples are estimated using the well-known parallel-plate capacitance CP with the disk capacitor calculated in the uniform field model: Cp = r 0 A , d (three)with r as the relative permittivity with the dielectric layer, 0 as the vacuum dielectric continuous, A because the region with the best electrode, and d because the thickness of the dielectric layer. On the other hand, this relation only holds for the situations exactly where the electric field between electrodes is usually deemed as uniform. That is mostly valid when the region from the electrodes significantly exceeds the thickness on the dielectric layer. When the electrode’s location becomes comparable (or smaller) to the dielectric thickness, the impact of fringing fields, originating from negative effects within the capacitive structure, gain an essential weight and contributes to a big part of the measured values [17]. Further effects (1 correction) need to also be taken into account in the case of our typical capacitive (SiO2 ) structures. They are namely related to depletion DMPO Cancer capacitances at the SiO2 /Si interface and to surrounding stray capacitances [32]. To this end, we apply finite element modelling solutions (FEM) to calculate capacitances CFEM working with COMSOL-Multiphysics together with the AC/DC module. The FEM calculations rely in certain around the measured values of micro-capacitive structures’ geometrical parameters, for example the equivalent radius R (connected to the area) plus the height hpad in the gold pad along with the thickness d on the dielectric layer. For the capacitance standards primarily based on SiO2 , the traceable geometrical parameters have already been determined following our recent operate in [32]. The micro-size capacitive struc.