Tures in this case present a compact dielectric thickness in comparison to the area of the electrodes. The geometrical condition d R (for any uniform field) is as a result satisfied, which validates the use of -Irofulven In Vitro Equation (3) inside the corresponding analytical calculations. For this, we viewed as r,SiO2 with a relative uncertainty of 1 . Nevertheless, even though the effect in the fringing fields is modest for the case of regular samples’ structures, we nevertheless consider it as a minor additional correction term to the initial approximation expression in Equation (three). An analytical expression of this correction has been located empirically and results in an error term reduced than 20 for R/d ten within a good agreement with the numerical calculation at the level of 1 [32]. For the case on the high- samples studied right here, the dimensions with the circular gold electrodes and dielectric layers’ thicknesses are described in detail in Section 3.1.2 with R/d 1, which makes the contribution in the fringing fields to the measured capacitances high. It really is consequently mandatory to think about a new analytical expression to appropriate the initial approximation (uniform field) of parallel-plate capacitor CP . For this, we found the following expression: C = CP 1 1 where h(d, R) = 1 ln 1 h(d, R) , 3ln(r ) d R d , R (four)(5)and is definitely an adjustable parameter depending slightly on hpad , = 0.097 for hpad = 50 nm. For d/R ranging from two to ten, h(d,R) increases virtually linearly as a function of d/R using a slope weakly dependent on r in agreement with [34]. In case of d/R 1, this leads to a first order approximation C = r 0 R, (6)( , ) = 1 ,(5)Nanomaterials 2021, 11,and ‘ is definitely an adjustable parameter depending slightly on hpad, ‘ = 0.097 for hpad = 50 nm. For d/R ranging from 2 to ten, h(d,R) increases virtually linearly as a function of d/R using a slope weakly dependent on r in agreement with [34]. In case of d/R 1, this leads to a 6 of 19 very first order approximation = , (6)independent with the electrode separation as expected for capacitance of uncoupled circular independent of the electrode separation as anticipated for capacitance of uncoupled circular electrodes [35,36]. The capacitance calculation employing the relations (3) to (5) agrees with electrodes [35,36]. The capacitance calculation working with the relations (three) to (five) agrees with FEM FEM calculation at the level of 3 for 0.2 d/R 2.6 and for a wide range of r values, from calculation in the level of 3 for 0.2 d/R 2.6 and for a wide selection of r values, from 200 2001500, as shown in Figure 3. In addition, the observed deviations weakly rely on the to to 1500, as shown in Figure 3. In addition, the observed deviations weakly depend onr the r values, without exceeding 1 . As a result, the FEM method will probably be preferred to values, with out exceeding 1 . Therefore, the FEM approach is going to be preferred to analytical analyticalaones for capacitance calculation on high- on high- On the other hand, Having said that, the ones for Olesoxime manufacturer precise a precise capacitance calculation samples. samples. the analytical analyticalwill be applied be evaluate the evaluate theofuncertainty on the capacitance process approach will to applied to uncertainty the capacitance calculation (by calculation (by propagating the uncertainties onand R)values d andestimate the uncertainty propagating the uncertainties on input values d input then to R) and after that to estimate the uncertainty around the dielectric constant determination. Theon the correction tocorrection on the dielectric constant determination. The uncertainty unc.