He red markers the the orange markers for pads. The outcomes of theset correspond towards the red markers and and orange markers for the second set. the second set.three.three. Uncertainty Budget three.3. Uncertainty Price range The uncertainties around the resulted values of the high- dielectric constants derive from the uncertainties around the resulted values of the high- dielectric constants derive from a series of uncertainties connected to the a variety of actions in our metrology workflow described series of uncertainties connected to the a variety of steps in our metrology workflow described a thus far (such as calibration, characterization and modelling steps). Table two facts most important as a result far (like calibration, characterization and modelling actions). Table two information primary uncertainty sources corresponding to every sample characterized within the present operate. uncertainty sources corresponding to every single sample characterized inside the present perform.Table 2. Uncertainty sources integrated within the current metrological workflow presented within this operate Table 2. Uncertainty sources incorporated inside the current metrological workflow presented within this perform plus the combined uncertainty uc corresponding towards the dielectric continuous values measured on PZT plus the combined uncertainty uc corresponding to the dielectric continuous values measured on PZT and PMN-PT samples. and PMN-PT samples. Uncertainty Sources PZT PZT u PMN-PT PMN-PT (1st Series) (1st Series) u u (six.5; 20.five) (6.five; 20.5) (three.five; 19.7) (three.5;five.5 19.7) five.5 3.3 (0.2; 0.six) 3.3 3.1 (0.2; 0.six) 1.eight PMN-PT PMN-PT (2nd Series) (2nd Series) u u (6.5; 23.six) (6.5; 23.six) (3.four; 22.9) (three.four; five.five 22.9) five.five three.2 (0.two; 0.six) 3.two three.1 (0.two; 0.6) 1.Uncertainty Sourcesu Capacitance calculation Capacitanceucalculation Location, A Region, ud Thickness,uA(2.5; 9.7) (two.5; 9.7) (1.3; 9.five) (1.3; 9.5) two.Thickness, ud Capacitance measurements Type-A (Histogram, repeatability) Capacitance measurements SMM calibration Type-A (Histogram, repeatability) OthersCombined uncertainty, uc SMM calibration Inositol nicotinate medchemexpress Others2.1 three.two (0.1; 0.two) 3.2 three.1 (0.1; 0.2) 1.three.3.1 1.three.1 9.1 1.three.1 10.six 1.Combined uncertainty, uc three.five 9.1 10.6 The uncertainty around the calculated capacitance values is -Irofulven MedChemExpress estimated from the RSS in the uncertainty associated to pads’ region, dielectric thickness and analytical expression provided by the relations (3) to (5). The identical outcomes have already been obtained using the FEM system. The uncertainty in the measured capacitance values is equal towards the RSS from the kind A uncertainties (combining repeatability along with the typical deviation with the histogram Gaussian distribution of every capacitance) and kind B uncertainty mainly because of the SMM calibration uncertainty. The other kind B uncertainties are related for the residual influence of stray capacitances and relative humidity leading to a combined uncertainty with aNanomaterials 2021, 11,15 ofconservative worth less than 0.eight [32]. The uncertainties corresponding to errors due to stray capacitances have been estimated utilizing the analytical expressions given in [502]. The sum of residual errors on account of the stray capacitances occurring between the sample (metallic pads and dielectric top rated surface), on 1 side, and also the cantilever, the tip cone and the tip apex, around the other side, doesn’t exceed 18 aF. Considering a rectangular distribution as well as the measured capacitance variety, the corresponding relative uncertainty varies in between 0.04 and 1.8 . 4. Discussion We demonstrate that SMM is often a potent tool to quantify the dielectric constants of components inside the m.
