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Regions, as shown in firstinsets of Figure 8b,e, suggests that the actualrespect to linear match. Nevertheless, the the derivative on the parasitic capacitance with variation the gold pad areas, as shown inside the insets of Figure 8b,e, suggests that the actual variation of Cpar has growing dependence around the location of your gold pad electrodes. Within this regard, the polycrystalline nature from the PZT [16,44] and PMN-PT surfaces in our case is anticipated to have an important part within a pronounced effect around the dispersion for smaller sized pads compared to larger pad regions, exactly where an averaging on the polycrystalline effect prevails, as clearly visible around the SEM pictures in Figure 5c,f. Employing the model of a parasitic capacitance, as described above, an equivalent parasitic layer is introduced to account for the variations of Cpar.Nanomaterials 2021, 11,13 ofEquation (eight) shows that the ratio in the equivalent permittivity for the equivalent thickness of this parasitic layer is straight proportional towards the first derivative of your parasitic capacitance: par 1 dCpar = . (eight) 0 dA dpar The excellent of the interfacial layer under the gold pads is directly dependent around the surface roughness in the high- samples. The measurement in the actual interface roughness below the gold electrodes is just not IL-4 Protein Protocol accessible. Nonetheless, the larger the roughness, the larger the equivalent thickness in the parasitic layer could be. For this, we take into account a array of unique values for the parasitic capacitance thickness dpar in between two nm and 14 nm. Though the lowest value reflects low neighborhood roughness below a gold pad, the highest value of 14 nm corresponds for the average peak-to-valley value calculated over the entire surface excluding the circular gold pads. PF-06454589 Purity & Documentation Applying these values, we extract a bounded variety for the probable variations on the equivalent relative permittivity with the parasitic capacitance par as shown in Figure 8c,f for the PZT and PMN-PT samples, respectively. We come across that, for the PZT sample, the equivalent parasitic permittivity r,par remains mostly below 80, except for the higher values of dpar . These values are well beneath the extracted dielectric continual for the PZT film (i.e., r,PZT = 445 16). This suggests that the equivalent parasitic layer is mainly formed by air voids and potentially confined water. Lately reported benefits on the anomaly low permittivity of confined water, where r 80 [45], go alongside this suggestion. The variations in r,par for the PMN-PT sample shows a related behaviour for the case of a low roughness interface represented by small values of dpar . Nonetheless, the AFM evaluation in Figure four clearly indicates a a lot larger surface roughness for the PMN-PT sample. Hence, the higher values of dpar (i.e., dpar = ten and 14 nm) constitute a greater representation of the variations inside the dielectric constant of your parasitic capacitance for the case of PMN-PT. It is actually noticeable in this case that r,par is largely higher than 80 (dielectric constant of bulk water), practically for all gold pad locations, as shown in Figure 8f. r,par increases because the area with the gold electrodes increases, reaching values comparable to that extracted for the PMN-PT film (i.e., r,PMN-PT = 641 44). This points towards the truth that the rough PMN-PT surface leads to a parasitic layer beneath the gold pads mostly incorporating peaks from the ferroelectric material using a reduce density of voids, specially for larger gold pads. This analysis highlights the vital function from the interfacial surfac.

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