## 3 Results
### Dynamic Characterization  
#### 3.3.1 One-Direction Bending  
To investigate the key characteristics of the developed sensor, a series of dynamic measurements followed by applying appropriate steps of compression and decompression of the device were performed as described in Section 2.2. Sensors that underwent a heating treatment of 1 h or 20 h, as well as sensors that did not undergo sintering, were characterized for comparison purposes. Additionally, the piezoresistive layer was subjected to bending with consecutive compression and elongation steps as described in the following sections. The properties outlined in Section 2.2 have been identified for all devices.  
The deduced variation in the resistance of the sensing element when applying consecutive steps of compression and decompression is depicted in Figure 9a,c,e. The corresponding increase in the initial resistance (%) with respect to the displacement for both the compression and decompression cycles is presented in Figure 9b,d.f.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sintering Time** & **No Sintering** & **11 min** & **60 min** & **20 h** \\ \hline Standard Deviation of Resistance change (\(\sigma_{\text{AR}}\)) & 6.02 & 3.84 & 1.69 & 0.53 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Standard deviation during strain-free measurements for samples with increasing annealing time.  
Figure 8: Standard deviation of resistance during static characterization for different values of current applied.  
Figure 9: _Cont._Figure 9: _Cont._  
It should be noted that after performing extensive testing with varying degrees of displacement, it was determined that the optimal range of displacement beyond which the hysteresis and linearity of the sensor began to decline was 0 to 0.6 mm. The degradation of these characteristics is possibly attributed to the fracture of the conductive paths within the piezoresistive material. The values of the deduced gauge factor and hysteresis (mean value) of the characterized devices are shown in Figure 10. Additionally, Table 2 provides a summary of the specific results along with the corresponding standard deviation for resistance change per step of displacement, which is a characteristic measure indicating the linearity of the sensor, as previously mentioned (see Section 2.2). As we can observe from the specific data, both the gauge factor and linearity of the sensor were significantly improved for samples sintered for 1 and 20 h; this finding is analyzed in the Section 4.  
Figure 9: Variation in resistance versus time and increase in initial resistance versus displacement for samples with no sintering (**a**,**b**); sintered for 1 h (**c**,**d**); sintered for 20 h (**e**,**f**).  
A correlation analysis was performed to examine the relationship between the gauge factor and hysteresis, and sintering time using the Pearson correlation method. The specific method is a widely used approach for numerical variables, assigning a value between \(-1\) and \(1\), that indicates the strength of the relationship between two variables. A value of \(0\) indicates no correlation, a value of \(1\) suggests a strong positive correlation, and a value of \(-1\) suggests a strong negative correlation [33]. The findings presented in Table 3 indicate a strong positive correlation between heat treatment time and gauge factor (\(0.94\)), a negative correlation between heat treatment time and hysteresis values (\(-0.75\)), and a strong positive correlation between sintering time and linearity, which aligns with previously reported results.