## 6 Discussion  
The dimensions of the testing device were reduced by about 350 nm. One of the reasons for this was the oxidation thinning process. From the Deal-Groove model [26], the oxide thickness had increased by 91 nm and 120 nm when the silicon that was covered with 800 nm oxide was oxidized for 6 h and 8 h, in a dry oxidation process at 1100 \({}^{\circ}\)C, which consumed 42 nm and 56 nm of silicon, respectively. The consumption of silicon during the second oxidation was not known, since the remaining oxide thickness after stripping the oxide on the SiNWs was not controlled or measured. Assuming that the remaining oxide thickness was 400 nm, considering the over-etching time in the stripping, the consumption of the silicon layer was only a few nanometers. The rest of the difference would have been caused by the lithography process. The smaller width of the structure caused a larger gap between the parallel plates, which reduced the electrostatic force and capacitance change. The electrostatic force reduced by 25% from the designed value, which made the actuation voltage higher on testing. The displacement sensitivity was about 12 V/\(\upmu\)m, which was smaller by 35%, because the initial gap was wider. The measured noise level of the voltage output of the circuit was 10.3 mVrms, which corresponded to a displacement of 0.9 nm. This was about 1% of the total displacement and it was sufficient for the experiments. Figure 8: Fracture surface of Specimen A.  
Figure 9: (**a**) Force–displacement plots and (**b**) tensile stress–strain plots. Lines indicates linear fittings. Note that fitting is done on a linear range (up to 80 nm displacement) for Specimen C.  
The force-displacement curves of the test results showed good linearity up to an 80 nm displacement. Then, nonlinearity was observed at larger displacements, which was likely as a result of the nonlinearity of the electrostatic transducer. The electrostatic force of the parallel plate actuator was proportional to the square of the voltage and inversely proportional to the square of the gap. We have took into account this effect in the design, but we did not consider the effect of lateral bending of the thin and long electrodes. The whole device structure was further analyzed using the finite element analysis (Coventor-Ware, Coventor, Cary, NC, USA). There was bending of the electrode beams, however, the capacitance change against the displacement showed a small nonlinearity, which did not explain the voltage-displacement observed nonlinearity in the force-displacement relationship. On the other hand, the voltage-displacement curve in Figure 10a indicates that the displacement did not follow the square of the voltage at a displacement of more than 80 nm. At this displacement range, we found that the device started to tilt around the tensile axis (Figure 10b) and that the force was reduced as a result of the reduction of the overlapped area of the parallel plate electrostatic actuators. Insufficient support at both sides of the device caused the tilt. Therefore, the force might have been overestimated at the large displacement region. However, it was difficult to calculate the amount of the overestimation in our measurement results, as the actual tilting angle might have been different from the simulated results, because the rotation was unstable and might have changed. Large deviations were seen in the slopes of the stress-strain curves, the main reason for which was the thick non-uniformity of the SiNWs. As we can see in some of the specimens in Figure 6 and in the enlarged view of specimen A in Figure 11, the bottom of the SiNW had a large degree of waviness and the calculated Young's modulus showed a large deviation. The thickness of the specimens was measured at the fracture surface and was the smallest in this specimen, which caused the overestimation of stiffness. From the SEM image in Figure 6, the thickness variations ranged from 10 to 100%.