4. Simulation of devices with different piezoelectric bridge

We will see that this device vibrates at a frequency lower than its first resonant frequency and that its vibration frequency depends on the characteristics of the structure (Nature of the piezoelectric material, nature of the metallic conductors, starting interface z0 and zr between Casimir electrodes and return Coulomb electrodes, dimensions of the Casimir reflectors, coefficient of proportionality p ¼ FCO=FCA … ). Except precision the interface zr between the Coulomb's electrode is chosen the same that those of Casimir reflector z0

#### 4.1 Piezoelectric materials = PZT (lead zirconia titanium)

#### 4.1.1 Interface between Casimir electrodes as a function of time for different trigger values of MOS transistors

For a starting interface between Casimir electrode of z0 <sup>¼</sup> <sup>200</sup><sup>∗</sup> <sup>10</sup>�<sup>10</sup> (m) and a coefficient of proportionality p ¼ FCO=FCA ¼ 2, we obtain the following evolution in time of the Casimir interface:

We notice a phase of rise of the Casimir electrode faster than that of descent. The period of vibrations is 6.18 10�<sup>7</sup> s therefore with a vibration frequency of 1.613 10<sup>6</sup> Hertz, while the first resonant frequency of the same structure is 6.54 10<sup>6</sup> hertz.

The moving electrode drops to zs ¼ 198:8 Angstroms from the fixed electrode SS3. The current peak for this coefficient of proportionality p <sup>¼</sup> 2 is 2:58 10�<sup>8</sup> A. This current is obtained by adjusting the threshold voltage of the enriched and depleted MOS transistors to a value Vt = 0.6553 V for a length L = width = W = 4 10�<sup>6</sup> m and with a grid oxide thickness SiO2 = tox of 250 10�<sup>10</sup> m (see Figure 13)! Let us simply change the coefficient p ¼ FCO=FCA of proportionality to p = 200, then we get (see Figure 14):

We notice for the ratio p ¼ FCA=FCO = 200 (Figure 14), a phase of "rise" of the Casimir electrode also much faster than that of "descent" but also more dynamic than for the ratio of previous p = 2 The vibration frequency of the device of 5.07 10<sup>5</sup> hertz, while the first resonant frequency of the structure is still 6.54 10<sup>6</sup> hertz!

The moving electrode is now approaching to zs ¼ 188:9A° of the fixed electrode SS3, so the vibration amplitude of the structure is 200–188.9 = 11.1 Angstroms!

This current is obtained by adjusting the threshold voltage of the enriched and depleted MOS transistors to a value Vt = 6.89 V for the same geometries as above

Perspective Chapter: Device, Electronic,Technology for a M.E.M.S. Which Allow… DOI: http://dx.doi.org/10.5772/intechopen.105197

#### Figure 13.

Figure 14. MOS threshold voltage = f (starting interface z0): FCO / FCA chosen = 200: PZT.

#### Figure 15.

Maximum current = f (length of the Casimir electrode ls), starting interface = 200 A °, selected coefficient of proportionality p = FCO / FCA = 2.

(see Figure 15). We must therefore adjust the threshold voltages to precisely adjust the ratio p ¼ FCO=FCA for which the Coulomb force is triggered. This is a point that can be easily obtained technologically (see the technological part of this report)! In

conclusion, as the vibration frequency of the structure depends, among other things, on the coefficient of proportionality p and therefore on the current that one wishes to obtain, the structure does not vibrate at its first resonant frequency.
