4.1.6 Variation of the proportionality ratio p ¼ FCO=FCA: PZT

In a non-intuitive way, the current simply increases linearly by a factor of 40 (Figure 26) if we increase the proportionality ratio p ¼ FCO=FCA by a factor of 500. On the other hand, the threshold voltage of the MOS switches increases by a factor 8 for the same variation of the interface (Figure 27).

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

Figure 22.

Current of the MOS = f (ratio = FCO / FCA), start Interface = 200 A ° piezoelectric material = PZT.

Figure 23. Threshold voltage of the MOS = f (ratio = FCO / FCA), start Interface = 200 A ° piezoelectric material = PZT.

#### Figure 24.

Plot of the evolution of the Casimir inter-electrode interval as a function of time over two periods and an FCO / FCA ratio = 1000: Casimir inter-electrode interface = 200 A°.

#### Figure 25.

Plot of the evolution of the Casimir inter-electrode interval as a function of time over two periods and an FCO / FCA Ratio = 1000: Casimir inter-electrode interface = 200 A °.

#### Figure 26.

Plot of the evolution of the Casimir inter-electrode interval as a function of time over two periods and a ratio FCO / FCA = 2. Casimir inter-electrode interface = 200 A °.

#### Figure 27.

Materials = PMN-PT: Coulomb and Casimir force as a function of the inter-electrode interface. Start interface = 200 A °.

The MOS N or P switch transistors enriched in parallel have the following geometries: Width W = 4 mm and length L = 4 mm

#### 4.2 Use of other piezoelectric materials

In the presentation above we used PZT but, in order to increase the density of electric charges at the terminals of the piezoelectric bridge, piezoelectric material

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

Figure 28. Materials = PMN-PT: Coulomb and Casimir force as a function of time. Start interface = 200 A °.

PMN-PT can be used which can be deposited by RF-magnetron sputtering and of composition, for example: PMN-PT = (1-x) Pb (Mg1/3 � Nb1/3) O3-xPbTiO3; d31 <sup>¼</sup> <sup>1450</sup><sup>∗</sup> <sup>10</sup>�12C<sup>=</sup> kg <sup>∗</sup> <sup>m</sup><sup>∗</sup> <sup>s</sup>�<sup>2</sup> ð Þ and a Young's modulus of Ep <sup>¼</sup> <sup>150</sup><sup>∗</sup> 109 (Figure 28). We will also simulate the results obtained with AlN (aluminum nitride) d31 <sup>¼</sup> <sup>2</sup>:4<sup>∗</sup> <sup>10</sup>�12et Ep <sup>¼</sup> Ep <sup>¼</sup> <sup>32</sup> <sup>∗</sup> <sup>10</sup><sup>10</sup> , another piezoelectric material or AlN widely used in microelectronics because it is easily removable and lead-free!

#### 4.2.1 Piezoelectric material = PMN-PT

With the MATLAB simulation of a structure using PMN-Pt we obtain the evolution over time of the Casimir and Coulomb forces as well as the FCO=FCA ratio of Figures 7, 11, 13, 24, 29–39 below. For a ratio of 1000, the maximum current delivered by the vibrating structure, the threshold voltage of the MOSE and MOSD and the vibration frequency of the structure are respectively: 1:2 10�4A, Vt = 3.2 V and 957,000 Hertz

## 4.2.1.1 Evolution of the Casimir interface as a function of time during two periods: PMN-PT

The FCO=FCA ratio = 10,000 induces a period of 3:85 10�<sup>6</sup> s and a rise time of 21:3 10�<sup>9</sup> s with a deflection of the bridge of 105 A°. The structure vibrates at

#### Figure 29.

Materials = PMN-PT: Coulomb force for zr = 200 A ° ( Blue )and zr = 400 A ° (Red) and Casimir force (Yellow , z0 =200 A °) as a function of the inter-electrode interface Starting interface = 200 A °.

#### Figure 30.

Materials = PMN-PT: Ratio p = FCO / FCA as a function of time. During a period of vibration. Start interface = 200 A °, Maximum ratio chosen = 450 A °.

259.7 kHz. At the rise sequence, the structure exceeds the initial 200 A° by 20 A° due to inertia (Figure 29).

The ratio FCO=FCA = 1000 induces a period of 2.96 10�<sup>6</sup> s and a rise time of 44.5 10�<sup>9</sup> s with a deflection of the bridge of 50 A° The structure vibrates at 337.8 kHz.

For p = 1000 (Figure 24), we notice a vibration amplitude of 50 A° with a period of 2.96 10�<sup>6</sup> s, with faster rise of the mobile electrode producing a slight rebound of 5A, because of the inertia of the structure.

For the ratio FCO=FCA ¼ 2 (Figure 30) a vibration amplitude of just 0.27 A° and a period of 1.8610�<sup>7</sup> s is obtained This low deformation of the PMN-PT piezoelectric bridge is mainly due to the extremely high piezoelectric coefficient d31 of 1450 (pC/ N) of PMN-PT compared to 120 (pC/N) for PZT (Figure 28). It is also observed that weak overshoot of the initial interface (200 A°) for the mobile electrode increases with the ratio (FCO=FCA).

#### 4.2.1.2 Evolution of the forces of Casimir and Coulomb: PMN-PT

We obtain the evolution of the Casimir and Coulomb forces as a function of the inter-electrode interface (Figure 13) and over time (Figure 31) as well as the

#### Figure 31.

Materials = PMN-PT: Coulomb Force / Casimir Force ratio as a function of the Casimir inter-electrode interface. Start interface = 200 A °.

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

Figure 32.

Materials = PMN-PT: peak current delivered by the structure as a function of the FCO / FCA ratio. Start interface = 200 A °.

FCO=FCA ratio as a function of time for an entire period (Figure 7). For an interval between Casimir electrode z0 = 200 Angstroms, we observe (Figure 7) that the Coulomb return force becomes more important than the Casimir force, if we induce a deflection of the piezoelectric bridge of 20 A° more for an interval zr = 400 Angstroms between return electrodes than for zr = 200 that.

The attraction of the electrodes by the Casimir force induces a deformation of the piezoelectric bridge, therefore electric charges, which can be used in the Coulomb force. The break circuits triggered at time t = 2.44 10<sup>6</sup> s suddenly induce a rise of the mobile electrode, therefore a sudden decrease in electric charges. We observe the gradual evolution towards the chosen ratio of 450 and then the sudden drop in this ratio as the electrodes regain their initial position (Figure 32).

### 4.2.1.3 Ratio as a function of Casimir interval and current peak as a function of the ratio: PMN-PT

We observe (Figure 33) that for PMN-PT a deflection of 10 A° and a length of the piezoelectric bridge of 150μm of the mobile Casimir electrode is sufficient to have an Fco/Fca ratio = 1000. A Ratio of 2 gives a peak current of 7 10<sup>7</sup> A, while a ratio of 1000 produces a peak current of about 3:5 10<sup>4</sup> A (Figure 34) for the same period of homogenization of the charges of about 10<sup>9</sup> s!

#### Figure 33.

Materials = PMN-PT: current peak as a function of time obtained over 2 cycles. Starting interface = 200 A °. Ratio p = FCO / FCA = 1000.

Figure 34. Materials = PMN-PT: Voltage peak across the 4 \* 10-5 H solenoid as a function of the time obtained over 2 cycles. Starting interface = 200 A °, Ratio p = FCO / FCA = 1000.

#### 4.2.1.4 Peak current as a function of time and peak voltage across the inductance for 2 periods: PMN-PT

The following figures illustrate the peak current generated by the automatic vibrating structure with an inserted magnification showing the shape of this peak as a function of time (Figure 11) and its exponentially decrease during about 10–9 s. This current of about 3.5 10–4 A flowing through an inductor LIN of 4 10<sup>5</sup> Henri naturally generates a voltage of 4 Volts (Figure 35).

Note in Figure 11 the exponential form of the current peak of a duration appearing in each period. It is the same for the voltage peaks at the terminals of the inductance (Figure 35).

As this current peak cross an inductor, it induces by itself a voltage peak.

The current peak that appears with each cycle of vibration is uniquely due to the homogenization of the electrical charges on the two parts of the return electrode. This current peak follows the equation.

#### Figure 35.

Materials = PMN-PT: Voltage peak across the 4 \* 10-5 H solenoid as a function of the FCO / FCA Ratio. Start interface = 200 A °.

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

$$I\_{IN} = -\frac{Q\_{mn2}}{R\_m C\_s} \left( \text{Exp} \left( -\frac{t}{R\_m C\_s} \right) \text{ with } \text{Q}\_{mn2} = \text{d}\_{31} \text{lp } \text{F}\_{\text{CA}} \text{ }^\* \text{a}\_{\text{p}}/2 \text{.} \right)$$

This charge transferred from the electrode on the face 1 of the piezoelectric bridge to the return electrode, which is initially grounded, does not depend on the common width bp = bs = bi of the structures. This point is important and facilitates the technological realization of these structures since it limits the difficulties of a deep and straight engraving of the different structures. On the other hand, the intensity of this peak current depends linearly on the lengths lp and ls of the structures (Figure 22).

However, the duration of the exponential peak te ¼ RmCS ln 2ð Þ is independent of the geometries of the structure. These only intervening in the frequency of vibration of the structure and in the intensity of the peak.

### 4.2.1.5 Peak voltage across the inductance and threshold voltage according to the desired FCO/FCA ratio: PMN-PT

We observe (Figure 36) that the automatically peak voltage obtained without any energy expenditure increases by a factor of 16 and goes from 0.25 V to 4 V when the ratio p ¼ FCA=FCO increases from 2 to 1000. Likewise, the threshold voltage MOSE and MOSD authorizing these ratios increases from 0.2 V to 3.2 V (Figure 37).

#### 4.2.1.6 Vibration frequency as a function of the FCO=FCA ratio and peak current as a function of the initial Casimir interval chosen: PMN-PT

Note (Figure 38), that for an initial interface z0 ¼ 200 A°, the maximum vibration frequency of the structure is 3.50 MHz for a ratio Fco/Fca = 2. It falls to 750 kHz for a ratio of 1000. These frequencies remain lower than that of the first resonance of the structure which is the order of 7.94 Megahertz! For an p ¼ Fco=Fca ratio = 500, the maximum current delivered by the structure drops as a function of the initial Casimir interval (Figure 39).

#### Figure 36.

Materials = PMN-PT: Threshold voltage of the Enriched or Depleted MOTS according to the FCO / FCA ratio. Start interface = 200 A °.

#### Figure 37.

Materials = PMN-PT: vibration frequency as a function of the FCO / FCA ratio. Start interface = 200 A °. Start interface = 200 A °.

#### Figure 38.

Materials = PMN-PT: Current peak across the 2 \* 10-4 H inductance as a function of the starting interval between Casimir electrodes. Start interface = 200 A °.

Figure 39. Piezoelectric Material = AlN Casimir, Coulomb Force = f (Time) starts Interface = 200 A °.

This vibration frequency of the Casimir structure approaches that of the first resonance for weaker interfaces and less than 200 A°. We are then unfortunately confronted with the technological possibility of mastering such a weak interface.

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

It seems that the piezoelectric material PMN-PT coupled with a conductor like aluminum is an interesting couple for our vacuum energy extraction structure!
