1. Introduction

#### 1.1 Obtaining an electric current from vacuum?

We know that the quantum vacuum, the energy vacuum, the absolutely nothing, does not exist!

This statement has been proven multiple times and noted in particular by:

• Lamb's shift (1947) of atomic emission frequencies.


#### 1.2 Brief presentation of Casimir's force

The vacuum energy is the zero-point energy of all fields (tensorial and scalar) in space, which for the standard model includes the electromagnetic field, gauge fields, fermionic fields, as well than the Higgs field. In quantum field theory, this vacuum energy defined as zero, is the ground state of fields! In cosmology, vacuum energy is a possible explanation for Einstein's cosmological constant. It has been observed and shown theoretically that this so-called zero-point energy, is non-zero for a simple quantum harmonic oscillator, since its minimum energy is equal to E=h ν/2 with ν the natural frequency of the oscillator, and h the Planck's constant.

Originally [1], the Casimir effect is derived from statistical fluctuations in total vacuum energy and is the attraction (in general) between two plates separated by a vacuum. In this approach, this Casimir energy is the part ECA of the vacuum energy which is a function of the zS separation of the Casimir plates, with:

$$\mathbf{E}\_{\rm CA} = \mathbf{S} \left( \frac{\pi^2 \hbar \,\mathbf{c}}{740 z\_{\rm S}^3} \right).$$

This Casimir energy is proportional to the reduced Planck constant h, to the speed of light c and to the surface S of the reflectors (in the limit where the edge effects of the plates are negligible, which then imposes large dimensions of the reflectors compared to that of the separation of the plates).

The force of Casimir FCA between the two reflectors is then the derivative compared to zs of this energy thus: This Casimir force,

$$F\_{CA} = \frac{d(E\_{CA})}{dz} = \mathcal{S}\left(\frac{\pi^2 \hbar \ c}{240 \, z\_{\mathcal{S}}^4}\right) \tag{1}$$

proportional to the surface, defines a pressure FCA/S which depends only on the distance zs <sup>4</sup> between the reflecting plates. This local approach greatly facilitates the formulations of Casimir's forces [1, 2]. The force of Casimir is then attractive and can be understood like a local pressure namely, the so-called virtual radiation pressure and exerted by vacuum fluctuations on the mirrors. These homogeneous, isotropic, and constant fluctuations of the vacuum, manifested by radiation and virtual particles, are modified by the presence of reflecting mirrors. These particles, however real, are called virtual because their lifetimes are noticeably short (for an electron of the order of 6:10�<sup>22</sup> seconds) before recombining to return to a vacuum!

The presence of the reflective plates excludes wavelengths longer than the distance zs between the plates. They thus induce a pressure difference of the virtual

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

particles generated by the vacuum between the internal and external space of the 2 plates. This difference results in a force that pushes the plates together.

The Casimir force between two perfectly conductive and smooth plates, without conductive charge, at zero temperature is written as the difference of the radiation pressures calculated outside and inside the cavity and is then written (Figure 1):

$$\mathbf{F}\_{ca} = \mathcal{S}\left(\frac{\pi^2 \hbar \, c}{240 \,\, z\_S^4}\right).$$

The famous physicist Evgueni Mikhaïlovitch Lifchits gave a general formula, which supplements that of Casimir because it considers the effect of temperature [3]. Indeed, when the temperature is no longer zero, the radiation of the black body must then be considered and the Casimir force at temperature T then becomes that of Lifchits [4].

$$F\_{ca} = \mathcal{S}\left(\frac{\pi^2 \hbar c}{240} \frac{1}{z\_{\mathcal{S}}^4} + \frac{\pi^2}{45} \frac{(k\mathcal{T})^4}{\left(\hbar c\right)^3} - \frac{k\mathcal{T}\pi}{z\_{\mathcal{S}}^3} \exp\left(\stackrel{-\frac{\mu k}{kT\_{\mathcal{S}}}}{}\right)\right) \tag{2}$$

With k the Boltzmann constant and T the temperature. This modification is important for large distances, typically L≥3 mm at ambient temperature.

We will use Eq. (1) to calculate and simulate the structure defined in the following diagram (Figure 2) because the intervals between electrodes are much smaller than μm and the effect of temperature is negligible.

Figure 1. Casimir effect.

Figure 2. General representation of the structure.
