1.6.4 Thermophoretic force (Fth)

The thermophoretic force occurs from the effect of temperature gradient in the neutral gas in the plasmas, and it is in the opposite direction to the temperature gradient. This force occurs due to transfer of momentum by the gas molecules from the hotter region to the colder portion of the gas. It can be written as:

$$F\_{th} = \frac{\mathbf{1}\mathbf{6}\sqrt{\pi}}{\mathbf{15}} \frac{\mathbf{a}^2 \kappa\_T}{\nu\_{T,n}} \nabla T\_n \tag{4}$$

where vT,n describes the thermal speed of the neutral gas of plasma, κ<sup>T</sup> defines the translational effects in the λ, and Tn tells about the temperature of the neutrals. It can be occurred in the discharge by heating one of the electrodes. The force of gravity acting on the dust particles in plasma is balanced by the temperature gradient [11].

### 1.7 Application of dusty plasmas in industry

Plasma-based material processing technologies are extensively employed in the designing and commercialization of very large-scale integrated circuits (VLSI). Usually, chemically reactive plasmas are useful to sputter, etch, or otherwise alter the surface characteristics especially for silicon. Surface characteristics are approximately done at length scale of 0.2 μm wide and 4 μm deep in silicon films by such kind of mechanisms. The presence of dust is of critical concern to the microelectronic industry since particle contamination of semiconductor materials was estimated to account for more than 50% of device failures. Dust contamination diminishes the yield and recital characteristics of fabricated devices. Simply, the dust particles fall into the surface topographies of semiconductors either interfering with the etching process, preventing the adhesion of thin films or contaminating the final products. The occurrence of even the smallest dust particles became a crucial problem as the microelectronics industry moved to smaller and smaller structures.

### 1.7.1 Dust is a good thing

In those days, it was investigated that dust particles in plasma can have very interesting and useful properties, e.g., very small sizes, uniform size distribution, Non-Newtonian Dynamics with Heat Transport in Complex Systems DOI: http://dx.doi.org/10.5772/intechopen.82291

(rf) parallel plate glow discharge plasmas, particles reside beneath the negative electrode where the downward electric field offers an upward electric force that

This force is generated due to impacts of dust particles with the neutral gas species (atoms and molecules) and it is proportional to the neutral pressure in the

Fn <sup>¼</sup> Nmnv<sup>2</sup>

where N defines the density of neutral species, mn denotes the mass of neutral species, and vdn represents the average relative velocity between the neutral elements and dust species. The resulting damping force also acts on the dust particles if the dust particles drift with drag force in the opposite direction to its motion.

The thermophoretic force occurs from the effect of temperature gradient in the neutral gas in the plasmas, and it is in the opposite direction to the temperature gradient. This force occurs due to transfer of momentum by the gas molecules from

> a<sup>2</sup>κ<sup>T</sup> νT,n

where vT,n describes the thermal speed of the neutral gas of plasma, κ<sup>T</sup> defines the translational effects in the λ, and Tn tells about the temperature of the neutrals. It can be occurred in the discharge by heating one of the electrodes. The force of gravity acting on the dust particles in plasma is balanced by the temperature

Plasma-based material processing technologies are extensively employed in the designing and commercialization of very large-scale integrated circuits (VLSI). Usually, chemically reactive plasmas are useful to sputter, etch, or otherwise alter the surface characteristics especially for silicon. Surface characteristics are approximately done at length scale of 0.2 μm wide and 4 μm deep in silicon films by such kind of mechanisms. The presence of dust is of critical concern to the microelectronic industry since particle contamination of semiconductor materials was estimated to account for more than 50% of device failures. Dust contamination diminishes the yield and recital characteristics of fabricated devices. Simply, the dust particles fall into the surface topographies of semiconductors either interfering with the etching process, preventing the adhesion of thin films or contaminating the final products. The occurrence of even the smallest dust particles became a crucial problem as the microelectronics industry moved to smaller and smaller structures.

In those days, it was investigated that dust particles in plasma can have very interesting and useful properties, e.g., very small sizes, uniform size distribution,

the hotter region to the colder portion of the gas. It can be written as:

Fth <sup>¼</sup> <sup>16</sup> ffiffiffi π p 15

dnπa<sup>2</sup> (3)

∇Tn (4)

stabilizes the weight of the particle with force.

vacuum chamber. Mathematically, it is written as:

1.7 Application of dusty plasmas in industry

1.6.3 Neutral drag force (Fn)

Non-Equilibrium Particle Dynamics

1.6.4 Thermophoretic force (Fth)

gradient [11].

1.7.1 Dust is a good thing

174

and chemical activity. There are many applications of plasma-produced particles. For example, large and active surface in catalysis is profitable. They are also essential in ceramic industry for sintering, in the modern technology of composite materials, and in fabrication of hard coatings [12] and solar cells [13]. Also, by injecting particles in plasma can furnish unique objects, like coated or layered grains with desired surface structure, color, and fluorescent properties. These particles are used as toners in copying machines [14] or in some optical devices [15].
