1.6.3 Neutral drag force (Fn)

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 vacuum chamber. Mathematically, it is written as:

$$F\_n = N m\_n \upsilon^2\_{dn} \pi a^2 \tag{3}$$

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

During the last decade, in microelectronics industry, dust particles become the major cause of contamination and reduce the yield and performance of fabricated devices. In early 1990s, more than 50% devices were failed due to the particle contamination. The adhesion of thin films was reduced due to the submicron particles deposited on the surface, also causes dislocations. In semiconductor technology, the elimination of even smallest dust particles has become an urgent issue to develop smaller structures and thin films. Firstly, it was thought that the cause of most of the contamination is that the processed surfaces were handling in the clean rooms but soon it was seemed that plasma is the major source of dust particles and causes the loss of costly wafers. Now, the dust contamination is well

We start, as usual, the Green-Kubo relations (GKRS) for the hydrodynamic transport coefficients of uncharged particles [16]. It is well-known form and has been shown the standard GKRS of fluids to the YDPLS [17–22]. The typical GKRS used for the estimation of thermal conductivity of interacting dust particles for

∞ð

<sup>J</sup><sup>Q</sup> ð Þ<sup>t</sup> :J<sup>Q</sup> ð Þ <sup>0</sup> � �dt (5)

<sup>m</sup> :Fij � � (6)

ϕij (7)

0

where in Eq. (5), k<sup>B</sup> is the Boltzmann's constant, V is the system volume,T is the absolute temperature, and JQ is the heat flux vector. The expression for the micro-

In the above expression, Fij is the total interparticle force on particle i due to j,

where ϕij is the Yukawa pair potential between particle i and j. Evans [23] has developed the non-Hamiltonian linear response theory (LRT) used for a moving

rij = r<sup>i</sup> � r<sup>j</sup> are the position vectors, and P<sup>i</sup> is the momentum vector of the ith particle. Ei is the energy of particle i and is given by the expression as:

> Ei <sup>¼</sup> <sup>p</sup><sup>2</sup> i 2m þ 1 2 ∑ i6¼j

r<sup>i</sup> � r<sup>j</sup> � � <sup>p</sup><sup>i</sup>

as toners in copying machines [14] or in some optical devices [15].

1.7.2 Dust in plasma processing devices (dust is a bad thing)

Non-Newtonian Dynamics with Heat Transport in Complex Systems

DOI: http://dx.doi.org/10.5772/intechopen.82291

2. HNEMD algorithm and computational technique

<sup>λ</sup> <sup>¼</sup> <sup>1</sup> 3kBVT<sup>2</sup>

scopic heat flux vector JQ can be given by:

system representing the equation of motion:

J<sup>Q</sup> V ¼ ∑ N i¼1 Ei pi <sup>m</sup> � <sup>1</sup> 2 ∑ i6¼j

controlled.

YDPLS:

175

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.
