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Numerical investigation of heat and mass transfer flow under the influence of silicon carbide by means of plasma-enhanced chemical vapor deposition vertical reactor

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Abstract

The effect of characteristics flow (contour of velocity), mass transfer (Sherwood number) and heat transfer (Nu number) on the growth rate of silicon carbide by means of plasma-enhanced chemical vapor deposition vertical reactor is investigated. The species transport and thermal fluid transport with chemical reaction are taken into account. The steady-state laminar fluid flow and gas flow having ideal behavior are considered. A mixture of silane and propane (2% molar) as main reactant gases and hydrogen (96% molar) as propellant gas are injected into the reactor. Four different diameters of shower head, three different substrate rotation speeds and five different temperatures of the substrate are used. The finite volume method is employed to solve the problem. The governing equations are solved by upwind differencing scheme. The assumption of speed–pressure coupling leads to use of semi-implicit method for pressure-linked equations to solve the governing equation. It is found that the deposition rate reduces with the shower head diameter and value of substrate temperature and enhances with rotational speed of the substrate. Furthermore, the best shower head diameter to achieve maximum rate of deposition is 1 mm. At the end, a comparison as a limiting case of the considered problem with the existing studies is made. Comparing the results of this experiment with prior studies has shown acceptable consistency.

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Abbreviations

\(A_{\text{r}}\) :

Pre-exponential factor of reaction

\(c_{\text{p}}\) :

Specific heat of gas mixture (J mol−1 K−1)

\(c_{j,r}\) :

Molar concentration

\(D_{i}\) :

Effective diffusion coefficient

D :

Diameter (m)

\(E\,\) :

Energy (J)

\(E_{\text{r}}\) :

Activation energy of the reactions

\(g\) :

Gravity force

\(j_{i}\) :

Mass flux of species

\(k_{{{\text{f}},{\text{r}}}}\) :

Rate constant of forward reaction

\(M_{i}\) :

Molar mass of species

\(m\,\) :

Mass (kg)

\(P\) :

Power (watt)

\(P\) :

Pressure (Pa)

SCCM:

Standard cubic centimeters per minute

SDR:

Surface deposition rate (Kg m−2 S−1)

\(R\) :

Gas constant (J mol−1 K−1)

\(R_{i}\) :

Species net molar reaction rate

\(R_{i,r}\) :

Net molar reaction rates of species i

\(T\,(^\circ {\text{C}})\) :

Temperature of gas mixture

\(U\,({\text{ms}}^{ - 1} )\) :

Velocity of gas mixture

\(\beta_{\text{r}}\) :

Thermal index

\(\eta_{j,r}^{'}\) :

Speed index for positive reaction of reactant or product j

λ :

Coefficient of heat conduction

µ :

Dynamic viscosity of gas mixture

\(\rho\) :

Density of gas mixture

δ :

Unit tensor

\(\tau\) :

Viscous stress

\(w_{i}\) :

Mass fraction of species

i, j:

Represent ith/jth species

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Kamel Milani Shirvan

  2. Department of Mathematics and Statistics, IIUI, H-10 Sector, Islamabad, 44000, Pakistan

    Rahmat Ellahi

  3. Department of Mechanical Engineering-Mechatronics, University of Sistan and Baluchestan, Zahedan, Iran

    Tahereh Fanaie Sheikholeslami

  4. Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

    Amin Behzadmehr

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  1. Kamel Milani Shirvan
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  2. Rahmat Ellahi
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Correspondence to Rahmat Ellahi.

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The authors have declared that they have no actual or potential conflict of interest including any financial, personal or other relationships with other people or organizations.

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Shirvan, K.M., Ellahi, R., Sheikholeslami, T.F. et al. Numerical investigation of heat and mass transfer flow under the influence of silicon carbide by means of plasma-enhanced chemical vapor deposition vertical reactor. Neural Comput & Applic 30, 3721–3731 (2018). https://doi.org/10.1007/s00521-017-2954-3

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