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

  • Kamel Milani Shirvan
  • Rahmat Ellahi
  • Tahereh Fanaie Sheikholeslami
  • Amin Behzadmehr
Original Article


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.


PECVD Heat and mass transfer Substrate rotation SiC 

List of symbols


Pre-exponential factor of reaction


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


Molar concentration


Effective diffusion coefficient


Diameter (m)


Energy (J)


Activation energy of the reactions


Gravity force


Mass flux of species


Rate constant of forward reaction


Molar mass of species


Mass (kg)


Power (watt)


Pressure (Pa)


Standard cubic centimeters per minute


Surface deposition rate (Kg m−2 S−1)


Gas constant (J mol−1 K−1)


Species net molar reaction rate


Net molar reaction rates of species i

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

Temperature of gas mixture

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

Velocity of gas mixture

Greek symbols


Thermal index


Speed index for positive reaction of reactant or product j


Coefficient of heat conduction


Dynamic viscosity of gas mixture


Density of gas mixture


Unit tensor


Viscous stress


Mass fraction of species


i, j

Represent ith/jth species


Compliance with ethical standards

Conflict of interest

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.


  1. 1.
    Tong L, Mehregany M, Tang WC (1993) Amorphous silicon carbide films by plasma-enhanced chemical vapor deposition. In: Proceedings IEEE micro electro mechanical systems. Fort Lauderdale, FL, pp 242–247Google Scholar
  2. 2.
    Mackenzie KD, Reelfs B, DeVre MW, Westerman R, Johnson DJ (2004) Characterization & optimization of low stress PECVD silicon nitride for production GaAs manufacturing. Unaxis USA Inc., St. Petersburg, FLGoogle Scholar
  3. 3.
    Choi WS, Hong B, Jeon Y, Kim K, Yi J (2004) Synthesis and characterization of diamond-like carbon protective ar coating. Korean Phys Soc 45:864–867Google Scholar
  4. 4.
    Ding J, Zhao Y, Yuan N, Shubo M, Wang C, Ye F, Kan B (2011) Effect of electrode architecture and process parameters on distribution of SiH3 in a PECVD system. Vacuum 86:344–349CrossRefGoogle Scholar
  5. 5.
    Jeong YM, Lee JK, Jun HW, Kim GR, Choe Y (2009) Preparation of super-hydrophilic amorphous titanium dioxide thin film via PECVD process and its application to dehumidifying heat exchangers. Ind Eng Chem 15:202–206CrossRefGoogle Scholar
  6. 6.
    Chowdhury A, Mukhopadhyay S, Ray S (2008) Effect of gas flow rates on PECVD-deposited nanocrystalline silicon thin film and solar cell properties. Solar Energy Mater Solar Cells 92:385–392CrossRefGoogle Scholar
  7. 7.
    Baek JS, Kim YJ (2007) Characteristics of thermal-flow fields in a PECVD reactor with various operating conditions. Korean Phys Soc 51:1113–1118CrossRefGoogle Scholar
  8. 8.
    Wang ZJ, Feng X, Shang XF (2011) The simulation of polycrystalline silicon thin film deposition in PECVD system. Adv Mater Res 189:2032–2036CrossRefGoogle Scholar
  9. 9.
    Colomboa FB, Carreño MNP (2012) Simulation of PECVD SiO2 deposition using a cellular automata approach. ECS Trans 49:297–304CrossRefGoogle Scholar
  10. 10.
    Marin M, Marinescu C (1998) Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies. Int J Eng Sci 36(1):73–86MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Marin M, Lupu M (1998) On harmonic vibrations in thermoelasticity of micropolar bodies. J Vib Control 4(5):507–518MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Marin M (2010) A domain of influence theorem for microstretch elastic materials. Nonlinear Anal RWA 11(5):3446–3452MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Sher Akbar N, Tripathi D, Khan ZH, Anwar Bég O (2016) A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects. Chem Phys Lett 661:20–30CrossRefGoogle Scholar
  14. 14.
    Sher Akbar N, Tripathi D, Anwar Bég O (2016) Modeling nanoparticle geometry effects on peristaltic pumping of medical magnetohydrodynamic nanofluids with heat transfer. J Mech Med Biol 16(06):1650088–1650108CrossRefGoogle Scholar
  15. 15.
    Sher Akbar N, Kazmi N, TripathiD Mir NA (2016) Study of heat transfer on physiological driven movement with CNT nanofluids and variable viscosity. Comput Methods Progr Biomed 136:21–29CrossRefGoogle Scholar
  16. 16.
    Sher Akbar N, Tripathi D, Anwar Bég O (2017) MHD convective heat transfer of nanofluids through a flexible tube with buoyancy: a study of nano-particle shape effects. Adv Powder Technol 28(2):453–462CrossRefGoogle Scholar
  17. 17.
    Sher Akbar N, Bintul Huda A, Tripathi D (2017) Thermally developing MHD peristaltic transport of nanofluids with velocity and thermal slip effects. Eur Phys J Plus 131(9):332CrossRefGoogle Scholar
  18. 18.
    Kleijin CR (1995) Chemical vapor deposition processes, chapter 4. Artech House, BostonGoogle Scholar
  19. 19.
    Pflűger A, Schröder B (2002) Simulations of the gas flux distribution for different gas showers and filament geometries on the large-area deposition of amorphous silicon by hot-wire CVD. J Non Cryst Solids 299–302(1):36–41CrossRefGoogle Scholar
  20. 20.
    ChengWT Li HC, Huang CN (2008) Simulation and optimization of silicon thermal CVD through CFD integrating Taguchi method. Chem Eng J 137(3):603–613CrossRefGoogle Scholar
  21. 21.
    Pawlowski RP, Theodoropoulos C, Salinger AG, Mountziaris TJ, Moffat HK, Shadid JN, Thrush EJ (2000) Fundamental models of the metalorganic vapor-phase epitaxy of gallium nitride and their use in reactor design. J Cryst Growth 221:622–628CrossRefGoogle Scholar
  22. 22.
    Hamby ES, Demos AT, Kabamba PT, Khargonekar PP (1995) A control oriented modeling methodology for plasma enhanced chemical vapor deposition processes American Control Conference, USAGoogle Scholar
  23. 23.
    Soong CY, Chyuan C, Tzong RY (1998) Thermo-flow structure and epitaxial uniformity in large-scale metalorganic chemical vapor deposition reactors with rotating susceptor and inlet flow control. Jpn J Appl Phys Part 1 37:5823–5834CrossRefGoogle Scholar
  24. 24.
    Zhi-Meng W, Qing-Song L, Xin-Hua G, Ying Z, Jian S, Jian-Ping X (2006) Effect of substrate temperature and pressure on properties of microcrystalline silicon films. Chin Phys 15(6):1320–1324CrossRefGoogle Scholar
  25. 25.
    Cho HS, Choi DJ (2009) The study of dielectric constant change of a-SiC: H films deposited by remote PECVD with low deposition temperatures. Korean Phys Soc 55(5):1920–1924Google Scholar
  26. 26.
    Pokhodnya K, Sandstrom J, Dai X, Boudjouk P, Schulz DL (2009) Comparative study of low-temperature PECVD of amorphous silicon using mono-, di-, trisilane and cyclohexasilane. In: 34th IEEE photovoltaic specialists conference (PVSC). Philadelphia, PA, pp 001758–001760Google Scholar
  27. 27.
    Liu L, Liu W, Cao N, Cai C (2013) Study on the performance of PECVD silicon nitride thin films. Def Technol 9:121–126CrossRefGoogle Scholar
  28. 28.
    Qing-Song L, Zhi-Meng W, Xin-HuaG Ying Z, Jian S, Jian-Ping X (2006) Effect of substrate temperature on the growth and properties of boron-doped microcrystalline silicon films. Chin Phys 15(1):213–218CrossRefGoogle Scholar
  29. 29.
    Hamui L, Monroy BM, Kim KH, López-Suárez A, Santoyo-Salazar J, López-Lópeze M, Cabarrocas PRI, Santana G (2016) Effect of deposition temperature on polymorphous silicon thin films by PECVD: role of hydrogen. Mater Sci Semicond Process 41:390–397CrossRefGoogle Scholar
  30. 30.
    Huang H, Winchester KJ, Suvorova A, Lawn BR, Liu Y, Hu XZ, Dell JM, Faraone L (2006) Effect of deposition conditions on mechanical properties of low-temperature PECVD silicon nitride films. Mater Sci Eng A 435–436:453–459CrossRefGoogle Scholar
  31. 31.
    Phillips B, Rodriguez RG, Lau LD, Steidley SD (2004) Effect of showerhead configuration on coherent Raman spectroscopically monitored pulsed radio frequency plasma enhanced chemical vapor. Plasma Chem Plasma Process 24(2):307–323CrossRefGoogle Scholar
  32. 32.
    Cheng H, Wu A, Xia J, Shi N, Wen L (2009) Effects of Substrate temperature on the growth of polycrystalline Si films deposited with SiH4 + Ar. J Mater Sci Technol 25(4):489–491Google Scholar
  33. 33.
    Moravej M, Babayan SE, Nowling GR, Yang X, Hicks RF (2004) Plasma enhanced chemical vapour deposition of hydrogenated amorphous silicon at atmospheric pressure. Plasma Sources Sci Technol 13:8–14CrossRefGoogle Scholar
  34. 34.
    Lee CH, Wong WS, SazonovA Nathan A (2015) Study of deposition temperature on high crystallinity nanocrystalline silicon thin films with in-situ hydrogen plasma-passivated grains. Thin Solid Films 597(31):151–157CrossRefGoogle Scholar
  35. 35.
    Gu L, Yang H, Wen G, Li Y, (2011) Substrate temperature influence on properties of amorphous silicon-germanium thin films prepared by RF-PECVD. In: Symposium on Photonics and Optoelectronics (SOPO)Google Scholar
  36. 36.
    Sarmid S, Oeraman K, Ismail B, Sakrani S (2006) Effect of substrate temperature on the properties of diamond-like carbon deposited by PECVD in methane atmosphere. In: Proceedings of Annual Fundamental Scion Seminar 2006, AFSS 20061, 6–7 June 2006Google Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Mathematics and StatisticsIIUIIslamabadPakistan
  3. 3.Department of Mechanical Engineering-MechatronicsUniversity of Sistan and BaluchestanZahedanIran
  4. 4.Department of Mechanical EngineeringUniversity of Sistan and BaluchestanZahedanIran

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