# Chemical Vapor Deposition in Barrel Reactor

For large-volume production of epitaxial growth of the silicon, the barrel reactor shown in Fig. 1(c) from Basics of Chemical Vapor Deposition is widely adopted. Transport phenomena in a barrel reactor are very complex and cannot be treated as axisymmetric (Curtis, 1976; Lord, 1987). The 3-D numerical model of transport phenomena in an idealized barrel reactor presented by Yang et al. (1992) will be introduced here. The physical model of the CVD reactor is shown in Fig. 1. The polygonal susceptor that is used in a barrel reactor is simplified as a circular cylindrical shape. The precursor gas that includes reactant silane and carrier-gas hydrogen enters two nozzles located on the top of the reactor at two different locations: θ = 0° and 180°. The precursors are induced into the reactor at an injection angle of φ. The flow is assumed to be laminar and the governing equations are eqs. (1)-(5) $\frac{D\rho }{Dt}+\rho \nabla \cdot \mathbf{V}=0$ and $\rho \frac{D{{\omega }_{i}}}{Dt}=-\nabla \cdot {{\mathbf{J}}_{i}}+{{{\dot{m}}'''}_{i}}\begin{matrix} , & i=1,2,...N-1 \\ \end{matrix}$ from Governing Equations of Chemical Vapor Deposition in the cylindrical coordinate system.

Yang et al. (1992) considered the following partial pyrolysis chemical reaction in the gas phase: ${{\operatorname{SiH}}_{4}}(g)\to \text{Si}{{\text{H}}_{\text{2}}}\text{(g)+}{{\text{H}}_{\text{2}}}\text{(g)} \qquad \qquad(1)$

with the following reaction rate: ${{{\dot{m}}'''}_{\text{Si}{{\text{H}}_{\text{2}}}}}=-5\times {{10}^{12}}\rho {{\omega }_{\text{Si}{{\text{H}}_{\text{4}}}}}\exp \left( -\frac{2.2\times {{10}^{8}}}{{{R}_{g}}T} \right) \qquad \qquad(2)$

The following two chemical reactions occurred on the surface of the susceptor: ${{\operatorname{SiH}}_{4}}(g)\to \text{Si(s)+2}{{\text{H}}_{\text{2}}}\text{(g)} \qquad \qquad(3)$ ${{\operatorname{SiH}}_{2}}(g)\to \text{Si(s)+}{{\text{H}}_{\text{2}}}\text{(g)} \qquad \qquad(4)$

where the chemical reaction in eq. (3) was assumed to be kinetically controlled and eq. (4) is considered to be diffusion controlled. The rate of kinetically-controlled production of Si is obtained by ${{\dot{{m}''}}_{\text{Si}}}=\frac{1}{{{M}_{\text{Si}}}}\frac{{{k}_{1}}{{p}_{\text{Si}{{\text{H}}_{\text{4}}}}}}{1+{{k}_{2}}{{p}_{{{\text{H}}_{\text{2}}}}}+{{k}_{3}}{{p}_{\text{Si}{{\text{H}}_{\text{4}}}}}} \qquad \qquad(5)$

where MSi is molecular mass of silicon, ${{k}_{1}}(\text{mol Si/}{{\text{m}}^{\text{2}}}\text{-s})=1.25\times {{10}^{9}}{{e}^{-18500/T}}$, ${{k}_{2}}=1.75\times {{10}^{3}}(at{{m}^{-1}})$, ${{k}_{3}}=4\times {{10}^{4}}(at{{m}^{-1}})$, and ${{p}_{{{\text{H}}_{\text{2}}}}}$ and ${{p}_{\text{Si}{{\text{H}}_{\text{2}}}}}$ are the partial pressures of hydrogen and silane in atmospheric pressure. The temperature at the top surface of the reactor is assumed to be a linear profile, while the bottom surface of the reactor is assumed to be adiabatic. The temperature of the susceptor stem is assumed to be maintained at the temperature of the inlet gas temperature so that there is no deposition on the stem. Other boundary conditions for velocity, temperature, and concentration are conventional. Figure 2: Temperature contour and flow fields at different planes (injection angle $\phi ={{0}^{\circ }}$, susceptor rotation Ω = 0 rpm
(a) $\theta ={{0}^{\circ }}$ (b) $\theta ={{90}^{\circ }}$

Yang et al. (1992) obtained the numerical solution of the fluid flow, heat and mass transfer, and silicon deposition rate using the SIMPLE algorithm (Patankar, 1980); and the representative temperature and flow field are shown in Fig. 2. The dimensions of the reactors are: L = 80 cm, Lin=3.8 cm, Lu=22 cm, Ls=38 cm, Le=6 cm, ri=1 cm, rs=15 cm, r0=19 cm, and re=6 cm. The susceptor temperature is Ts = 1300 K, and the susceptor stem temperature is Ti = 300 K. The flow is very complex because the natural convection caused by a hot susceptor interacts with the forced convection induced by incoming injection flow. The distribution of the deposition rate shown in Fig. 3 indicates that the deposition rate varies significantly on the susceptor surface. The deposition rate is significantly higher at the location near the nozzles that induced the reactant than at other locations.

## References

Curtis, B.J., 1976, “Temperature Asymmetries and Fluctuation in a Barrel Reactor,” Journal of the Electrochemical Society, Vol. 123, pp. 437-439.

Lord, H.A., 1987, “Convective Transport in Silicon Epitaxial Deposition in a Barrel Reactor,” Journal of the Electrochemical Society, Vol. 134, pp. 1227-1234.

Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC.

Yang, L., Farouk, B., and Mahajan, R.L., 1992, “Three-Dimensional Predictions of Silicon Deposition in a Barrel Type CVD Reactor,” Journal of the Electrochemical Society, Vol. 159, pp. 2666-2673.