# Chemical Vapor Deposition in Horizontal Reactor

Since the susceptor in a horizontal reactor is heated from below, and the precursor flows along the horizontal direction, the temperature gradient in the precursor is perpendicular to the gas velocity. However, in this case, the forced convective boundary layer assumption is not valid, because the gas velocity is very low. In addition, Rayleigh-Bénard natural convection may occur on the susceptor because it is a nearly horizontal surface heated from below. Therefore, convection in a horizontal reactor is a mixed convection problem that combines the effects of forced and natural convection. The convection in the horizontal reactor is characterized by a low Reynolds number (under 50 based on channel height) and large temperature difference (400 to 1000 °C), which may lead to a complex flow structure and flow instability.

Chiu et al. (2000) observed the flow structures in a horizontal converging channel heated from below [see Fig. 1(a) from Basics of Chemical Vapor Deposition]. The cross-section of the channel is

Figure 1: Side and tail views of flow patterns in a converging channel with 8° tilt

25.4×5.08 cm (width×height: W×H) and the length of the channel is 91.4 cm. The length of the heated section, which can be tilted up to 10°, is 16.51 cm. They concluded that three flow regimes may exist, depending on Reynolds and Grashof numbers: (1) steady state laminar flow without roll, (2) longitudinal rolls, and (3) transverse rolls (see Fig. 1). The Reynolds number and Grashof number in Fig. 1 are defined as follows:

$\operatorname{Re}=\frac{{{u}_{\infty }}H}{\nu } \qquad \qquad(1)$

$\text{Gr}=\frac{g\beta ({q}''H/k){{H}^{3}}}{{{\nu }^{2}}} \qquad \qquad(2)$

where β is the coefficient of thermal expansion (1/K) and H is the height of the reactor.

The flow regime map obtained by Chiu et al. (2000) for a converging channel with 8° tilt is shown in Fig. 2.

Steady-state laminar flow without roll exists when both the Reynolds number and the Grashof number are low. While longitudinal rolls are observed at a higher Reynolds number, transverse rolls occur at a higher Grashof number. The transition from longitudinal rolls to transverse rolls occurs at a critical mixed convection parameter of $\text{Gr}/{{\operatorname{Re}}^{2}}\approx 6000$.

The heat transfer of the converging channel heated from below is also investigated by Chiu et al. (2000), and the following empirical correlations are recommended:

$\overline{\text{Nu}}=1.350{{\operatorname{Re}}^{0.0531}}\text{G}{{\text{r}}^{0.0594}}\begin{matrix} , & \text{for straight channel} \\ \end{matrix}\text{ }(\theta ={{0}^{\circ }}) \qquad \qquad(3)$

$\overline{\text{Nu}}=2.398{{\operatorname{Re}}^{0.0576}}\text{G}{{\text{r}}^{0.0192}}\begin{matrix} , & \text{for converging channel} \\ \end{matrix}(\theta ={{8}^{\circ }}) \qquad \qquad(4)$

Figure 2: Flow regime map for a converging channel with 8° tilt

where the average Nusselt number is defined as

$\overline{\text{Nu}}=\frac{{q}''H}{k\Delta \bar{T}} \qquad \qquad(5)$

and $\Delta \bar{T}$ is the difference between the average temperature of the susceptor and the incoming temperature of the precursor.

There are also numerous efforts to model CVD in the horizontal reactors and detailed reviews are available in the literature (Jensen et al., 1991; Mahajan, 1996). Some earlier studies adopted boundary-layer assumptions and neglect buoyancy, Soret, and Dufour effects, but Mahajan and Wei (1991) relaxed the boundary layer assumption and systematically studied the effects of buoyancy force, Soret, Dufour, and variable properties. The configuration as studied by Mahajan and Wei (1991) is shown in Fig. 1(a) from Basics of Chemical Vapor Deposition, in which the reactant, silane, and the carrier gas, hydrogen, enter the horizontal channel from the left and the CVD occurs on a susceptor tilted by θ. The monocrystalline silicon can be deposited on a susceptor as the result of chemical reaction.

The governing equations for the problem are eqs. ($\frac{{D\rho }}{{Dt}} + \rho \nabla \cdot {\mathbf{V}} = 0$) – ($\rho \frac{D{{\omega }_{i}}}{Dt}=-\nabla \cdot {{\mathbf{J}}_{i}}+{{{\dot{m}}'''}_{i}}\begin{matrix} , & i=1,2,...N-1 \\ \end{matrix}$) in the Cartesian coordinate system, with the Dufour heat flux as

$\mathbf{{q}''}=-k\nabla T+\alpha {{R}_{g}}T\frac{{\bar{M}}}{{{M}_{2}}}{{\mathbf{J}}_{1}} \qquad \qquad(6)$

where $\bar{M}$ is the averaged molecular mass, M2 is the molecular mass of the hydrogen, and ${{\mathbf{J}}_{1}}$ is the mass flux of reactant due to ordinary and thermal diffusions.

Figure 3: Growth rate of the silicon film grown obtained by different models

The deposition rate of the monocrystalline silicon can be obtained by

${{\mathbf{\dot{m}}}_{\text{Si}}}=-\frac{{{M}_{\text{Si}}}cD}{{{\rho }_{\text{Si}}}}{{\left. \nabla {{x}_{1}} \right|}_{\text{Susceptor Surface}}} \qquad \qquad(7)$

where MSi and ρSi are respectively molecular mass and density of silicon, c is molar concentration of the precursor, and x1 is mole fraction of silane.

To compare the computational results with the experimental results by Eversteyn et al. (1970), Mahajan and Wei (1991) took the physical dimensions and the processing parameters were taken to be similar to those of Eversteyn et al. (1970): the height of the reactor was 2.05 cm, and the temperatures of the susceptor and the top wall were 1323 K and 300 K, respectively. The partial pressure of the carrier gas (hydrogen) and the reactant (silane) were 760 torr (1 atm) and 0.76 torr (0.001atm), respectively. The inlet velocity of the precursors was 0.175 m/s, and their temperature was 300 K.

Figure 3 shows comparison of the growth rates of the silicon in a horizontal reactor with a tilt angle of γ = 2.9° obtained by different models, along with experimental data. It can be seen that curve a, with average properties and without Soret or Dufour effects, agreed with experimental results very well. When the Soret effect is included, the predicted deposit rate – represented by curve b – is significantly below the experimentally measured deposit rate. Addition of the Dufour effect did not improve the agreement with the experimental data. When variable properties are accounted for, the predicted result – represented by curve c – again agreed with the experimental results. This interesting phenomenon indicates that the Dufour effect has very insignificant effect on the deposition rate, and the Soret effect and variable property effect can cancel each other. However, it is necessary to point out that the agreement of curve a and experimental results is coincidental, and the Soret and variable property effects should be included in the analysis.

## References

Chiu, W.K.S., Richards, C.J., and Jaluria, Y., 2000, “Flow Structure and Heat Transfer in a Horizontal Converging Channel Heated from Below,” Physics of Fluids, Vol. 12, pp. 2128-2136.

Eversteyn, F.C., Severin, P.I.W., vida Brekel, C.H.J., and Peck, H.L., 1970, “A Stagnation Layer Model for the Epitaxial Growth of Silicon from Silane in a Horizontal Reactor,” Journal of the Electrochemistry Society, Vol. 117, pp. 925-931.

Jensen, K.F., Einset, E.O., and Fotiadis, D.I., 1991, “Flow Phenomena in Chemical Vapor Deposition of Thin Films,” Annu. Rew. Fluid Mech. , Vol. 23, pp. 197-232.

Mahajan, R.L., 1996, “Transport Phenomena in Chemical Vapor-Deposition Systems,” Advances in Heat Transfer, Academic Press, San Diego, CA.

Mahajan, R.L., and Wei, C., 1991, “Buoyancy, Soret, Dufour, and Variable Property in Silicon Epitaxy,” ASME Journal of Heat Transfer, Vol. 113, p. 688-695.