Multiphysics Model of Silicon Epitaxy CVD

case study

This Case Study reproduces a modeling study published in the literature by Habuka et al. [1] on epitaxial deposition of silicon film on a silicon substrate in a horizontal hot-wall reactor. The steady-state FEM model incorporates fluid flow, heat transfer, dilute species transport, and one-step Arrhenius kinetics at the wafer surface. Additionally, the transport properties of the gas species are all temperature dependent. Simulation results are compared with those in [1].


Epitaxy refers to a deposition of a crystalline layer on a crystalline substrate. It may be further classified as homo-epitaxy or hetero-epitaxy depending on whether the layer deposited is made of identical material as the substrate. Silicon epitaxy is a Chemical Vapor Deposition (CVD) process that is widely used in the semiconductor industry. The process involves decomposition of chlorosilanes (e.g., SiCl4, SiHCl3, SiH2Cl2, SiH4) at high temperature (~ 900°C – 1150°C), with hydrogen as the reducing agent and carrier gas. Trichlorosilane (TCS), SiHCl3, a liquid at room temperature, is the preferred silicon source. Hydrogen gas is bubbled through liquid TCS to produce a dilute mixture of gaseous TCS in hydrogen carrier gas. TCS has a moderately high deposition temperature of 1150°C at atmospheric pressure for deposition of single crystal silicon.

The steps in the vapor-phase epitaxy involve the following processes:

  • convective transport of reactants from the reactor entrance to the substrate region,
  • gas-phase reactions, as well as decomposition of reactants and products in the hot region close to the heated substrate (wafer),
  • species transport from gas stream through boundary layer to the wafer surface by diffusion,
  • adsorption of reactants on the wafer surface,
  • surface reactions,
  • etching of the deposited silicon by the HCL byproduct before it diffuses into the main flow, and
  • finally, convective transport of byproducts out of the chamber.

The silicon epitaxy chemistry is complex and can be modeled as composed of the following reversible steps in which the TCS reacts with hydrogen to produce dichlorosilane (DCS), SiH2Cl2, decomposition of both DCS and TCS to SiCl2, followed by reduction of SiCl2 to silicon on wafer surface [2]:

SiHCl3 + H2 ↔ SiH2Cl2 + HCl.

SiH2Cl2 ↔ SiCl2 + H2.

SiHCl3 ↔ SiCl2 + HCl.

SiCl2 + H2 ↔ Si + 2 HCl.

The global, one-step approximation of the above reactions by Habuka et al. [1] is as follows:

SiHCl3 + H2 → Si + 3 HCl.

The kinetic rate coefficient for this global reaction is of the Arrhenius form: kr = A exp(-Ea/(RT)). Habuka et al. [1] calibrated their model to their experimental data and reported the activation energy as, Ea = 138,000 J/mol. The pre-exponential term was found to be A = 2650 m4/mol/s.

Two-dimensional FEM Model of Silicon Epitaxy

Figure 1 shows the geometry used in the 2-D model obtained from Habuka et al. [1]. The end-to-end length of the reactor is 0.705 m and the total height is 0.4 m. The chamber is radiantly-heated from above and below as shown, and operates at atmospheric pressure. The upper part of the left wall and the entire right wall are kept cool at room temperature (27°C), and the sections of the top and the bottom wall immediately above the susceptor are at specified temperatures. The rest of the walls are insulated. A gaseous mixture, consisting of trichlorosilane (SiHCl3, nominal mass fraction = 0.71) and hydrogen, is injected into the chamber at room temperature and a velocity of 0.67 m/s from the top left corner of the chamber, and exits from the bottom right corner. The 8” wafer is located at the center of the 12” susceptor, 0.205 m from the left end of the chamber. The wafer and susceptor are heated to the deposition temperature, Tsus, which ranges from 1120°C to 1180°C, with a nominal value of 1150°C. The temperatures of the hot sections of the top and bottom walls, Twall, were measured by Habuka et al. [1], and found to be in the range 457°C497°C corresponding to the Tsus range specified above. Hence, the following relationship was used in the simulations:

Twall = 457 + 0.667 * (Tsus-1120) ; (in °C).

The susceptor and wafer temperatures are assumed to be independently controlled to generate excellent uniformity.


Figure 1: Schematic of the two-dimensional reactor [1]. Shaded walls are insulated. Figure not to scale.

Figure 1: Schematic of the two-dimensional reactor [1]. Shaded walls are insulated. Figure not to scale.


The two-dimensional finite element model was developed using COMSOL Multiphysics. The model uses the Non-Isothermal Fluid Flow, Heat Transfer and Transport of Dilute Species physics components of the software. The temperature dependence of all the transport properties of the three species (TCS, H2 and HCl) were obtained from relationships given by Newman and Pollard [3]. The model takes less than five minutes to run a simulation.

Figure 2 shows the velocity vectors with superposed temperatures for nominal conditions (TCS mass fraction of 0.71, wafer temperature of 1150°C, and top and bottom quartz wall temperatures of 477°C). The gas is heated up considerably by the susceptor and the wall, and speeds up along the wafer surface. Figure 3 shows the distribution of the TCS mole fraction within the chamber with depletion near the wafer. Had gas-phase decomposition been considered, the depletion profile (TCS boundary layer) near the wafer would have been slightly broader. Figure 4 shows comparison of deposition rate uniformity with Habuka et al. [1]. Results from SC’s model compare quite well with those of Habuka et al. [1], the average deposition rate difference being about 10%. Figure 5 shows the effect of wafer rotation which was simulated by averaging the deposition profile with the same profile flipped about the vertical axis through the center of the wafer. It is seen that the rotation significantly improves deposition uniformity, assuming that the rotation period is much smaller than the deposition period (which is almost always the case).


Figure 2: Gas velocity vectors superposed with velocity magnitude (speed).

Figure 2: Gas velocity vectors superposed with velocity magnitude (speed).


Figure 3: Surface plot of TCS mole fraction.

Figure 3: Surface plot of TCS mole fraction.


Figure 4: Deposition profile along flow direction. Comparison with Habuka, et al. [1].

Figure 4: Deposition profile along flow direction. Comparison with Habuka, et al. [1].



Figure 5: Deposition rates with and without wafer rotation.

Figure 5: Deposition rates with and without wafer rotation.


Deposition rates computed for various TCS mass fractions are plotted in Figure 6. These results agree well with Habuka’s experimental data. The slight over-prediction of the deposition rate may be attributed to three potential causes. First, the temperatures at the adiabatic parts of the wall are relatively high, and in reality, there is probably some deposition on the walls leading to reactant depletion downstream. Second, there is always a small amount of HCL etching of deposited silicon that reduces the overall deposition rate [4]. Habuka et al. did not consider etching in this particular study and so we left it out from ours, too. Finally, Habuka et al.’s rate constants were determined from fitting the data to their model, and there are numerical differences in the results of the two models.


Figure 6: Average deposition rate as function of average molecular weight of gas at inlet. Nominal molecular weight is 6.67 kg/kg-mole (when TCS mass fraction = 0.71).



Physics-based CVD models such as this model of silicon epitaxy are useful in many ways including model-based control, design of next-generation chambers, troubleshooting, virtual sensing and process optimization. If you would like more information regarding physics-based model development and its application to your system, please contact us.



  1. M. Habuka, Katayama, M. Shimda, K. Okuyama, “Numerical Evaluation of Silicon Thin Growth from SiHCl3-H2 Gas Mixture in a Horizontal Chemical Vapor Deposition Reactor,” Jpn. J. Appl. Phys., No. 33, p.1977-1985, 1994.
  2. S. Wolf, Silicon Processing for the VLSI Era, Vol. 1: Process Technology, 2nd Edition, Lattice Press, 1999.
  3. Pollard and Newman, J. Electrochem. Soc., Vol. 127, p. 744, 1980
  4. H. Habuka, T. Suzuki, S. Yamamoto, A. Nakamura, T. Takeuchi and M. Aihara, “Dominant Rate Process of Silicon Surface Etching by Hydrogen Chloride Gas,” Thin Solid Films, No. 489, pp.104-110, 2005.