A numerical model was developed to predict gas-phase nucleation of particles during silane pyrolysis. The model includes a detailed clustering mechanism for the formation of hydrogenated silicon clusters containing up to ten silicon atoms. This mechanism was coupled to an aerosol dynamics moment model to predict particle growth, coagulation, and transport. Both zero-dimensional transient simulations, at 1-2 atm pressure, and one-dimensional steady-state stagnation-point flow simulations, at 1-2 Torr pressure, were conducted. The effects of carrier gas, temperature, pressure, silane concentration, and flow rate were examined. The results predict that hydrogen as carrier gas, compared to helium, suppresses nucleation, and that particle formation for the case of hydrogen carrier gas increases strongly with increasing initial silane-to-hydrogen ratio. For the conditions examined, predicted particle nucleation rates increase dramatically with increasing temperature. The effect of total pressure depends on the pressure regime: at 1-2 atm pressure particle formation is predicted to be insensitive to pressure, whereas at 1-2 Torr particle formation is predicted to increase strongly with increasing pressure. The predicted effects on particle formation of temperature, pressure, carrier gas, and silane concentration are all qualitatively consistent with published experimental results. In the stagnation-point flow simulations the flow rate is found to affect particle dynamics because of the opposed effects of convective transport toward the heated water and thermophoretic transport away from the wafer.

The creation of wavy disturbances (Tollmien–Schlichting waves) by a localized two-dimensional disturbance source vibrating periodically at a fixed frequency in a Blasius boundary layer is discussed. The initial-boundary value problem mathematically models the vibrating ribbon experiment of Schubauer and Skramstad. By considering the ribbon vibration to start at t=0, in the model one gets the transient and the eventual periodic part of the solution. The results of the full simulation are compared with the time-asymptotic solution.

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Within shock waves, the translational motion of the gas is more energetic in the direction perpendicular to the shock than in the direction parallel to the shock. To represent this translational nonequilibrium, new continuum conservation equations are developed. These equations are derived by solving the Boltzmann equation with a first-order Chapman–Enskog expansion of an anisotropic velocity distribution function. This results in a gas model with anisotropic pressure, temperature, and speed of sound. The governing equations are solved numerically for one-dimensional steady shock waves in a Maxwellian gas. The numerical results are compared to those obtained using the direct simulation Monte Carlo method. The new continuum model captures many of the features of shock waves. In particular, this paper finds that translational nonequilibrium is present at all Mach numbers. For Mach numbers greater than 1.5, the perpendicular temperature overshoots the post-shock temperature. At the point where this temperature reaches a maximum, the model predicts that for any shock wave, the square of the perpendicular-direction Mach number is one-third; this is substantiated by the DSMC results.

Convective, diffusive, and thermophoretic particle transport in a parallel-plate semiconductor reactor is investigated. Measurements that illustrate particle transport in the reactor are presented and a Eulerian continuum particle transport formulation is used to quantitatively explain the measurements. Experimental and numerical results show that particles formed in the parallel-plate region are confined in a thin sheath (∼2 cm) between the “hot” wafer and “cold” showerhead inlet. This sheath is located at the point where downward convective transport balances upward transport by thermophoresis. The particle sheath location is independent of particle size but is dependent on gas flow rates and temperature of the wafer and showerhead inlet. In addition, experimental and numerical results show that as particles exit the parallel-plate region, the radial thermophoretic particle transport can produce “ring-like” contaminant deposits on the outer wall of the reactor under certain flow conditions. We propose a simple reactor design modification and an analytic design criterion to avoid particle deposition on the chamber walls.