Particle Transport in Parallel-Plate Reactors

Rader, Daniel J.; Geller, Anthony S.

doi:10.2172/10355

Cited by 4 publications

(13 citation statements)

References 39 publications

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“…This small inertial assumption creates a great deal of simplification with respect to the solution of the multidimensional particle transport equation. However, it limits the problem class that CADS may be applied to [12]. Routines for the evaluation of the particle diffusion coefficient, , are also included within CADS.…”

Section: Equations That Cads Solvesmentioning

confidence: 99%

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CADS:Cantera Aerosol Dynamics Simulator.

Moffat¹

2007

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This manual describes a library for aerosol kinetics and transport, called CADS (Cantera Aerosol Dynamics Simulator), which employs a section-based approach for describing the particle size distributions. CADS is based upon Cantera, a set of C++ libraries and applications that handles gas phase species transport and reactions. The method uses a discontinuous Galerkin formulation to represent the particle distributions within each section and to solve for changes to the aerosol particle distributions due to condensation, coagulation, and nucleation processes. CADS conserves particles, elements, and total enthalpy up to numerical round-off error, in all of its formulations. Both 0-D time dependent and 1-D steady state applications (an opposing-flow flame application) have been developed with CADS, with the initial emphasis on developing fundamental mechanisms for soot formation within fires. This report also describes the 0-D application, TDcads, which models a time-dependent perfectly stirred reactor. 4

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Section: Equations That Cads Solvesmentioning

confidence: 99%

“…For air, it turns out that requires particles of ~25 m, which are larger than normal soot particles. Support for inertial effects may be added later to CADS; as there are important applications that may only be approached via the inclusion of these effects [12].…”

Section: Particle Terminal Velocitiesmentioning

confidence: 99%

CADS:Cantera Aerosol Dynamics Simulator.

Moffat¹

2007

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“…Based on comparisons with calculations from a nite-element, NavierStokes solver, Rader and Geller (1999) found that Equation (1) provides a good approximation of the ow for Re < 4; for larger Reynolds numbers the asymptotic solution becomes less accurate, although it continues to capture the qualitative features of the ow.…”

Section: Fluid Transportmentioning

confidence: 99%

“…Rader and Geller (1999) used numerical simulations to explore the limits within which the ow can be approximated as quasi-1-D. They found that, for Reynolds numbers below about 8, the nonuniform region is restricted to an annulus extending about one plate-separation distance radially inward from the susceptor's outer edge.…”

Section: Fluid Transportmentioning

confidence: 99%

“…The effect of Reynolds number on collection ef ciency was explored by Rader and Geller (1999) using the analytic approximation for the ow eld given in Equation (1). For Reynolds numbers between 0 and 8 (spanning the Re range of the majority of low pressure commercial tools), they found only modest variations in the absolute collection ef ciency.…”

Section: Ef Ciency At Intermediate Peclet Numbersmentioning

confidence: 99%

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Particle Deposition in Parallel-Plate Reactors: Simultaneous Diffusion and External Forces

Rader

Geller

Choi

2002

Aerosol Science and Technology

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Particle deposition resulting from uniform external forces and Brownian motion is modeled in a parallel-plate reactor geometry characteristic of a wide range of semiconductor process tools: uniform, isothermal, downward ow exiting a perforated-plate showerhead separated by a small gap from a parallel, circular wafer. Particle transport is modeled using a Eulerian approach neglecting particle inertia and interception. Particles are assumed to originate in a planar trap located between the plates, such as would result for particles released from a plasma-induced particle trap after plasma extinction. Flow between in nite parallel plates is described by an analytic quasi-one-dimensional creeping ow approximation, where the showerhead is treated as a porous plate. An analytic, integral expression for particle collection ef ciency (fraction of particles that end up on the wafer) is derived as a function of four dimensionless parameters: the ow Reynolds number, a dimensionless trap height, a dimensionless particle drift velocity, and the particle Peclet number. Numerical quadrature is used to calculate particle collection ef ciency in terms of the controlling dimensionless parameters for external forces, which either enhance or inhibit particle deposition. Example calculations of collection ef ciency are also presented in dimensional terms for a representative set of process conditions. Strategies to reduce particle deposition include the use of a protective external force and manipulation of the trap to keep it as far from the wafer as possible.

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Showerhead-Enhanced Inertial Particle Deposition in Parallel-Plate Reactors

Rader¹,

Geller²

1998

Aerosol Science and Technology

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ABSTRACT. Particle deposition is modeled in a parallel-plate reactor geometry characteristic of a wide range of semiconductor process tools: uniform downward flow exiting a perforated-plate showerhead separated by a small gap from a circular wafer resting on a parallel snsceptor. Because the area available to flow is constricted inside the showerhead, high gas velocities within showerhead holes can accelerate particles and lead to inertia-enhanced particle deposition on the wafer below. Numerical models are presented for determining the extent of inertia-enhanced deposition in a parallel-plate geometry for particles originating upstream of the showerhead. The problem is treated in two steps, for which particle and fluid transport are determined: 1) within a showerhead-hole, and 2) between the showerhead and susceptor. Analytic expressions are presented for the gas velocity in the showerhead holes. Particle transport analysis leads to an analytic expression for the dimensionless particle velocity at the exit of the showerhead as a function of the dimensionless showerhead thickness, the showerhead porosity, and the particle Stokes number. The fluid flow field in the inter-plate region is calculated by both an analytic 1-D creeping-flow approximation and by a numerical 2-D finite element method; for Reynolds numbers less than about four, the two methods are found to be in good agreement. To calc~~late the net effect of inertia-enhanced deposition, the analysis of particle acceleration in the showerhead is coupled with that for interplate transport. The final result is the particle collection efficiency (fraction of particles entering the reactor that deposit on the wafer) as a function of the dimensionless parameters characterizing: showerhead porosity, showerhead thickness, inter-plate Reynolds number, dimensionless particle drift velocity (a measure of the strength of applied external forces), and particle Stokes number. Conditions are found under which particle acceleration in the showerhead greatly enhances particle deposition on wafers. Numerical predictions are presented for the critical Stokes number, which is the nondimensional particle size at which inertial effects lead to substantial particle deposition even in the absence of external forces. Specific guidelines for reducing inertia-enhanced particle deposition include: increase the number of and/or enlarge the size of the showerhead holes, make the showerhead very thin, keep the inter-plate gap large, apply an external force that resists deposition, use low mass flow rates, avoid low pressure, or use a high molecular weight gas. For Reynolds numbers less than four, particle deposition efficiencies calculated with the analytic inter-plate flow field approximation are found to be in good agreement with numerical 2-D simulations. AEROSOL SCIENCE AND TECHNOLOGY 28:105-132 (1998) NOMENCLATURE radius of showcrhead holes (cm) showerhead hole area (cm2) showerhead area (cm2) gas mean molecular velocity = (8RTlvM) (cmls) diameter of showerhead holes (cm) par...

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Particle Transport in Parallel-Plate Reactors

Cited by 4 publications

References 39 publications

CADS:Cantera Aerosol Dynamics Simulator.

CADS:Cantera Aerosol Dynamics Simulator.

Particle Deposition in Parallel-Plate Reactors: Simultaneous Diffusion and External Forces

Showerhead-Enhanced Inertial Particle Deposition in Parallel-Plate Reactors

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