lecture_9_chex42

lecture_9_chex42 - Coupled Mass Transport and Reaction in...

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Unformatted text preview: Coupled Mass Transport and Reaction in LPCVD Reactors Coupled Mass Transport and Reaction in LPCVD Reactors Dilute A in B e.g., SiH 4 in H 2 2R w 2R t r z z=- /2 z= /2 r=0 r=R w c=c b Separate reactor into two regions, intrawafer & annular Continuity Continuity Eqn Eqn : Convection : Convection-Diffusion Diffusion-Reaction Reaction Eqns Eqns Assumptions ! Dilute species i in major carrier gas (e.g., H 2 ) i=SiH 4 ! Isothermal ! Constant D i and density Assume stagnant in the intrawafer region ~ 0 No rxn in the gas Steady state t c R c u c D i i i i i = + r 2 Equations and Boundary Conditions for the Equations and Boundary Conditions for the intrawafer intrawafer region region 1 2 2 = + z c r c r r r 2 2 / z @ r z c D / z @ r z c D R r @ c c r @ r c s s w b = = = = = = = = r s = surface reaction rate (net loss rate of SiH 4 ); related to the deposition rate ! If r s is linear in c then there is an analytic solution ! If r s is nonlinear we have to seek numerical solution Approximate solution Approximate solution Fin Approximation Fin Approximation ! Take r s =kc & average over z direction ! Averaging over the small dimension (z) is called the fin approximation: an approximation which is very good for 2-D regions with high aspect ratio (R/ ) 2 1 1 1 1 2 2 2 2 2 2 2 2 = = + = + = + = = kC r C r r r D D kC D kC r C r r r z C z C r C r r r dz z c dz r c r r r / z / z / / / / = = 2 2 2 2 2 2 1 / / / / / / dz ) z , r ( c dz dz ) z , r ( c ) r ( C let volume area surface R R w w = = 2 2 2 2 note Nondimensionalization Nondimensionalization & Solution & Solution D kR D kR c C R r w w b w 2 2 2 2 2 1 = = = =...
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This note was uploaded on 12/29/2011 for the course CHE 142 taught by Professor Ceweb during the Fall '09 term at UCSB.

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lecture_9_chex42 - Coupled Mass Transport and Reaction in...

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