EE143 N Cheung Notes on CVD Kinetics Deposition depends on the sequence of events 1 Diffusion of Reactants to surface 2 Absorption of Reactants at surface 3 Chemical reaction at surface 4 Desorption of products from surface 5 Diffusion of products from surface 1 and 5 are mass transfer mechanisms The slowest event will be the rate determing step 1 Temperature Dependence of Deposition rate i From the above Si deposition example for low T rate R e E kT Surface Reaction limited where E 25 100 kcal mole for most CVD processes or 1 4 eV atom ii For high temperature R Tn 1 5 n experimental 2 0 Mass Transport limited 1 For mass transport limited reactions R D diffusion constant and D T3 2 P for gaseous diffusion n1 v n2 v v dn Proof F 4 4 4 dx where mean free path of gas collision v dn F Ddx D 2 kT Since P and v T D T3 2 P 2 Growth Rate Model Note This model is a special case of the Grove Deal model for thermal oxidation Here we don t have to consider the diffusion througfh the oxide layer In this model fluxes of products are ignored i e their mass transfer coefficients those of reactant Let F1 flux from bulk of gas to substrate surface hG CG CS where hG mass transfer coefficient CG CS reactant conc at bulk of gas and substrate surface respectively Let F2 flux consumed in film growth reaction kS CS where kS surface reaction rate coefficient Steady state F1 F2 F CG kShG CS 1 k h and F k h CG S G S G 2 Since CG Y CT where Y mole fraction of reactant CT total of molecules cm3 in gas mixture dy F thickness growth rate where atomic density of film dt kShG CT CT 1 dy Y 1 Y dt k h 1 S G k h s G Comments dy a dt is determined by the smaller of hG and kS i e mass transfer control or surfacereaction control dy b dt Y mole fraction of reactant in bulk of gas mixture and 3 3 Boundary Layer Theory for Stagnant Gas Layer The boundary layer thickness x is shown in the figure below and L is the length of the substrate e g substrate or wall of reactor The gas velocity u is a function of x and y and is equal to zero at plate s surface and is equal to U in the free gas stream Let viscosity of gas Then frictional force unit area along the x direction u y Let us consider a volume element of unit depth i e into the paper height x and width dx u u Total friction force on element 1 dx dx decelerating force y y Total accelerating force on element du du dx du x dx dt x dx dx dt x dx dx u where is the gas mass density u du Balanced forces x udx and u x y can be solved exactly y Approximate Solutions u U u U Let u U y x y x x then x A 1 2 B parabolic dependence where A B are constants U L 1 2 L 2 x dx The average boundary layer thickness L 3 UL 3 0 4 L ReL ReL is called the Reynold Number of the reactor When ReL is small 2000 viscous flow dominates When ReL very large 2000 turbulent flow dominates The Exact Solutions The stagnant layer thickness with u 0 99U is equal to x x 5 0 U 1 2 See H Blasius NACA Tech Mem 1949 p 1217 In the CVD growth rate model it was assumed that mass transport across stagnant layer proceeds by diffusion CG CS DG then F1 DG hG where DG diffusivity For mass transfer limited deposition model 5 dy 1 dt hG U
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