Revisit gas d c D J=D C-C dynamics. dx d(x Boundary layer Layer thickness, 8(x) 入 And we saw gas dIffuSivity D (unlike solid 2 gas vel: uo boundary layer wafer water X=L Fuld dynamics:6(*=nr p=mass density, n= viscosity puo 6(x)a=2r/ 2 L Reynolds #:Re Puo L 3√ Re ease of gas flc So √Re 2 Mon.. Sept. 15. 2003
Revisit gas J1 = hg(Cg - Cs) dC D J1 = D = (Cg - Cs) dynamics: dx d(x) Boundary layer Layer thickness, d(x) lvx And we saw gas diffusivity D = (unlike solid) 2 z u gas vel: u0 boundary layer Cg d (x) d (x) us = 0 Cs wafer wafer x x = L hx Fluid dynamics: d(x) = r = mass density, h = viscosity ru0 L 1 h 2 L Reynolds #: Re = ru0L d = Ú d(x)dx = 23 L ru0L ≡ 3 Re ease of gas flow h L 0 D 3 D Æ Re So: hg = d 2 L Mon., Sept. 15, 2003 6
Several processes In serles SImplify cvD to 2 steps: △C B J,=kc 2 Reaction rate constant, ks Stlcking coeficient yr as in oxidation but no 0≤%AB≤ sold-state diffusion here reaction occurs at surface AB bounces Good off surface ad heston Let's analyze, solve for J2 Mon.. Sept. 15. 2003
Several processes in series Simplify CVD to 2 steps: Boundary AB layer Dg J1 = d DC J2 B A J2 = k Cs s Reaction rate constant, k Sticking coefficient gAB, s …as in oxidation, but no 0 ≤ gAB ≤ 1 sold-state diffusion here, reaction occurs at surface. AB bounces Good off surface adhesion Let’s analyze, solve for J2… Mon., Sept. 15, 2003 7
Two man CVD layer =2△C1=bC8=C B =kC In steady state: J-J2n C, J,=kC h,(Co-C)=kcs tk h tk ectrical analog小=h R-R++R2 G=1/RG2G1+2) Two processes In serles; slowest one Imts film growth Mon.. Sept. 15. 2003
J1 = J2, hg ( Cg - Cs ksCs J2 = ksCs = hgks hg + ks Cs = Cg hg hg + ks Cg , Boundary layer J2 = ksCs B A AB J2 J1 = hg( ) Cg - Cs process: J1 = Dg d DC In steady state: ) = Two main CVD J1 = J2, 1+R2 1G2 /(G1+G2) Electrical analogy: R = R G = 1/R= G Two processes in series; slowest one limits film growth Mon., Sept. 15, 2003 8
Two men cVD Boundary A: layer J1=△CJ=1(C2-C) 6 A J2=kc hk 2 h tk hk cc FIm growth rat≡y=J # h +k N h k Slower process controls growth Mon.. Sept. 15. 2003
Boundary layer J2 = ksCs B A AB J2 J1 = hg( ) Cg - Cs Two main CVD process: J1 = Dg d DC J2 = ksCs = hgks hg + ks Cg ≡ v = J # area - t Ê ËÁ ˆ¯˜ 1 N # vol Ê ËÁ ˆ¯˜, v = hg ks hg + ks Cg Nf = Cg Nf 1 hg + 1 ks Film growth rate Slower process controls growth Mon., Sept. 15, 2003 9