《Microelectronics Process》Gas flux across concentration gradient

3.155J/6.152J Microelectronic Processing Technology Fall Term. 2003 Bob Handley Martin schmidt Luiz #1 out:Oct.22.2003 Due:Oct.22.2003 Ideal gas: PV=NkBT, N/=n=C(concentration) 2k. T k。T Gas kinetics: y Mean free path: 1 d= molecular diameter nd-p Oxidation, CVD Gas flux across concentration gradient: J=h(Cg-Cs ), Cs=concentration at surface Flux for chemical reaction: J(#/vol s)=k Cs, where k=koexp[-AG/(kBT)I Film growth velos/ hk ii where Nr is number of deposited species/cm Diffusio Diffusion length: a=2v(Dr) Fixed dose: C( =mdR exp 4D =C(0, Dexe-4l Inexhaustable source: C(,t=Csurerfd Dt Dose=Q=」c(=,l)d Concentration profile: C(x)=C, exp (r-R OAv(2T)AR,]cm

3.155J/6.152J Microelectronic Processing Technology Fall Term, 2003 Bob O'Handley Martin Schmidt Quiz # 1 Out: Oct. 22, 2003 Due: Oct. 22, 2003 Ideal gas: PV = NkBT, N/V = n = C (concentration) kBT Gas kinetics: v = 2kBT , Mean free path: λ = 2πd2 P , d = molecular diameter. x πm Oxidation, CVD: Gas flux across concentration gradient: J = h(Cg - Cs), Cs = concentration at surface. Flux for chemical reaction: J (#/(vol s) = k Cs , where k = koexp[-∆G/(kBT)]. J Film growth velocity: v f = = Cg / Nf where Nf is number of deposited species/cm3 . N 1 1 f + h k Diffusion: Diffusion length: a = 2√(Dt). Q  2   Fixed dose: C z( ) ,t = Dt exp− z  = C(0, t)exp− z 2   π  4Dt   4Dt  Inexhaustable source: C z, t ( )  = Csurferfc   2 z Dt   , ∞ Dt Dose ≡ Q = ∫ C(z,t)dz = 2 C0 0 π Ion implantation:  ( )= Cp exp− (x − Rp ) 2  Concentration profile: C x .  2∆R2  p   Cp = Q/[√(2π) ∆Rp] cm-3. 1