Diffusion of a thin surface layer into a solid When a thin surface layer diffuses into a solid, what is c(z, t)? Q= initial amount of dopant 'dose) assumed to be a delta-function ∫c(a t dz=Q=const. (#/area) C|t=0 Bound cond dC(0) Bound cond 0 Solutlon Is a Gausslan C(a,)=0 C(x)= √mDr4Dr 0 Initial cond: C(z0)=0(z diffusion length a=2√Dr Dose in sample constant in time 3.155J/6.152J.2003Diffusion of a thin surface layer into a solid When a thin surface layer diffuses into a solid, what is C(z,t)? Q = initial amount of dopant (‘dose’), • Ú C z, t)dz = Q = const. (# /area) assumed to be a delta-function ( -• t1 t2 t = 0 C Bound cond: dC(0, t) Bound cond: = 0 Solution is a Ga ussia n. dz C ( •,t ) = 0 2 Q È z ˘ C z( , t ) = exp - pDt ÎÍ 4 Dt˚˙ z 0 Initial cond: C z( ,0 ) = 0 ( z 0 ) diffusion length a = 2 Dt Dose in sample constant in time 3.155J/6.152J, 2003 3