RemInder Analytical Solutlons to Dlifuslon Equatlons Solution for a limitless source of dopant(constant surface concentration Bound cond d dc C(0,t)=Surf Const C urf Bound cond dt dz. C(∞,t)=0 C(z,t=Curfc t>0 Initial cond: C(Z, 0)=0 where erfc(x)=1-erf() and t,=predep time Dose Q-(2/ Curt vDt Dose in sample increases as ti/2 3.155J/6.152J.2003Reminder: Analytical Solutions to Diffusion Equations Solution for a limitless source of dopant (constant surface concentration): Bound cond: ∂C = D ∂2C C (0, t ) = Csurf C (∞, t ) = 0 t Bound cond: Const Csurf ∂t ∂z 2 È z ˘ C z( , t) = Csurf erfcÍ2 Dt ˙˚ , t > 0 Î z Initial cond: C (z, 0) = 0 where erfc(x) = 1-erf(x) and tp = predep time Dose Q = (2/√p) Csurf √Dtp Dose in sample increases as t1/2 3.155J/6.152J, 2003 2