Solutions for other L.C. B.C. can be obtained by superposition I Predeposition A Const C (Limitless source C(∞,t)=0 C(02=0 不J q=u=(2D) erf 4Dt 6.155/3.155J9/29/
6.155/ 3.155J 9/29/03 12 erf t = 0 C 0 Solutions for other I.C./B.C. can be obtained by superposition: II. Predeposition (Limitless source of dopant) x2 = z 2 4Dt Æ (z - z0 )2 4Dt Cimp ( ) z,t = 2p exp -x2 [ ] 0 u= z 2 Dt Ú dx > erf u( ) = erf z 2 Dt ÊË ˆ¯ C (, t ) C( ) 0,t = C0 C z( ) ,0 = 0 z Const C0 t C( ) •,t = 0 0
Other L.C. /B.C.(cont 0.995 erfClu=l-erf 012 a= diffusion length=2√Dr t>0 Dt (D≈1015)×(t=10)→a≈0.2um D Dose=JC(1÷3V2 Const Co Co limited by solid solubil C(∞,t) Dose, Q, mount of dopant in sample 0)=0 increases as t1/2 6.155/3.155J9/29/03
6.155/ 3.155J 9/29/03 13 Other I.C./B.C. (cont.): C z( ) ,t = Csurferfc z 2 Dt ÈÎÍ ˘˚˙, t > 0 a = diffusion length = 2 Dt (D § 10-15) ¥ (t = 103) fi a § 0.2 mm erfC u( ) =1-erf u( ) z C z erf z( ) 0 1 2 1 0.995 C (, t ) C( ) 0,t = C0 C z( ) ,0 = 0 z Const C0 t Dose, Q, amount of dopant in sample, increases as t1/2. Dose > Q = C(z,t)dz = 2 Dt 0 p • Ú C0 = ap C0 C0 limited by solid solubility