solid solubility in silicon
Post on 02-Feb-2016
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Solid solubility in silicon
• Basic diffusion– Constant surface-concentration
t=0 C(x,0)=0
boundary conditions: C(0,t)=Cs where Cs=surface-concentration (cm-3)
C(,t)=0 ”at large depth”
Dt
xerfcCtxCS 2
),(
x
C Cs t2
t1
t2>t1
D= Diffusion coefficient (cm2/s)
t=time (s)
– Constant dose (quantity)
boundary conditions :
x=0 lead to
Dt
x
Dt
StxC
4exp),(
2
S= dopants per surface unit (cm-2)
0),(
),(0
tC
SdxtxC
Dt
StC
S
x
Ct1
t2t2>t1
t increase, Cs decrease Cs !
Equal Area below the curves
• Diffusion coefficient
kT
EDD aexp
0T= temperature in Kelvin
k=8.61710-5 (eV/K) ”Boltzmans-constant”
Ea= activation energy (eV)
D0= Diffusion coefficient
extrapolated for infinity temperature
D is the intrinsic diffusion coefficient and is valid when C<ni
ni=intrinsic charge carrier concentration for a specified temperature.
When C>=ni then D is extrinsic diffusion
Graf: Intrinsisk ladningsbärrar konc.
Graf: Intrinsisk diffusivitet
Graf: Erfc och exp fkn.
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