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 = Nk
B
T,N/V = n = C (concentration)
k
B
T
Gas kinetics,v =
2k
B
T
,Mean free path,λ=
2πd
2
P
,d = molecular diameter,
x
πm
Oxidation,CVD,
Gas flux across concentration gradient,J = h(C
g
- C
s
),C
s
= concentration at surface,
Flux for chemical reaction,J (#/(vol s) = k C
s
,where k = k
o
exp[-?G/(k
B
T)],
J
Film growth velocity,v
f
= =
C
g
/ N
f
where N
f
is number of deposited species/cm
3
.
1 1
N
f
+
h k
Diffusion,
Diffusion length,a = 2√(Dt),
Q
2

Fixed dose,Cz,t
()
=
Dt
exp
z
= C(0,t)exp
z
2
π? 4Dt 4Dt?
Inexhaustable source,Cz,t
()
= C
surf
erfc
2
z
Dt
,
∞
Dt
Dose ≡ Q =
∫
C(z,t)dz =
2
C
0
π
0
Ion implantation,
()
= C
p
exp
(
x? R
p
)
2
.Concentration profile,Cx
2?R
2
p

C
p
= Q/[√(2π)?R
p
] cm
-3
,
1