Design specific variation in pattern transfer by via/contact etch ...

Intra-Feature Radical Transport Resistance
Mechanisms of the neutrals transport inside a feature:
• The “line-of-sight” – reagents are disappeared after first collision with wall
• “Knudsen diffusion” – reagents do not react with walls
For Knudsen diffusion - Clausing factor is the probability that
a randomly directed species incident at the top of a verticalwalled
feature will reach the other end.
For the Clausing factor k we can use :
1
for round via of the depth L and radius R k =
1
3 PL
1+
16 S
3 L
1+
8 R
And k = for the rectangular shaped feature of the
perimeter P, area S and the depth L.
CF 2 flux impinged the via bottom
2π
λ
π
c λ
⎛ 2 R
B 1 CF
⎜
2
Γ =
N CF ( r1
, ϕ )
2
2 2
2
3 h
1 k
8π
R ∫∫
⎜ ∫∫
+
0 0 ⎜
D
8 R
⎝
rdrdψ
2 2 2 [ λ + r + r − 2r
r cos(
ϕ −ψ
) ]
⎞
⎟
⎟r1dr
dϕ
⎟
⎠
CF 3 1
0 0
1
1
2
2π
⎝
B cO
( )
( h + λ)
ΓO r,
ψ = ∫ ∫
8π
0
⎛ λ ⎞
R⎜1+
⎟
h ⎠
0
N
O-atom flux impinged the via bottom
O
( r , ϕ)
1
⎡
⎢
⎢⎣
λ
h
ψ
Reactiv
e
surface
r
r
1
θ
Copyright ©2008, Mentor Graphics.
2
r
1
2
( ) ( ) 2
2 2 2⎛
⎞ ⎛ ⎞
h + λ + r + r 1+
+ 2r
r 1+
cos ϕ −ψ
1
⎜
⎝
r dϕdr
1
λ
⎟
h ⎠
1
1
⎜
⎝
ϕ
λ
⎟
h ⎠
12
⎤
⎥
⎥⎦
3