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

Mass-balance
Differential equation for radical distribution at the
flux-BC surface
• averaging the diffusion equations along the plasma thickness (L),
• using the flux BC
• and assuming that diffusion is much faster than the gas flow
Flux BC:
Radical fluxes Γ i 0 coming from plasma impinges a wafer surface. Fluxes impinged a
PR surface and an etched feature are consumed with different probabilities: χ i PR
and χ i (χ i is AR dependent parameter).
Density of consumed flux of neutrals, which is the difference of the densities of
incoming and reflected fluxes depends on the PD:
Γ
C
dS 2
=
r
Γi
= 2
πh
( r )
N
∫
R
i
r
c
4
( r )
r
χ
i
h
π
r
2 2π
R
∫∫
( r + r ) ρ(
r , φ )
1
0 0
i
i
r1dr
1dφ1
( χ PR ( 1−
ρ(
r1
, φ1)
) + χ ( AR)
ρ(
r1
, φ1)
)
2 r r 2 ( h + r1
− r )
1
1
2
dr1
⎡
r 2
⎛ r ⎤
1 ⎞
⎢1
+ ⎜ ⎟ ⎥
⎢⎣
⎝ h ⎠ ⎥⎦
2
2
=
( r,
φ)
2
2
⎪⎧
⎡∂
n
⎤⎪⎫
i 1 ∂ ni
1 ∂ni
nicF
0 = D⎨⎢
+ ⋅ + ⋅ −
2 2 2 ⎥⎬
⎪⎩ ⎣ ∂r
r ∂φ
r ∂r
⎦⎪⎭
4L
2 r
r r r r d r ′
F(
r,
φ)
= ∫ ˆ χ(
r ′ + r ) ρ(
r ′ + r ) r 2
2
⎛ r ′ ⎞
⎜
⎜1+
⎟ 2
⎝ h ⎠
+ γ − kV
n
r ⎧χ
⎫
ˆ χ(
r ′ ) = ⎨ ⎬
⎩χ
PR ⎭ Stenger, AIChE Journal, 33, 1187-1190 (1987)
Y
φ 1
r r 1
dS 1
X
Θ
r r δδ Ω = sin Θ Θδδ
Θ Θδϕ
δϕ
2
r r r
12
r r r
r = r − r
1
Surface “2”
dS 2
Surface “1”
Copyright ©2008, Mentor Graphics.
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