Method for determining via/contact pattern density effect in via/contact etch rate
View Patent ↗A method for determining an effect of via/contact pattern density in via/contact etch rate of a wafer includes determining a neutral etchant species number flux intersecting each via/contact mouth as a function of local layout characteristics and determining variations in the neutral etchant species flux number as a function of the via/contact pattern density in a wafer scale. The comparison of these number fluxes provides the capability to discriminate an underetched or an overetched via/contact from normal vias/contacts satisfying an etch tolerance criterion. Chip designers can modify the layout design to minimize via/contact failures. Chip manufacturers can modify the etching process to minimize via/contact failures.
1. A method for improving wafer yield in response to analysis of effects of via or contact pattern density on via or contact etch rate of a wafer, comprising the steps of:
(a) determining a neutral etchant species number flux intersecting each via or each contact mouth as a function of local layout characteristics;
(b) determining variations in a neutral etchant species concentration as a function of the via or contact pattern density in a via or a contact layout; and
(c) adjusting the layout and etching process to reduce via failures.
2. The method for improving wafer yield according to claim 1 , further comprising identifying underetched or overetched vias or contacts.
3. The method for improving wafer yield according to claim 1 , wherein the determining step (a) comprises:
(a1) calculating a region of intersection (r) of solid angle, through which neutral etchant species have a line of sight access to a via j or contact j mouth, with an effective reactive surface situated at a distance λ above a wafer surface, wherein λ is a mean free path;
(a2) generating a circle with a radius equal to 2 r around the via or the contact j ;
(a3) counting a number of vias or contacts (n r ) located inside the 2 r -circle;
(a4) generating circles of radius equal to r around via or contact centers of each via or contact located inside the 2 r -circle;
(a5) calculating areas of overlap between the r-circle of a center via or contact in the 2 r -circle and r-circles of the rest of the vias or contacts in the 2 r -circle;
(a6) calculating a sum (S j ) of the areas of overlap with a weighting factor of 1/k, wherein k is a number of overlapped r-circles;
(a7) calculating S j for all vias or contacts in the layout; and
(a8) calculating an incident neutral flux (Γ j ) crossing the mouth of the via or contact j .
4. The method for improving wafer yield according to claim 3 , wherein for the calculating step (a1),
r
=
2
λ
AR
,
wherein AR is a via or contact aspect ration, wherein
AR
=
h
PR
+
h
Me
+
h
Via
d
Via
,
wherein h PR is a thickness of a photoresist layer, h Me is a thickness of a metal layer, h Via is a thickness of a via or contact height, and d Via is a via or contact diameter.
5. The method for improving wafer yield according to claim 3 , wherein for the calculating step (a6),
S
j
=
∑
k
=
1
n
1
k
S
k
,
wherein n is a number of vias or contacts located inside the 2 r -circle, and S k is an area of the k-overlapped regions.
6. The method for improving wafer yield according to claim 3 , wherein for the calculating step (a8), Γ j =Γ n S j , wherein Γ n is a total number flux consumed by all a wafer regions containing n vias or contacts.
7. The method for improving wafer yield according to claim 1 , wherein the determining step (b) comprises:
(b1) calculating a total neutral flux consumption (Γ m ) by a sub-region of the wafer;
(b2) determining a neutral etchant species concentration (N m ) of m number of vias or contacts in the sub-region;
(b3) determining a neutral etchant species concentration (ζ 0 ) near a wafer edge; and
(b4) solving a system of linear equations to derive neutral concentrations (ζ i ) for every i th sub-region.
8. The method for improving wafer yield according to claim 7 , wherein for the calculating step (b1),
Γ
m
≈
Γ
o
(
δ
Ω
2
π
)
S
∑
mk
eff
≈
N
m
c
_
4
1
2
π
(
Θ
λ
2
)
S
∑
mk
eff
=
N
m
c
_
ΘmS
∑
8
πλ
2
k
eff
=
φ
m
N
m
,
wherein m is a number of vias or contacts in the sub-region, δΩ is a solid angle through which via j or contact j mouth is “visible” from a flux generating point located at an effective reactive surface, Θ is an area of the via j or the contact mouth, S Σ is a total area covered by m r-circles corresponding to m vias or contacts, c is a gas thermal velocity, k eff is a coefficient describing a probability that radicals penetrating a via or contact mouth are consumed by etch reactions, and λ is a mean free path.
9. The method for improving wafer yield according to claim 7 , wherein for the determining step (b2), a mass balance equation for the sub-regions is
2
L
λ
2
γ
-
Γ
m
-
2
L
λ
D
∑
k
=
1
4
(
N
m
-
N
m
k
λ
=
0
,
wherein 2L is an electrode gap in a capacitive coupled plasma reactor, or the characteristic size of the plasma region in vertical direction for any other type of plasma reactor, γ is a rate of homogeneous generation of neutral etchant species in a discharge, N mk is a neutral species concentration in a 4 neighbor sub-regions, D is a diffusion coefficient of neutrals, and λ is a mean free path, wherein the mass balance equation can be modified to the system of linear equations:
ξ
m
(
φ
m
2
LD
+
4
)
-
∑
k
=
1
4
ξ
m
k
=
1
,
where
ξ
i
=
N
i
D
γ
λ
2
and
φ
m
=
c
_
Θ
mS
∑
8
π
λ
2
k
eff
.
10. The method for improving wafer yield according to claim 7 , wherein for the determining step (b3),
ξ
o
=
S
w
-
n
d
S
d
λ
2
Q
2
LD
,
wherein S w is a wafer area, S d is an area of a single die, Q is an inlet feed gas flow rate, 2L is an inter-electrode gap, or the characteristic size of a plasma region in a vertical direction for any other type of the plasma reactor, n d is a number of dies on a wafer, and λ is a mean free path.
11. The method for improving wafer yield according to claim 1 wherein the determining step (a) comprises the calculation of relative fluxes of neutral etchant species intersecting each via/contact mouth.
12. The method for improving wafer yield according to claim 11 further comprising a comparison of said relative fluxes to discriminate under-etched or over-etched vias/contacts from the normal ones satisfying the etch tolerance criterion.