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

Design Design Design specific specific variation variation variation in 

in 

pattern pattern transfer transfer by by via/contact 

via/contact 

etch etch process: process: full full-chip full full-chip full chip chip analysis 

analysis

� Introduction 

Agenda 

� Pattern density variation in die-scale modeling 

� Microloading and aspect ratio (AR) induced etch rate 

variation – Physics behind 

� Calibration 

� Use models 

Copyright ©2008, Mentor Graphics. 

2

Etch Step in Pattern Transfer Simulation Flow 

� Etch step is important part of the pattern transfer technology in chip 

manufacturing 

� While the existing capabilities of the predictions of post-illumination and 

post-photoresist development contours are in line with the current 

requirements, predictions of the post-etch contours are not so good. 

� Etch process is characterized by strong pattern density dependency 

Optical simulation 

Photoresist 

simulation 

Etch simulation 

Pattern Transfer in the Case 

of Contact Hole Etch 

Phot 

o 

BARC 

BARC/ME 

BARC/ME/OE 

Full Etch 

NCCAVS PAG, Sunnyvale, 

CA, 2005 

By D. Farber, B. Dostalik, B. 

Goodlin, et al (TI) 

It would be quite beneficial for both the design and process development 

communities to have a design automation tool capable of analyzing the design 

quality regarding the shape distortions (etch bias) caused by the employed 

etch recipe and, visa verse, the ability of the developed recipe to handle 

pattern density variation of a design to be manufactured. 


3

Plasma-assisted etch 

� Plasma-assisted etch is a sequence 

of chemical reactions between 

etched material and plasmagenerated 

chemical species 

resulting 

products 

generation of volatile 

� In order to initiate and sustain etch 

process the etchant species should be 

continuously generated and delivered 

to those surface segments where the 

material removal takes place – the 

bottoms of etched features. 

� In order to have a uniform across-chip 

etch rate, the combination of fluxes of 

neutrals and ions impinged the etched 

surface should be a constant. 

+ 


4

Effects of Aspect Ratio & Microloading 

Etch rate variation across layout caused 

by: 

� Across-layout variation in concentration 

of neutrals in the above-wafer plasma 

region - Microloading 

� Variation in resistance to the interfeature 

transport of neutrals - AR 

� Variation in plasma visibility - AR 

Neutrals concentration 

across layout 

Variation of solid angle of 

visibility 

Ω Ω 

Proc. of SPIE Vol. 

6520 65204D-1 

� AR variations are responsible for the distortion 

in etch rate, sidewall slope and etch depth 

developed in neighboring features 

� Microloading is responsible for those 

distortions developed in the identical features 

located in different neighborhoods 

characterized by different pattern densities 

Layout and averaged patter density 


5

PD Dependency in Etch Processing - Microloading 

� Effect of the pattern density on etch is characterized 

by a specific correlation length depending on a 

particular process recipe 

� The correlation length provides the size of layout area 

which effects etching of a particular feature 

� Correlation length is in order of magnitude of the mean 

free path of the gas species - λ 

C. Hedlund, H. O. Blom, and S. 

Berg, “Microloading effect in 

reactive ion etching,” J. Vac. 

Sci. Technol. A 12, 1962–1965 

(1994) 


6

• Neutral radical generation 

• Consumption/reflection 

• Non-uniform concentration 

• Diffusion 

Main Factors of Microloading 

Reactive 

surface 

Wafer 


7

Flux Boundary Condition Surface 

Across-die distribution of radical concentration 

c 

Γ = 

8π 

surface 

Radical Flux at Top of the Feature 

λ 

π λ 

∫ ϕ ∫ ( ϕ ) 

2 

r 

d 1 N r1 

, 1 

r1dr 

1 

3 

0 0 2 

r 

r 

2 r r 2 ( h + r + r1 

) 

Γ 

Y 

C 

dS2 

r 

Γi 

= 2 

πh 

Pattern-dependent Flux Consumption 

( r) 

∫ 

δδ Ω = sin Θ Θδδ 

Θ Θδϕ 

δϕ 

φ 1 

r 2 2 

Ni 

( r) 

ci 

h 

= 

4 π 

R 

r 

χ 

r 

r r r 

∫∫ 

1 

πR 

dS 1 

( r+ 

r) 

ρ( 

r, 

φ ) 

1 

0 0 

Θ 

r r 2 

r r 12 

r r r 

r = 

r − r 

Surface “2” 

dS 2 

i 

i r1dr 

1d 

1 φ 

( χPR( 

1−ρ( 

r1, 

1 φ ) ) + χ ( AR) 

ρ( 

r1, 

1 φ ) ) 

2 r r2 

( h + r1 

−r 

) 

1 

1 

X 

2 

dr1 

⎡ 

r 2 

⎛r 

⎤ 

1⎞ 

⎢1+ 

⎜ ⎟ ⎥ 

⎢⎣ 

⎝h⎠ 

⎥⎦ 

2 

1 

2 



2 

8 

=

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 


dS 2 



2 

9 

i

Mass-balance 

Differential equation for across-die distribution of 

the radicals 

Due to complex character of dependency of the introduced 

parameters on the plasma recipe as well as the difference in 

generation rates of different radicals it is reasonable to introduce a 

dimensionless form for radical concentration: 

This transformation leads to the dimensionless form of the mass 

balance equation: 

2 

γ 

⎛ γλ ⎞ cn0 

n0 

= andθ 

0 = n0 

/ = 

Here: 

k 

⎜ 

V 

D ⎟ 

⎝ ⎠ 3γλ 

Solution of these mass balance equations generates across-die 

distributions of concentrations of all radicals participating in etch 

reactions. Gas-kinetic properties of radicals (D, λ, c) are calculated 

based on Chapman-Enskog kinetic theory. 

Approximate solution of the mass-balance equation 

clearly demonstrates that an across-die distribution 

of radicals is characterized by a complex PD 

dependency, more complicated than the 

“traditional” reverse PD: 1/PD. 

n 

θ = 

2 ⎛ γλ ⎞ 

⎜ 

⎟ 

⎝ D ⎠ 

r ⎡ 1 3 λ r ⎤ r 

1−θ 

( r) 

⎢ + F ⎥ r 

⎣θ0 

4 L ⎦ 

2 ( r ) + λ ∆θ 

( ) = 0 

Approximate solution 

2 ⎡ 1 3 λ r ⎤ 

1− 

λ ∆⎢ 

+ F( 

r ) ⎥⎦ 

r 

≈ 

⎣θ0 

4 L 

θ ( r ) 

⎣θ0 

4 L 

θ ( r ) ≈ 

⎦ 

⎡ 1 3 λ r ⎤ 

⎢ + F( 

r ) ⎥⎦ 

⎣θ0 

4 L 

F = ∫ 

r r r r 

PD – GDSII 

2r 

d r′ 

r 2 ⎛ r′ 

⎞ 

⎜1+ 

⎟ 2 

⎝ h ⎠ 

( r, 

φ) 

ˆ χ( 

r′ 

+ r ) ρ( 

r′ 

+ r ) 2 

Sticking 

coefficients 

Visibility factor 


10

Radical Flux to the Feature 

� When a radical distribution across “effective 

reactive” surface is known we can determine a flux 

coming to the feature from a small area of the 

“effective reactive” surface and to integrate it 

through the all area of visibility. 

λ 

π λ 

∫ ϕ ∫ ( ϕ ) 

2 

r 

d 1 N r1 

, 1 

r1dr 

1 

3 

0 0 2 

c 

Γ = 

8π 

r 

r 

2 r r 2 ( h + r + r1 

) 

Output of the Microloading Analysis 

Consumption 

Flux 


11

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 


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

Die-level analysis: 

Calculation of distribution of 

neutral species participating in 

etch driven reactions at die level – 

microloading 

Etch Modeling Backbone 

CD/Contour 

Simulation 

Engine – Etch 

Model 

Feature-level analysis: 

Plasma visibility variation – plasma 

region visible from every segment of 

the feature etch profile 

Etch mechanism 

Wafer-scale variations & 

process parameters: 


13

Etch Model 

� Etch model, representing mathematical formulation 

of etch mechanism, provides a relation between 

fluxes of all etch-important species coming to any 

point at the etched surface and the etch rate at this 

point. 

Example of modeling SiO 2 Etch by Fluorocarbon Plasmas 

CF x radical fluxes result in SiO 2 etch and C xF y polymer deposition 

O-atom flux is a major cause of the polymer removal 

Precursors for the etch reactions are formed at the polymer-SiO2 interface 

by ion-induced energy reactions: “-Si-O-” + E = “Si-” + “O-”. Energy flux 

reaching the interface is controlled by the polymer thickness. 

Radical reactions between Si- and O- from SiO 2 and F and C from gas 

phase and polymer layer are responsible for the silicon oxide etch 

Reaction Kinetics 

x C is the carbon fraction in C xF y polymer layer; 

θ is the fraction of precursors formed at the SiO 2 - 

polymer interface 

Η CxFy is the thickness of polymer layer. 


14

Thin & Thick Polymer Regimes 

T. Tatsumi, M. Matsui, M. Okigawa, and M. Sekine, J. Vac. Sci. Technol. B 18, 1897-1902 (2000) 

Thin polymer regime 

Thick polymer regime 


15

S n 

( Z1 

+ 

8 

M 2 Z ) 9 ⎝ ⎠ 

2 

( M1 

+ M 2 ) 

Ion energy loss: ∂E 

Ion Energy Loss in Polymer Layer 

Nuclear stopping power: Electronic stopping power: 

2 

1 

1 

( Z ) 3 

3 

1Z 

⎛ 

2 M ⎞ 1 4M1M 

2 3 

= 10. 

6 

⎜ 

⎟ 

2 Se ( E) 

( E) 

E 

� For ion energy loss: 

( H ) 

− 

∂x 

= 

NS 

� From Tatsumi -JVST B18, 1897 (2000), µ = 2.97. 

�� For E = 1450 eV: E H ≈ E 0 − 0 . 088 H 

E 

� Etch stop will happen at 

the polymer thickness: 

H cr 

( E ) 

0 

1 

3 

E0 

= 

2. 

97 

,[nm] 

n 

= 

( E) 

+ NS (E) 

e 

1 

1 

2 

15 6 1 2 

3. 84 1 

⎟ 

1 

⎟ 

− ⎛ Z Z ⎞⎛ 

E ⎞ 

e Z ⎜ ⎟ ⎜ 

⎝ Z ⎠ M 

2 

3 

2 ⎛ ⎞ 

⎛ ⎞ 

⎜ µ ⎟ 

⎜ 

3 ⎟ 

3 

≈ 

⎜ 

E0 

− βE0 

H 

⎟ 

≈ E0 

− µ E0 

H = E0⎜1 

− H 1 ⎟ 

⎝ ⎠ 

⎜ 3 ⎟ 

⎝ E0 

⎠ 

( ) ( ) 3 

( ) ( ) 

T. Tatsumi, M. Matsui, M. Okigawa, and M. Sekine, J. Vac. 

Sci. Technol. B 18, 1897-1902 (2000) 

⎝ 

Experiment vs. Prediction 

⎠ 


16

Approximation of “Thin Polymer” Layer 

� Rate of generation of active precursors on SiO2 surface by 

ions penetrated the adsorbed layer is much higher than the 

rate of their disappearance by means of etch reactions 

� Rate of the reaction between silicon and fluorine atoms is 

faster than the rate of reactions of polymer formation. ( ) ⎟⎟ 

M k′ 

Γ 

C D CF2 

H ≈ 

C 

ρ S kRΓO 

+ ketch 

C ⎛ k ′ Γ ⎞ 

etchk 

D CF 

≈ Γ ⎜ 

2 

ER K etchk 

D CF 1− 2 ⎜ 

C 

ηΓi 

E0 

kRΓO 

+ ketch 

Polymer Polymer thickness thickness (nm) (nm) 

Polymer thickness (nm) 

6 

5 

4 

3 

2 

1 

Exp 

Cal 

O2=8 cc 

0 

0 500 1000 1500 

6 

5 

4 

3 

2 

1 

Exp 

Cal 

Ion Energy (eV) 

O2=8 cc 

0 

0.00E+00 1.00E+17 2.00E+17 3.00E+17 

CF2 flux (cm-2 s-1) 

ER of SiO2 (nm/min) 

ER of SiO2 (nm/min) 

600 

500 

400 

300 

200 

100 

Exp 

Cal 

O2=8 cc 

0 

0 500 1000 1500 

600 

500 

400 

300 

200 

100 

Exp 

Ion Energy (eV) 

O2=8 cc 

Cal Tatsumi, T., Hikosaka, Y., Morishita, 

S., Matsui, M., and Sekine, M., “Etch 

rate control in a 27 MHz reactive ion 

etching system for ultralarge scale 

integrated circuit processing,” J. Vac. 

Sci. Technol. A 17, 1562-1569 (1999). 

0 

0.00E+00 1.00E+17 2.00E+17 3.00E+17 

CF2 flux (cm-2 s-1) 

⎝ 


17 

⎠

“Thick Polymer” Approximation 

Ion-energy transfer through polymer layer is a limiting step in SiO 2 etch rate 

MC 

H = 

ρS 

k 

ER = K 

etch 

C 


k 

Γ 

D CF2 

⎛ kDΓ 

⎜ 

⎜1− 

⎝ ηΓi 

E 

CF2 

⎛ H ⎞ 

ηΓi 

E0⎜1− 

⎟ = K 

⎝ H * ⎠ 

0 

⎛ 

⎜ 

⎜ k Γ k′ 

Γ 

R O D 

⎜1− 

C 

⎞ ⎜ ketch 

ηΓi 

E 

⎟ 

⎠ 

⎜ 

⎝ 


CF2 

⎛ kDΓ 

⎜ 

⎜1− 

⎝ ηΓi 

E 

⎛ 

⎜ 

⎜ µ MC 

ηΓi 

E0⎜1− 

1 

⎜ 3 

⎜ 

E0 

ρS 

k 

⎝ 

0 

1 

CF2 

C 


0 

2 

⎞ 

⎟ 

⎠ 

⎞ 

⎟ 

⎟ 

⎟ 

⎟ 

⎟ 

⎠ 

k′ 

DΓCF 

2 

⎛ k′ 

DΓ 

⎜ 

⎜1− 

⎝ ηΓi 

E 

CF2 

0 

⎛ 

⎜ 

⎜ k Γ k′ 

Γ 

R O D 

⎜1− 

C 

⎞ ⎜ ketch 

ηΓi 

E 

⎟ 

⎠ 

⎜ 

⎝ 

CF2 

0 

1 

⎛ k′ 

DΓ 

⎜ 

⎜1− 

⎝ ηΓi 

E 

Matsui, M., Tatsumi, T. and Sekine, M., “Relationship of etch reaction and reactive species flux in C4F8/Ar/O2 plasma for SiO2 selective etching 

over Si and Si3N4,” J. Vac. Sci. Technol. A 19, 2089-2096 (2001). 

CF2 

0 

2 

⎞ 

⎟ 

⎠ 

⎞⎞ 

⎟⎟ 

⎟⎟ 

⎟⎟ 

⎟⎟ 

⎟⎟ 

⎠⎠ 


18

Etch Stop Condition 

� Etch stops when ions lose all their energy while penetrating the C-F layer. A 

condition for the etch stop is follows: 

k′ 

D 

LE ( Γ ) 

k 

i 

R 

Γ 

O 

Γ 

CF 

2 

= 

ρS 

M 

C 

� Knowledge of distributions of ion-neutrals fluxes along the etched surface: 

allows to determine a regions where etch is completely stopped 

1 

3 

E0 

µ 

Γ 

( , y), 

Γ ( x, 

y), 

Γ ( x, 

y) 

2 

i 

x CF 

O 


19

VEB+ - based correlations 

x 

Normalized Etch Rate 

VCE 

1.01 

1.00 

0.99 

0.98 

0.97 

0.96 

0.95 

0.94 

0.93 

P=P3 fitting with theta_0 

0.92 

VCE4 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

1.02 

1.00 

0.98 

0.96 

0.94 

0.92 

Distance x from edge of the large open area [um] 

P1=0.005 Torr 

P2=0.02 

P3=0.05 

P4=0.1 

VCE1 

VCE2 

VCE3 

y = 1.1734x - 0.1695 

R 2 = 0.9262 

0.90 

0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 

Measurements 

VCE1 

Linear (VCE1) 


20

VCE Input/Output 


21

Input/output to VCE tool - I 

VCE 

Input (process info): 

• Etchant radicals 

• Flux variation 

• Pressure 

• CD variation 

• Wall temperature • Etch rate variation 

• Etch depth var. 

Input (layout info): GDSII 


22

Calculation of Gas Kinetic Parameters 

- Calculation of binary diffusivities 

σ + σ 

2 

D 

ij 

T 

⎛ 

⎜ 

1 

⎜ 

⎝ M 

i 

= 0. 

0018583 

2 

Pσ 

ij 

i j A C E G 

Here σ ij = Ωij 

= + + + and 

* B 

* 

* 

* 

exp DT exp FT exp HT 

3 

1 

+ 

M 

* T 

, T = 

( T ) ( ) ( ) ( ) 

, 

ε 

Ω 

ij 

ij 

j 

⎞ 

⎟ 

⎠ 

ε ij 

= 

k 

B 

ε ε i j 

k k 

A = 1.06036, B = 0.15610, C = 0.193, D = 0.47635, E = 1.03587, F = 1.52996, G = 1.76474, H 

= 3.89411. Total gas pressure P in [atm], temperature T in [K] and cross-section σ σij in [A]. 

Parameters T* and Ω ij are dimensionless. The resulting binary diffusivities D ij are in [cm 2 s -1 ]. 

( 1− 

x ) 

- Effective diffusivity of i-th radical in the gas mixture: i D xk is the mole fraction of 

i = 

the k-th component 

xk 

= 100 

8RT 

⎛ 

⎜ 

1 

π ⎝ M 

1 

+ 

M 

∑ 

k ≠i 

Dik 

ij 

- Calculation of binary velocities ⎜ ⎟ . Velocities are in [cm/s]. 

( ) 

1− 

xi 

Effective velocities: ci 

= 

x and mean free path for i-th radical 

k 

c 

∑ 

k ≠i 

ik 

c 

i 

j 

⎞ 

⎟ 

⎠ 

D 

λi 

= 3 

c 


i 

i 

B 

B 

23

Reactor (wafer) scale 

simulation (3-rd party tool) 

Input/output to VCE tool - II 

Process recipe 

Die-level model –VCE 

Missing link 

GDSII 



• Etch rate variation 



24

Calibration Methodology 

� The major difference between the fully-coupled multi-scale simulations and the approach proposed in 

this paper is in a calibration-based nature of predictability of the latter one. 

� All unknown parameters of the employed model, such as plasma generation-recombination rates, 

chemical reaction rates, sticking coefficients, interaction radiuses, etc, are calibrated/optimized based on 

measured post-etch geometries of the different features characterized by a variety of AR and PD. 

� This calibration confines our model with the particular type of the reactor and process. While it is 

perfectly well with the process-aware design optimization, however, the calibration-based approach 

introduces some restrictions on the use-model for the design-aware process optimization. Calibrated 

model can be used mostly for exploring the effect of small variation in process parameters on the PDinduced 

variability by means of the proper link with a reactor-scale model. 

center 

Hole/Pitch=0.140/0.600um Hole/Pitch=0.135/0.220um Hole/Pitch=0.138/0.600um Hole/Pitch=0.140/0.600um 


25

Calibration Methodology 

� Allocate a number of vias/contacts not less than the number of model parameters. The best practice 

is to pick the features from the regions characterized by different pattern densities 

� Measure either etch rates, post-etch via depth, or CD for these features 

� Run the VCE and extract from the data-base the relative fluxes of all radicals coming to the 

measured features: γ ij 

� Run a optimization module to extract parameters values providing the best fit between calculated 

and measured characteristics. 

Calculated depths 

184 

180 

176 

172 

R 2 = 0.9226 

168 

164 168 172 176 180 184 

Measured depths 

Correlation of 92% was achieved for process node: 

55 nm; test chip size of 25.2x30.7 mm 

(a) (b) 

Measured values (plotted by triangles) and calculated 

values (squares) of vias (a) with top diameter 110 nm, and 

(b) with top diameter 67 nm. 


26

VCE Capability 

Based on accurate calculation of an across-die flux variation of radicals 

participating in etch reactions we can predict: 

Across-die etch rate variation 

Via 3 layer Via5 layer 


27

No dummy fill 


Effect of dummy fill on across-die CD variation 

With dummy fill 


28 

CD map full range = 6e -3


Across-die etch hot-spots distribution 


29

VCE/LE Capabilities 

Post-etch contours 

• Three steps of litho simulation for poly layer 

Post-exposure 

Post-photoresist 

Post-etch 


30

APPLICATIONS of VCE 


31

Hot-spot check: Bottom CD variation 

� VCE calibrates the bottom CD 

model based on the customer 

provided measurements of postlitho 

top CD and post-etch bottom 

CD for a number of features 

�� VCE predicts bottom CD 

variation through the entire chip 

78.00 

76.00 

74.00 

72.00 

70.00 

68.00 

1 3 5 7 9 11 13 15 17 

Measured values 

(plotted by diamonds) 

and calculated values 

(squares) of vias with 

top diameter of 67 nm 

(as-designed) 

77 

76 

75 

74 

73 

y = 0.6716x + 24.4 

R 2 = 0.6722 

72 

70.00 72.00 74.00 76.00 78.00 


32

Process-Aware Design Optimization vs. 

Design-Aware Process Optimization 

Upon completion of the hot spot check the following correction 

actions can be undertaken: 

DESIGN PROCESS 

• Intelligent dummy-fill 

• Mask correction at the MDP stage 

• Tuning the process parameters 

• Modification of the processing gas 

composition 


33

Design optimization by means of dummy via 

insertion 

VCE predicts bottom 

CD variation through 

the entire chip: 

�� Before dummy 

placement 

� After dummy 

placement 

CD Map 

No dummy fill With dummy fill 

∆ Max – ∆ Min : 

no-fill / fill = 

1.32 

CD map full range = 6e -3 


34

Process optimization 

• VCE predicts bottom CD variation through the 

entire chip for different process recipes 

� Two cases characterized by the identical etch process recipes 

are considered. The only difference between these two cases is 

that some amount of CHF3 was added to the inlet gas flow in the 

Case 2. 

� Addition of CHF3 dramatically reduces the fluorine atom 

concentration in the plasma bulk. 

� The later causes an excessive polymer deposition at the etched 

feature sidewalls and bottom that results in a bigger etch CD bias. 


35

Reactor (wafer) scale 

simulation (3-rd party tool) 

Input/output to VCE tool -II 

Process recipe 

Die-level model –VCE 

Missing link 

GDSII 



• Etch rate variation 



36

F Concentration, mass fraction 

Reduced Fluorine concentration 

Case 1 

edge 

Copyright ©2008, Mentor Graphics. Case 2 

37

Case 1 

Molar Fractions 

Summary of Reactor-scale simulation 

C CF CF2 CF3 CF4 F F2 

0.0006693 0.0099706 0.0107488 0.0139769 0.8800164 0.0837992 0.0008187 

Radical Fluxes (#/cm2/sec) 

CF CF2 CF3 F 

5.418E+15 9.415E+15 1.579E+15 9.474E+16 

Ion Fluxes (#/cm2/sec) 

CF+ CF2+ CF3+ Sum 

1.430E+15 2.760E+15 1.310E+16 1.729E+16 

Case 2 

Max. Ion Current: 4.85 mA, Vrf_b=181V 

Plasma Potential =+178.8V 

Aver. RFpotential -147.2 Vb/-314.1Vt 

E o = 326 V 

Molar Fractions 

C CF CF2 CF3 CF4 F F2 CHF3 HF 

0.0002971 0.0065974 0.0101139 0.0177320 0.8162692 0.0457770 0.0005838 0.0914919 0.0111377 

Radical Fluxes (#/cm2/sec) 

CF CF2 CF3 F 

2.835E+15 8.031E+15 2.713E+15 4.879E+16 

Ion Fluxes (#/cm2/sec) 

CF+ CF2+ CF3+ Sum 

5.870E+14 1.690E+15 8.070E+15 1.035E+16 

Max. Ion Current: 2.26 mA, Vrf_b=271V 

Plasma Potential =+95.5V 

Aver. RFpotential -388 Vb/-253 Vt 

E o = 484 V 


38

Averaged pattern density 

R=1000µm 

Neutral flux maps 

Neutral Flux (x10 15 cm -2 s -1 ) 

CF+CF2+CF3 F 


39

CD variation maps: case1 vs case2 

Pattern density ∆CD : case 1 

∆CD : case 2 

Case 1 

Case 2 

Via 

a) b) 

a) ) ∆ ∆average 

: 

case2 / case1 = 1.41 

b) ) ) ∆∆ 

∆ ∆Max 

– ∆Min : 

case2 / case1 = 1.49 


40 

CD map full range = 6e -3

OBSERVATION: FIB inspection of 0.26 um via after etching. (a) dense vias; (b) isolated via. 

Dense vias etch faster than isolated via, i.e. inverse micro-loading effect. 

Dense vias 

(a) (b) 

KV areas 

� Via etch process optimization was done for regular 

patterns on test wafer 

� Employed patterns represent a small part of the 

entire test-chip design 

� An etch rate variation caused by microloading is 

governed by a large-scale pattern density variation – 

much larger than used patters. This scale is order of 

magnitude of the mean free path of radical species 

participating in etch reactions. 

� A full-chip analysis is required for understanding 

the real pattern dependency of the etch step 

SEMbar (1) 

SEMbar (2) 

Test-chip SEMbar 

Copyright ©2008, Mentor Graphics.

Non-etchable Non suppressed 

Includes all area 

Pattern Density & Radical Fluxes Maps 

Density 

CF2 flux F flux 


CF2 flux 

F flux 

SEMbar (1) in all01 

Flux Distributions 

SEMbar (2) in all01 SEMbar isolated 


Across-Die Distribution of Etch Stop Threshold 

Pattern density Probability of etch stop (ES) Above-threshold ES location 

� SEMbar1 and SEMbar2, which are identical regarding the local pattern density, are characterized by 

different radical flux distribution, that transfers into different post-etch feature profiles. 

� Radical flux variation in SEMbar is determined by the global pattern density distribution rather than the 

local one inside this segment of layout. 

� Calculated full-chip radical flux distributions suggest that the etch stop is more probable at the iso-via 

location than in SEMbar. 

� An accurate design/process optimization could be achieved only by analyzing test-chip design with 

Mentor-VCE tool. 


Calibration/Prediction – Resist Model 

� CM1(Compact Model 1) is a Mentor Graphics resist model. 

It provides a dense simulation by considering acid and base neutralization, diffusion length during the 

exposure, baking, and resist development phases. 

� The output of the model is a resist contour 

obtained from the exposure threshold T : 

� Each term M i(I) is of the form: 

Simulated, nm 

285 

275 

265 

255 

245 

235 

225 

215 

205 

+/-b is the neutralization operator (+ for acid, - for base concentration), 

y = 0.80x + 43.77 

R2 R = 0.805 

2 = 0.805 

195 

195 205 215 225 235 245 255 265 275 285 

Measured, nm 

M 

( ) ) n 

∑ci 

Mi 

I = 

k n 

1/ 

∇ I b ⊗Gs 

, p 

= ± 

CD, nm 

300 

280 

260 

240 

220 

200 

180 

( ) T 

Measured 

Simulated 

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 

Via No. 

� Optical diameter = 2.56um 

� NA = 0.659 

� Model is calibrated on BARC opening 

CD. 

� Result : R2 = 0.81 


Calibration/Prediction –ARC Etch 

� Correction for Microloading nature of BARC etcing is added: 

CD BARC. 

o 

CDLitho 

γ 

i 

CD BARC . o − CD Litho = δ '+ 

αγ O [ 1 − β ( 1 − κD 

)] 

CD 

Litho 

. o = CD Litho ⋅ { δ + αγ [ 1 − β ( 1 − κD 

)] } 

α, β, δ, κ : calibration parameters. 

CD BARC 

O 

: Simulated BARC CD opening prior to main 

etching. 

: Simulated resist opening CD using CM1 resist 

model (calibrated on BARC opening CD 

measurements) 

: Normalized flux of neutral i. 

: Density of resist opening. 

� D(r 

The ) term ββββ(1-κκκκD) is introduced to explain carbon assisted 

polymer formation. Carbon in resist film is considered to be the 

source. 

� CDSEM measurement error of 3nm is taken into 

account. TRS 2001 eds. Metrology, p.8 

� Result : R 2 = 0.82 

CD, nm 

Simulated, nm 

300 

280 

260 

240 

220 

200 

180 

285 

275 

265 

255 

245 

235 

225 

215 

205 

Measured 

Simulated 

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 

y = 0.85x + 33.52 

R2 = 0.823 

Via No. 

195 

195 205 215 225 235 245 255 265 275 285 

Measured, nm 


Calibration/Prediction - Main Etch 

� BARC CD widening due to PR loss during main etching is considered: 

CDBARC 

− CDBARC. 

o = α0 

'+ α1γ 

F[ 

1−α 

2( 

1− 

α3D)] 

≥ 0 

CD 

CDBott 

− CD 

CD 

CD 

Bott 

BARC. 

o 

BARC 

BARC 

= CD 

= CD 

BARC 

γ 

+ β1( 

γ 

⎧β0 

= β0'+ 

1 

⎨ 

⎩α 

0 = α0 

'+ 

1 

γ CF γ CF 2 γ CF 3 

= β0 

'+ 

β 1 + β2 

( ) + β3( 

) ≤ 0 

γ γ γ 

BARC . o 

CF 

F 

F 

γ 

⋅[ 

β0 

+ β1( 

γ 

F 

γ 

) + β2 

( 

γ 

⋅ { αα 

+ αα 

γγ 

[ 1 − −αα 

( 1 − −αα 

D )]}[ ββ 

+ 

0 

γ 

) + β2 

( 

γ 

1 

CF 

F 

) 

CF 

F 

F 

2 

2 

γ 

+ β3( 

γ 

CF 

F 

) 

3 

2 

F 

γ 

+ β3( 

γ 

α 0, α 1, α 2, α 3, β 0, β 1, β 2 , β 3 : calibration parameters. 

CD bott : simulated Bottom CD after main etching. 

CF 

F 

) 

3 

] 

0 

CF 

� Result : R 2 = 0.70 

F 

) 

3 

] 

Simulationed, nm 

CD, nm 

285 

275 

265 

255 

245 

235 

225 

215 

205 

195 

300 

280 

260 

240 

220 

200 

180 

Measured 

Simulated 

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 

y = 0.81x + 44.52 

R2 = 0.701 

Via No. 

195 205 215 225 235 245 255 265 275 285 

Measured, nm 


Bias Map 

Design 

� Normalized CD Bias : 

Area 1-2: 

Area 4: 

Area 5: 

Etch CD Bias Prediction 

∆ 

n 

CDBott 

− CD 

= 

CD 

Area 4 

BARC. 

o 

BARC 

. o 

γ CF γ CF 2 γ CF 3 

= { α0 

+ α1γ 

F[ 

1−α 

2( 

1− 

α3D)]}[ 

β0 

+ β1( 

) + β2 

( ) + β3( 

) ] −1 

γ γ γ 

� Bias is represented in terms of CD BARC.o_predicted . 

� Large bias is expected in RED regions, and could become hot 

spots. 

� 12x12 via blocks (area 1-2 vs. area 5) : Long range 

microloading may lead to different level of bias maps 

although these two patterns are locally identical. 

Area 1-2 Area 5 

F 


F 

F 

∆ n ≤ -0.2 

∆ n = 0 

∆ n ≥ 0.1

Mentor Graphics Corp., 

San Jose, CA, USA 

�J-H Choy 

�H. Hovsepyan 

�N. Khachatryan 

�A. Kteyan 

�H. �H. Lazaryan 

�L. Manukyan 

�Yu. Granik 

�A. Markosian 

�V. Sukharev 

Thank you! 

TEAM: 

Toshiba Corp., Japan 

�Seiji Onoue, 

�Takuo Kikuchi, 

�Tetsuya Kamigaki 

Institute of Microelectronics, 

Singapore 

�Vladimir Bliznetsov

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

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