1CMP Research Lab

Effect of kinematics and abrasive

particle dynamics on material removal

rate uniformity during polishing

Armin Saeedi Vahdat1,2 and S V Babu2

1Dept. of Mechanical and Aeronautical Engineering

2Center for Advanced Material Processing (CAMP)

Clarkson University

Potsdam, New York 13699-5725

April16, 2015

2CMP Research Lab

Motivation and Objective

Scaling down the structures

and increasing wafer size MRR uniformity becomes

more challenging

CMP kinematics based on slurry

distribution and particle

trajectories have a big impact on

MRR profiles.

(Pressure and temperature profiles

are also very important)

3CMP Research Lab

Chemical Mechanical Polishing Kinematics

e0 : Distance between pad and wafer centers, r0 : Wafer radius

et : Carrier oscillatory motion function

ωp : Platen rotational/angular

velocity ωw : wafer rotational/angular

velocity

Rotary Dynamics

Reciprocation Dynamics

ωw tωp t

e0X, x

Y

y

et r0

wafer

Pad

4CMP Research Lab

Velocity Field on Wafer SurfaceRelative velocity of a

point on the wafer:0(e e )A p t p tv r r e

rr r r rr r r&

ωw tωp t

e0X, x

Y

y

et r0

waferr A

Pad

2 2

0 0 0(1 ) / 1 (1 ) /A pv e y e x e

2 2

0 0 0 0 0/ ( ) (1 ) / 1 / (1 ) /A p t p tv e e e y e e e x e &

For typical rotary-type

polishers:

0 0,t p te e e e &

/w p where

5CMP Research Lab

Velocity Field on Wafer Surface

When α = 1 (ωp = ωw)

2 2

0 0 0

0 0

( (1 ) / ) (1 (1 ) / )A pv e y e x e

1 4 2 4 3 1 4 2 4 3

Uniform velocity field all over the wafer

0A pv e

Assuming uniform pressure distribution, Preston’s equation

suggests uniform MRR:

(x, y) (x, y) (x, y)p AMRR k v p0(x, y) .p pMRR k p e cont

However experimental results suggests α = 1 is

not a proper velocity ratio option in order to get

uniform MRR profile.

6CMP Research Lab

Particle Trajectories and MRRParticles trapped between pad

asperities and wafer are active

particles

activeinactive

MRR uniformity depends on:

Active particles trajectories

distribution

Material removed along each

trajectory (particle size)

Non active abrasives cause

zero/negligible MRR

7CMP Research Lab

Description of a Particle Location

Initial location of each active particle of pad:

0

0

cos

sin

A

A

XR

Y

0 0R e r

0m m

2 2 21 0 0

0

cos2

m

R e r

R e

Location of all Active particles

participating in MRR on wafer

follows these conditions

r0

φ0

RA

X, x

Y y

φm

e0

8CMP Research Lab

φ0+ωp tR

A

Y

y

et

Description of a Particle TrajectoryTime dependent trajectory of a particle in fixed/global

coordinate:

0

0

cos ( t)(t)

sin ( t)(t)

pA

pA

XR

Y

Assumption:

Particle leaves the wafer

area and rotates with pad

velocity and eventually

reenters the wafer area.??

9CMP Research Lab

Description of a Particle Trajectory

Time-dependent particle locations

in fixed and moving coordinates

are related as:

ωw t X

Yy yʹ

x

xʹ

A

e0 +et

φ0+ωp t

0(t) (t)

(t) (t) 0

A A t

A A

X x e e

Y y

cos( t) sin( t)(t) (t)

sin( t) cos( t)(t) (t)

p pA A

p pA A

x x

y y

Carrier oscillatory motion is described using its amplitude and

frequency:

sin ( )t e ee A tZhao, Dewen, et al. "Kinematic optimization for chemical mechanical polishing based on statistical analysis of particle trajectories." Semiconductor

Manufacturing, IEEE Transactions on 26.4 (2013): 556-563.

10CMP Research Lab

Description of a Particle Trajectory

0 0

0

cos( t) sin( t) cos ( t) ( sin ( ))(t)

sin( t) cos( t) sin ( t)(t)

p p p e eA

p p pA

R e A tx

Ry

Time dependent trajectory of a particle in local coordinate

system can be expressed:

11CMP Research Lab

Five Particle Trajectories (No Oscillation)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

Five particles are located

on pad asperities

When α = 1 (ωp = ωw)

12CMP Research Lab

Five Particle Trajectories (No Oscillation)α=0.90

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

α=0.91

α=0.92

α=0.93

13CMP Research Lab

Five Particle Trajectories (No Oscillation)α=0.94

α=0.95

α=0.96

α=0.97

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

14CMP Research Lab

Five Particle Trajectories (No Oscillation)α=0.98 α=0.99

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

For α=0.91, 0.93,0.94,0.97 the trajectories are better distributed

all over the wafer surface.

A ring with lower trajectory density is observed.

15CMP Research Lab

Five Particle Trajectories (No Oscillation)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)-100 0 100

-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)The observed ring is an

artifact which is

induced due to the initial

particle locations

16CMP Research Lab

Five Particle Trajectories

No oscillation With Oscillation

The trajectory distribution density at the center of the wafer

can be improved by making the carrier oscillate

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

17CMP Research Lab

100 Particle Trajectories

When number of particles increase, the trajectory distribution

appears uniform but it is not.

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-10 -5 0 5 10-10

-5

0

5

10

x (mm)

y (

mm

)

Therefore a quantitative technique is required to measure the

distribution of particle trajectories across the wafer.

18CMP Research Lab

Kinematics Parameters and Sliding Length

n

Particle 1

t=t0 + ∆tSliding

distance L11

nn Particle 1

t=t0 + 2∆t

Sliding

distance

L12

Sliding distance of each particle inside each

area element is calculated during polishing

time.

n

Particle 2

t=t0 + ∆t

Sliding

distance L21

n

n

Particle 2

t=t0 + 2∆t

Sliding

distance L22

19CMP Research Lab

Sliding Distance, MRR and WIWNU

( , ) ( , ) ( , )pV x y k p x y L x y

( , ) ( , )( ) ( , )v p

p p

V x y L x yMRR k R p x y

T T

Uniform pressure profile ( )( , )

p

v

p

const

k R pMRR L x y

T

14 2 43

Hence Sliding distance distribution is an indicator of WIWNU

(%) 100 100MRR L

mean mean

WIWNUMRR L

Material volume removed based on particle trajectory length:

Mono-dispersed particles

20CMP Research Lab

WIWNU vs Active Particle Number

Using large number of particles in simulations is impractical

So determine the number of active particles that leads to a

realistic simulation

102

104

106

-10

0

10

20

30

Particles Number

WIW

NU

(%)

n =10,000 is a good choice for

number of particles

Zhao, Dewen, et al. "Kinematic optimization for chemical mechanical polishing based on statistical analysis of particle trajectories." Semiconductor

Manufacturing, IEEE Transactions on 26.4 (2013): 556-563.

21CMP Research Lab

WIWNU Distribution

Question: Whey does WIWNU converge a) to a constant

value and b) that is still large?

102

104

106

-10

0

10

20

30

Particles Number

WIW

NU

(%)

Answer: The MRR increases toward

the edge of the wafer even when the

whole wafer surface is covered by

active particles

-150 -100 -50 0 50 1000

0.5

1

1.5

x (mm)

Norm

aliz

ed S

lidin

g D

ista

nce

22CMP Research Lab

WIWNU vs α Parameter

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 10

5

10

15

20

WIW

NU

(%

)

α = 0.91 results in

lowest WIWNU.

α = 1 results in worst

WIWNU results.

-150 -100 -50 0 50 1000

0.5

1

1.5

x (mm)

Norm

aliz

ed S

lidin

g D

ista

nce

-150 -100 -50 0 50 1000

0.5

1

1.5

x (mm)

Norm

aliz

ed S

lidin

g D

ista

nce

Mono-dispersed slurry

is assumed

23CMP Research Lab

WIWNU vs Oscillatory Motion

1 2 3 4 5 6 7 8 9 102

3

4

5

6

7

p /

e

WIW

NU

(%)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.73

4

5

6

7

Ae / r

0

WIW

NU

(%)

sin ( )t e ee A t

6

p

e

Oscillatory motion

0

5e

rA

WIWNU is improved

(%) 3.36%WIWNU

24CMP Research Lab

Quantitative Example of CMP Kinematics

For0

93 / min

200

p r

e mm

0

0.91 93 / min 85 / min

15 / min6

305

w p

p

e

e

r r

r

rA mm

For polishing of 300 mm wafers on a rotary-type polishing

tool with mono-dispersed slurry:

However, some special cases need to be avoided:

93 / minp w r 0 0e eA or and

(%) 4%WIWNU Small variations in these numbers create a

small change in the obtained WIWNU

(%) 18%WIWNU

25CMP Research Lab

Large Particles Influence on WIWNU

MRR depends on the size of the

abrasivesFilm

Small

Particle

Large

Particle

2( )pk R R

Qin, Kuide, Brij Moudgil, and Chang-Won Park. "A chemical mechanical polishing model incorporating both the chemical and mechanical effects."

Thin Solid Films 446.2 (2004): 277-286.

When film thickness is larger than

particle penetration depth

Particle size dependency of MRR is projected

in the Preston’s constant

When large particles are present in the slurry along with the

nominal particle size

Large and small particles effects will both be projected in the

MRR profile.

26CMP Research Lab

Large Particles Influence on WIWNU

1 2 3

2 2 2 2

1 2 1 3 1 1( / ) ( / ) ... ( / )n

p

v R R R n R

p

k pMRR R L R R L R R L R R L

T

(%) 100vMRR

T mean

WIWNUMRR

n

Small

Particle

Sliding distance

LR1

nn

Large Particle

Sliding distance

L22

27CMP Research Lab

Effect of Large Particles The number of larger particles is assumed to be 1%-5% of the

total number of active particles

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

-150 -100 -50 0 50 100 150-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

Trajectories of large particles are calculated while changing

their position every 2 seconds

28CMP Research Lab

Large Particles Size and Concentration Effects

2 4 6 8 102

4

6

8

10

12

RL / R

s

WIW

NU

(%)

1%

2%

3%

4%

5%

Large particles size can drastically deteriorate WIWNU

indicating the significance of a proper slurry filtration process.

29CMP Research Lab

Scratch Growth

For the special case of α = 1 (ωp = ωw), since each particle

travels the same path over and over during the polishing

-100 0 100-150

-100

-50

0

50

100

150

x (mm)

y (

mm

)

Scratch growth on a

constant path

Large particles and undesired

debris can create major scratches

on the wafer surface.

For α ≠ 1 (ωp ≠ ωw), since each particle travels various paths

during the polishing the effect of large particles is distributed

across the wafer which may minimize their unwanted effects

α = 1

30CMP Research Lab

Conclusions and Remarks

• A mathematical model to describe particle trajectories

during polishing was developed.

• MRR and WIWNU were determined based on the extracted

particle trajectories.

• The results showed that ωw=ωp leads to the worst MRR

uniformity.

• When ωw= 0.91 ωp, the most uniform MRR is obtained.

• The oscillatory motion frequency and amplitude can also be

optimized to improve MRR profile uniformity.

• This model is capable of explaining the effect of large

particles on WIWNU and scratch growth.

31CMP Research Lab

Questions and Comments

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Thank you for your attention.