VIBRATION MODELING IN

CMP M Brij Bhushan

IIT Madras Jul-14-2010

1

Outline 2

Introduction

Model description

Implementation details

Experimentation details

Verification of simulation output with experimental

data

Application

Summary and Conclusion

Future work

Acknowledgement

Life @ OSU

What is CMP?

Planarizing process, combination of Chemical and Mechanical

forces.

Hybrid of chemical etching, mechanical abrasion and free

abrasive polishing.

Used on metals (Al, Cu, W, etc.), dielectrics (SiO2, etc.) and

hard ceramics (SiC, TiN, etc.)

Achieves local and global planarization, most preferred in

semiconductor industry.

The overall CMP market exceeds $10 billion and is growing at

a rate of ~ 50% per year.

With wafer sizes going above 300mm and feature sizes going

below 30nm, chief determinant of wafer yield and cost.

4

Ref: http://www.icknowledge.com/misc_technology/CMP.pdf

What is CMP? 5

Quality challenges in CMP

Complex process dynamics and interactions among: Equipment

Consumables (i.e. slurry, pad, carrier film)

Process parameters

Large number of parameters affecting the process

High capital costs

Quality Indices: Process –

Material Removal Rate (MRR)

Repeatability

Product – Within wafer non-uniformity (WIWNU)

Surface roughness

Defects

6

High requirement of quality vs. cost – need for understanding the

process dynamics and improve process monitoring

Prior work in CMP modeling & sensing 7

7

CMP

Pheno/Empirical models •Preston (1927)

•Jeong et al. (1996)

•Lucca et al. (2001)

•Noh et al. (2004)

•Venkatesh et al. (2004)

•Hernandez et al. (2001)

•Wang et al. (2001, 03)

•Park et al. (2000)

Physical

modeling

Process

modeling

Computational

models •Srinivas-Murthy et al.

(1997)

•Byrne et al. (1999)

•Nguyen et al. (2004)

Analytical models •Ida et al. (1964)

•Saka et al. (2001)

•Qin et al. (2004)

•Zhao et al. (2002)

•Warnock et al. (1991)

•Vlassak et al. (2004)

•Burke et al. (1991)

•Sivaram et al. (1992)

•Burke et al. (1991)

•Cook et al. (1990)

•Cho et al. (2001)

•Watanabe et al. (1981)

•Suzuki et al. (1992)

•Wang et al. (2005)

•Borucki (2002)

Process

monitoring

End point detection •Bibby and Holland (1998), Simon (2004),

Saka (2004), Yu (1993,95), Moore (2004)

•Murarka (1997), Sandhu (1991), Sandhu

and Doan (1993), Chen (1995), Mikhaylich

(2004)

Defect detection •Tang et al. (1998)

•Vasilopolous et al. (2000)

•Surana et al. (2000)

•Dennison (2004)

•Steckenrider (2001)

•Braun (1998)

•Chan et al. (2004)

•Li and Liao (1996)

•Wang et al. (2000)

•Zhang et al. (1999)

•Xie et al. (2004)

Gaps in technical approach 8

Modeling Gaps:

It is still not fully been understood how the process parameters

affect the performance

Significant analytical work focuses only on the static loading

aspects

Sensors have been used to monitor and predict process features –

mainly statistical

Experimental gaps:

MEMS wireless sensors not much explored

Vibration – one of the few real-time parameters, experimental

data is scarce.

Need for Real-time estimation of state of the process and

dynamics from the sensor features → advanced prediction

capability for online CMP process control (active control)

Sensor based modeling of CMP 9

Sensors are used for process monitoring and modeling.

Sensors – Give information about state of the machine, process, and pad/wafer.

Few real-time sensors available – optical, vibration, acoustic emission, ultrasonic, thermal, etc.

We used MEMS wireless vibration sensors MEMS

Light-weight

Robust

Low energy consumption

Wireless Can be placed in close proximity to the object.

Flexibility

Vibration Dynamic response higher than other sensors

One of the best for real-time monitoring

Approach

An attempt to develop a model of CMP dynamics that can physically capture the cause of the various vibration features observed:

Obtain pad parameters such as elasticity (E), curvature of asperities (κs), pad asperity density (ηs), etc.

Obtain the mean distance of separation (do) for static loading conditions

Use these parameters in the dynamic simulation model

Verify the features of the simulation data with those obtained from the sensor signals

10

Process Machine ( m, K, c, Po, λ )

( Eeff , ηs , ks,

do, ϕ(z) )

Forces in CMP 11

Original position of wafer above

the asperities (mean of vibrations)

~N(0, σ 2)

z d0

x(t)

Mean of the asperity

distribution (fixed)

x = 0

Vibration

Amplitude

• Relatively flat, hard wafer in contact with a rough pad surface.

• Pad asperity heights and wafer position are measured from the mean pad surface

plane.

•Vibrations are developed due to the elastic deformations in the pad asperities.

Gaussian

asperity

distribution

Forces in CMP 12

When the wafer rests on the pad at a distance x from the

mean, the prob. of making contact with any asperity of height

z(z>x) is:

The expected total load is:

ηs is the asperity density on the surface.

ks is the curvature of the asperity summits.

E* is the 2-D Young’s modulus of the pad material.

Anom. is the nominal area of the pad surface.

Ref: Greenwood, J. A. & Williamson, J. B. P. 1966 Contact of nominally flat surfaces.

Static distance of separation (do) 13

do was calculated using minimizing the function:

Ran for various values of do in the appropriate range to search for minima

(tending to 0); do calculated to 0.1% error; integral discretized

Variation in do value with change in Po is in accordance with Greenwood’s

results (Greenwood & Williamson 1966)

Structural Excitation 14

Po is the constant down-force acting on the wafer.

c is the system’s damping coefficient.

ks is the spring constant of the additional elasticity in the system.

do is the distance of the mean position from the datum.

Po

Wafer – mass (m)

Harmonic Perturbation

CMP setup always has

slight lack of local/global

planarity.

Level difference is given by:

As θ is very small,

If the wafer RPM is N, a

perturbation is introduced

to the disturbance given by:

15

λ

Variation of pad elasticity with x

Pad material is not

homogenous with

deflection.

Can be decomposed into

asperity region and bulk

region.

Bulk has large effective

elasticity, Eeff value – all

air voids compressed.

16

Bulk

Asperity

Variation of pad elasticity with x 17

Wafer

Pad

Wafer

Pad

Lower down-force Higher down-force

• Greater do

• Lower value of Eeff

• Large number of voids

beneath the asperity layer

• Smaller do

• Higher value of Eeff

• Lesser number of voids

beneath the asperity layer.

Variation of structure stiffness with x 18

Additional spring-force due to the structure, introduced into the system.

Stiffness also changes with x.

Change in stiffness similar to Eeff.

SEM cross-section of a polishing pad.

– L. Borucki (2002)

Implementation details 19

Overall differential equation: 𝑚𝑥 + 𝑐𝑥 + 𝑘 𝑥 − 𝑑0 = 𝑃0 −[𝛽0 + 𝛽1 𝑥 + 𝑥3 + 𝛽2 𝑥 + 𝑥3

2 + 𝛽3 𝑥 + 𝑥33

+ … ]

x3 is the harmonic perturbation introduced into the system:

𝑥 3 +2𝜋

𝑇

2

𝑥3 = 0

2 degree of freedom, non-linear model of the CMP process

Model was implemented in Simulink

Solver : variable step, ODE45 (Dormand-Prince)

Simulation time: 0 to 40 seconds

Initial conditions:

Force(RHS) = Po

Acceleration = 0

Velocity = 0

Displacement = do

20

Disturbance block:

Add a perturbation as a sine wave.

Check whether the displacement stays

above a basic minimum value (6 um, in

this case).

Feed the displacement into the RHS

force calculation block.

21

22

23

Experimentation details

Machine:

Buehler Ecomet 250 grinder-polisher.

Sensors:

Freescale MMA62xxQ

Low-g, dual-axis sensor

High resolution in the range of 1.5g to 10g.

Low noise

Low current device

Wireless communication system:

Tmote sky 250kbps 2.4GHz IEEE 802.15.4 Chipcon

Wireless Transceiver

8MHz Texas Instruments MSP430 microcontroller (10k RAM, 48k Flash)

Integrated ADC, DAC, Supply Voltage Supervisor, and DMA Controller

Ultra low current consumption

24

Experimentation details 25

Design of experiments (DOE):

Full factorial design having three factors and two levels :

Wafer - Copper work piece

Wafer RPM is constant at 60

Slurry - alumina slurry having an abrasive size 0.05μm

Polishing pad - Microcloth pad from Buehler.

Run ID Load (lbf) Pad RPM Slurry ratio

R1 10 500 1:3

R2 10 300 1:3

R3 5 500 1:3

R4 5 300 1:3

R5 10 500 1:5

R6 10 300 1:5

R7 5 500 1:5

R8 5 300 1:5

Experimental Data

26

125.3 Hz

Region of interest in the FFT spectrum: 27

Vibration sampled at 300Hz

Region below 100Hz corresponds to the machine frequency

Region above 100Hz corresponds to the process frequency and is

of interest (100Hz to 150Hz)

30 0 60 90 120 150 30 60 90 120 150

28

Simulation

Time-domain features captured

Beat phenomenon,

frequency 1Hz (~wafer

RPM)

Regions of high and

low amplitudes.

High amplitude bursts.

Time-frequency

variations.

29

Frequency-domain features captured

Dominant frequency

Spectral shape

(continuous spectrum

with two dominant

frequency bands)

30

125.9 Hz

129.8 Hz

Effect of varying down-force 31

As Po increases, clustering increases

Increased bursts at high amplitudes

Amplitude difference between high and low-

amplitude regions increases

Energy in the 112-139 Hz band increases

Some harmonic distortion evident in the model

32 Experimental Simulation

33 Experimental Simulation

6.02

7.00

0.029

0.043

Effect of wear 34

The peaks of the taller asperities flatten out

The mean of the asperity distribution shifts downwards

Reduced height of asperity ⇒ σ decreases

The pad now rests at a lower do value

Assumed Gaussian distribution holds – in reality, distribution gets slightly skewed (Borucki, 2002)

do do

New pad Old pad

Effect of wear 35

Experimental Simulation

Anticipated applications of model 36

Enhance the predictability of the CMP process.

Enable development of feed-forward control systems

which have a faster action time.

Tool for iterative optimization of yield, quality under

changing settings.

Summary and conclusions 37

2-DOF deterministic, non-linear, differential

equation model developed to capture the physical

sources of CMP vibrations

Variation of elastic properties was found to be the

cause of variations and bursts in the time and

frequency pattern

Incorporated the beat phenomenon due to the lack

of planarity of the wafer-pad interface

Future Work 38

Harmonic balancing

Studying more about wear of the pad and its effect

on vibration signals

Inclusion of velocity and its effects into the model

Acknowledgements 39

Dr. Karl N Reid, for giving me the opportunity

Dr. Satish Bukkapatnam and Dr. Ranga Komanduri for being the driving force and the guiding light for my work

Research group at OSU - all the faculty and the MS and PhD students

All the fellow interns from IITs and IT-BHU