emmanuel a. baisie* and zhichao li xiaohong zhang€¦ · pad conditioning in chemical mechanical...

Int. J. Manufacturing Research, Vol. 8, No. 1, 2013 103

Copyright © 2013 Inderscience Enterprises Ltd.

Pad conditioning in chemical mechanical polishing: a conditioning density distribution model to predict pad surface shape

Emmanuel A. Baisie* and Zhichao Li Department of Industrial and Systems Engineering, North Carolina Agricultural and Technical State University, 1601 E. Market Street, Greensboro, NC 27411, USA E-mail: [email protected] *Corresponding author

Xiaohong Zhang Seagate Technology, 1 Disc Drive, Bloomington, Minneapolis, MN 55435, USA

Abstract: Diamond disc pad conditioning is traditionally employed to restore pad planarity and surface roughness in chemical mechanical polishing (or planarisation) (CMP). In this paper, a conditioning density distribution model is developed to predict the pad surface shape resulted from the diamond disc conditioning in CMP. A kinematic study is carried out to calculate and simulate the diamond grit trajectories. An analytical model is then proposed to correlate the conditioning density distribution with the wear of the polishing pad. In this study conditioner design is considered while function defined sweeping profiles and a visual measure of conditioner-pad contact distribution are introduced. Furthermore, the pad surface shape is predicted by the model and compared with experimental data. Results show that the model is effective to predict the pad surface shape.

[Received 25 April 2011; Revised 24 August 2011; Accepted 23 October 2011]

Keywords: semiconductor materials; chemical mechanical polishing (or planarisation); CMP; conditioning; dressing; pad shape; kinematics model; conditioning density.

Reference to this paper should be made as follows: Baisie, E.A., Li, Z.C. and Zhang, X.H. (2013) ‘Pad conditioning in chemical mechanical polishing: a conditioning density distribution model to predict pad surface shape’, Int. J. Manufacturing Research, Vol. 8, No. 1, pp.103–119.

Biographical notes: Emmanuel A. Baisie is a PhD Research Assistant at the Industrial and Systems Engineering Department of North Carolina Agricultural and Technical State University in USA. Prior to this, he was a Teaching Assistant at the Mechanical Engineering Department of Kwame Nkrumah University of Science and Technology in Ghana where he received his BS in Mechanical Engineering. His research focuses on modelling, simulation and optimisation of semiconductor ‘front-end’ manufacturing processes.

104 E.A. Baisie et al.

Zhichao Li is an Assistant Professor at North Carolina Agricultural and Technology State University in USA. He received his MS in Mechanical Engineering from Tianjin University (China) in 2002 and a PhD in Industrial Engineering from Kansas State University (USA) in 2006. His research interests include modelling and development of machining and finishing processes (like grinding, lapping and chemical mechanical polishing, and wire sawing, etc.) for brittle materials. He has authored and co-authored more than 40 research papers.

Xiaohong Zhang is a Process Engineer at Seagate Technology. She received her BS and MS in Mechanical Engineering from Tsinghua University (China) and a PhD in Industrial Engineering from Kansas State University (USA) in 2007. Her research area of interests is focused on mechanical shaping of silicon wafers and chemical mechanical planarisation (CMP).

1 Introduction

Chemical mechanical polishing (or planarisation) (CMP) is widely used to planarise semiconductor wafers and smooth the wafer surface (Li and Miller, 2000; Steigerwald et al., 1997; Hocheng et al., 2000; Quirk and Serda, 2001). A typical CMP process is illustrated in Figure 1. A wafer is held by a rotating wafer carrier and a down force is applied on the wafer carrier to press the wafer against a rotating polishing pad. Slightly corrosive colloidal slurry containing fine abrasive particles is released onto the pad surface. The polishing pad plays a key role in both the mechanical and chemical aspects (Hooper et al., 2002). It is made of porous material that is capable of holding the abrasive particles in the slurry. In this process, the wafer surface is polished due to the relative motion between the wafer and the polishing pad in the presence of the slurry. The slurry chemically weakens the wafer surface to facilitate material removal. The material removal occurs as a consequence of a combination of chemical reaction (between the slurry chemicals and the wafer surface) and the repeated mechanical interaction (between the wafer surface and the polishing pad) under an applied down force.

In CMP, as more and more wafers are polished, the pad planarity and surface roughness could be deteriorated by surface ‘glazing’ resulted from pad wear and debris (Steigerwald et al., 1997; Bajaj et al., 1994; Tsai et al., 2009; Hooper et al., 2002; Li and Miller, 2000; Hocheng et al., 2000). This leads to a reduction in material removal rate (MRR) and poor wafer uniformity (Tsai et al., 2009; Bajaj et al., 1994; Hooper et al., 2002). Traditionally, diamond disc conditioning is employed to condition the pad surface to restore pad planarity and surface asperity. As shown in Figure 1, a metal disc (with one side embedded by protruding diamond abrasives) is held by a conditioning head and pressed against the pad surface. A robotic arm is programmed to sweep the conditioning head back and forth from the pad centre to the pad periphery. The pad surface is then conditioned by the diamond abrasives to regenerate pad pores and asperities as the disc rotates and sweeps.

Pad conditioning in chemical mechanical polishing 105

Figure 1 Schematic of CMP process showing conditioner-pad interaction (see online version for colours)

Several researchers have investigated the effects of diamond disc conditioning on the pad characteristics and CMP performance (Liang et al., 1997; Baisie et al., 2009; Achuthan et al., 1996; Ting et al., 2007; Tso and Ho, 2007; Kihyun et al., 2008; Chen et al., 2000; Feng, 2007). Zhou and Davis (1999) reported variation of pad shape during conditioning. Their study showed that conditioning results in a concave pad shape and the concavity increases with conditioning time. Chang et al. (2007) investigated the relationship between the pad conditioning time and the pad surface shape. It was reported that longer conditioning time results in higher concavity of the pad surface shape. Baisie et al. (2010) developed a mathematic model using a surface element method to simulate and predict the pad surface shape resulted from diamond disc conditioning. In the study, effects of conditioning parameters (including sweeping profile, pad rotating speed, conditioner rotating speed, and conditioner diameter) on the pad surface shape are investigated.

Despite the advancement of experimental and theoretical studies on the diamond disc pad conditioning in CMP, attaining a flat pad surface shape resulted from diamond disc conditioning still remains a challenge in CMP (Zhou and Davis, 1999; Chang et al., 2007; Feng, 2007). There is still a need to develop more accurate models to adequately characterise the pad surface shape especially in the effects of conditioning parameters (such as conditioner sweeping profile, pad/conditioner rotating speed, and conditioner design, etc.) on the pad surface shape (Baisie et al., 2009).

Studies have suggested that the amount of pad wear experienced at a point has a strong correlation with the conditioning density at that point (Byrne et al., 1999; Hooper et al., 2002; Hua et al., 2009; Qin et al., 2009; Tsai, 2010). Initially, Hooper et al. (2002) developed a simple model where CD is determined by the sweeping velocity of the arm Varm, and the radial position on the pad, Rpad(CD =1 / Varm·Rpad). Later, Feng (2007) developed a more elegant kinematic conditioning density, CD function (based on the polishing trajectories generated by a conditioner) as a measure of dressing performance


and by inference to predict pad wear rate. In the study, it was observed that to have flat distribution of pad wear rate, the ratio of disk-radius to pad-radius must be as small as possible. Feng concluded that several concerns needed to be investigated further. Among them are; different sweeping motion, non-uniform grit distribution, the assumption of a slow sweeping motion, and ultimately the search for an optimal set of parameters to satisfy a certain criterion. Yeh and Chen (2010) also commented that Feng’s model – despite its utility – does not consider the fact that a specific area of the pad may require several ‘cuttings’ to restore it. Thus, Yeh suggested a modification of the conditioning density definition to include the influence of other related information. In addition, a mathematical correlation between CD and the pad shape is not mentioned and only numerical examples are provided to verify the model.

With regard to these issues, a conditioning density distribution model is developed to predict the pad surface shape resulted from the diamond disc conditioning in CMP. A kinematic study is carried out to calculate and simulate the diamond grit trajectories. An analytical model is then proposed to correlate the conditioning density distribution with the wear of the polishing pad. In this model, different sweeping motions as well as user defined grit distribution are considered. Furthermore, the pad surface shape is predicted by the model and compared with experimental data.

2 Model development

2.1 Assumptions

A typical pad conditioning cycle is illustrated in Figure 2. The pad and conditioner rotate about their central axis at angular speeds of ωp and ωc respectively. At the start of a conditioning cycle, the rotating conditioner is fed down to the pad from its initial position and pressed against the pad surface under a constant pressure P. The conditioner then moves along the radial direction of the pad at a velocity v(t). As the conditioner touches the pad periphery, it lifts up from the pad surface and moves back to its initial position to repeat next conditioning cycle.

In practice, the travel distance of the conditioner centre is divided into q equal sections as shown in Figure 2. In Figure 2, q = 10. The length of each section is

2,p cR R

wq−

= where Rp is the pad radius and Rc is the conditioner radius. The time it

takes for the conditioner to pass the section k(k = 1, 2, 3, …, q) is defined as tk. tk is equal

to wv

and is adjustable. A sequence of tk which sums up to tcycle is defined as a sweeping

profile. The radial distance travelled by the conditioner from the pad centre by time t can be obtained as:

( )( )( ) , mod cycled D t L vdt where t t t′ ′ ′= = + =∫ (1)

Usually, L is set to be equal to the conditioner radius Rc or larger. In the case where L is larger than Rc, the central area of the pad with radius L – rc will remain unconditioned.


Figure 2 Illustration of a diamond disc conditioning cycle

It is assumed that all of the diamond grits embedded on the metal disc protrude with a pyramid shape and have the same protrusion height as shown in the Figure 1 inset. In the conditioning process, each diamond grit is in continuous contact with the pad and will generate an individual trajectory on the pad surface. The concentration of these trajectories on the pad depicts the conditioning density. Then pad material removal due to conditioning is assumed to be directly proportional to the conditioning density.

2.2 Model derivation

The relative velocity between conditioner and pad is represented generally as:

( )/p c p c p p cv v v ω d ω ω r= − = × + − × (2)

where vp is pad velocity, vc is conditioner velocity and r is the radius of a point on the conditioner relative to the conditioner centre. Figure 3 illustrates the kinematic model to generate the diamond grit trajectories. At an instant of time t in the conditioning session, the position of a diamond grit relative to the pad axes (Xpad, Ypad) can be obtained from equation (2) as:

( ) ( )( )( ) ( )( )

( ) cos cos

( ) sin sin

p p c

p p c

x X t d w t r w w t θ

y Y t d w t r w w t θ

= = ⋅ + ⋅ − −

= = ⋅ + ⋅ − − (3)


Figure 3 Position of diamond grit relative to the pad x-y coordinates

As illustrated in Figure 3, (ri, θi) defines the position of the ith diamond grit (out of Nd total diamonds) relative to the conditioner centre. For multiple diamonds on the conditioner, the collection of trajectories on the polishing pad is described by:

( )( )( )( )( )

coscos( )( )sin( ) sin

1 1

d dp c ip

ip p c ii

N N w w t θw tX td r

w tY t w w t θi i

⎡ ⎤− −⎡ ⎤⎡ ⎤⊕ = ⋅ + ⊕ ⎢ ⎥⎢ ⎥⎢ ⎥ − −⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦= =

(4)

Equation (4) is utilised with a commercial software package MATLAB (The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760, USA) to plot the conditioner trajectories. The parameters are the input variables Np, Nc, Rp, T, tcycle and the set {ri, θi} describing the conditioner diamond grit arrangement. Np and, Nc, the rotation speeds in RPM for the pad and conditioner are converted to ωp and ωc respectively in rad/sec. All length units are in inches and time is in seconds. Figure 4 illustrates a typical single diamond grit trajectory over one cycle when the sweeping velocity is constant (v(t) = 0.1818 in/s). Figures 5 to 7 illustrate the trajectories produced for various conditioner diamond arrangements. The


trajectory plots reveal that for different diamond arrangements, pad conditioning differs in extent of coverage of conditioner-pad interaction.

Figure 4 Trajectory on pad created by 2″ conditioner with single diamond, (a) diamond grit arrangement (b) diamond grit trajectory (see online version for colours)

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Figure 5 Trajectories on pad created by 5 grit/2″ conditioner with radial diamond arrangement, (a) diamond grit arrangement (b) diamond grit trajectory (see online version for colours)

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Figure 6 Trajectories on pad created by 12 grit/2″ conditioner with annular diamond arrangement, (a) diamond grit arrangement (b) diamond grit trajectory (see online version for colours)

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Figure 7 Trajectories on pad created by 49 grit/2″ conditioner with combined, (a) diamond grit arrangement (b) diamond grit trajectory (radial × annular) diamond arrangement (see online version for colours)

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Conditioning density is defined as the average of total trajectory length per unit area in the radial direction (Feng, 2007). Considering an infinitesimal part of the trajectory, the length s of the curve generated within the time interval [ti, ti+1] can be given as;


12 2lim

i

i

t

t

s x y+

= Δ + Δ∑ (5)

which yields

[ ] [ ]1 2 2( ) ( )

i

i

t

tS X t Y t dt

+′ ′= +∫ (6)

Figure 8 shows the measurement of trajectory length and how a surface map can be used to account for the conditioner-pad contact distribution. The scratch points indicate positions of diamond grit at specified intervals of time. In this study, the conditioning density is evaluated for a set of annular segments along the radius of the pad. Since the motion of the conditioner is restricted in one radial direction, part of the conditioner trajectory can be considered to fall within a specific segment j when t (say trj and tRj) is known for the segment boundary radii (say rj and Rj). The length of a diamond grit trajectory travelled between the times that the grit i traverses segment j can be determined as:

[ ] [ ]2 2( ) ( ) (1,2,3 )R j

rj

tij i it

S X t Y t dt j n′ ′= + ∀ =∫ … (7)

where

, ( 1)p pj j

R RR j r j

n n= = −

and

1 1( ) , ( )j j jjR r d rd Rt D d t D d− −=== = (8)

Figure 8 Development of surface map from trajectory length per unit area (see online version for colours)


Figure 9 shows the development of pad shape from trajectory length. For the entire collection of diamonds on the conditioner, the trajectory distribution is described by:

1

(1, 2,3, )dN

j ij ji

S S n=

= ∀ =∑ … (9)

This distribution does not directly reflect the amount of pad removal since pad wear is affected by the size of the conditioned area. To account for the conditioned area, the average conditioning density CDj for a specified segment j is given as:

( )2 2(1,2,3 )j

jj j

NSCD j n

π R r= ∀ =

−… (10)

where cycle

TNt

= and T = total conditioning time.

Figure 9 Development of pad shape from trajectory length (see online version for colours)

Since it is of interest to finally determine the pad shape, conditioning density is computed for the set of n annular segments of equal width. These values are then correlated with an


average pad wear thickness ΔH(rpj) for corresponding radii rpj of the pad. The description of pad shape development is illustrated in Figure 10.

( )pj j j pj jH r K CD r r RΔ = ⋅ < < (11)

Figure 10 Simulation results for typical conditioning case (UNIFORM), (a) segment trajectory length and conditioning density (b) surface map (c) 3-D pad shape (see online version for colours)

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Coefficient K is utilised to account for other process conditions. Kinvolves advanced physics and is reported to be dependent on the pad roughness, asperities, elasticity, surface chemistry and abrasion effects as well as conditioner characteristics (Nanz and Camilletti, 1995). In this study, the value of K is modified by substituting the experimental data into the simulation results. Considering the initial pad thickness Ho, the pad surface shape [pad thickness H(rp)] along the radial direction of the pad can be obtained from the wear prediction as:

( ) ( )p o pH r H H r= −Δ (12)

The plot of pad thickness values [H(rp)] against the pad radius describes one half of the pad shape.

3 Simulation and model verification

3.1 Simulation

The MATLAB software package is utilised to explore simulation results for key stages in the model development. For a typical conditioning case called UNIFORM, the parameters are chosen as Np = 75 RPM, Nc = 70 RPM, Rp = 12″, T = 660 s, tcycle = 55 s and v(t) = 0.1818 in/s. A 2″ conditioner with combined (radial × annular) arrangement of 200 diamond grits is used. The pad surface is divided into 24 annular segments.

Figure 10(a) shows the distribution of total contact distance Sj of the conditioner and corresponding CDj on the pad surface. The surface map shown in Figure 10(b) reveals the areas where conditioning is more intense. For a UNIFORM conditioner sweeping speed, it is seen that the total contact distance experienced by the conditioner increases for the outer segments. A 3-D view of the pad surface shape for a UNIFORM sweeping profile is shown in Figure 10(c). Since the pad conditioning takes place in one side of the revolving pad, the pad shape is symmetrical about the pad’s axis of rotation. Interestingly, the 3-D view reveals a central bump and an inner surface which is correlated with the sweeping profile bounded by a peripheral wall. It is observed that the size of base of the central bump is related to L.

3.2 Model verification and discussion

The model is verified with published experimental (Freeman and Markert, 1996). Three experimental sweeping profiles (FLAT 1, FLAT 2, and BELL) which correspond to three sweeping velocity functions are listed in Table 1. FLAT 1 increases linearly in time from the pad centre to the periphery. FLAT 1 is proposed to test a hypothesis that the conditioning time should increase linearly along the pad radius to compensate for the increase of the pad area. FLAT 2 has a constant sweeping profile to test the hypothesis that the pad surface profile is independent of the increase of the pad area along radial direction. BELL is proposed to generate a bell shape sweeping profile by increasing the time at the beginning and the end and reducing the time around the middle. To simulate each sweeping pattern, the relationship between data values for the swept distance and cumulative conditioning time is fitted with a curve to derive the respective sweeping distance equations;


2

6 4 3 2

0.1818 ( ) 20.0011 ( ) 0.2415 ( ) 0.1036 1

6 10 ( ) 0.0008 ( ) 0.0315 ( ) 0.1487 ( ) 0.1092

vdt

t for FLATt t for FLAT

t t t t for BELL−

′⎧ ⎫⎪ ⎪′ ′= − + +⎨ ⎬⎪ ⎪′ ′ ′ ′× − + − +⎩ ⎭

∫ (13)

Table 1 Sweeping profiles used for model verification

Sweeping profile

Pad centre Pad periphery

vdt∫ 0″ 1″ 2″ 3″ 4″ 5″ 6″ 7″ 8″ 9″ 10″

FLAT 1 tk(sec) - 4.1 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2

Σtk(sec) 0 4.1 8.1 12.5 17.3 22.5 28.1 34.1 40.5 47.3 54.5

FLAT 2 tk(sec) - 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

Σtk(sec) 0 5.5 11 16.5 22 27.5 33 38.5 44 49.5 55

BELL tk(sec) - 8.1 5.4 4 2.2 2.4 2.6 2.8 5.8 9.8 13

Σtk(sec) 0 8.1 13.5 17.5 19.7 22.1 24.7 27.5 33.3 43.1 56.1

Source: After Freeman and Markert (1996)

The experimental process parameters are presented in Table 2. Figure 11 shows the model simulation results overlain with experimental data when the same conditioning parameters are used. For the simulation results of FLAT 1 shown in Figure 11(a), a sharp linear increase in pad wear can be observed near the pad centre area followed by a slower linear increase and terminated with a sharp linear decrease around the pad periphery area. For FLAT 2 a constant wear can be observed in between a sharp increase wear near the pad centre and a sharp decrease wear near the pad periphery as shown in Figure11(b). This confirms the initial hypothesis that the pad surface profile is largely independent of the increase of the pad area along radial direction. In a similar nature the results for BELL [shown in Figure 11(c)] reveal a bell-shaped wear profile. Table 2 Experimental conditions

Polish parameters Conditioning parameters

Time 2 min #sweeps 1 post polish

Downforce 41.37 kPa Time 1 min

Pad temp 37.78ºC Downforce 15.38 kPa

Platen RPM 36 rpm End RPM 70 rpm

Pad type RodelEX1400 Platen speed 75 rpm

Back pressure 0 kPa Platen ∅ 60.96 cm

Flow rate 150 ml/min Profile Variable

Oscillation 10 mm End effector 5.08 cm ∅ / 200 diamond grits

Source: After Freeman and Markert (1996)


Figure 11 Simulation results vs. experimental results of three sweeping profiles, (a) FLAT 1 (simulation data vs. experimental data) (b) FLAT 2 (simulation data vs. experimental data (c) BELL (simulation data vs. experimental data) (see online version for colours)

(a)

(b)

(c)

From all three results, it is observed that the pad wear always shows a sharp linear increase near the pad centre and a sharp linear decrease near the pad periphery to form transition regions. These transition regions are resulted from the inability of all the diamond grits to have full interaction with the pad during their revolution since the entire diameter of the conditioner does not sweep over the central and peripheral areas. The


effect of transition regions could be mitigated by reducing the conditioner disc size, allowing conditioner overhanging and possibly allowing step function modifications to the sweeping profile although further investigation is required. It can be concluded that the sweeping profile has a great effect on the pad surface shape. Different sweeping profiles will generate significantly different pad surface shapes.

The good agreement between the simulation results and published experimental data indicates that the model developed from the conditioning density can be used to accurately predict pad surface shape resulted from diamond disc conditioning. The slight deviations observed in the comparison can be attributed to sweeping pattern approximation and experimental conditions such as conditioning tests setup, pad deformation and surface non-uniformity, and process variations due to polishing wafers.

4 Conclusions

CMP pad surface shape is affected by diamond disc conditioning which is applied to reverse the degradation of desired pad surface conditions during polishing. The paper utilises an analytic method to predict the pad surface shape from area density of conditioner-pad interaction given sweeping profile (defined by a function), conditioner disc design and process kinematic parameters. A surface map is introduced and utilised to account for the trajectory length per unit area as a visual measure of conditioner-pad contact distribution. Major conclusions can be summarised as follows:

1 The developed model is able to simulate the kinematics of diamond disc pad conditioning and accurately predict the pad surface shape.

2 The model is able to account for specific conditioner diamond grit arrangement (regular/random/annular/full/, etc.). It is observed that under different diamond grit arrangements, resulting pad conditioning is seen to differ in the extent of actual conditioner-pad interaction.

3 By investigating three sweeping profiles, it is confirmed that the sweeping profile has a great effect on the pad surface shape and the pad shape is largely independent of the increase of the pad area along radial direction.

4 There always exist some transition regions near the pad centre and the pad periphery. These transition regions show either a sharp linear decrease or a sharp linear increase pad thickness. These transition regions are resulted from the inability of all the diamond grits to have full interaction with the pad during touchdown and lift off stages of the conditioning cycle. This could be mitigated by reducing the conditioner disc size, allowing conditioner overhanging and possibly allowing step function modifications to the sweeping profile.

Considering the current understanding of pad shape development and the availability of metrics to measure conditioning performance, future work can consider a non-linear optimisation model to determine the optimal set of parameters to achieve desired pad shape.


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emmanuel a. baisie* and zhichao li xiaohong zhang€¦ · pad conditioning in chemical mechanical...

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