Modelling of delamination of ultra low-k material during ...mpfs/papers/LS2007CMP.pdf · Modelling of delamination of ultra low-k material during chemical mechanical polishing F

Modelling of delamination of ultra low-k material during chemical

mechanical polishing

F. Liua,* and M. P. F. Sutcliffea

aDepartment of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

Received 8 June 2006; accepted 26 October 2006

Two sets of experiments are performed to examine the delamination mechanism of ultra low-k material during chemical

mechanical polishing (CMP): (i) a macro-scale polishing test using a metallographic polisher and (ii) a micro-scale scratch test on a

micro-tribometer. Delamination has been observed at higher pressures in both sets of experiments and the relationship between

delamination rate and pressure has been established. Contact mechanics models are proposed to correlate results from the two sets

of experiments, combining a Weibull model of failure with a statistical asperity contact model. Results confirm the usefulness of the

combined testing procedure in predicting safe polishing pressures during CMP.

KEY WORDS: chemical mechanical polishing, ultra low-k, delamination, micro-tribometer

Nomenclature

a, b Pad asperity contact radius, acrylic ball contact

radius

A* Ratio between true and nominal contact area�A Mean asperity contact area in pad-wafer contact

A0 Acrylic ball indenter swept area in micro-tribom-

eter tests

Ak Individual asperity contact area

Aw Wafer surface area

D Acrylic ball deflection in compression test

E* Elastic modulus of ball-wafer contact system

Ep� Elastic modulus of IC1000TM polishing pad

fk Individual asperity contact force

Fn, Ft Down-force and tangential force on micro-trib-

ometer

‘ Defect length

L Total sliding distance

Lc Critical sliding distance established in micro-

tribometer tests

M Number of asperities in contact between pad and

wafer

�nðncÞ Critical number of cycles (number of contacts) to

delamination established in micro-tribometer tests

Nw Total number of defects on wafer sample

pm Hertz pressure in micro-tribometer tests

�p True mean contact pressure in polishing tests

P0 Probability of no defects failing on a wafer sample

P1 (Ps) Probability of one defect failing (surviving)

Pf Failure rate established in micro-tribometer tests

Pn Nominal polishing pressure

r Individual asperity peak radius

R Acrylic ball radius

T Polishing time to give 50% chance of delamina-

tion failure

v Polishing speed

V(V0) Material volume (normalising material volume) in

Weibull analysis

z Pixel height in filtered pad surface matrix

Greek letters

d Asperity deflection

D Horizontal resolution used in profilometry mea-

surements

l Coefficient of friction

qa Density of asperities in contact as a function of �p

qd Density of defects as a function of pmk Mean number of asperity contacts to give 50%

chance of delamination failure

r (r0) Material stress (normalising stress) in Weibull

analysis

1. Introduction

In the semiconductor industry, the fabrication ofintegrated circuits (IC) is based on multilayer integra-tion of different semiconductor materials and theirelectrical interconnects in a three-dimensional circuitrynetwork. Chemical mechanical polishing (CMP) hasevolved as a standard process to produce nanoscaleflatness and high planarity after material deposition, sofacilitating deposition of the next layer of material.

Chemical mechanical polishing of interlayer dielectricsis one of the most common operations in IC fabrication.Silicon dioxide has been used as the interlayer dielectric inconjunction with aluminium interconnects for more thantwo decades. A major drawback of silicon dioxide is itshigh dielectric constant (k value), which results in a highRC time constant. With the scaling down of the featuresize and the increase of the transistor density on highperformance ICs, the propagation delay due to this in-creased RC time constant has become a major barrier to

*To whom correspondence should be addressed.

E-mail: [email protected]

� 2006 Springer Science+Business Media, LLC

Tribology Letters (� 2006)

DOI: 10.1007/s11249-006-9171-z

raising the device speed [1]. Integration of copper anddielectrics with a low dielectric constant (low-k,k £ 2.8) has proved to be an effective solution. As ICmanufacturers move towards 65 nm technology, materi-als with even lower k values are required. By introducingmicropores into the low-k material [1], materials with avery low dielectric constant can be produced (k £ 2.2);these are known as ultra low-k (ULK) materials.

However, porous ultra low-k materials generally havepoor mechanical strength, which can cause serious fab-rication problems. The soft and fragile nature of theporous ultra low-k materials makes them susceptible tomechanical damage during the CMP process. Delami-nation is the most commonly seen form of failure, withthe ultra low-k layer being removed due to themechanical breakdown of the ULK/Cu diffusion barrieror ULK/etch stop interface [2], causing defects on theprocessed wafer.

Various attempts have been made to investigate thedelamination mechanism of ultra low-k materials. Sik-der et al. [3] and Ganesan et al. [4] performed experi-ments using Cu-patterned low-k and ultra low-k wafers.Delamination on these wafers was observed at higherpressures. It was found possible to monitor delamina-tion by measuring acoustic emission (AE). Later Zantyeand Sikder et al. [5] characterised the interfacial adhe-sion of various low-k and ultra low-k films. Wang et al.[6] also conducted experiments on SiLKTM low-kmaterial and concluded that delamination is pattern-dependent. At the mean time, modelling work e.g. [7,8]has also been carried out for low-k/ultra low-k CMP.However, these models only provide prediction for thematerial removal rate of low-k/ultra low-k materials.Although relevant delamination theory was first estab-lished as early as the 1970’s by Suh [9] to predictmaterial removal rate of metals, no tribological models,either analytical or numerical, are currently available toprovide understanding of the delamination mechanismsof ultra low-k films. Since the fragility of ultra low-kmaterials is likely to persist in the near future [2],delamination during CMP will remain a major problemcompromising the production yield. It would be ex-tremely beneficial to the IC industry if a quantitativemethod can be developed to predict delamination forultra low-k materials.

The current paper presents a combined testing methodto predict delamination on ultra low-k wafers. CMPexperiments have been conducted on a metallographicpolisher. A micro-tribometer has been used to study thedelamination mechanism at a micromechanics scale, bysimulating the contact pressure on the asperity levelencountered in the CMP experiments. The statisticalmodels proposed in the paper correlate the results fromboth parts of the experiments, providing a quantitativeunderstanding of delamination of ultra low-k materialand a way to evaluate and optimise processing routes.

2. Polishing experiments

2.1. Polishing experiments setup

Polishing experiments were carried out using a PresiMecapol 230 metallographic polisher which functions asa small scale version of an industrial CMP machine. Thepolisher has a standard bench-top configuration asshown in figure 1. The wafer sample used in this work isCu-patterned Orion� ultra low-k wafer provided byAviza Technologies. Orion� is a nano-porous carbon-doped organosilicate glass with a pore size of 1–4 nm.The wafer was pre-polished by Aviza Technologiesaccording to the IC industrial standard for low-k/ultralow-k CMP to remove the bulk Cu layer, leaving the Culines and the Orion� layer exposed. The wafer was thenbroken into 20 mm � 40 mm coupons for the polishingexperiments. The scanning electron micrograph cross-section of figure 2 shows the four-layer structure of thewafer, with a 200-nm-thick Orion� film deposited on a50 nm SiC etch stop layer. A 500 nm SiO2 layer issandwiched between the SiC layer and a Si substrate.The polishing consumables used in the CMP experi-ments were a Rohm and Haas IC1000TM polishing padin conjunction with their LK301 silica-based low-kslurry. Pad conditioning was performed ex situ betweentwo tests using a Kinik DiaGrid� diamond conditioner.

2.2. Experimental procedure

The purpose of the polishing experiments was toinvestigate the relationship between the applied pressureand delamination on the wafer coupon. The wafercoupon was aligned with the centre of the sample holderin each test. Both the sample holder and platen speedswere set to 20 rpm for all the tests. The distance betweenthe two centres was fixed to 0.045 m by securing thepolishing head. This setup gave an average polishingspeed across the coupon of approximately 0.12 m/s. Theslurry was fed onto the pad through the external

Figure 1. Schematic of bench-top polisher: offset between sample

holder and pad centres d = 0.045 m.

F. Liu and M. P. F. Sutcliffe/Modelling of delamination of ultra low-k material

agitated dispenser at a flow rate of 100 ml/min. Thepolishing time in the polishing experiment was con-trolled by the digital timer of the polisher. The samplewas taken off the machine at ten second intervals andexamined under an optical microscope.

2.3. Results and discussions

The nominal pressures applied in the polishingexperiment covered the range from 7 kPa to 58 kPa.Delamination was observed at the edge of the couponunder all pressures, even at the beginning of polishing.This is due to the exposure of the interface between theOrion� layer and the SiC layer at the cut edge. Sincethis delamination would be avoided when polishing acomplete wafer by chamfering the wafer edge, it is dis-regarded in the tests. Only delaminations starting awayfrom the edges of the sample were seen as significant.

At pressures below 28 kPa, no delamination could beobserved in the centre of the wafer coupons after up to120 seconds of polishing. The Orion� film was subjectto smooth wear. However, at higher pressures, delami-nation began to occur in the centre of the coupons. Ithas been found that delamination always took place firstin the large open areas of unpatterned Orion� film andpropagated until it reached the Cu lines, as shown infigure 3. This observation matches the results of otherresearchers [6,10] studying CMP of low-k/ultra low-kmaterial. Profilometric scans were taken across the del-aminated area using a Dektak IIA contact profilometer.These revealed that the step height of the delaminationwas 200 nm, indicating that delamination occurred atthe interface of the Orion� film and the SiC layer.

The evolution of the Orion� film delamination is afunction of pressure and time, as shown in figure 4 for amean polishing speed of 12 m/s. Each asterisk corre-sponds to the time at which delamination was firstobserved in a given sample. The horizontal dashed linedelineates a threshold pressure of about 28 kPa, belowwhich no delamination in the centre of the specimenoccurred during polishing. The curved dashed line givesthe boundary on the pressure-time map between safe

polishing (to the bottom-left of the line) and delamina-tion. The effect of an increase in pressure is to reduce thesafe polishing time, for pressures above the thresholdlevel of 28 kPa. In all tests, delamination occurred atrandom locations on the coupons. This is consistentwith the hypothesis that random interfacial adhesivedefects are the major cause of delamination on ultralow-k stacks [5,11]. These defects may have developedduring the CVD process of the Orion� layer or havebeen induced by the bulk Cu pre-polishing process. Bothpossibilities exist in IC manufacturing and therefore thepolishing experiment results are representative of thereal industrial problems. Nevertheless the origin of thesedefects remains a source of interest for further work.

3. Micro-tribometer experiments

3.1. Micro-tribometer setup

The polishing pad in CMP can be modelled as arough surface with protruding asperities. When theasperities are brought into contact with the wafer sur-face, the true contact pressure on the asperity scale ismuch higher than the nominal pressure on the waferscale [12]. To further understand the delaminationmechanism, micro-tribometer tests were undertaken to

Figure 2. Scanning electron micrograph cross-section of patterned

Orion� wafer [courtesy of Aviza Technologies].

Figure 3. Delamination on patterned Orion� wafer.

Figure 4. Process map showing regions of safe polishing and delam-

ination as a function of polishing time and pressure.


bring the contact down to the asperity scale, with acontact size of the order of an asperity contact andequivalent contact pressures predicted for CMP.

A schematic of the micro-tribometer [13] is shown infigure 5. An acrylic ball indenter of radius 0.73 mm ispressed against an ultra low-k wafer sample through asolid spring. The solid spring is coupled with a piezo-drive with closed-loop control to achieve a constant loadon the sample. By using springs of different stiffness, thedown-force can range from 0.01 N to 20 N with aresolution of 0.01 N.

The sample is held by a holder which is attached to aload cell. The load cell measures the normal and tan-gential forces induced by the indenter. A reciprocatingstage coupled with a precision motor/encoder unit pro-vides horizontal motion. The output signals of the loadcell are passed through a low-pass filter to eliminate highfrequency noise. The filtered signals are then fed into ahost computer for data logging and processing. Thecoefficient of friction l can then be obtained as

l ¼ Ft

Fnð1Þ

where Ft and Fn are the measured tangential and normalforces respectively.

The elastic modulus E* of the contact system can beestimated via a compression test in which the ball iscompressed between a steel plate and the wafer sample.The Hertz contact equation relates the down-force Fn tothe ball deflection D via

Fn ¼4

3E �R

12

D

2

� �32

ð2Þ

where R is the ball radius. The modulus of the loadingplates, which is considerably greater than this, is disre-garded in the calculation. By recording the applieddown-forces and ball deflections, E* was derived as2.7 GPa. This E* was used in the micro-tribometerexperiments to calculate the contact pressures, againassuming that the elastic deformation of the siliconwafer is insignificant compared with that of the polymerball. The Hertz theory also gives the contact pressure pm

and contact radius b between the ball and sample in themicro-tribometer experiments as

b ¼ 3FnR

4E�

� �13

ð3Þ

pm ¼2

3

6FnE�2

p3R2

� �13

ð4Þ

3.2. Experimental procedure

The theoretical Hertz contact pressures in the micro-tribometer experiments were between 42 MPa and116 MPa, corresponding to loads between 0.1 Nand 2 N. The Hertz pressures used in the experimentsand their corresponding contact radius obtained fromequations 3 and 4 are listed in table 1. The pressuresapproximately match the range of mean true contactpressures predicted in section 4 for the polishingexperiments.

The acrylic ball was loaded on the sample throughthe solid spring and the down-force was then fine-tuned to a high accuracy by adjusting the verticaldisplacement of the piezodrive. The LK301 slurry wascontinuously injected onto the sample using a plasticpipette. The sliding distance (reciprocating stroke) ofthe stage, which was controlled by the host computer,was set at 500 lm for the 42 MPa tests. At higherpressures, the sliding distance was reduced to accountfor the increase in contact radius in order to maintaina constant scratch area. This constant area is requiredto investigate the volume dependence of failure viaWeibull statistics, which is detailed later in this sec-tion. The experiments were carried out in the unpat-terned area on the Orion� wafer to study thedelamination mechanism observed in the polishingexperiments. After each test, the sample was cleanedin an ultrasonic cleaner with water to remove thepolymer and slurry residues. Then the groove depth ofthe scratch was measured using a Dektak IIA contactprofilometer. Special attention was paid to any cor-relation between the coefficient of friction anddelamination on the Orion� film.

Figure 5. Micro-tribometer.

Table 1.

Down-force and corresponding Hertz pressure and contact radius in

micro-tribometer experiments.

Down-force

(N)

Hertz pressure

(MPa)

Contact radius

(lm)

0.1 42 27

0.2 53 34

0.5 73 47

1.0 92 59

2.0 116 74


3.3. Experiment results

The optical micrograph in figure 6 shows a groove onthe wafer sample after a typical test. At lower pressures(below 53 MPa), the friction coefficient l changes sig-nificantly during the test as the ball penetrates throughdifferent layers of material. Four example traces areshown in figure 7(a), for a pressure of 42 MPa. Ini-tially, l has a high value between 0.4 and 0.7. At around1000 cycles, there is increased noise in the friction signalas the ball meets the Orion�/SiC interface; l then risesas the ball bears on the SiC layer. Since SiC is a dense,hard material, it takes more than 300 cycles to penetratethe 50 nm layer. After the ball touches the soft SiO2

layer, l begins to drop quickly. The SiO2 is worn awayin less than 200 cycles before a spike appears on l,indicating the ball has reached the SiO2/Si substrateinterface. As the ball slides on the Si substrate l slowlyincreases. In all the tests at 42 MPa, the drop in l tookplace after around 1500 cycles, indicating that nodelamination occurred in these tests since no early dropin l was observed.

At higher pressures (above 53 MPa), the micro-trib-ometer experiment reveals delamination of the Orion�film in the form of an early drop of l. This is illustratedin the friction traces shown in figure 7(b) for a pressureof 73 MPa. In some tests l drops after only around 100cycles of sliding while in other tests this drop occurs ataround 300 cycles. The early drop in l is associated withdelamination of the Orion� film, so that the ball tou-ches the Si substrate at an early stage. By subtracting thenumber of cycles needed to wear away the SiC layerfrom the number of cycles at which the l drop occurs,the critical sliding cycles to delamination can be obtained.It was found that, where delamination occurred, thenumber of cycles to delamination had a relatively smallvariation. For example, the standard deviation in cyclesfor delaminated tests at 73 MPa was approximately

25% of the mean number of cycles. Both the failure rate(number of failures/number of tests) and the number ofcycles needed to cause delamination of the Orion�wafer are functions of the applied Hertz pressure, asshown in table 2. It is observed that, as the pressureincreases, the failure rate rises, while the number of cy-cles before delamination falls.

The variation of material removal rate of the Orion�film with applied Hertz pressure was also inferred fromthe micro-tribometer tests, as shown in figure 8. Thematerial removal rate does not have the Prestonianlinear relationship with applied pressure, but shows asteep rise in removal rate at a pressure of around70 MPa. This rise may be due to crushing of the micro-pores in the Orion� material at a critical pressure.

3.4. Weibull analysis

Weibull statistics have proved successful in modellingthe mechanical failure of semiconductor materials underboth normal stress and shear stress [14,15]. Here we useWeibull statistics to represent the micro-tribometerdelamination results detailed in table 2.

In its simple two-parameter form, the Weibulldistribution gives the variation of failure rate Pf withapplied stress r for a volume V0 of material as

ln ln1

1� PfðV0Þ

� �¼ m ln r�m ln r0 ð5Þ

where r0 is a normalising stress and m is the Weibullmodulus for the material. Therefore a plot of ln ln (1/(1)Pf (V0))) against ln r has a linear relationship ifWeibull model is appropriate. The volume dependenceof the Weibull distribution is given by

lnð1� PfðVÞÞ ¼ �V

V0

rr0

� �m

ð6Þ

where V is any arbitrary volume under test. In the mi-cro-tribometer experiment, the volume of the Orion�film under test is directly proportional to the scratcharea of the ball indenter.

Since the stresses in the solid and at the Orion�/SiCinterface are proportional to the Hertz pressure pm forlinear elastic solids, the stress r in equations (5) and (6)can be substituted by the Hertz pressure pm in the micro-tribometer tests. The Weibull plot of ln ln (1/(1)Pf (V0)))against ln pm is shown in figure 9 for the micro-trib-ometer test results of table 2. The standard distance(500 lm at 42 MPa and shorter distances at higherpressures) test result shows that delamination of theOrion� film follows the Weibull distribution with aWeibull modulus of 3.7 and a normalising pressure of132.6 MPa.

To investigate the dependence of failure rate on thevolume of the film under test predicted by the Weibull

Figure 6. Optical micrograph of Orion� wafer after micro-tribometer

test.


model, a second set of tests was carried out, with thesliding distance twice the standard distance at eachpressure. The predictions of the Weibull model given byequation 6 for this double distance stroke, using theparameters found from the standard distance tests, arecompared with the measured failure rates in figure 9.The double distance tests were conducted at two Hertzpressures, 73 MPa and 92 MPa. It can be seen that theexperimental result at 73 MPa agrees well with theprediction. However at 92 MPa, the result shows asmaller size offset than the Weibull prediction. This ismost probably due to the fact that in the double distancetests the ball indenter was worn at twice the rate of thestandard distance experiment, causing the contactpressure to drop significantly, and hence reducing thefailure rate.

4. Contact mechanics

Bhushan et al. [16] defined three pad-wafer contactmodes in CMP: direct contact, semi-direct contact andnon-direct contact. In the direct contact mode, the waferis supported only by the deformed pad asperities.Models such as Yu et al.’s early work [12] and the morerecent work by Chekina et al. [17] are based on thismode. In the semi-and non-direct contact modes, thewafer is assumed to be supported partially or solely bythe fluid film and elastohydrodynamic lubrication(EHL) theory is applied to predict the contact pressure.This also enables the modelling of slurry particletransport and entrainment mechanisms. Such modelsrange from Jeng et al.’s [18] partial asperity contactmodel using 1D EHL simulation to Shan et al.’s [19]and Jin et al.’s [20] recent models that extended EHL to

Figure 7. Evolution of friction during micro-tribometer tests at (a) 42 MPa (b) 73 MPa. Four repeat experiments are shown.

Table 2.

Summary of failure rate and critical number of cycles to delamination.

Hertz pressure 42 MPa 53 MPa 73 MPa 92 MPa 116 MPa

Failure rate, Pf (Number of failure/number of tests) 0% (0/50) 4% (2/50) 9% (9/100) 21% (13/60) 50% (25/50)

Critical number of cycles to delamination, �n – 200 50 10 10


2D and 3D. Considering the low polishing speed in low-k/ultra low-k CMP, for which the global elastohydro-dynamic effect is less prominent, we base our model onthe direct contact mode. At the range of nominal pres-sures used in CMP between 20 kPa and 120 kPa, theasperities are assume to behave elastically and thereforecan be treated individually as Hertzian contacts.

Most existing models e.g. [12,19–22] have treated thepolishing pad according to the Greenwood-Williamsontheory [23] as a rough engineering surface with pro-truding asperities whose heights follow the Gaussiandistribution. The asperities are assumed to be cappedwith spherical peaks of uniform radius. To predict thereal contact pressure between the asperities and thewafer surface, it is important to have an accuratemeasurement for the asperity heights and peak radii.

The IC1000TM polishing pad used in the polishingtest is a foamed polyurethane pad with micropores onthe surface. Non-contact 3D optical profilometry hasproved to be successful in the study of polishing padtopography [24,25]. In this work, the surface of a freshlyconditioned IC1000TM polishing pad was examined

using a Zygo Newview 200 white light interferometricprofilometer with a sample area of 480 lm � 640 lm.The pad sample was gold-coated to increase the reflec-tivity and the global surface slope of the resulting heightmatrix was removed by applying the built-in removeplane function in the profilometer control softwareMetropro. The height matrix was then filtered by using azero-phase forward and reverse digital filter (filtfiltfunction in Matlab [26]) to remove unwanted high fre-quency noise. After filtering, an asperity peak is identi-fied if a pixel is found to have a greater height value thanits surrounding pixels. The asperity heights can then bederived by subtracting the value of the mean plane fromthe values of the peak pixels in the filtered matrix. A cut-off frequency of 0.02/ lm and a filter order of 10 werechosen in order to smooth the profile of the asperitiesand model contact on the scale of tens of micrometers(the flat areas between the micropores). An alternativefilter would be needed to model nanoscale roughness onthese flats. Further details and validation of this methodare given in [27,28]. The final topography of theIC1000TM pad after the filtering process is shown infigure 10, indicating how the pore-scale roughnesstopography has been isolated using this filteringprocedure.

The radii of asperity peaks identified from thesmoothed pad profile are then given by [29]

ri;j ¼ �2D2

ziþ1;j þ zi�1;j þ zi;jþ1 þ zi;j�1 � 4zi;jð7Þ

where ri,j is an asperity peak radius, D the samplinglength of the Zygo profilometer (horizontal resolution),zi,j an asperity height, and zi+1,j, zi-1,j, zi,j+1, zi,j-1 are theheights of its four neighbouring pixels. Because of thesmooth nature of the filtered surface, this estimate of ri,jis reasonably robust.

For the conditioned pad, a typical distribution ofheights and radii of peaks is represented in figure 11,

0

10

20

30

40

50

60

0 50 100 150Pressure (MPa)

Mat

eria

l rem

ova

l rat

e(A

ng

stro

m/c

ycle

)

Figure 8. Effect of Hertz pressure on material removal rate during

micro-tribometer tests.

Figure 9. Weibull analysis of Orion� film delamination during the

micro-tribometer tests showing the effect of pressure pm on failure rate

Pf.

Figure 10. Surface topography of freshly conditioned IC1000TM

polishing pad filtered with 0.02/ lm cut-off frequency.


demonstrating that the Greenwood-Williams assump-tion of uniform asperity radius is not appropriate.Hence a numerical model was used to calculate thecontact conditions. Each asperity was modelled as anindependent Hertzian contact, as with the Greenwood-Williamson model, but the actual distributions ofasperity heights and peak radii were used. Ten pro-filometric scans were performed in different locationson the pad to ensure the heights and radii used in thenumerical model were representative of the whole pad.Following the standard procedure for such models[30], the load at each asperity contact was found as afunction of asperity geometry, and the separationbetween the wafer surface (assumed smooth) and themean plane of the rough pad surface. The variation intrue mean contact pressure and contact area withnominal applied pressure was found by reducing theseparation distance until the total contact forcereaches equilibrium with the down-force.

Assuming at equilibrium the total number of asperi-ties in contact is m, the contact force and contact area ofthe kth asperity is given by the Hertz equations as

fk ¼4

3E�pr

12

kd32

k ð8Þ

Ak ¼ prkdk ð9Þ

where Ep* is the pad modulus (measured as 550 MPa

[28]), and dk the asperity deflection in contact. The truemean contact pressure is then given by

�p ¼

Pmk¼1

fk

Pmk¼1

Ak

ð10Þ

The ratio A* between the true contact area and thenominal contact area Aw can be obtained as,

A� ¼

Pmk¼1

Ak

Awð11Þ

Results in the range of nominal pressures appropriate tothe polishing experiments (7–58 kPa) as a function ofthe applied nominal pressure are presented in figure 12.The predicted contact area ratio is small, typically of theorder 0.1%, while the true mean contact pressure is inthe range of 45–82 MPa. Another advantage of thenumerical model is that the number of asperities incontact per unit area (asperity density) and the meanradius of the contact patches can also be obtained.These results are used in the next section to modeldelamination of the Orion� film.

5. Correlation between micro-tribometer and polishing

experiments

In this section we describe a contact mechanicsmodel, based on the surface topography measured in theprevious section, to relate the micro-tribometer andpolishing experiments. The relationship between trueand nominal pressures for the pad contact, given infigure 13 is used to determine the appropriate Hertzpressure pm in the micro-tribometer experiments whichcorresponds to a given nominal pressure pn in the pol-ishing experiments. In effect it is assumed that all theasperity contacts in the polishing test have the same truemean contact pressure �p given by equation (10), ratherthan the spread of pressures expected theoretically, witha corresponding mean contact area �A given by

�A ¼

Pmk¼1

Ak

mð12Þ

Figure 11. Asperity radius and height distribution of IC1000TM pad.

0 20 40 60 80 1000

20

40

60

80

100

Nominal contact pressure (kPa)

Tru

e m

ean

co

nta

ct p

ress

ure

(M

Pa)

0

0.25

0.5

0.75

1

1.25

Tru

e co

nta

ct a

rea

rati

o

PressureArea ratio

x10-3

Figure 12. Numerical model for the pad topography showing the

effect of nominal contact pressure on true mean contact pressure and

area ratio.


The relationship between the critical number of cyclesto delamination �n in the micro-tribometer experimentsand the polishing time to delamination t in the polishingexperiments is not straightforward. Two alternativemodels with different assumed failure mechanisms areproposed. In both cases it is assumed that delaminationinitiates at a defect (for example at the Orion�/SiCcovalent bonding layer), but in the first case a fatigue-type approach is adapted, while in the second case awear-type model is used. Further information on theactual failure mechanism is needed to decide on themore appropriate model.

5.1. Fatigue model

In this model it is assumed that delamination from adefect is associated with the number of asperities slidingacross it during polishing. We term this a fatigue model,as fatigue is typically controlled by the number of cyclesto failure. It is hypothesised that during each contactevent the delamination sees one cycle of loading.

It is assumed that each sliding stroke of the ballindenter in the micro-tribometer test corresponds to oneasperity contact. The micro-tribometer test then givesthe critical number of asperity contacts to failure nc, as afunction of Hertz pressure pm, as

nc ¼ 2�n ð13Þ

where �n is the number of cycles to delamination foundin the micro-tribometer experiment.

Next we need to establish the rate at which defects inthe polishing test suffer an asperity contact. To idealisethe problem, it is assumed that the wafer has an arealdensity of susceptible defects qd (which depends onpressure) in the form of lines of length k, and that the

relative wafer motion is perpendicular to the defectorientation, as illustrated in figure 14. The asperitydensity qa is found from the numerical contactmechanics model of section 4, at the given nominalcontact pressure pn. The mean number of asperitiescontacts k sliding across the defect, at a polishing speedv, in time t, is then given by

k ¼ qa‘vt ð14Þ

The density of susceptible defects q d on the wafer, as afunction of Hertz pressure pm, is established from thedelamination failure rate Pf measured in the micro-tribometer tests, as

qd ¼Pf

A0ð15Þ

where A0 is the area that the ball indenter sweeps duringthe test. This area, illustrated in figure 13, is readilycalculated from the contact radius b defined in equation(3) and sliding distance L as

A0 ¼ 2bL ð16Þ

The total number of defects Nw on the wafer coupon ofsurface area Aw is given by

Nw ¼ qdAw ð17Þ

With the very small fractional true contact area pre-dicted for the polishing process, the probability ofcontact between defects and asperities is very low, and itis appropriate to assume that the number of asperitycontacts n that a defect sees has a Poisson distributionwith mean k. The probability P1 of a defect seeing morethan nc contacts, and hence failing, is then given by [31],

P1 ¼ Pðn > ncÞ ¼X1n¼nC

e�k kn

n!ð18Þ

The probability that a single defect does not fail (i.e.the probability of survival) equals

Ps ¼ 1� P1: ð19Þ

and so the probability that none of the Nw defects on thewafer coupon has failed during polishing is given by,

P0 ¼ PNws ¼ 1�

X1n¼nC

e�k kn

n!

!Nw

ð20Þ

This summation is calculated numerically. Equation (20)shows that the probability P0 that no defects in thewafer fail is a function only of the critical number ofcontacts nc, the mean number of asperity contacts k andthe total number of defects Nw. Alternatively, the meannumber of asperity contacts k required for a givenprobability of delamination (here taken for the polishingtests as 50%), can be found given nc and Nw. The pol-ishing time to give a 50% chance of delamination is

Figure 13. Schematic of the contact between asperities and a defect in

the polishing experiments.


related to the mean number of asperity contacts viaequation (14), to give,

t ¼ kqa ‘v

ð21Þ

where the polishing speed v used is a mean value of0.12 m/s seen in the polishing experiments.

To summarise, for a given nominal polishing pressurepn, the pad contact model (section 4) is used to find thecorresponding true mean contact pressure �p andasperity density qa. Then the micro-tribometer test, witha Hertz pressure pm the same as �p gives the criticalnumber of contacts to failure nc, while equation (15)provides the defect density qd. Equation (20) is used tocalculate the mean number of asperity contacts k to givea 50% chance of delamination failure, and equation (21)gives the corresponding time t. The defect length ‘ is theonly parameter that has to be obtained by estimation inthis statistical model. Figure 14 summarises the abovealgorithm, showing the calculation procedure for pre-dicting the polishing time to delamination in the pol-ishing experiments based on the micro-tribometerexperimental results.

5.2. Wear model

In the above fatigue model, each stroke of sliding inthe micro-tribometer experiment corresponds to anasperity contact in the polishing test. However, thecontact radius of the ball indenter is significantly largerthan the average asperity contact radius in the polishingtest. The defect is therefore subject to a much longersliding distance in each stroke under the micro-tribom-eter than during asperity contact in the polishingexperiment. An alternative view of failure supposes thatthe sliding distance in the polishing and micro-tribom-eter tests controls delamination failure. This wouldcorrespond to a wear-type process, where wear of the

film ultimately leads to subsurface delamination, per-haps when a critical film thickness is reached. Thedevelopment of the model follows closely that of thefatigue model, and only the critical differences aredescribed.

The wear model is illustrated in figure 15. Eachasperity passing over the defect contributes a slidingdistance of 2a, while in each stroke of sliding on themicro-tribometer the ball indenter contributes 2b, wherea is the mean asperity contact radius given by

a ¼ffiffiffiffi�A

p

rð22Þ

and b the ball indenter contact radius given by equation(3) corresponding to a Hertz pressure pm. The criticalsliding distance Lc in the micro-tribometer at a givenHertz pressure pm is given by

Lc ¼ 2ncb ð23Þ

and the mean sliding distance L in the polishing test(equivalent to the mean number of asperity contacts kfor the fatigue model), is given by

L ¼ 2qa‘vta ð24Þ

The probability of no failures among Nw defects on thewafer coupon is found by replacing nc with Lc and kwith L in equation (20), to give

P0 ¼ ð1� P1ÞNW ¼ 1�X1k¼LC

e�LLk

k!

!NW

ð25Þ

As with the fatigue model, the value of L, correspondingto a 50% probability of delamination, is used to predictthe mean time for delamination t by

t ¼ L

2qa‘vað26Þ

Micro-tribometer experiments

Polishingexperiments

Hertz pressure of micro-tribometer, pm

True mean contact pressure, p

(corresponding to a nominal pressure pn)

Critical number of cycles to

delamination, n andfailure rate Pf

Polishing time to delamination, t

Numerical contact mechanics model

Asperity density a

and defect density

dat p

Polishing speed, v

ρ

Figure 14. Overview of model relating micro-tribometer results to

polishing results.Figure 15. Schematic of the contact between the micro-tribometer and

a defect (the area within the dashed lines represents the area swept out

by the defect).


5.3. Results and discussions

Calculations based on the 73 MPa micro-tribometertest are given to illustrate the model. The values of allthe parameters used are listed in table 3. The probabilityof failure of a single defect, and the probability that nodefects fail within the 1440 defects expected on thesample, are given in figure 16 as a function of the meannumber of asperity contacts k. As k approachesthe critical number of contacts for failure defined by themicro-tribometer experiment (nc = 100 in this case), theprobability of one asperity failing rises rapidly. Mean-while, the probability of no asperity failing decreasessharply with increasing mean number of asperity con-tacts k. Because of the large number of defects present,to avoid failure in every defect there has to be a verysmall chance of a single defect failing. It is predicted thatthere is a 50% chance of delamination with a meannumber of asperity contacts of around 70. To illustratethe calculations, consider the 73 MPa Hertz pressuretest corresponding to a 37 kPa nominal polishing pres-sure, found by using the numerical pad contact model insection 4. The contact model also gives asperity densityqa = 3.24 � 107/m2. Knowing the polishing speed

v = 0.12 m/s and assuming the defect lengthk = 0.5 lm, equation 21 is then used to find the pol-ishing time t = 36 s to give a 50% chance of delami-nation. Similar results are seen for the wear model, as afunction of sliding distance L.

The two models are used to relate the micro-trib-ometer results of table 2 with the polishing results. Thepredicted polishing times t to give a 50% chance ofdelamination are plotted as a function of nominalpressure in figure 17, and compared with the polishingexperiment results, re-plotted from figure 4. The defectlength k has been chosen to best fit the results, withvalues of 0.5 lm and 20 lm chosen for the fatigue andwear models, respectively. Further information aboutthe size of relevant defects in the Orion� low-k waferwould be needed to distinguish between these twomodels. In both cases the fit between the measured data,and that inferred from the micro-tribometer experi-ments, is very encouraging. The shape of the boundarybetween safe polishing and delamination is well cap-tured by the model, and the values of k required arephysically plausible. It is worth noting that the sharpdecrease in the polishing time to delamination as thepolishing pressure rises from 20 kPa to 40 kPa arises

Table 3.

Parameters used for modelling based on 73 MPa true mean contact pressure.

Parameter Value Source

Corresponding nominal pressure in CMP, pn 37 kPa Contact model

Critical number of contacts to failure, nc ¼ 2�n 100 Micro-tribometer test

Micro-tribometer failure rate (at 73 MPa), Pf 9% Micro-tribometer test

Micro-tribometer swept area, A0 0.5 mm2 Micro-tribometer test

Wafer coupon area, Aw 800 mm2 Polishing test

Total number of defects, Nw 1440 Nw = Pf � Aw /A0

Critical sliding distance, Lc ¼ 2ncb ¼ 4�nb 9400 lm Micro-tribometer test

Mean polishing speed, v 0.12 m/s Polishing test

50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

Mean number of asperity contacts,λ

Pro

bab

ility

Failure of a singledefect

No failure in Nw

defects

Figure 16. Effect of the mean number of asperity contacts k on the

probability of failure in a single defect, or on a wafer sample with 1440

defects. Parameters used are for a true mean pressure of 73 MPa, with

the critical number of contacts nc = 100.

Figure 17. Prediction of polishing time to failure using fatigue and

wear models.


from the significant increase of the true mean contactpressure seen in Figure 13 over this range of pressures.

6. Conclusions

The following conclusions can be drawn from thecombined testing procedure.

1) Delamination of Orion� ultra low-k material duringCMP occurs at higher nominal pressures (> 28 kPa).The polishing time to delamination is a function ofapplied pressure.

2) The effect of true mean asperity contact pressure onthe delamination failure rate can be investigatedusing a micro-tribometer. Delamination of Orion�ultra low-k material can be modelled with Weibullstatistics, with the probability of delamination failureincreasing with increasing applied pressure.

3) Given the pad surface topography, the real averagecontact pressure during CMP can be establishedthrough a numerical asperity contact mechanicsmodel using Hertz contact theory.

4) A statistical asperity contact model has been devel-oped to correlate the polishing and micro-tribometertests. This forms the basis of a predictive model whichcan be used to predict the polishing time to delami-nation as a function of applied pressure. Althoughthe model established in this work is based on thepolishing experiments performed on a metallographicpolisher, this procedure is equally applicable for testscoupling microtribometer measurements with indus-trial CMP. This combined testing procedure can beused in the semiconductor industry to define safepolishing conditions for low-k/ultra low-k CMP.

Acknowledgements

The authors are most grateful to the Kinik CompanyLtd (Mr. Wu), Massachusetts Institute of Technology(Prof. Boning), Rohm and Haas Electronic Materials(Drs. Muldowney and van der Velden and Mr O’Don-nell) and Aviza Technologies (Dr. Buchanan) for theiradvice and supply of consumables and to Prof. Hutch-ings of Cambridge University for his advice.

References

[1] C.L. Borst, W.N. Gill, and R.J. Gutmann, Chemical–Mechanical-

polishing of Low Dielectric Constant Polymers and Organosilicate

Glasses (Kluwer Academic Publishers, 2002).

[2] M.R. Oliver, Integration Issues with Cu CMP (Press release, Rodel

Inc, 2003).

[3] A.K. Sikder, P. Zantye, S. Thagella, A. Kumar, B.M. Vinogra-

dov, and N.V. Gitis, Delamination studies in Cu-Ultra low-k

stack. Proc. CMP-MIC Conference, 2003.

[4] R. Ganesan, T. Das, A.K. Sikder, and A. Kumar, Wavelet-based

identification of delamination defect in CMP (Cu-low-k) using

nonstationary acoustic emission signal. IEEE Trans. Semicon-

ductor Manufact., Vol. 16, No. 4, 2003.

[5] P. Zantye, A.K. Sikder, and A. Kumar, Investigation of the

interfacial adhesion and its correlation with chemical mechanical

polishing for various low-k and Cu-low k multi-layered thin films.

Proc. MRS spring meeting, 2004.

[6] S. Wang, G. Grover, C. Baker, J. Chamberlain, and C. Yu,

Advanced processing: CMP of Cu/low-k and Cu/ultralow-k

layers. Solid State Technology, 2001.

[7] S. Thagella, A.K. Sikder, and A. Kumar, J. Electrochem. Soc. 151

(2004).

[8] D.B. Ouma, D.S. Boning, J.E. Chung, W.G. Easter, V. Saxena, S.

Misra, and A. Crevasse, Characterization and modeling of oxide

chemical mechanical polishing using planarization length and

pattern density concepts. IEEE Trans. Semiconductor Manufact.,

Vol. 15, No. 2, 2002.

[9] N.P. Suh, The delamination theory of wear. Wear, 25, 1973.

[10] V. McGahay, Challenges in Cu/low-k integration for multilevel

BEOL wiring. NCCAVS Joint CMP/TF/PE User Group Meet-

ing, 2004.

[11] P. Zantye, A. Kumar and A.K. Sikder, Chemical mechanical

planarization for microelectronics applications. Material Science

and Engineering, R45, 2004.

[12] T. Yu, C.C. Yu, and M. Orlowski, A statistical polishing pad

model for chemical mechanical polishing. IEEE Proc. of IEDM,

1993.

[13] H.R. Le, M.P.F. Sutcliffe, and J.A. Williams, Tribol. Lett. 18(1)

2005.

[14] A. Goyal, J. Cheong, and S. Tadigadapa, J.Micromech.Microeng.

14 (2004).

[15] A. Villa, B. De Masi, A. Corigliano, A. Frangi, and C. Comi,

Mechanical characterization of epitaxial polysilicon in MEMS’’,

Computational Fluid and Solid Mechanics, 2003.

[16] M. Bhushan, R. Rouse, and J.E. Lukens, J. Electrochem. Soc.

142(11) (1995).

[17] O.G. Chekina, L.M. Keer, and H. Liang, J. Electrochem. Soc.

145(6) (1998).

[18] Y-R Jeng, P-Y Huang, and W-C Pan, J. Electrochem. Soc.

150(10) (2003).

[19] L. Shan, J. Levert, L. Meade, J. Tichy, and S. Danyluk, J. Tribol.

122 (2000).

[20] X. Jin, L.M. Keer, and Q. Wang, J. Electrochem. Soc. 152(1)

2005.

[21] Y. Xie, and B. Bhushan, Wear 200 (1996).

[22] J. Seok, C.P. Sukam, A.T. Kim, J.A. Tichy, and T.S. Cale, Wear

254 (2003).

[23] J.A. Greenwood and J.B.P. Williamson, The contact of nominally

flat surfaces. Proc. R. Soc., London, Ser. A. 295 (1966).

[24] H. Lu, B. Fookes, Y. Obeng, S. Machinski, and K.A. Richardson,

Mater. Characterization 49 (2002).

[25] A.S. Lawing, Proc. of the 7th International Chemical-Mechanical

Planarization for ULSI Mutilevel Interconnection Conference

(Santa Clara, 2002).

[26] Using Matlab, The MathWorks Inc., 1996.

[27] F. Liu, Chemical mechanical polishing of low-k material MPhil

thesis (Cambridge University, 2005).

[28] L. Cheng, Tribology and asperity contacts in chemical mechanical

polishing (MPhil thesis, Cambridge University, 2004).

[29] D.B. James, Pad properties during polishing and their effects on

polishing performance. CAMP 6th International CMP Symposium

(2001)).

[30] K.L. Johnson, Contact Mechanics (Cambridge University Press,

1985, pp. 411–416).

[31] A. Papoulis and S. U. Pillai, Probability, Random Variables and

Stochastic Processes, 4th edn. (McGraw-Hill, 2002, pp. 140).


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