stress induced delamination methods for the study of adhesion of pt thin films to si

Acta Materialia 52 (2004) 2081–2093

www.actamat-journals.com

Stress induced delamination methods for the study of adhesionof Pt thin films to Si

Alan Lee, B.M. Clemens, W.D. Nix *

Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305-2205, USA

Received 6 November 2003; received in revised form 6 November 2003; accepted 6 January 2004

Abstract

Adhesion of Pt films to Si substrates with a native oxide has been investigated using two methods of quantitative adhesion

characterization. The nanoindentation induced delamination method uses an impression to store compressive strain in an overlayer

film to induce delamination at the Pt/SiO2 interface. Likewise, the telephone cord delamination method involves sputtering a thick

compressively stressed overlayer onto the Pt/SiO2 films to induce telephone cord delamination patterns in the Pt film. Crack ex-

tension forces and interface toughnesses are calculated from the dimensions of the circular blister or the telephone cords using

currently available models. Focused ion beam (FIB) observations show that the nanoindentation method is difficult to implement

because of extensive crack formation in the substrate beneath the indentation, causing interface toughnesses from this test to be

gross overestimates. The telephone cord measurements, by comparison, give realistic interface toughnesses, allowing us to show that

decreasing the argon pressure during Pt sputtering significantly increases the adhesion of the films to the substrate.

� 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Nanoindentation; Adhesion; Pt sputtering; Mode mixity; Telephone cords; Blister; Delamination; Spalling

1. Introduction

The need for high capacitance densities in DRAM

and RF devices has prompted the search for high per-

mittivity dielectrics capable of storing large amounts of

charge. The development of these novel high-K dielec-trics is partially motivated by the need for on-chip ca-

pacitors in the next generation of processors. Planar

superparaelectric barium strontium titantate (BST) has

been identified as one likely candidate, with its extremely

high charge storage capacity, ranging from 80 to 150

FF/lm2 [1–4].

To implement this new material into production re-

quires a conductive electrode material with a high workfunction, which is needed to limit steady-state leakage

current across the capacitor [3]. In addition, the elec-

trode material must be stable against oxidation at pro-

* Corresponding author. Tel.: +1-650-725-2605; fax: +1-650-725-

4034.

E-mail address: [email protected] (W.D. Nix).

1359-6454/$30.00 � 2004 Acta Materialia Inc. Published by Elsevier Ltd. A

doi:10.1016/j.actamat.2004.01.003

cessing temperatures and must also be relatively smooth

upon deposition to avoid microstructural irregularities

during processing. Most important for this work, the

electrode must adhere well to the underlying diffusion

barriers and dielectric layers throughout processing.

Platinum has been singled out as a candidate electrodematerial that meets all of the above criteria. Here, we

investigate two methods of adhesion characterization,

the nanoindentation induced delamination method and

the telephone cord delamination method, examining their

limits and applying them to the Pt/SiO2 interface, a

model system.

2. Test methods

2.1. The nanoindentation induced delamination method

The nanoindentation induced delamination method

utilizes the Marshall and Evans [5] model wherein an

indentation creates a plastic impression on the film

surface. The residual strain in the plastic impression in

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2082 A. Lee et al. / Acta Materialia 52 (2004) 2081–2093

turn causes the film to buckle upwards to minimize the

strain energy, leaving a circular crack at the interface

beneath the indentation. The result is a circular blister

on the film as shown schematically in Fig. 1.

The Marshall and Evans model provides a relation-ship between the crack extension force for the interface

crack, G, and the observed circular delamination of ra-

dius, a, in the plane of the film at the interface. If the

residual compressive stress in the film plus the stress

associated with indentation is greater than the critical

stress required for buckling, then the film will buckle

from the interface and a ring crack will form in the in-

terface and expand until the driving force for crack ex-tension drops below a critical value. A blister with

radius a is then visible on the film. Using the Marshall

and Evans model, the observed buckle of radius a can

then be used to extract the critical crack extension force

sustainable by the interface.

The nanoindentation induced delamination method is

highly impractical for very thin films, especially ones

that are soft or have a very strong interface. The Mar-shall and Evans model was developed for a single film

on a substrate. The strain energy in the film is often too

small to induce delamination. To overcome this limita-

tion Gerberich and others [6–10] have deposited thick

overlayers capable of storing large amounts of strain

energy over the interface of interest. This allows for

deeper indentations, which create greater driving forces

for buckling. Adaptations such as the one by Kriese andGerberich [6] have allowed the Marshall and Evans

model, initially developed for monolithic films, to be

applied to multilayer systems.

We have adopted the overlayer system as a means of

increasing the driving force for delamination in both the

nanoindentation induced delamination and telephone cord

Fig. 1. Schematic diagram of indentation induced delamination. In-

dentation causes dilated plastic zone to form which drives buckling

and delamination.

delamination methods. The system under study is a

thin layer of Pt sputtered on Si with a native oxide, or

Pt/SiO2/Si. A thick molybdenum overlayer is then

sputtered onto the Pt. Since the overall thickness of the

Pt film is usually less than 1% of the thickness of the Mooverlayer, the system can be approximated as a single

layer film. This, in turn, means that the Marshall and

Evans model can be used instead of the more complex

multilayer treatment. In addition to molybdenum,

tungsten overlayers were also used to induce delamina-

tion in samples during telephone cord delamination

measurements. The tungsten overlayer thicknesses in

these cases accounted for about 95% of the total thick-ness of the Pt and overlayer, thus the bilayer can still be

reasonably approximated as a single film. Since sput-

tered tungsten overlayers store considerably more strain

energy than molybdenum overlayers, they were used

only on interfaces for which molybdenum overlayers

where not able to induce delamination. Tungsten films

grown on the weaker interfaces induce large-scale

spalling before comparatively thick overlayers can begrown. Thus tungsten overlayers were not used for weak

interfaces. The single film approximation would not be

valid for the very thin overlayers that would be needed

to produce controlled delamination for weak interfaces.

The Marshall and Evans relationship used to calcu-

late the crack extension force, G, is given by

G¼ ð1� mÞhE

ð1(

� aÞr2R þr2

0

ð1þ mÞ2

"�ð1� aÞ 1

�� rc

r0

�2#)

;

ð1Þ

where

r0 ¼bEV0a2h

; rc ¼ cEðh=aÞ2; b ¼ 1

2pð1� mÞ ;

c ¼ 14:68

12ð1� m2Þ : ð2Þ

Here, a is 0.383 for buckled films and 1 for unbuckled

films, a is the crack radius, h is the film thickness, V0 is

the total plastic volume displaced by the indenter, rR is

the residual stress in the film and all of the other termshave their usual meaning.

2.2. The telephone cord delamination method

Telephone cord delaminations are typically found in

thin-film systems with weak interfaces and very high

compressive stresses in the films [11–13]. Like nanoin-

dentation induced delamination, the film buckles fromthe interface to relieve strain energy present in the highly

stressed film. In this case, however, the stress in the film

itself is enough to initiate buckling without the need for

the extra driving force created by nanoindentation. In

the plane of the film, the delaminations are roughly si-

nusoidal in appearance and resemble telephone cords, as

Fig. 2. Telephone cord delamination for Pt grown at an Ar pressure of

6 mTorr with a residually stressed Mo overlayer, 2.5 lm in thickness.

The pie slice shows the portion of the delamination that can be

modeled using the pinned circular blister model.

A. Lee et al. / Acta Materialia 52 (2004) 2081–2093 2083

can be seen in Fig. 2. Once these telephone cord blisters

form, interface toughnesses can then be calculated bymeasuring the dimensions of the blister and using re-

cently developed models relating the crack extension

force to the width of the telephone cord.

Early models of the mechanics of telephone cord

delaminations were developed by Hutchinson and Suo

[12]. They modeled the rare straight-sided blister by

treating it as a two-dimensional clamped Euler column

and coupling it with the solution for an edge crack on aninfinitely deep substrate. The crack extension force re-

sulting from their model is given by

G ¼ G0 1

�� rrc

�1

�þ 3

rc

r

�; ð3Þ

where

G0 ¼1� t2f� �

h

2Ef

� �r2; ð4Þ

and

rc ¼p2

12

Ef

1� t2f

� �hb

� �2

: ð5Þ

Here, G0 is the strain energy per unit area in the film

under plane strain conditions, rc is the classical buckling

stress of a clamped wide plate, r is the compressive stress

in the film, Ef is the elastic modulus and tf is Poisson�sratio for the film, h is the film thickness, and b is the halfwidth of the delamination.

This model applies to straight-sided blisters. How-

ever, most blisters are sinusoidal in appearance, resem-

bling the shape of a telephone cord. Some have simply

measured the width of these sinusoidal telephone cords

at a straight portion of the cord and used the straight-

sided analysis to determine the interface toughnesses

[27]. The accuracy of this method is uncertain since a

curved crack front differs from a straight one in terms of

crack extension force and mode mixity.

Recently, Moon et al. [13] have used a pinned circular

blister analysis by Hutchinson and Suo [12] to model

wavy telephone cords. As can be seen in Fig. 2, thesections of a wavy telephone cord resemble slices of a

circular blister pinned at its center. If the telephone cord

under the shaded area were rotated 360�, it would span a

full circular blister pinned at its center. Modeling of the

problem involves numerically integrating the non-linear,

axi-symmetric von Karman equations with the appro-

priate clamped boundary conditions and then using the

solutions to solve for the energy release rate and phaseangle. In practice, plots of energy release rates vs. film

properties and telephone cord width are used to deter-

mine numerical values of G.The advantage of this method over the previous

straight-sided method is that it takes into consideration

the curved edges of the blister. Assuming that the blister

can be modeled accurately in this way provides for a

very simple way of obtaining the energy release rate atthe interface when wavy telephone cords are present.

Both of the previously discussed blister models give

the strain energy release rate of the film at the film/

substrate interface as a function of the film properties,

stress, and blister dimensions. We have also used

Hutchinson and Suo�s analysis to estimate the Mode I

and Mode II interface toughnesses for the straight-sided

and wavy telephone cord blisters once the Gs are known[12]. The analysis is well-described by Moon et al. [13].

By using the plots of phase angle, w, vs. the ratio of

compressive stress in the film to the critical buckling

stress, r=rc, for various types of delaminations (shown

in Moon et al. as Fig. 10(a)), the mode mixity of the

crack front of the blisters can be determined through

telephone cord blister measurements and film parame-

ters. Furthermore, using the mode mixity-dependentinterface toughness relation given by Hutchinson and

Suo as

CcðwÞ ¼ CIc 1�

þ tan2ðð1� kÞwÞ�; ð6Þ

and setting the crack extension force for the delami-

nating film equal to the interface toughness [12]

G ¼ CcðwÞ; ð7Þthe Mode I toughness, CIc for the interface can be esti-

mated. Here, k is a mode-sensitivity parameter which is

commonly set to 0.25. It determines the ratio CIIc=CIc at

the crack front. Interfaces with moderate mode depen-dence are found to be characterized by k < 0:30 [14].

Once the Mode I toughness, CIc, and phase angle, w, areknown, the Mode II toughness, CIIc, can be calculated

[12].

It is important to emphasize here that the interface

toughness actually changes as the blister grows because

the mode mixity changes. This is a result of the changing


phase angle of the crack front as the delamination grows

in size. Interfaces are much weaker under Mode I

loading than they are under Mode II loading. This

phenomenon is usually attributed to shielding of the

crack tip by asperities behind the crack front, as well asto changes in the plasticity of the crack tip itself as a

function of loading [26]. As the size of a blister grows,

the phase angle approaches )90� and the crack front

takes on an increasing Mode II component [13]. Since

the Mode II toughness is greater than the Mode I

toughness, the toughness of the interface changes in

such a way that the interface becomes effectively tougher

as the blister grows wider.The critical crack growth criteria of Eq. (7) shows

that a crack will continue to grow as long as the strain

energy release rate for the crack is greater than the

toughness of the interface at that particular load-

ing condition. In order to simplify the presentation of

Eq. (7), it is common to divide both sides by ð1þtan2ðð1� kÞwÞÞ so that the mode dependence is buried

into the crack extension force and the interface tough-ness in pure Mode I loading becomes the criteria for

crack advancement. This new crack extension force is

often referred to as a mode adjusted crack extension

force. Fig. 3 shows a qualitative plot of mode adjusted

crack extension force vs. blister width, b, similar to the

one given by Hutchinson and Suo [12]. Note that the

normalized stress, r=rc, is proportional to the square of

the blister radius, r, for a pinned blister and the squareof the blister width, b, for a straight-sided blister, so as

the blister size increases, so does the normalized stress.

Shown in the figure are crack extension curves for three

films with different residual compressive stresses and

strain energy. Assume that the critical interface tough-

ness in pure Mode I loading of all three films is identi-

cally CIc. In the case of the film with the lowest strain

energy, a delamination will never form or grow since theinterface toughness is always greater than the strain

Fig. 3. Mode adjusted crack extension force vs. delamination width.

energy release rate in the film. Moving to a higher strain

energy curve produces strain energies that exceed the

critical interface toughness from b1 to b2. This shows

that if a blister the size of b1 is produced in the film, it

will continue to grow until it reaches the dimension b2since the strain energy release rate of the film is greater

than that which can be supported by the interface. At b2the crack will stop growing. Experimentally, the initial

defect of size b1 can be produced by scratching the

surface of the film. In this way, telephone cords can be

initiated in an otherwise smooth film which has not yet

met the pre-existing flaw size criterion. As the strain

energy in the film is increased even further, the pre-existing flaw size necessary for crack growth decreases to

b3. Once the crack starts to grow, it also grows to a

larger size b4 before it stops.

Though many other quantitative techniques have

been developed to quantify adhesion, the simplicity of

the nanoindentation induced and telephone cord del-

aminations makes these two techniques particularly

attractive. In principle, there are no difficult samplepreparation steps, large-scale plasticity effects, or addi-

tional thermal processing steps that may affect the ad-

hesion characteristics of the system involved for either

method. The only sample preparation required is the

sputtering of a strong, compressively stressed refractory

metal film onto the sample surface. Either technique

might be useful for characterizing the adhesion of thin

films in device structures. Thus, we are assessing theirviability in this paper.

3. Experimental

All films were grown on 3 in. (1 0 0) orientated silicon

wafers. The films consisted of a thin layer of platinum

on the native silicon oxide and a thick capping layer ofcompressively stressed molybdenum or tungsten to in-

crease the driving force for delamination. The samples

were sputter deposited in a sputter deposition chamber

located in the Vapor Phase Synthesis Laboratory of the

Geballe Laboratory for Advanced Materials at Stanford

University. The chamber is a UHV chamber equipped

with four planar dc magnetron sputtering guns. Argon

was the only sputtering gas used for the system. All Mooverlayers were deposited at 3 mTorr of Ar. That was

the lowest pressure of Ar which produced a stable

plasma in the chamber during Mo deposition. Low Ar

pressures during sputtering are known to create films

with large compressive stresses. At lower pressures, the

mean free path of the reflected argon neutrals are higher

so that they bombard the substrate with higher energies

[15]. This atomic peening mechanism causes depositedatoms to be implanted deeper into the film, resulting in

compressive stresses [16–18]. Furthermore, we were able

to increase the compressive stresses grown in the over-


layers slightly by varying the background pressure dur-

ing Mo deposition. As a result, the Mo overlayers grown

maximize the driving force for delamination.

Tungsten overlayers were grown at 3 and 6 mTorr of

Ar pressure. Both Ar sputtering pressures, however,produced comparable compressive stresses. These were

considerably higher than the stresses produced in Mo

overlayers.

In addition to generating compressive stresses, atomic

peening is also expected to have some effect on the ad-

hesive properties of the film. In particular, we have

found that interface adhesion of platinum films grown

on native silicon oxide through sputtering can be con-trolled by changing the argon pressure during deposi-

tion. Lower deposition pressures are associated with

greater energy of reflected neutral and depositing species

due to decreased scattering during transit from the tar-

get to the substrate. This energetic bombardment during

the initial stages of growth can affect the physical and

chemical nature of the interface. For example, greater

intermixing and removal of loosely bound impuritiesmight be expected at lower pressures. This could lead to

better adhesion for films grown at low Ar pressures. For

this reason, Pt layers on native silicon oxide were grown

at various Ar pressures. Indeed, we have found that the

subsequent properties of the interface range from well

adhered for lower argon pressures to very weak for

higher pressures.

All rates of deposition, and hence the thicknesses ofthe overlayers, were determined by depositing a very

thin film for a given amount of time and then using low

angle X-ray diffraction to determine its thickness.

The silicon wafers were baked in the chamber at 130–

170 �C for 30 min before deposition to ensure a clean

and dry interface. Platinum layers 16 nm in thickness

were then sputtered at various Ar pressures ranging

from 3 to 15 mTorr. Complete coverage of Pt on Si hasbeen shown to occur at a Pt thickness of around 3.2 nm

[19]. Profilometer measurements, as well as sputtering

models, have also shown that there is a 53% variation in

the thickness of the film due to the distribution of the

sputtering flux from the target [20]. One hundred and

sixty angstroms of Pt is therefore more than enough to

ensure that the Pt fully covers the substrate at all places

and thus controls adhesion. Finally, thick overlayers ofmolybdenum or tungsten were deposited on every

sample at an argon pressure of 3 mTorr for Mo over-

layers and 3 or 6 mTorr for W overlayers without re-

moving the sample from high vacuum after the platinum

layers were grown.

The average stresses of all films were measured using

wafer curvature [21–23]. The curvature of each individ-

ual wafer was measured before and after deposition. Thechange in curvature from the resultant force exerted by

the deposited film as well as its thickness was then used

to calculate the average biaxial stress in the film. Due to

the non-uniform flux from the target in the chamber,

corrections to film thicknesses were made to account for

the radial variation in film thickness in the 3 in. wafers.

As a result, an area-averaged film thickness was used for

all wafer curvature stress calculations [24].All nanoindentation samples were cut into smaller

pieces and indented with the NANO XPe nanoindenter

manufactured by Nano Instruments, Inc. A Berkovich

diamond tip was used for indentation. Indentations were

then imaged under AFM to characterize the buckling

radius and other parameters such as the pileup height.

Several of these samples were also cut and imaged under

a focused ion beam at Advanced Micro Devices Inc., inorder to study the delamination occurring at the film/

substrate interface.

Telephone cord delaminations were typically ob-

served to form after the removal of the sample from the

deposition chamber. Most wafers were left intact and

blisters were imaged with an optical microscope. Due to

the differing optical properties between the SiO2 and Pt,

a visual inspection was sufficient to determine whetherdelaminations took place at the Pt/SiO2 or Pt/metal in-

terface. In all cases, telephone cords caused delamina-

tion between the Pt/SiO2 interface.

4. Results and discussion

4.1. Nanoindentation induced delamination

Nanoindentation induced delamination was used in this

study to characterize the toughness of the Pt/SiO2 in-

terface. Samples were made with molybdenum overlay-

ers typically 2 lm in thickness and indentations were

made to various depths.

The quantitative analysis developed by Marshall and

Evans [5] for extracting G from indentation experimentsrequires that the film form a circular buckle at the in-

terface directly beneath the indentation impression.

Atomic force microscopy images taken from indentation

experiments initially suggested a mode of delamination

where the film is neatly debonded from the substrate.

Fig. 4 shows two profiles of indentations obtained from

AFM images. The first profile shows an indentation

which does not exhibit buckling. As can be seen, mate-rial pileup occurs along the sides of the triangular Ber-

kovich impression but not at the corners where tensile

stresses typically arise in the film. The second profile

shows an indentation in which a noticeable amount of

material is present at the corners of the impression

where considerable pileup should not occur. This is a

strong indication that buckling has occurred. Using

these AFM images, the radii of the buckled circularblisters caused by the indentation and residual stresses in

the film were measured and the crack extension force

was calculated using the Marshall and Evans model.

Fig. 4. Cross-section of indentations taken with AFM. The top profile shows no signs of buckling while the bottom profile shows large vertical

displacements where buckling should occur. Right image shows AFM view of indentation after buckling. Black line shows where profiles are taken.


Table 1 shows the buckled radii and computed Gs for 2lm thick molybdenum films grown with Pt sputtered at

3 and 6 mTorr of argon pressure. The delaminated zone

is larger for the 6 mTorr interface, leading to the con-

clusion that the Pt interface produced at 6 mTorr of

argon is weaker than that produced with 3 mTorr argon,as expected.

The interface toughnesses, G, extracted from the

model are, however, unrealistically high for both films,

as seen on Table 1. No amount of error in measurement

could possibly account for these unusually high values.

As shown below, telephone cord measurements on

similar films with Pt layers deposited at 6 mTorr Ar

pressure show crack extension forces which are 15–30times less. Though considerably lower, the telephone

cord measurements are clearly closer to the real tough-

nesses. The observation of spontaneous blistering was

a clear sign of weak interfaces with low interface

toughnesses.

In order to investigate the unusually high Gs obtainedfrom the Marshall and Evans model, focused ion beam

(FIB) images were taken to assess the condition of theinterfaces after indentation. Fig. 5(a) shows an image of

an indentation cross-section for a film with Pt deposited

at 3 mTorr of argon pressure. The thick overlayer on top

of the silicon substrate is the molybdenum film. The Pt

layer sandwiched between the overlayer and the sub-

strate is too thin to see in these images. Substrate

Table 1

Buckling radius and corresponding G values extracted from the Marshall an

Ar pressure during

Pt sputtering (mTorr)

Overlayer

stress (GPa)Indentation depth (2.2 lm

Buckling radius

(lm)

App

toug

3 )1.1 32.7 195

6 )0.9 40.5 84

cracking is very apparent beneath the indentation. Lat-

eral and cone cracks, in particular, form readily in the

substrate. Lateral cracks run parallel to the surface and

appear directly beneath the indentation impression.

These cracks most likely formed during unloading and

are commonly observed with elastic–plastic indentations[25]. They represent a serious problem if the lateral

cracking is so pronounced that it allows a large amount

of substrate material underneath the indentation to

separate from the bulk of the substrate and remain at-

tached to the film. When this happens, the indentation

results become very difficult to interpret since the degree

of cracking in the substrate material is unpredictable,

allowing some overlayers to buckle away from thesubstrate while pinning others completely. Moreover,

the bending stiffness of the overlayer changes depending

on how much substrate material is still attached to the

overlayer. In this case, the stress distribution in the

overlayer becomes much more complicated and no

longer fits the assumptions of the Marshall and Evans

model.

Conical cracks also present a major problem. Conecracks typically form during loading of brittle materials

with very dull indenter tips [25]. They initiate as a ring

around the indentation site and propagate downwards

as shown in the FIB images. Complications with the

Marshall and Evans model arise when the cone cracks

cause the interface crack to be deflected into the sub-

d Evans model

) Indentation depth (3.0 lm)

arent interface

hness (J/m2)

Buckling radius

(lm)

Apparent interface

toughness (J/m2)

46.9 190

54.4 106

Fig. 6. (a) Indentation, nominally 2.2 lm deep, on a Mo overlayer on a

Pt film grown at a Ar pressure of 3 mTorr, showing neither substrate

cracking nor interface delamination. (b) Indentation, nominally 2.2 lmdeep, on a Mo overlayer on a Pt film grown at an Ar pressure of

6 mTorr, showing extensive interface delamination.

Fig. 5. (a) Indentation, nominally 3 lm deep, on a Mo overlayer on a

Pt film grown at an Ar pressure of 3 mTorr, showing extensive sub-

strate cracking. Lateral cracks run parallel to the surface directly under

the impression and cone cracks form at the edge of the impression. (b)

Indentation, nominally 2.4 lm deep, on a Mo overlayer on a Pt film

grown at an Ar pressure of 6 mTorr, showing similar substrate

cracking. Extensive interface delamination indicates weaker interface

adhesion compared to (a).


strate. Though the Berkovich indenter is usually not dull

enough to induce noticeable conical cracking in silicon,

the presence of the Mo overlayer, with an approximate

hardness of 13 GPa, has a ‘‘tip blunting’’ effect which

changes the stress field in the substrate and hence causes

cone cracks to form in the Si substrate. FEM modelingusing the ABAQUS FEM package shows a considerable

difference between the stress fields formed at the silicon

surface when a thick molybdenum overlayer is present,

compared to indentation without an overlayer. Fur-

thermore, the simulations show that for certain film-

substrate systems, tensile stresses form in the substrate

during indentation at the site where conical cracks first

nucleate as ring cracks. This is consistent with the for-

mation of conical cracks in general and why they presentproblems in the nanoindentation induced delamination

experiments.

The difficulties associated with substrate cracking

invalidates the assumptions of the Marshall and Evans

model and further complicates the interpretation of

experimental results. Considering the FIB images in

Figs. 5 and 6, it would be tempting to draw conclusions

about the qualitative differences of interface toughness


between Pt films sputtered at different argon pressures.

Intuitively, despite cracking, weaker interfaces are ex-

pected to delaminate more readily and show a larger

delaminated zone at the interface in question. The 2200

nm deep indentations on the Pt films deposited at 3 and6 mTorr show that buckling occurs only in the samples

deposited at 6 mTorr, as seen in Figs. 6(a) and (b), in-

dicating that the interface may be weaker under those

conditions. Likewise, comparisons at larger indentation

depths of 3000 nm show that the delamination zone

between the film and the substrate for films deposited at

6 mTorr is larger and more pronounced than that for

films deposited at 3 mTorr, as seen in Figs. 5(a) and (b).Since conical and lateral cracks are present in most of

the images, however, the previously mentioned compli-

cations make it impossible to conclude whether the

3 mTorr Pt interface actually adheres better than the

6 mTorr Pt interface.

Although the hard Mo overlayer can be blamed for

the extensive substrate cracking, that layer is necessary

in order to perform nanoindentation induced delamina-

tion experiments. Without the presence of the elastic

strain stored into the hard overlayer by nanoindenta-

tion, there would not be enough driving force to initiate

buckling in the first place. Soft overlayers might reduce

the ‘‘tip blunting’’ effect caused by hard overlayers but

they might not store enough strain energy to cause de-

lamination. Also, since a certain amount of material

must be displaced in order to provide the driving forcefor delamination, using very steep sided indenter tips to

limit cone cracks would probably not work. It is these

competing problems that ultimately limit the usefulness

of nanoindentation induced delamination, particularly for

systems involving hard overlayers on brittle substrates.

4.2. Telephone cord delamination

4.2.1. Controlling driving force and stress measurements

The telephone cord delamination method of adhesion

testing is useful whenever telephone cords spontane-

ously form on a film surface. This occurs only if the

strain energy stored in the film is large relative to the

adhesion of the film to the substrate. If the strain energy

is too large, however, the film will simply spall without

forming telephone cords. Therefore in order to charac-terize films of varying adhesion, it is important to be

able to control the strain energy stored in the film.

The strain energy per unit area of a film, as shown in

Eq. (4) for the case of plane strain, grows linearly with

increasing film thickness but is proportional to the

square of the stress. The stored energy can be controlled

by controlling the thickness and varying the stress in the

overlayer through different deposition conditions. Thisis not difficult to do when the adhesion energies of the

films in question are as low as 3 J/m2 or less. When

adhesion is good, however, it becomes difficult to store

enough energy into the film to cause spontaneous tele-

phone cord blisters to form.

Fig. 7(a) shows the variation in compressive stress as

a function of nominal film thickness for molybdenum

and tungsten thin films, sputtered at 3 mTorr argonpressure unless otherwise noted. As discussed previ-

ously, the background vacuum pressure was adjusted to

10�7 Torr during Mo deposition in order to promote

more highly stressed films. The relationship between film

thickness and stress is very repeatable and predictable.

The linear relationship shows that for every 1000 nm of

molybdenum grown, the average stress in the overlayer

drops by about 300 MPa in this particular range of filmthickness. Likewise, the stress in the tungsten drops by

about 300 MPa for every 100 nm grown for thicknesses

between 100 and 220 nm. The importance of these re-

lationships is that they allow one to estimate the stress in

the film when wafer curvature measurements are not

possible. Specifically, this method was used to find the

stress in the outer parts of the films when large scale

spalling occurred at the center of the wafers.As discussed above, depositions in the chamber show

up to a 53% variation in thickness from the center of a

3 in. wafer to the edge. Since thinner films support

higher stresses, it was assumed that the stress in any

section of the wafer is the same as the average stress in a

uniform film grown to the same average thickness. Ex-

periments support this assumption, as shown below.

Fig. 7(b) shows the same sets of data points as inFig. 7(a) plotted as G0, or the stored energy in the film

vs. film thickness, where once again

G0 ¼ð1� t2Þhr2

2E: ð4Þ

The trend shows the underlying difficulty associated

with delaminating films with strong interfaces. Because

the film stress decreases with increasing thickness and

because the stored energy depends on the square of the

stress, simply growing thicker films eventually does notresult in higher driving forces for delamination. Mo-

lybdenum films grown to thicknesses of 2500 nm have

driving forces comparable to films grown to thicknesses

of 1500 nm. From the graphs in Fig. 7(b), the plateau in

stored energy appears to start at a Mo thickness of

about 1500 nm. Tungsten films were grown to only small

thicknesses so that the plateau in stored energy has not

been experimentally determined. Assuming that thestress vs. thickness relationship for W films is linear, a

plateau would appear at 3500 nm with 5.5 J/m2 of stored

energy. Experimentally, deviations from the expected

trend of stresses have produced higher driving forces for

several samples. Regardless, these results show an in-

herent limitation in the telephone cord method. The

upper limit of adhesion energies that can be measured

by this technique are dependent on how much com-pressive stress can be produced in the overlayer.

100 120 140 160 180 200 2203.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

Com

pres

sive

stre

ssin

film

(GP

a)

Nominal W film thickness (nm)

run a (6 mTorr)run b (3 mTorr)run c (6 mTorr)

500 1000 1500 2000 25000.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Com

pres

sive

stre

ssin

film

(GP

a)

Nominal Mo film thickness (nm)

run 1run 2run 3run 4

all at 3 mTorr

500 1000 1500 2000 25001.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

G0

,S

tore

dst

rain

ener

gy(J

/m2 )

Nominal Mo film thickness (nm)

run 1run 2run 3run 4

all at 3 mTorr

100 120 140 160 180 200 2201

2

3

4

5

6

7

G0

,S

tore

dst

rain

ener

gy(J

/m2 )

Nominal W film thickness (nm)

run a (6 mTorr)run b (3 mTorr)run c (6 mTorr)

(a) (b)

Fig. 7. (a) Residual compressive stress vs. nominal film thickness for Mo and W overlayers showing that the stress falls linearly with increasing film

thickness. (b) Computed elastic strain energy stored in the films as a function of overlayer thickness. The strain energy for Mo overlayers reaches a

plateau at an overlayer thickness of about 1500 nm.


For films in which the slope of stress vs. thickness is

large, the maximum driving force for delamination maynot occur at the center of the wafer where the film is

thickest. Fig. 8 shows plots of stress vs. thickness and

stored energy vs. thickness for two hypothetical films

with two different slopes (thickness-dependent stresses).

For the film with the smaller slope, the stored energy

increases with film thickness throughout the range of

film thicknesses. In this case, the highest stored energy

will occur at the center of the wafer. This is consistentwith our experiments, which show that spontaneous

telephone cord delamination and blistering usually be-

gin at the center of the wafer. For large slopes, however,

the maximum stored energy occurs away from the cen-

ter. As seen in Fig. 8(b), a steeper slope in the stress vs.

thickness plot results in a stored energy function with a

peak at an intermediate overlayer thickness. If these

overlayers are grown to thicknesses larger than the

thickness at which the stored energy peaks, then spon-taneous delamination will be more likely to occur away

from the center of the wafer. This has been observed in

several of the grown molybdenum films which are lar-

gely smooth except for several rings of telephone cord

blisters which circle the wafer halfway from the center to

the edge of the wafer, as seen in Fig. 9. These observa-

tions support the assumption that the compressive

stresses vary radially in the deposited overlayers.

4.2.2. Adhesion results

It was found that the adhesion of the interface in-

creased with decreasing argon pressure during Pt de-

position. Fig. 10(a) shows a plot of the critical crack

extension force for the Pt/SiO2 interface as a function of

Ar sputtering pressure during Pt deposition. Calculated

0 500 1000 1500 20000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Str

ess

(GP

a)

Nominal film thickness (nm)

film 1film 2

0 500 1000 1500 20000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

G0

,Sto

red

stra

inen

ergy

(J/m

2 )

Nominal film thickness (nm)

film 1film 2

(b)

(a)

Fig. 8. (a) Stress vs. film thickness for two hypothetical films 1 and 2,

for which the stress falls slightly and markedly, respectively, with in-

creasing film thickness. (b) Corresponding strain energy (per unit area)

for films 1 and 2 as a function of film thickness. The strain energy for

film 2 reaches a maximum at 750 nm; the strain energy in film 1 peaks

at a much larger film thickness.

Fig. 9. Telephone cord delaminations forming in a circular pattern on

a wafer with a Pt film grown at 12 mTorr of Ar with a 1 lm thick Mo

overlayer.


Gs using both the straight-sided and wavy telephone

cord models are shown. Fig. 10(b) shows a plot of the

critical crack extension force as well as computed ModeI and Mode II interface toughnesses for the wavy tele-

phone cord blisters. Table 2 shows relevant data and

film properties for each particular sample.

Each experimental data point is based on at least ten

different telephone cord sections. The dependence of

crack extension force on the observed variation in tele-

phone cord width, however, is very small. The standard

deviation of Gs is usually around 1% of G or less. Mostof the error lies in the uncertainty of the stress in the

film. Wafer curvature measurements give only an aver-

age stress in the film and even then, requires that the

exact film thicknesses be known. We estimate that there

is, at most, a 10% uncertainty in our wafer curvature

measurements. Error bars have been included, reflecting

the Gs obtained using the upper and lower stress limitsin the film.

Also, direct wafer curvature measurements were not

possible for the Pt films deposited at 10.5 and 15 mTorr

due to large scale spalling, so the stress was found by

extrapolation using the method previously discussed.

The trend of improved adhesion with decreasing Ar

sputtering pressure during Pt deposition is very appar-

ent. At high argon sputtering pressures of around 12–15mTorr, the Pt/SiO2 interfaces are so weak that the films

fail not only by telephone cord blisters, but also by

large-scale spalling. As the Ar pressure is decreased to

around 9 mTorr, the films still form telephone cord

blisters but no longer undergo spalling. At 6 mTorr and

below, the adhesion is sufficiently high that telephone

cord blisters are very rare and difficult to attain with

molybdenum overlayers, forcing the use of the higherstressed tungsten overlayers. The analysis from the

telephone cord measurements show that adhesion con-

tinues to improve as the Ar sputtering pressure during

Pt deposition is decreased from 6 to 3 mTorr. Previously

shown FIB images from nanoindentation experiments

were only able to qualitatively hint at this trend.

Interface toughnesses calculated from the straight

blister and pinned circular blister models are in verygood agreement. Theoretically, the wavy telephone cord

analysis should be more accurate since none of the

measured telephone cords were actually of the straight-

sided blister variety. Only the wavy telephone cord

analysis takes into account that the crack fronts of the

blisters are curved; the use of the straight-sided blister

model is simply an approximation. In general, straight

telephone cords occur in only a very narrow range of

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0

1

2

3

4

5

6

7

No DelaminationTelephone CordsSpalling

G0

,Sto

red

stra

inen

ergy

(J/m

2 )

Ar pressure during Pt deposition (mTorr)

Fig. 11. A plot of G0 vs. Pt deposition pressure for many samples. The

plot also indicates whether telephone cord delamination, spalling, or

no delamination occurred for each individual sample.

2 4 6 8 10 12 14 16

0

1

2

3

4

5

6

7

8

9

10

11

12

Ene

rgy/

Are

a(J

/m2 )


Gw

(pinned circular blister)G

s(straight-sided blister)

2 4 6 8 10 12 14 16

0

1

2

3

4

5

6

7

8

9

10

11

12

Ene

rgy/

Are

a(J

/m2 )


Gw

(pinned circular blister)G

Ic,w

GIIc,w

(b)

(a)

Fig. 10. (a) A plot if the fracture energy of the Pt/SiO2 interface as a

function of argon sputtering pressure during Pt deposition. Calculated

G values using both the straight-sided and wavy telephone cord models

are shown. (b) A plot of the fracture energy, Gw, Mode I and Mode II

interface toughnesses for the wavy telephone blisters.


film conditions and are therefore much rarer than their

wavy counterparts [13]. For our current experiments,

we think that the pinned circular blister model is moreaccurate.

Table 2

Important values for samples used to create Figs. 10(a) and (b)

Pt pressure

(mTorr)

Gw

(J/m2)

Standard

deviationw

Ww

(�)CIc;w

(J/m2)

C(

3 8.66 <0.01 )89.3 1.32 9

6 6.3 0.01 )84.5 1.26 8

9 4 0.06 )81.1 0.95 6

10.5 2.7 <0.01 )82.3 0.6 4

12 1.31 <0.01 )83.2 0.28 1

15 0.68 0.01 )86.7 0.12 0

All wavy telephone cord values are denoted by subscript w and straight

mixity of the straight telephone cord calculations are exclusively Mode II.

The Mode I and Mode II interface toughness curves

were calculated from the G curve for the wavy telephone

cord model using Hutchinson and Suo�s methodology

[12]. As expected, they follow the trend of the crack

extension force curve, increasing with decreasing depo-sition pressure. Interface toughness is known to be

highly dependent on the mode mixity of the loading at

the crack front [12]. Interfaces tend to be much weaker

in Mode I loading as compared to Mode II loading, as

previously mentioned. Table 2 shows the average cal-

culated mode mixities at the crack front of the sides of

the wavy telephone cords for each sample. The crack

fronts are predominately Mode II.It should be noted that if the straight-sided telephone

cord analysis were used, the Mode I toughness CIc,

would be underestimated since straight telephone cords

are almost exclusively Mode II at the sides. Also, since

the ratio CIIc=CIc > 1 and determined only by a mode

sensitivity parameter k, usually set to 0.25, underesti-

mating CIc results in an underestimate of the Mode II

toughness, CIIc and the overall adhesion of the film.

IIc;w

J/m2)

Gs

(J/m2)

Standard

deviations

Ws Blisters

measured

.24 6.61 0.01 )90 15

.82 5.01 0.02 )90 10

.65 3.6 0.04 )90 17

.2 2.22 0.013 )90 14

.96 1.07 <0.01 )90 21

.84 0.52 <0.01 )90 12

telephone cord values are denoted by subscript s. Note that the mode


For every sample that exhibited telephone cord de-

lamination, there were many others that did not due

to insufficient driving forces in the overlayer. Fig. 11

shows a plot of G0 vs. Pt deposition pressure for many

samples. The plot also indicates whether telephone cordblisters, spalling, or no delamination occurred for each

individual sample. This plot further emphasizes that

there is a threshold of strain energy in the overlayer that

must be produced before consistent delamination will

take place.

5. Concluding remarks

Two different methods for quantitative adhesion

measurements have been investigated. The nanoindenta-

tion induced delamination method is very simple and

straightforward but difficult to implement. Values for

adhesion obtained from these experiments on Pt/SiO2 are

out of line with expected toughnesses due to extensive

lateral and conical crack formation in the Si substratedirectly beneath the indentation site. Conical cracks are

troublesome because they deflect the interface crack into

the substrate, effectively stopping interface delamination.

Lateral cracks cause problems when they allow part of

the substrate to remain attached to the underside of the

overlayer after it has buckled. Though cone cracks are

associated with only blunt indenter tips, the hard mo-

lybdenum overlayer has a ‘‘tip blunting’’ effect on thestress fields of sharp Berkovich tips so that conical cracks

still form in the substrate. These issues make the nano-

indentation induced delamination method particularly

difficult to implement for this materials system.

Telephone cord delaminations are a more promising

means of quantifying adhesion of weak interfaces. The

data show that this technique can be used to extract

reasonable Pt/SiO2 adhesion values which show changesin adhesion due to differing processing conditions.

Sample preparation is also relatively simple compared to

many other existing techniques requiring additional

thermal treatments or complicated sample fabrication

steps. The biggest drawback to the telephone cord

method is the upper limit of measurable adhesion en-

ergies. Large compressive stresses must be present in the

overlayer in order to induce spontaneous delamination.For the case of molybdenum overlayers, the highest

attainable stress for a 2 lm film was slightly above 1

GPa. This allowed crack extension forces as large as 4.5

J/m2 to be measured. Using tungsten films, we have

extended the range of measureable crack extension for-

ces to 10 J/m2. Larger applicability of this method will

depend on finding and growing films capable of storing

higher compressive stresses in order to increase the totaldriving force for delamination.

Despite limitations of both methods, the data shows

that Pt adhesion on silicon wafers with a native oxide is

directly controllable by varying the argon sputtering

pressure during Pt film growth. Telephone cord mea-

surements show a steady increase in adhesion energies

from argon sputtering pressures of 15 mTorr down to 3

mTorr. Although nanoindentation experiments provedinconclusive, the telephone cord tests show that adhe-

sion continues to improve below 6 mTorr. We therefore

conclude that there is a steady increase of adhesion of

these films over the range of from 15 to 3 mTorr argon

sputtering pressures during Pt deposition, most likely

caused by a more diffuse Pt/SiO2 interface or chemical

changes at the Pt/SiO2 interface as a result of increased

atomic peening from the energetic argon neutrals cre-ated in the sputtering process.

Acknowledgements

The authors are indebted to Prof. P.C. McIntyre of

Stanford University for his support and encouragement

of this research and for his help with the manuscript. We

also thank Prof. John Hutchinson of Harvard for his

help with the mechanics of telephone cord blisters and

Dr. Neville Moody of Sandia National Laboratories for

his advice and assistance regarding interface adhesion

measurements. In addition, we gratefully acknowledgethe assistance of Jonnie Barragan of AMD in Sunny-

vale, CA for her help in providing the FIB images of

interface delamination and substrate cracking. Financial

support by the National Science Foundation under a

GOALI-FRG, DMR-0072134 is also gratefully

acknowledged.

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stress induced delamination methods for the study of adhesion of pt thin films to si

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