dislocation depletion in thin films

Dynamics of confined defects in metals:Mechanistic insights from atomistics

Kedarnath Kolluri, Rauf Gungor, Dimitrios Maroudas

Acknowledgments: Mayur Valipa, Miguel Amat

Outline•Motivation

• Confined interconnects in semiconductor materials

• Confined defects in pillars and nanowires

•Mechanical behavior of free-standing copper thin films

• stress-strain behavior of pre-strained thin films

• Mechanisms that lead to the observed behavior

• Comparing with other FCC metals

• Comparison motivated by mechanistic understanding of

copper thin films

Confined metallic systems in semiconductors

3D view of interconnects after removal of the ILD layers (www.ibm.com)

Cross-sectional view of the dual damascene structure (www.ibm.com)

Schematic of the strained SiGe p-channel heterostructure MOSFET

Silicon Nanowire Transistor (NIST Illustration)

http://www.ibm.com

http://www.ibm.com

http://www.ibm.com

http://www.ibm.com

Line defects in metals: Edge dislocation

138

Crystals with fcc lattice structures are generated by stacking close-packed layers

on top of one another in a fashion illustrated in Fig. A.6. Given a layer A, close packing

can be extended by stacking the next layer so that its atoms occupy B or C sites. Here

A, B, and C refer to the three possible layer positions in a projection normal to the close-

packed layers. The stacking sequence corresponding to an fcc crystal is

…ABCABCABCABC…, while that for a hcp crystal is …ABABABABA…. When a

partial dislocation is created in a fcc crystal, the fcc stacking sequence changes to the

hcp stacking sequence; the stacking sequence in the crystal with a stacking fault can be

…ABCABCACABCABC….

Figure A.6. Projection normal to the (111) plane showing the three types of stacking

layer positions A, B, and C. Various vectors in an fcc lattice also are shown.

Let us suppose that the close-packed layer shown in Fig. A.7 corresponds to the

bottom side of the glide plane of a dislocation, and that the atoms above the layer are

originally in sites such as the one denoted by (a). The passage of the perfect dislocation

with Burgers vector b = (a0/ 2)[101] from the bottom of the figure to the top results in

the atom originally at (a) being displaced to (c). Motion of the atom along the straight

path from (a) to (c) involves a large dilatation (assuming a hard-sphere model) normal

to the slip plane, and hence a larger misfit energy than does the motion along the path

138

Crystals with fcc lattice structures are generated by stacking close-packed layers

on top of one another in a fashion illustrated in Fig. A.6. Given a layer A, close packing

can be extended by stacking the next layer so that its atoms occupy B or C sites. Here

A, B, and C refer to the three possible layer positions in a projection normal to the close-

packed layers. The stacking sequence corresponding to an fcc crystal is

…ABCABCABCABC…, while that for a hcp crystal is …ABABABABA…. When a

partial dislocation is created in a fcc crystal, the fcc stacking sequence changes to the

hcp stacking sequence; the stacking sequence in the crystal with a stacking fault can be

…ABCABCACABCABC….

Figure A.6. Projection normal to the (111) plane showing the three types of stacking

layer positions A, B, and C. Various vectors in an fcc lattice also are shown.

Let us suppose that the close-packed layer shown in Fig. A.7 corresponds to the

bottom side of the glide plane of a dislocation, and that the atoms above the layer are

originally in sites such as the one denoted by (a). The passage of the perfect dislocation

with Burgers vector b = (a0/ 2)[101] from the bottom of the figure to the top results in

the atom originally at (a) being displaced to (c). Motion of the atom along the straight

path from (a) to (c) involves a large dilatation (assuming a hard-sphere model) normal

to the slip plane, and hence a larger misfit energy than does the motion along the path

Line defects in metals: Stacking faults

Theory of Dislocations, Hirth & Lothe

single crystal pillars were annealed at 300 °C to remove anyremaining defects. Figure 4 presents flow stresses of allaforementioned samples as well as the FIB-fabricatedsamples and a comparison to the axial stress correspondingto the theoretical shear strength calculated by Ogata et al.20

All data points represent the pillars which deformed homo-geneously during compression testing, as can be seen in Fig.2!b".

It is clear from the graph that the electroplated pillars,which were never subjected to the Ga+ ions, not only haveflow stresses higher than bulk gold but also exhibit a similarrise in strength as the diameter is reduced. It is also clear thatGa+ removal and pretest-annealing resulted in data that fallson the curve formed by the FIB pillars. This result leads us tobelieve that observed size effect is not linked to a specificfabrication technique. While some minimal Ga+ might be

FIG. 2. !a" Stress-strain behavior of #001$-oriented pillars: flow stresses increase significantly as the pillar diameter is reduced. !b" SEMimage of a compressed pillar after deformation. Slip lines in multiple orientations are clearly present and indicate a homogeneous shapechange.

FIG. 3. !a" Stage II work-hardening is clearly present in thestress vs strain curve for the largest pillar whose diameter is7.45 !m. !b" The lack of stage II work-hardening is evident in thestress vs strain curve for a small pillar whose diameter is 400 nm.

FIG. 4. Flow stress vs pillar diameter for all FIB, electroplated,annealed, and Ar plasma-treated pillars as compared to a range oftheoretical strengths and the yield strength of bulk gold.

NANOSCALE GOLD PILLARS STRENGTHENED THROUGH! PHYSICAL REVIEW B 73, 245410 !2006"

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Mechanical behavior of bulk

J. Greer et al. Phys. Rev. B. 73, 245410 (2006)

R. Madec et al., Phys. Rev. Lett. 89, 255508 (2002)http://www.geol.ucsb.edu

Au

http://www.geol.ucsb.edu/faculty/hacker/geo102C/lectures/dislocation2.jpg

http://www.geol.ucsb.edu/faculty/hacker/geo102C/lectures/dislocation2.jpg

Mechanical response is confined systems is differentsingle crystal pillars were annealed at 300 °C to remove anyremaining defects. Figure 4 presents flow stresses of allaforementioned samples as well as the FIB-fabricatedsamples and a comparison to the axial stress correspondingto the theoretical shear strength calculated by Ogata et al.20







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Au

single crystal pillars were annealed at 300 °C to remove anyremaining defects. Figure 4 presents flow stresses of allaforementioned samples as well as the FIB-fabricatedsamples and a comparison to the axial stress correspondingto the theoretical shear strength calculated by Ogata et al.20







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formation. Stress-strain curves of FIB pillars whose diam-eters range between 290 nm and 7450 nm as well as thestrength of bulk gold at 2% strain are presented in Fig. 2!a".Uniaxial loading in the #001$ direction, chosen for our ex-periments and corresponding to a high-symmetry orientation,would result in the activation of 12 different %111& / #011̄$ slipsystems, with the pillar deforming uniformly around its di-ameter as it is compressed. In this orientation, despite thepresence of the end constraints, the pillar remains centrally-loaded and preserves its cylindrical shape throughout the de-formation process.

Each curve represents a single test at a specific pillar di-

ameter, measured at approximately L /3 below the pillar top.The smallest pillar reaches a compressive stress of 800 MPaat 10% strain. While in some cases the initial stages of de-formation are not purely elastic due to the gradual onset ofyielding, the initial loading slopes of the well-aligned testsgive elastic moduli very close to the Young’s modulus ofgold in the #001$ direction, 43 GPa. The fully elastic unload-ing slopes closely match the expected value, as well.

Another important aspect of these stress-strain curves isthe lack of stage II work-hardening associated with the acti-vation of multiple slip systems in the course of deformationof single crystals. In a typical single crystal, the dislocationsfrom different active slip planes interact with each other andform sessile dislocations, creating a large number of barriersfor the movement of other dislocations, thereby requiringever-higher stresses with the increasing strain. A typicalwork-hardening slope is on the order of ! /20, where ! is theelastic shear modulus. This behavior is prevalent in the com-pression of the largest pillar whose diameter is a little over7 !m, as shown in Fig. 3!a".

Contrary to this, the stress-strain behavior observed hereagrees more with stage I-type deformation, or the “easyglide” section of a low-symmetry oriented single crystal de-formation curve. Moreover, a representative stress-straincurve in this work is composed of a number of discrete slipevents separated by elastic loading segments, while the over-all stress level remains nearly constant as the strain increasesas shown in Fig. 3!b". This suggests that the hardeningmechanism here is the opposite to that of conventionalstrain-hardening, with the elastic loading sections indicativeof the absence of dislocations rather than their multiplication.

One of the major concerns with the FIB fabrication tech-nique is the possibility of Ga+ ion implantation into thesample, and that this is the cause for the observed increase instrength. Several approaches were used to address this issue.First, Auger depth profiling analysis with subsequent surfacelayer removal was employed. The initial concentration of Gawas 1.7 at. % on top of the pillar and 0.8 at. % on its side.The “side” of the pillar here refers to the middle third of thespecimen since in that area the deformation is closest to be-ing homogeneous. The conformal surface layer was removedby etching the rotating pillar in low-energy Ar+ plasma.Depth profiling and surface etching were repeated to assessthe ever-decreasing concentration of Ga. The final etch stepresulted in the total removal of 5 nm from the pillar surface,reducing the overall Ga concentration by '50%, and thegallium-to-gold ratio from 0.079 to 0.016. The significantchange in gold-to-gallium ratio indicates that Ga ions werelocated near the surface rather than implanted into thesample. These cleaned pillars were subsequently tested incompression, which indicated that surface removal had littleeffect on strength. The full Auger analysis can be found inRef. 19!a".

To further investigate the possible effects of Ga+ ion im-plantation, we developed an alternative fabrication techniquebased on lithography/electroplating.18 The electroplated pil-lars were annealed at 300 °C before testing to establish acoarse grain size. While these pillars are polycrystalline, theycontain only 2–3 grains extending across the pillar width. Tocomplete the analysis of possible surface modification, some

FIG. 1. !a" A representative #001$-oriented gold pillar machinedin the FIB. Pillar diameter=290 nm, pillar height=1.2 !m. !b" Alarge pillar !7.45 !m diameter" and a small pillar !250 nmdiameter".

JULIA R. GREER AND WILLIAM D. NIX PHYSICAL REVIEW B 73, 245410 !2006"

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J. Greer et al. Phys. Rev. B. 73, 245410 (2006)Au

Mechanical behavior of a Ni nano-pillarLETTERS

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Figure 1 Two consecutive in situ TEM compression tests on a FIB microfabricated 160-nm-top-diameter Ni pillar with �111⇥ orientation. a, Dark-field TEM image ofthe pillar before the tests; note the high initial dislocation density. b, Dark-field TEM image of the same pillar after the first test; the pillar is now free of dislocations.c, Dark-field TEM image of the same pillar after the second test. d,e, Force versus displacement curve of the first (d) and second (e) test. f, Instantaneous stress versuscompressive displacement for the two tests; the apparent yield stress is similar for both tests. All dark-field images are shown in a g= [111̄] condition, zone axis(ZA)= [11̄0].

starting at ⇤170 nm (Fig. 1d) coincided with predominantly elasticbehaviour. Post-test, dark-field observation under multiple two-beam conditions confirmed that this test left behind a dislocation-free pillar (Fig. 1b).

The pronounced decrease in dislocation density during thenanocompression test provides direct experimental support for thedislocation starvation mechanism that has been hypothesized onthe basis of experiments10,11 and simulations17,20. Neither the surfaceoxide layer19 nor the FIB damage layer21 trapped dislocations insidethe pillar during deformation. Presumably, the driving force for theescape of dislocations within the pillars is a combination of theapplied stress and the image forces from the surface22. The formerwill activate or nucleate dislocations and the latter will assist thedislocations in moving towards the free surfaces of the crystal.

The extent to which both pre-existing and newly generateddislocations ran out of the pillar was unexpected, and presentedan opportunity to examine the strength of a dislocation-free pillar.Figure 1e shows the force–displacement curve of the second teston the same pillar. The mechanical response was predominantlyelastic for the initial ⇤20 nm. Discrete plasticity then occurred,demonstrated by a series of discontinuities in the curve. Afterthe compressive displacement reached ⇤140 nm, the load steadilydecreased over the next ⇤185 nm. The video of this test clearlyshowed that this steady decrease in force was due to buckling of thepillar. The load rise following this buckling (starting at ⇤325 nm)occurred as the punch came into contact with material at the baseof the pillar (Fig. 1c).

One advantage of in situ testing is that the instantaneouscontact diameter can be measured from the still frames extractedfrom the recorded movies (30 frames s�1). This makes it possibleto determine an instantaneous contact stress imposed on the pillar

(force divided by the instantaneous contact area), which is moreaccurate than a simple engineering stress (force divided by theinitial area of the top of the pillar), providing the assumption ofsymmetrical deformation holds true. For the test shown in Fig. 1,this assumption is reasonable, and the instantaneous stress versusthe compressive displacement for the two tests corresponding toFig. 1d and e are plotted together in Fig. 1f. Interestingly, despitethe approximately 15 orders of magnitude di�erence in startingdislocation density, the apparent yield stress achieved in both testsis quite similar. Therefore, the initial defects due to FIB processingdid not significantly a�ect the stress response of the pillar. Thissuggests that the deformation of the pillar is controlled instead bythe nucleation of dislocations and their propagation through thepillar. The low impact of initial microstructure on the stress–straincurve is probably related to the fact that defects created by ionbeams typically do not extend much beyond the penetration depthof the ions, which for 30 keV Ga+ in Ni is only 10–20 nm even forlarge incident angles23.

However, owing to the tapered geometry of the microfabricatedpillars, the stress throughout the pillars is not homogeneousand the simple analysis used for calculating the instantaneousstress does not fully capture the complexity of the situation. Arecent computational study has reported that a taper angle tothe sidewalls of microfabricated pillar structures can result in anoverestimation of the elastic modulus and the apparent yield stressduring a microcompression test24. Given that the microfabricatedpillar shown in Fig. 1 had a sidewall taper angle of ⇤4.5⇥, it isexpected that the top of the pillar experienced a larger imposedstress during compression, which might result in inhomogeneousplastic deformation localized at the top of the pillar. This is infact what happened and Fig. 1b shows a remnant of this localized

116 nature materials VOL 7 FEBRUARY 2008 www.nature.com/naturematerials

©!2008!Nature Publishing Group!

!

Z. Shan et al., Nature Materials 7, 115 (2007)









copper thin films

Free-standing film as a model for confined metals

x

εxx

εxx

εyy

z

y

εyy

How its done

• Analysis based on constant strain and dynamic deformation

molecular-dynamics (MD) simulations

13

CHAPTER 2

ATOMISTIC SIMULATION AND STRUCTURAL

CHARACTERIZATION METHODS

In this Chapter, we discuss several computational methods employed in this

thesis for the atomic-scale simulations of thin metallic films and semiconductor

heterostructures and for the analysis of the simulation results. In Sec. 2.2, we discuss

the interatomic potentials for metals and semiconductors that are used in the atomistic

simulations for the description of interatomic interactions. The numerical details of the

atomistic simulations are given in Sec. 2.3. The various techniques and computational

tools for structural characterization and computation of materials properties from the

atomistic simulations are presented in Sec. 2.4 and Sec. 2.5, respectively. The

limitations of molecular-dynamics simulations, in the context of our studies, are

discussed in Sec. 2.6.

2.1. Molecular-Dynamics Simulations and Interatomic

Potentials

Atomistic simulations are used to study the structure, energetics, and dynamics

of a collection of interacting atoms following classical mechanics. For a system

containing N atoms with positions {ri}i=1

N and velocities {!i= dr

i/ dt}

i=1

N , the total

Hamiltonian is given by

H({ri}i=1

N) = T+ U =

1

2m

i!i

2+ U({r

i}i=1

N)

i=1

n

" (2.1)

• Embedded-Atom-Method (EAM) potential

• Supercell size: up to 1.54 million atoms

• Film thickness varied from 4 nm to 10 nm

• Applied equi-biaxial tensile strain through cell size expansion:

– applied strain rate: 107 s-1 - 1011 s-1

Deformation in Cu thinfilm: PrestrainingDeformation of Cu thinfilm: Prestraining

A defect-free single crystal is first biaxial strained to 8%

Deformation in Cu thinfilm: Prestraining

Top view: Light blue are in stacking faultsDark blue are fcc atomsothers are at dislocations

Deformation in Cu thinfilm: Prestraining

Side view: dark blue are in stacking faultsothers are at dislocationsFCC atoms are not shown

Response of thin Cu film (! 4nm) to further strain

Strain rate 4 orders of magnitute lower than that during prestraining

Stage I : Near elastic response and depletion of 15% of dislocationsStage II : Easy-glide; dislocation annihilationStage III : Insufficient plastic flow; stress increasesStage III+: Nucleation of additional dislocations; material failure


Stage I : Near elastic response and depletion of 15% of dislocationsStage II : Easy-glide; dislocation annihilationStage III : Insufficient plastic flow; stress increasesStage III+: Nucleation of additional dislocations; material failure


Dislocation starvation and creation occurs in cyclesSuch cycles observed in experiments of fcc nanopillars









copper thin films

Dislocation-stacking fault interactions causeannihilation









copper thin films

Comparing behavior of metals with different propensity for formation of stacking faults

Factors considered in choosing model materials

• Stable stacking fault energy, ϒs

• Ratio of unstable to stable stacking-fault energy, ϒs/ϒu

• Ideal shear strength

ϒ/ϒ u

x/bp

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!/!

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!/!

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!/!

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!/!

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AlCuNi

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AlCu

Ni

Response of different prestrained films (! 4nm) tofurther strain

In stage II:Ni and Cu Constant stress and dislocations annihilateAl Stress increases monotonicallyAl Dislocations annihilate at half the rate35% more annihilation in Ni and Cu than in Al

Response of different prestrained films (! 4nm) tofurther strain

In stage II:In Ni and Cu, plastic strain decreases monotonicallyIn Al, plastic strain remains constantCritical plastic strain beyond which stress increases in every thinfilmIn Al, plastic strain never exceeds critical plastic strain

Dislocations annihilate by collinear interactions in Al

Dislocations with same Burgers vector but in different glide plane

Initial

Dislocations annihilate by collinear interactions in Al

Dislocations with same Burgers vector but in different glide plane

3% strain

Summary:

• Dislocation interactions with stacking faults (SF) play an important role

• SF aid cross-slip and increase dislocation annihilation rate

• Dislocation annihilation occurs without SF as well, only much less

dislocation depletion in thin films

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