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Physical mechanisms of residual stress in metallic thin

films- A review of the literature -

February 19th, 2008Felix Lu

Applied Quantum Technologies / Duke University

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Outline

• Stresses & Strains• Residual stresses• Thin film formation• Growth modes• Mechanisms of intrinsic stress• Effect of sputtering

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Stresses & Strains

• Stress (σ) = force/area– Typically in Dynes/cm2, where 1 dyne =

10-5 N or 1 g·cm/s2

• Strain (ε) = (∆ length)/length (%)

σ = Eε, where E is Young’s modulus

Definitions

http://matthieu.lagouge.free.fr/phd_project/extractor.html

Unreleased structure Released structure with stress Thermally actuated structure

σ

εPlastic deformation

Elastic region Ultimate strength

Yield strength

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Stresses & Strains in MEMS structures

• Thin film stresses ~/> Yield strengthor ultimate strength

Approach to analyzing films

σf = 1

6R

Es ds2

(1-νs) df

Stoney equation for calculating interfacial stress in a plate

σf = stress, R = radius of curvature, Es = Young’s modulus, ds = substrate thickness, df = film thickness, νs = Poisson’s ratio of substrate

ds

df

Esνs

R

These surfaces stretched

This particular form of the Stoney equation assumes that film thickness << substrate thickness

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Types of residual stress

Extrinsic stress : due to post-deposition processing or external influences – Thermal property differences

– Impurity contamination

Intrinsic stress : stress in the as-deposited film– Caused by microstructure of the film

• Function of process parameters

Residual stress

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Origins of extrinsic stress

• Thermal stress –– deposition T ≠ measurement T

• Adsorption of polar molecules within porous structure of film. Polar molecules interact with each other which introduces extra forces.

Extrinsic stress

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Thin film formation

• Thermodynamics � surface free energies arguments…• But deposition process strongly influenced by kinetics

parameters, defects, … which determine when and how nucleation takes place…

� not in thermodynamic equilibrium• Basically…

– Film atoms do not wet the substrate surface � Volmer-Weber growth mode

– Film atoms wet the substrate surface� Frank-Van der Merwe growth mode

– Other cases where it is in between (mixed mode)…� Stranski-Krastanov growth mode

Materials Science

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Thin film formation

• Physical vapor deposition (PVD) of polycrystalline thin films– Evaporation– Sputtering

• Typically follow Volmer-Weber growth patterns for lower substrate temperatures

• Epitaxial growth typically follows Frank-van der Merwe growth mode.

And hybrids and variants

(Wikipedia)

Thermal evaporation

Sputtered atom

s ~5-40 eV

1,2E

vaporated atoms

~0.1 eV

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Volmer-Weber growth

Materials Science

After Koch (1994)

TEM of Ag films deposited in UHV on MgF2 coated glass substrates

Film becomes continuous (percolation or network stage3)

After C.V. Thompson (2004)

A simple polycrystalline grain structure

Defects, surface reconstruction, impurities affect orientation of nuclei 3

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Percolation

• delayed percolation � larger grains• higher nucleation densities

�grains are smaller � higher areal coverage

Control of percolation thickness important for applications:- Near percolation thickness, small changes in composition, bias, temperature

� large changes in electrical conductivity & optical transparency2

Thinner percolation thickness

Increase deposition rate

Lower substrate temperature

Plasma treatment of substrate surface

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Volmer-Weber mode characteristics

• Non-equlibrium supersaturation

• Crystallite does not maintain equilibrium shape (with crystal facets) due to kinetic reasons

• At percolation, film mostly continuous• Film thickness not increased until most channels

are filled – (Ostwald ripening or similar)

• If grain size preserved �columnar growth, otherwise, increase in lateral size of grains due to recrystallization

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Frank-van der Merwe and Stranski-Krastanov mode characteristics

• Frank-van der Merwe mode– Basically similar to Volmer-Weber mode

– “islands” are 2-D instead of 3-D– Goes through network stage, fills in remaining

channels and then forms continuous layer before growing next layer.

• Stranski-Krastanov mode– Mixed modes due to extrinsic factors

• Misfit stress, interfacial alloy or compound, etc.

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Mechanisms of intrinsic stress in Volmer Weber growth mode

Small angle grain boundaries• grains of differing orientations laterally touch.• areas of reduced density � grain boundaries.

• interatomic forces try to close gap � stretch grains �tensile stress

• tensile stress ~ grain boundary area ~ 1/(grain size)

• Tensile stress larger for fine grained films.

Intrinsic stress

After Koch (1994)

Domain walls (special type of grain boundary)

• presumed to be due to weak film/substrate adhesion

• islands grow with same orientation since not constrained by substrate

• atoms that fill the gaps between islands form the most bonds at the deepest part of the gap � higher density of atoms in gaps � compressive stress

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Mechanisms of intrinsic stress in Volmer Weber growth mode

Recrystallization processes• self diffusion allows reorganization of

disordered areas• grains become larger (no new material added)• tension increases a small amount as grain

boundaries are closed3,7

• due to smaller grain boundary area, as the grain boundaries shrink, the tension between surviving grain boundaries tends to increase.

Intrinsic stress

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Mechanisms of intrinsic stress in Volmer Weber growth mode

Capillarity stress

See Koch paper for more details and references on lattice expansion

Lattice expansion mechanism

Only seen if adhesion and/or compression is strong Substrate lattice spacing

Growing dropletLattice expands as drop grows

Grains press against each other creating compressionWeak adhesion allows gliding to relieve strain –until they contact each other…

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Mechanisms of intrinsic stress in Volmer Weber growth mode

• Impurities– Mostly oxygen and water– High dep rate and good vacuum to maintain “pure”

film, especially for more reactive elements.

• misfit stress– Lattice mismatch in epitaxy, limits film thickness if a

pseudomorphic interface is desired

• solid state reactions and/or interdiffusion– Reaction products can change volume at interface

Intrinsic stress

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Structure-property relationship

Very thin films (~2 Å) –lattice expansion (compressive)

Thicker films (~2-8 Å) -small angle grain boundaries (tension)

Percolation point (~8 Å) –tension maximum

Post-coalescence (> ~8 Å) –compression from capillarity stress

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Mechanisms of intrinsic stress in Volmer Weber growth mode

Intrinsic stress

Low mobility Volmer-Weber Growth

After Koch(1994); ( Abermann)

Relatively high melting point metals

High mobility Volmer-Weber Growth

After Koch(1994); (Abermann)

Relatively low melting point metals

Much smaller scale

Evaporated films in UHV

tensile

tensile

compressive

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Mechanisms of intrinsic stress in Volmer Weber growth mode

Influence of substrate temperature

After Koch(1994); Abermann

Cr deposited in UHV onto MgF2 coated glass

Cu film force vs. film thickness and time

After Koch(1994)

Deposited in UHV at 300K onto MgF2coated glass. O2pressure in mbars.

Increasing Tsub resembles high mobility VW growth

For highest O2 pressure:

1. Force maximum shifts to smaller thickness (higher nucleation density and smaller grain size

2. Reduced crystallization rate – many small grains which produce tension.

Influence of O2 partial pressure

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Control of intrinsic stress by impact energy

Intrinsic stress

After Pauleau (2001); Windischmann (1991)

At low impact energies, film is not fully densified(porous) � tensile due to grain stretching

At higher energies, the film becomes compacted and compressive

At even higher energies, the impacted atoms are plastically deformed (broken bonds).

Curve applies for:

1. Low deposition temperature Tdbelow Td/Tm ~0.1 where diffusion based strain relief is absent.

2. No impurity stresses (e.g. hydrogen, oxygen or water)

3. Continuous films.

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Structure Zone Model (SZM)

After Thornton (1977)

Low impact energy ~ thermal evap

Higher impact energy ~ sputtering

Holes in zone 1 between ~3-10, and 20-30 not explained. Presumably due to lack of data in that region?

1 micron = 1 milliTorr

Higher pressure ~ low impact energy

Zone 1 – little or no adatom diffusion; morphology influenced by substrate roughness, has open boundaries and is rather porous, with increasing porosity with increasing pressure.Zone T – Transitional region; fibrous structure, limiting case of zone 1 structures with infinitely smooth substrates

Zone 2 – surface diffusion controlled growth, columnar crystals are roughly the same size1,2

Zone 3 – bulk diffusion1,2

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Effect of impurities

After Kaiser (2005); Barna (1995)

• Impurities act similarly to the effect of low substrate temperature.

• Impurities concentrate at grain boundaries

• Critical impurity concentration � passivationlayer

• Passivation layer promotes secondary nucleation

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Summary

• PVD produces Volmer-Weber growth at low substrate temperatures.• Interaction of grains, grain boundaries produce stress.• Stress modulated by grain nucleation density• Grain nucleation density is a function of process parameters.• Surface mobility is a function of the melting point of metal, substrate

temperature, partial pressure• Higher substrate temperatures promote larger grain growth• Operational parameters are interchangeable 1,6

– E.g. using lower melting point metals ~ increase substrate temp.– E.g. Impurities during deposition ~ decrease in substrate temp.

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References1. John A. Thornton, “High Rate Thick Film growth”, Ann Rev. Mater. Sci. 1977, 7:239-602. Norbert Kaiser, Review of the fundamentals of thin film growth, Applied Optics, 1 June 2002 Vol

41, No 16, p 3053 3. R. Koch, J.Phys. Condens. Matter 6 (1994) 9519-95504. Carl V. Thompson, The origin and control of residual stress in polycrystalline films for applications

in microsystems, Slides (2004)5. Y. Pauleau, Generation and evolution of residual stresses in physical vapour-deposited thin films,

Vacuum 61 (2001) 175-1816. H. Windischmann, intrinsic stress in sputtered thin films, J. Vac. Sci. Technol. A 9 (4), Jul/Aug

1991, p. 24317. Milton Ohring, The Materials Science of thin films, Academic Press 19928. Abermann et al.(see reference 3)9. Barna at al., (see reference 3)Other useful references:• P.S. Alexopolous, and T.C. Sullivan, Mechanical properties of thin films, Annu. Rev. Mater. Sci.

1990, 20:391-420• Jerrold A Floro, Eric Chason, Robert C. Cammarata, and David J. Srolovitz, Physical Origins of

intrisic stresses in volmer weber thin films, MRS bulletin, Jan 2002 p 19• Brian W. Sheldon, Ashok Rajamani, Abhinav Bhandari, Eric Chason, S.K. Hong, R. Beresford,

Competition between tensile and compressive stress mechanisms during Volmer Weber growth of aluminum nitride films, Journal of Applied Physics 98, 043509 (2005)

• Erik Klkholm, Delamination and fracture of thin films, IBM J. Res Develop. Vol 31 No 5, Sept 1987• Frederik Claeyssens, Ph.D. Thesis, Fundamental studies of pulsed laser ablation, 2001, Dept of

chemistry, University of Bristol, UK, http://www.chm.bris.ac.uk/pt/diamond/fredthesis/