Brief Overview Of Residual Stress In Thin Films

Physical mechanisms of residual stress in metallic thin films - A review of the literature February 19th, 2008 Felix Lu Applied Quantum Technologies / Duke University 1

Outline • • • • • •

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

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Stresses & Strains Unreleased structure

Released structure with stress

Thermally actuated structure

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

• 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

Elastic region

σ

Ultimate strength Yield strength

Plastic deformation

ε 3

Definitions

Stresses & Strains in MEMS structures • Thin film stresses ~/> Yield strength or ultimate strength Stoney equation for calculating interfacial stress in a plate 1 σf =

6R

R df

Es ds2 (1-νs) df

ds

νs Es

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

These surfaces stretched

This particular form of the Stoney equation assumes that film thickness << substrate thickness 4

Approach to analyzing films

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 5

Residual stress

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.

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Extrinsic stress

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 7

Materials Science

Thin film formation

– Evaporation – Sputtering

And hybrids and variants

(Wikipedia)

Thermal evaporation

Evaporated atoms ~0.1 eV 2

• Typically follow Volmer-Weber growth patterns for lower substrate temperatures • Epitaxial growth typically follows Frank-van der Merwe growth mode.

Sputtered atoms ~5-40 eV 1,2

• Physical vapor deposition (PVD) of polycrystalline thin films

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Volmer-Weber growth TEM of Ag films deposited in UHV on MgF2 coated glass substrates

Defects, surface reconstruction, impurities affect orientation of nuclei 3

After Koch (1994)

A simple polycrystalline grain structure After C.V. Thompson (2004)

Film becomes continuous (percolation or network stage3) 9

Materials Science

Percolation Control of percolation thickness important for applications: - Near percolation thickness, small changes in composition, bias, temperature
large changes in electrical conductivity & optical transparency2

• delayed percolation
larger grains • higher nucleation densities Thinner
grains are smaller percolation thickness
higher areal coverage Increase deposition rate Lower substrate temperature Plasma treatment of substrate surface 10

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 11

Frank-van der Merwe and StranskiKrastanov 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. 12

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.

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

After Koch (1994)

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Intrinsic stress

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.

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Intrinsic stress

Mechanisms of intrinsic stress in Volmer Weber growth mode Lattice expansion mechanism Growing droplet Lattice expands as drop grows

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

Capillarity stress

Weak adhesion allows gliding to relieve strain – until they contact each other…

Grains press against each other creating compression

See Koch paper for more details and references on lattice expansion

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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

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Intrinsic stress

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 Evaporated films in UHV Relatively high melting point metals Low mobility Volmer-Weber Growth

Relatively low melting point metals High mobility Volmer-Weber Growth

tensile

tensile

compressive Much smaller scale

After Koch(1994); ( Abermann)

After Koch(1994); (Abermann)

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Intrinsic stress

Mechanisms of intrinsic stress in Volmer Weber growth mode Influence of O2 partial pressure

Influence of substrate temperature

Cu film force vs. film thickness and time

Cr deposited in UHV onto MgF2 coated glass

Deposited in UHV at 300K onto MgF2 coated glass. O2 pressure in mbars.

After Koch(1994); Abermann After Koch(1994)

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. 19

Control of intrinsic stress by impact energy 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 Td below Td/Tm ~0.1 where diffusion based strain relief is absent. 2. No impurity stresses (e.g. hydrogen, oxygen or water) 3. Continuous films. After Pauleau (2001); Windischmann (1991)

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Intrinsic stress

Structure Zone Model (SZM) 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

Higher pressure ~ low impact energy Low impact energy ~ thermal evap Higher impact energy ~ sputtering After Thornton (1977)

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

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Effect of impurities • Impurities act similarly to the effect of low substrate temperature. • Impurities concentrate at grain boundaries • Critical impurity concentration
passivation layer • Passivation layer promotes secondary nucleation

After Kaiser (2005); Barna (1995)

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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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References 1. 2.

John A. Thornton, “High Rate Thick Film growth”, Ann Rev. Mater. Sci. 1977, 7:239-60 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) 9519-9550 4. 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) 175-181 6. H. Windischmann, intrinsic stress in sputtered thin films, J. Vac. Sci. Technol. A 9 (4), Jul/Aug 1991, p. 2431 7. Milton Ohring, The Materials Science of thin films, Academic Press 1992 8. 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/ 24