Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I

Analysis for obtaining film stress from non-local curvature information

D. Ngo, X. Feng*, Y. Huang, A. J. Rosakis, M. A. Brown

*Corresponding author for this work

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362-370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney's Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483-2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.

Original languageEnglish (US)
Pages (from-to)1745-1754
Number of pages10
JournalInternational Journal of Solids and Structures
Volume44
Issue number6
DOIs
StatePublished - Mar 15 2007

Fingerprint

strain distribution
Film thickness
Thin Films
film thickness
Curvature
Substrate
curvature
Thin films
Arbitrary
Substrates
thin films
Radial Symmetry
inference
Temperature Distribution
Temperature distribution
temperature distribution
methodology
Strictly
Entire
symmetry

Keywords

  • Interfacial shears
  • Non-local stress-curvature relations
  • Non-uniform film thickness
  • Non-uniform misfit strain
  • Thin films

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

@article{a4d4ff416a514a4ab0cafa3a495a2ff1,
title = "Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information",
abstract = "Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362-370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney's Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483-2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.",
keywords = "Interfacial shears, Non-local stress-curvature relations, Non-uniform film thickness, Non-uniform misfit strain, Thin films",
author = "D. Ngo and X. Feng and Y. Huang and Rosakis, {A. J.} and Brown, {M. A.}",
year = "2007",
month = "3",
day = "15",
doi = "10.1016/j.ijsolstr.2006.10.016",
language = "English (US)",
volume = "44",
pages = "1745--1754",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "6",

}

TY - JOUR

T1 - Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I

T2 - Analysis for obtaining film stress from non-local curvature information

AU - Ngo, D.

AU - Feng, X.

AU - Huang, Y.

AU - Rosakis, A. J.

AU - Brown, M. A.

PY - 2007/3/15

Y1 - 2007/3/15

N2 - Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362-370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney's Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483-2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.

AB - Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis and co-workers [Huang, Y., Ngo, D., Rosakis, A.J., 2005. Non-uniform, axisymmetric misfit strain: in thin films bonded on plate substrates/substrate systems: the relation between non-uniform film stresses and system curvatures. Acta Mech. Sin. 21, 362-370; Huang, Y., Rosakis A.J., 2005. Extension of Stoney's Formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53, 2483-2500; Ngo, D., Huang, Y., Rosakis, A. J., Feng, X. 2006. Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform film stresses and system curvatures. Thin Solid Films (in press)] established methods for film/substrate system subject to non-uniform misfit strain and temperature changes. The film stresses were found to depend non-locally on system curvatures (i.e., depend on the full-field curvatures). The existing methods, however, all assume uniform film thickness which is often violated in the thin film/substrate system. We extend these methods to arbitrarily non-uniform film thickness for the thin film/substrate system subject to non-uniform misfit strain. Remarkably the stress-curvature relation for uniform film thickness still holds if the film thickness is replaced by its local value at the point where the stress is evaluated. This result has been experimentally validated in Part II of this paper.

KW - Interfacial shears

KW - Non-local stress-curvature relations

KW - Non-uniform film thickness

KW - Non-uniform misfit strain

KW - Thin films

UR - http://www.scopus.com/inward/record.url?scp=33846468826&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846468826&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2006.10.016

DO - 10.1016/j.ijsolstr.2006.10.016

M3 - Article

VL - 44

SP - 1745

EP - 1754

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 6

ER -