Abstract
The classical Stoney formula relating local equibiaxial film stress to local equibiaxial substrate curvature is not well equipped to handle realistic cases where the film misfit strain, the plate system curvature, and the film thickness and resulting film stress vary with in-plane position. In Part I of this work we have extended the Stoney formula to cover arbitrarily non-uniform film thickness for a thin film/substrate system subject to non-uniform, isotropic misfit strains. The film stresses are found to depend non-locally on system curvatures. In Part II we have designed a demanding experiment whose purpose is to validate the new analysis for the case of radially symmetric deformations. To achieve this, a circular film island with sharp edges and a radially variable, but known, thickness is deposited on the wafer center. The plate system's curvatures and the film stress distribution are independently measured by using white beam and monochromatic X-ray microdiffraction (μXRD) measurements, respectively. The measured stress field (from monochromatic μXRD) is compared to the predictions of various stress/curvature analyses, all of which have the white beam μXRD measurements as input. The results reveal the shortcomings of the "local" Stoney approach and validate the accuracy of the new "non-local" relation, most notably near the film island edges where stress concentrations dominate.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1755-1767 |
| Number of pages | 13 |
| Journal | International Journal of Solids and Structures |
| Volume | 44 |
| Issue number | 6 |
| DOIs | |
| State | Published - Mar 15 2007 |
Fingerprint
Keywords
- Non-local stress/curvature relations
- Thin film
- X-ray microdiffraction
ASJC Scopus subject areas
- Modeling and Simulation
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
Cite this
}
Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II : Experimental validation of the non-local stress/curvature relations. / Brown, M. A.; Rosakis, A. J.; Feng, X.; Huang, Y.; Üstündag, Ersan.
In: International Journal of Solids and Structures, Vol. 44, No. 6, 15.03.2007, p. 1755-1767.Research output: Contribution to journal › Article
TY - JOUR
T1 - Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II
T2 - Experimental validation of the non-local stress/curvature relations
AU - Brown, M. A.
AU - Rosakis, A. J.
AU - Feng, X.
AU - Huang, Y.
AU - Üstündag, Ersan
PY - 2007/3/15
Y1 - 2007/3/15
N2 - The classical Stoney formula relating local equibiaxial film stress to local equibiaxial substrate curvature is not well equipped to handle realistic cases where the film misfit strain, the plate system curvature, and the film thickness and resulting film stress vary with in-plane position. In Part I of this work we have extended the Stoney formula to cover arbitrarily non-uniform film thickness for a thin film/substrate system subject to non-uniform, isotropic misfit strains. The film stresses are found to depend non-locally on system curvatures. In Part II we have designed a demanding experiment whose purpose is to validate the new analysis for the case of radially symmetric deformations. To achieve this, a circular film island with sharp edges and a radially variable, but known, thickness is deposited on the wafer center. The plate system's curvatures and the film stress distribution are independently measured by using white beam and monochromatic X-ray microdiffraction (μXRD) measurements, respectively. The measured stress field (from monochromatic μXRD) is compared to the predictions of various stress/curvature analyses, all of which have the white beam μXRD measurements as input. The results reveal the shortcomings of the "local" Stoney approach and validate the accuracy of the new "non-local" relation, most notably near the film island edges where stress concentrations dominate.
AB - The classical Stoney formula relating local equibiaxial film stress to local equibiaxial substrate curvature is not well equipped to handle realistic cases where the film misfit strain, the plate system curvature, and the film thickness and resulting film stress vary with in-plane position. In Part I of this work we have extended the Stoney formula to cover arbitrarily non-uniform film thickness for a thin film/substrate system subject to non-uniform, isotropic misfit strains. The film stresses are found to depend non-locally on system curvatures. In Part II we have designed a demanding experiment whose purpose is to validate the new analysis for the case of radially symmetric deformations. To achieve this, a circular film island with sharp edges and a radially variable, but known, thickness is deposited on the wafer center. The plate system's curvatures and the film stress distribution are independently measured by using white beam and monochromatic X-ray microdiffraction (μXRD) measurements, respectively. The measured stress field (from monochromatic μXRD) is compared to the predictions of various stress/curvature analyses, all of which have the white beam μXRD measurements as input. The results reveal the shortcomings of the "local" Stoney approach and validate the accuracy of the new "non-local" relation, most notably near the film island edges where stress concentrations dominate.
KW - Non-local stress/curvature relations
KW - Thin film
KW - X-ray microdiffraction
UR - http://www.scopus.com/inward/record.url?scp=33846533039&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846533039&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2006.10.015
DO - 10.1016/j.ijsolstr.2006.10.015
M3 - Article
VL - 44
SP - 1755
EP - 1767
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
IS - 6
ER -