scholarly journals Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations

2001 ◽  
Vol 89 (11) ◽  
pp. 6116-6129 ◽  
Author(s):  
Hansuk Lee ◽  
Ares J. Rosakis ◽  
L. B. Freund
Keyword(s):  
Thin Film ◽  
Optical Measurement ◽  
Geometrically Nonlinear ◽  
Full Field ◽  
Film Substrate ◽  
Nonlinear Deformations ◽  
Ultra Thin Film

Appling of New Optical Measurement and Theory in Mechanical Properties of Thin Film

2011 ◽  
Vol 121-126 ◽  
pp. 4295-4299
Author(s):  
Hao MA Yun ◽  
Lu Ping Chao ◽  
J. S Hsu
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Mechanical Properties ◽  
Thermal Stresses ◽  
Optical Measurement ◽  
Phase Shifting ◽  
Deposition Condition ◽  
Full Field ◽  
Evaporation Technique ◽  
Film Substrate

The thesis aims to characterize the mechanical properties and stresses for thin films deposited on the circular substrates. First, the thin films with the same deposition condition were successively deposited on the distinct substrates using the evaporation technique. The phase-shifting Twyman-Green interferometer (PSTGI) was then employed to measure the warpage of the film-substrate structures and therefore the intrinsic stresses and thermal stresses can be calculated from the well-known Stoney’s formula. The coefficients of thermal expansion (CTE) and Young’s modulus of thin films were also obtained from the Stoney’s theory. Furthermore, the merit of full-field character of optical interferometry was used to propose a novel methodology using the Chen and Ou’s theory to improve the accuracy and to reduce the experiment procedures in the traditional measurement of the aforementioned mechanical properties. Finally, the measured results corresponding to the traditional and proposed methods were respectively substituted into their adopted theories to compare their difference. The results reveal that the accuracy of proposed methodology is considerably improved and the experimental procedures are reduced to those of the traditional methods.

Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
X. Feng ◽  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Field Measurements ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Multilayer Thin Film ◽  
Nonuniform Temperature ◽  
Curvature Invariant ◽  
Full Field ◽  
Curvature Measurements ◽  
Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to uniform film stress and system curvature states over the entire system of a single thin film on a substrate. By considering a circular multilayer thin film/substrate system subjected to nonuniform temperature distributions, we derive relations between the stresses in each film and temperature, and between the system curvatures and temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part, which reflects the effect of temperature of other points on the location of scrutiny. We also derive relations between the film stresses in each film and the system curvatures, which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. The interfacial shear tractions between the films and between the film and substrate are proportional to the gradient of the first curvature invariant, and can also be inferred experimentally.

Extension of Stoney’s Formula to Arbitrary Temperature Distributions in Thin Film/Substrate Systems

2006 ◽  
Vol 74 (6) ◽  
pp. 1225-1233 ◽  
Author(s):  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Field Measurements ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Curvature Invariant ◽  
Full Field ◽  
Polar Components ◽  
Temperature Distributions ◽  
Curvature Measurements ◽  
Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to nonuniform and nonaxisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system’s curvatures and the temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part that reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.

X-ray Standing Waves in X-ray Specular Reflection and Fluorescence Study of Nano-Films

1997 ◽  
Vol 30 (5) ◽  
pp. 833-838 ◽  
Author(s):  
S. I. Zheludeva ◽  
M. V. Kovalchuk ◽  
N. N. Novikova ◽  
A. N. Sosphenov ◽  
N. N. Salaschenko ◽  
...  
Keyword(s):  
Thin Film ◽  
Specular Reflection ◽  
Fluorescence Study ◽  
Reflection Curve ◽  
X Ray ◽  
Inorganic Films ◽  
Film Substrate ◽  
Mode Formation ◽  
Ultra Thin Film

The analysis of the wavefield intensity distribution connected with X-ray standing wave (XRSW) generation above the mirror surface at total reflection (TR) is presented for a vacuum/film/substrate sample along with experimental examples for organic and inorganic films for cases where the refractive index of the film is greater than that of the substrate. The thickness of an ultra-thin film may be estimated from the value of the XRSW period formed above the film/substrate interface at TR. In some cases, the thickness of an ultra-thin film may be roughly obtained just from the form of the X-ray reflection curve at incident angles smaller than the critical angle of the substrate. It is demonstrated that interference phenomena at TR, leading to waveguide mode formation inside the layered structure and responsible for a modulation of the X-ray reflection and fluorescence angular dependence, can be used for characterization of nano-films.

Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison

1994 ◽  
Vol 61 (4) ◽  
pp. 872-878 ◽  
Author(s):  
C. B. Masters ◽  
N. J. Salamon
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Ritz Method ◽  
Spherical Shape ◽  
Free Edge ◽  
Boundary Region ◽  
Film Stress ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress ◽  
Film Substrate

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

Curvature of a Film-Substrate System in the Nonlinear Deformation Range

1999 ◽  
Author(s):  
L. B. Freund ◽  
A. J. Rosakis ◽  
H. S. Lee
Keyword(s):  
Nonlinear Deformation ◽  
Deformation Mode ◽  
Geometrically Nonlinear ◽  
Field Observations ◽  
Si Substrate ◽  
Full Field ◽  
Mismatch Strain ◽  
Substrate Curvature ◽  
Film Substrate ◽  
The Relationship

Abstract The physical system considered is a thin film bonded to the surface of an initially flat circular substrate, in the case when a residual stress exists due to an incompatible mismatch strain in the film. The magnitude of the mismatch strain is often inferred from a measurement of the curvature it induces in the substrate. This discussion is focused on the limit of the linear range of the relationship between the mismatch strain and the substrate curvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and on the bifurcation of deformation mode from axial symmetry to asymmetry with increasing mismatch strain. Results are obtained on the basis of both simple models and more detailed finite element simulations. Preliminary full-field observations are reported on deformation of a 6 μm thick Al film deposited onto a 100 μm thick Si substrate subjected to thermal cycling.

On the Stoney Formula for a Thin Film/Substrate System With Nonuniform Substrate Thickness

2007 ◽  
Vol 74 (6) ◽  
pp. 1276-1281 ◽  
Author(s):  
X. Feng ◽  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Misfit Strain ◽  
Film Stress ◽  
Substrate Thickness ◽  
Full Field ◽  
Temperature Changes ◽  
Thin Film Stress ◽  
Curvature Measurements ◽  
Film Substrate ◽  
Stoney Formula

Current methodologies used for the inference of thin film stress through system 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 [Acta Mech. Sinica, 21, pp. 362–370 (2005); J. Mech. Phys. Solids, 53, 2483–2500 (2005); Thin Solid Films, 515, pp. 2220–2229 (2006); J. Appl. Mech., in press; J. Mech. Mater. Struct., in press] established methods for the film/substrate system subject to nonuniform misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (i.e., depend on the full-field curvatures). These methods, however, all assume uniform substrate thickness, which is sometimes violated in the thin film/substrate system. Using the perturbation analysis, we extend the methods to nonuniform substrate thickness for the thin film/substrate system subject to nonuniform misfit strain.

scholarly journals Finite Element Analysis of the 3ω Method for Characterising High Thermal Conductivity Ultra-Thin Film/Substrate System

Coatings ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 87 ◽  
Author(s):  
Weidong Liu ◽  
Liangchi Zhang ◽  
Alireza Moridi
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Theoretical Models ◽  
High Thermal Conductivity ◽  
Element Analysis ◽  
3Ω Method ◽  
Film Substrate ◽  
Ultra Thin Film

The 3ω method is an attractive technique for measuring the thermal conductivity of materials; but it cannot characterise high thermal conductivity ultra-thin film/substrate systems because of the deep heat penetration depth. Recently, a modified 3ω method with a nano-strip was specifically developed for high thermal conductivity thin film systems. This paper aims to evaluate the applicability of this method with the aid of the finite element analysis. To this end, a numerical platform of the modified 3ω method was established and applied to a bulk silicon and an AlN thin-film/Si substrate system. The numerical results were compared with the predictions of theoretical models used in the 3ω method. The study thus concluded that the modified 3ω method is suitable for characterising high thermal conductivity ultra-thin film/substrate systems.

scholarly journals A Comparison of X-Ray Microdiffraction and Coherent Gradient Sensing in Measuring Discontinuous Curvatures in Thin Film: Substrate Systems

2005 ◽  
Vol 73 (5) ◽  
pp. 723-729 ◽  
Author(s):  
Michal A. Brown ◽  
Tae-Soon Park ◽  
Ares Rosakis ◽  
Ersan Ustundag ◽  
Young Huang ◽  
...  
Keyword(s):  
Thin Film ◽  
Stress Measurement ◽  
Plate Theory ◽  
Measurement Tool ◽  
Wafer Level ◽  
Full Field ◽  
X Ray ◽  
Deformation State ◽  
Film Substrate ◽  
Si Wafer

The coherent gradient sensor (CGS) is a shearing interferometer which has been proposed for the rapid, full-field measurement of deformation states (slopes and curvatures) in thin film-wafer substrate systems, and for the subsequent inference of stresses in the thin films. This approach needs to be verified using a more well-established but time-consuming grain orientation and stress measurement tool, X-ray microdiffraction (XRD). Both CGS and XRD are used to measure the deformation state of the same W film/Si wafer at room temperature. CGS provides a global, wafer-level measurement of slopes while XRD provides a local micromeasurement of lattice rotations. An extreme case of a circular Si wafer with a circular W film island in its center is used because of the presence of discontinuous system curvatures across the wafer. The results are also compared with a theoretical model based on elastic plate analysis of the axisymmetric biomaterial film-substrate system. Slope and curvature measurements by XRD and by CGS compare very well with each other and with theory. The favorable comparison demonstrates that wafer-level CGS metrology provides a quick and accurate alternative to other measurements. It also demonstrates the accuracy of plate theory in modeling thin film-substrate systems, even in the presence of curvature discontinuities

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