Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry

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.

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

Journal of Applied Physics ◽

10.1063/1.1364650 ◽

2001 ◽

Vol 89 (11) ◽

pp. 6116-6129 ◽

Cited By ~ 45

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

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

Journal of Applied Mechanics ◽

10.1115/1.2744035 ◽

2006 ◽

Vol 74 (6) ◽

pp. 1225-1233 ◽

Cited By ~ 19

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.121-126.4295 ◽

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.

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

Journal of Applied Mechanics ◽

10.1115/1.2745392 ◽

2007 ◽

Vol 74 (6) ◽

pp. 1276-1281 ◽

Cited By ~ 88

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.

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

Journal of Applied Mechanics ◽

10.1115/1.2150500 ◽

2005 ◽

Vol 73 (5) ◽

pp. 723-729 ◽

Cited By ~ 16

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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Noncontact and Full-Field Measurement of Residual and Thermal Stress in Film/Substrate Structures

Surfaces ◽

10.3390/surfaces4010011 ◽

2021 ◽

Vol 4 (1) ◽

pp. 89-96

Author(s):

Dong Yang ◽

Xumeng Zhang ◽

Jianguo Zhu

Keyword(s):

Thin Film ◽

Thermal Stress ◽

High Temperature ◽

Correlation Method ◽

Image Correlation ◽

Full Field ◽

3D Digital Image Correlation ◽

Full Field Measurement ◽

Curvature Measurement ◽

Film Substrate

Residual stress and thermal stress of a film/substrate system are determined based on the curvature measurement with a 3D digital image correlation method (DIC) and calculation of the thin-film stresses by the extension of Stoney’s formula. A Ni film electroplated on a H62Cu plate is used to verify the proposed method. The full fields of nonuniform thin-film stresses are obtained in a room temperature to high-temperature environment of 200 °C, which can be potentially extended to higher temperatures. These results provide a fundamental approach to understanding thin-film stresses and a feasible measurement method for high temperature.

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Microtomy of spherical Al2O3 powders

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010007429x ◽

1983 ◽

Vol 41 ◽

pp. 74-75

Author(s):

E.J. Jenkins ◽

D.S. Tucker ◽

J.J. Hren

Keyword(s):

Thin Film ◽

Size Range ◽

Particle Aggregation ◽

Ion Milling ◽

Thin Sections ◽

Α Phase ◽

Convenient Means ◽

Van Der Waals Attraction ◽

Negative Feature ◽

Film Substrate

The size range of mineral and ceramic particles of one to a few microns is awkward to prepare for examination by TEM. Electrons can be transmitted through smaller particles directly and larger particles can be thinned by crushing and dispersion onto a substrate or by embedding in a film followed by ion milling. Attempts at dispersion onto a thin film substrate often result in particle aggregation by van der Waals attraction. In the present work we studied 1-10 μm diameter Al2O3 spheres which were transformed from the amprphous state to the stable α phase.After the appropriate heat treatment, the spherical powders were embedded in as high a density as practicable in a hard EPON, and then microtomed into thin sections. There are several advantages to this method. Obviously, this is a rapid and convenient means to study the microstructure of serial slices. EDS, ELS, and diffraction studies are also considerably more informative. Furthermore, confidence in sampling reliability is considerably enhanced. The major negative feature is some distortion of the microstructure inherent to the microtoming operation; however, this appears to have been surprisingly small. The details of the method and some typical results follow.

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Microstructural investigation of surface roughness in MBE-grown AlAs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100138646 ◽

1995 ◽

Vol 53 ◽

pp. 454-455

Author(s):

R. Rajesh ◽

R. Droopad ◽

C. H. Kuo ◽

R. W. Carpenter ◽

G. N. Maracas

Keyword(s):

Thin Film ◽

Real Time ◽

Growth Control ◽

Native Oxide ◽

Effusion Cell ◽

Surface Oxide Layer ◽

Microstructural Investigation ◽

Mbe Growth ◽

Film Substrate ◽

And Control

Knowledge of material pseudodielectric functions at MBE growth temperatures is essential for achieving in-situ, real time growth control. This allows us to accurately monitor and control thicknesses of the layers during growth. Undesired effusion cell temperature fluctuations during growth can thus be compensated for in real-time by spectroscopic ellipsometry. The accuracy in determining pseudodielectric functions is increased if one does not require applying a structure model to correct for the presence of an unknown surface layer such as a native oxide. Performing these measurements in an MBE reactor on as-grown material gives us this advantage. Thus, a simple three phase model (vacuum/thin film/substrate) can be used to obtain thin film data without uncertainties arising from a surface oxide layer of unknown composition and temperature dependence.In this study, we obtain the pseudodielectric functions of MBE-grown AlAs from growth temperature (650°C) to room temperature (30°C). The profile of the wavelength-dependent function from the ellipsometry data indicated a rough surface after growth of 0.5 μm of AlAs at a substrate temperature of 600°C, which is typical for MBE-growth of GaAs.

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