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.

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 The Effect of Stress on the Nanomechanical Properties of Au Surfaces

1996 ◽  
Vol 440 ◽  
Author(s):  
J. E. Houston
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Local Level ◽  
Maximum Shear Stress ◽  
Critical Role ◽  
Film Stress ◽  
Indentation Modulus ◽  
Nanomechanical Properties ◽  
Average Grain Size ◽  
Film Substrate

AbstractStress in thin films plays a critical role in many technologically important areas. The role is a beneficial one in strained layer superlattices where semiconductor electrical and optical properties can be tailored with film stress. On the negative side, residual stress in thin-film interconnects in microelectronics can lead to cracking and delamination. In spite of their importance, however, surface and thin-film stresses are difficult to measure and control, especially on a local level. In recent studies, we used the Interfacial Force Microscope (IFM) in a nanoindenter mode to survey the nanomechanical properties of Au films grown on various substrates. Quantitative tabulations of the indentation modulus and the maximum shear stress at the plastic threshold showed consistent values over individual samples but a wide variation from substrate to substrate. These values were compared with film properties such as surface roughness, average grain size and interfacial adhesion and no correlation was found. However, in a subsequent analysis of the results, we found consistencies which support the integrity of the data and point to the fact that the results are sensitive to some property of the various film/substrate combinations. In recent measurements on two of the original substrate materials we found a direct correlation between the nanomechanical values and the residual stress in the films, as measured globally by a wafer warping technique. In the present paper, we review these earlier results and show recent measurements dealing with stresses externally applied to the films which supports our earlier conclusion concerning the role of stress on our measurements. In addition, we present very recent results concerning morphological effects on nanomechanical properties which add additional support to the suggestion that near-threshold indentation holds promise of being able to measure stress on a very local level

Multilayer thin-film substrate for multichip packaging

2003 ◽  
Author(s):  
C.C. Chao ◽  
K.D. Scholz ◽  
J. Leibovitz ◽  
M.L. Cobarruviaz ◽  
C.C. Chang
Keyword(s):  
Thin Film ◽  
Multilayer Thin Film ◽  
Film Substrate

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.

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.

Measurement of the Effect of Temperature on Stress Distribution and Deformation in Multilayer Optical Thin Film Structures

1994 ◽  
Vol 356 ◽  
Author(s):  
Cynthia G. Madras ◽  
P. Y. Wong ◽  
I. N. Miaoulis ◽  
L. M. Goldman
Keyword(s):  
Thin Film ◽  
Plastic Deformation ◽  
Stress Distribution ◽  
Thermal Stresses ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Optical Thin Film ◽  
Melting Temperatures ◽  
Thermal Expansion Coefficients ◽  
Theoretical Predictions

AbstractThis study investigates methods of predicting the deformation and stress distribution in multilayer optical thin film structures. The thin film layers include materials of various thermal expansion coefficients, elastic moduli, and melting temperatures. Each layer is deposited at a different temperature, causing complex thermal and deposition stresses throughout the structure. In addition, since the deposition temperatures of some of the layers are high (>600°C), stress relaxation and plastic flow may occur in materials with low melting temperatures. A combination of theoretical predictions and experimental measurements is used to measure and quantify the deformation caused by residual and thermal stresses in the films as well as any plastic deformation that may have occurred. Results from a model using multilayer plate bending theory to determine the elastic deformation of the device due to thermal stresses are reported. These predictions, as well as a more common method of predicting film stress and curvature, are compared to experimentally measured curvature changes as a function of temperature in the samples. However, when plastic deformation begins to occur at high temperatures, the residual stress and degree of deformation are no longer predictable based on elastic theory alone, and have to be measured experimentally. Plastic deformation in the substrate is discussed as a cause of a high observed curvature following sample heating.

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