Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information

2007 ◽  
Vol 44 (6) ◽  
pp. 1745-1754 ◽  
Author(s):  
D. Ngo ◽  
X. Feng ◽  
Y. Huang ◽  
A.J. Rosakis ◽  
M.A. Brown
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Misfit Strain ◽  
Film Stress ◽  
Local Curvature ◽  
Non Local ◽  
Film Substrate ◽  
Curvature Information

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.

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.

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

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.

Effect of Film Thickness and Annealing Time on Residual Stress of High-k Al2O3 Film on Si-(100) Substrate

2013 ◽  
Vol 644 ◽  
pp. 161-164
Author(s):  
Wu Tang ◽  
Ji Jun Yang ◽  
Chi Ming Li
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Film Thickness ◽  
Annealing Time ◽  
Gate Dielectric ◽  
Electron Beam Evaporation ◽  
Film Stress ◽  
X Ray Diffraction ◽  
Thin Film Stress ◽  
High K

In this paper, Al2O3 thin film samples were deposited on Si-(100) substrate by electron beam evaporation with different thickness at substrate temperature 400°C and after that, annealed in the air at 500°C with different time. The structure, thickness and residual stress of these films were measured by X-ray diffraction (XRD), stylus profiler and electronic thin film stress distribution tester, respectively. The effects of several parameters on the properties of Al2O3 films were studied. In addition, the relations between thickness and residual stress of Al2O3 thin films as the high-k gate dielectric was analyzed. The results shown that the residual stress becomes smaller after annealing, the residual stress was depressed down to maximum value 300MPa from 580MPa for annealing time 30min, and depressed down to minimum value 220MPa from 580MPa for annealing time 60min. But eventually, it has a critical film thickness point on the scale.

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.

Identification of the Failure Mechanism of a Thin Film on a Thick Substrate by Means of Synchrotron X-Ray Topography Combined with Transmission Electron Microscopy

1987 ◽  
Vol 108 ◽  
Author(s):  
D. Goyal ◽  
W. Ng ◽  
A. H. King ◽  
J. C. Bilello
Keyword(s):  
Thin Film ◽  
Electron Microscopy ◽  
Thin Films ◽  
Transmission Electron Microscopy ◽  
Film Thickness ◽  
Film Stress ◽  
Silicon Substrates ◽  
X Ray ◽  
Transmission Electron ◽  
Thick Substrate

ABSTRACTWe have used synchrotron x-ray topographic techniques to study the stresses in thin films formed upon silicon substrates either by evaporation or sputtering. It is found that the film stress generally decreases with increasing film thickness for evaporated films, but film delamination occurs at a well defined film thickness. Transmission electron microscope studies have been performed on the same specimens in order to reveal what mechanisms are involved with the delamination of the films.

Elastic Analysis of Twinning in Misfitting Thin Films

1995 ◽  
Vol 389 ◽  
Author(s):  
N. Sridhar ◽  
J.M. Rickman ◽  
D.J. SroIovitz
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Film Thickness ◽  
Misfit Strain ◽  
Elastic Analysis ◽  
Domain Formation ◽  
Linear Elasticity Theory ◽  
Periodic Distribution ◽  
Twin Domain ◽  
Strain Tensors

ABSTRACTWe examine the conditions under which a misfitting thin film on a substrate will twin and the pattern of the twin microstructure that will form. Using linear elasticity theory, we present exact analytical results for the energy released due to the formation of a periodic array of twinned domains as well as that for a single embedded twin domain. While the analysis is applicable to general misfit strain tensors, we specifically analyze the energetics of twinned domain formation for a tetragonal film on a cubic substrate. The analysis shows that for a periodic distribution of twins, the equilibrium width of the domains of the two variants are identical. Our results also show that the equilibrium periodicity of the microstructure scales inversely with film thickness for large film thickness and decays exponentially with increasing film thickness for small film thicknesses.

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