Advanced resonant ultrasound spectroscopy for measuring anisotropic elastic constants of thin films

This paper presents an advanced resonant ultrasound spectroscopy (RUS) method to determine the elastic constants C_ij of thin films. Polycrystalline thin films often exhibit elastic anisotropy between the film growth direction and the in‐plane direction, and they macroscopically show five independent elastic constants. Because all of the C_ij of a deposited thin film affect the mechanical resonance frequencies of the film/substrate layer specimen, measuring resonance frequencies enables one to determine the C_ij of the film with known density, dimensions and the C_ij of the substrate. Resonance frequencies have to be measured accurately because of low sensitivity of the C_ij of films to them. We achieved this by a piezoelectric tripod. Mode identification has to be made unambiguously. We made this measuring displacement–amplitude distributions on the resonated specimen surface by laser Doppler interferometry. We applied our technique to copper thin film and diamond thin film. They show elastic anisotropy and the C_ij smaller than bulk values of C_ij. Micromechanics calculations indicate the presence of incohesive bonded regions.     

Morphological evolution driven by strain induced surface diffusion

We have developed a three-dimensional finite element method to simulate the morphological evolution of a strained surface via surface diffusion, with a view to understanding the self-assembly, shape transitions and stability of low-dimensional quantum structures. We model deposition of an elastic film on a large lattice mismatched substrate. The film surface evolves by surface diffusion, driven by a gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy, surface energy, surface energy anisotropy and the interaction between the film and the substrate. Our simulations reveal that surface energy anisotropy and elastic anisotropy have a strong effect on the morphological evolution and shape transitions of the self-assembled islands. Our simulation results show a good qualitative agreement with experimental results.     

Elastic anisotropy effect on indentation-induced thin film interfacial delamination

Effect of elastic anisotropy on indentation-induced thin film interfacial delamination, especially, at the initiation and early growth stage, is examined. The indentation load is modeled as a constant pressure over an expanding semi-spherical cavity. The delamination process is approached by a cohesive zone model. The rest of the problem is formulated within the general anisotropic elasticity theory, and solved numerically by the boundary element method employing a special Green’s function for multilayers. The material system of a Cu(0 0 1) film on a Si(0 0 1) substrate is studied as an example. The interfacial damage initiation and crack development under indentation are captured in the simulation. By comparing the predictions with the materials being modeled as isotropic and as anisotropic (of the cubic symmetry as they are), it is shown that the elastic anisotropy of the copper film plays a significant role in determining the delamination pattern. In the isotropic model, the delamination crack fronts are circular reflecting the problem axisymmetry. In contrast, crack fronts are square with rounded corners in the anisotropic case. This significant difference necessitates a three-dimensional anisotropic stress analysis of the indentation-induced delamination of strongly anisotropic films.     

Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

Spannungsanisotropie und Struktur von TiN-Schichten

Stress anisotropy and structure of TiN thin films In many sputtering processes the substrate is rotated or periodically moved with respect to the target in order to obtain a homogeneous film deposition. In that case anisotropic conditions of film growth exist which lead to anisotropic mechanical stresses. The stress anisotropy depends on the carrier velocity and can be attributed to the film structure. The stress measurements, therefore, will be related to measurements of composition by SNMS, to determination of stoichiometry by ellipsometry and to investigations of structure by X-ray diffraction.     

Experimental Determination of the Kapitza Conductance Across Thin Film Bolometer Interfaces

Thin film bolometers are widely used in low temperature experiments. They are always connected in an electrical measuring circuit which involves a current, so an unavoidable Joule heating effect is generated. As a result the detector temperature can be appreciably higher than that of the cell, especially in the low temperature range. It is therefore important to be able to determine the bolometer net heat loss in order to evaluate the temperature gradient which could take place. We propose a simple analysis that provides an experimental determination of the values of the heat conductance across the interfaces of a thin film bolometer deposited onto a substrate. In this way, both temperatures of the bolometer and of the part of the helium film which covers it, as well as the respective heat flows through the film and the substrate are easily obtained. This method could prove useful in the future for a better understanding of surface exchanges and surface characterization.     

Electromechanical instability in anisotropic dielectric elastomers

In this paper, we analyze the electromechanical instability of anisotropic dielectric elastomers. When an electric field and biaxial stress are applied to a dielectric elastomer, the homogeneous deformation of the dielectric elastomer may be unstable and pull-in instability and bifurcation instability may occur. Based on the previous investigations on the incompressible anisotropic elastic solids and dielectric elastomers, we outline the theory of anisotropic dielectrics. The electromechanical instability is considered for a thin layer of a dielectric elastomer sandwiched between two compliant electrodes. Analytic solutions are obtained for the classic neo-Hookean model of anisotropic materials. The results show that the stability of the dielectric elastomer is remarkably enhanced by anisotropy parameter.     

Non-uniform stress distribution and deformation bifurcation of thin film/substrate system subjected to gradient temperature

Stresses in thin films or coatings control the reliability of the thin film/substrate structure. By considering a circular thin film/substrate system subjected to gradient temperature, we derive relations between the non-uniform stresses in film and temperature, and between the non-uniform 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 “non-local” part which reflects the effect of temperature of other points on the location of scrutiny. Furthermore, the deformation bifurcation behavior of the thin film/substrate system is analyzed. As the thermo-mismatch strain in the thin film increases, the system may transit to a biaxial curvature state (non-spherical deformation), in other words, the bifurcation of curvature will occur.     

Energy based model to assess interfacial adhesion using a scratch test

A common way to improve the scratch resistance of a sensitive surface is to coat it with a thin film. However, the substrate/thin film adhesion must be well controlled and measurable. The contribution of the present work is to propose a global energy balance model of the blistering process for the scratching of a substrate/thin film system, which permits one to determine the adhesion of the system. The adhesion can be measured by following the delaminated area as a function of the scratching distance during blistering. The particular case of an experimental stable blistering process was studied and the corresponding substrate/thin film adhesion was derived using the global energy balance model.     

An interface crack between an orthotropic thin film and substrate

This work is concerned with a semi-infinite interface crack between a thin film and a substrate. The two materials are assumed to be linearly elastic and orthotropic. A solution is presented for the stress field due to an edge dislocation on the interface which is valid for any combinations of material parameters. It is found that the behavior of such a bi-material system is governed by 6 independent material parameters. The stress intensity factor is computed for general edge loadings by solving integral equations numerically, and the size of the K-dominant zone is also studied for a residually stressed thin film. The situations in which the K-field zone of dominance is very small are identified and discussed.     

Tunable In-Plane Anisotropy in Amorphous Sm–Co Films Grown on (011)-Oriented Single-Crystal Substrates

Amorphous Sm–Co films with uniaxial in-plane anisotropy have great potential for application in information-storage media and spintronic materials. The most effective method to produce uniaxial in-plane anisotropy is to apply an in-plane magnetic field during deposition. However, this method inevitably requires more complex equipment. Here, we report a new way to produce uniaxial in-plane anisotropy by growing amorphous Sm–Co films onto (011)-cut single-crystal substrates in the absence of an external magnetic field. The tunable anisotropy constant, k_A, is demonstrated with variation in the lattice parameter of the substrates. A k_A value as high as about 3.3 × 10⁴ J·m⁻³ was obtained in the amorphous Sm–Co film grown on a LaAlO₃(011) substrate. Detailed analysis indicated that the preferential seeding and growth of ferromagnetic (FM) domains caused by the anisotropic strain of the substrates, along with the formed Sm–Co, Co–Co directional pair ordering, exert a substantial effect. This work provides a new way to obtain in-plane anisotropy in amorphous Sm–Co films.     

Channel cracking in thin films on substrates of finite thickness

Solutions are presented for the elastic plane-strain problem of a crack in a coating on a compliant substrate of finite thickness. Analysis of the problem shows that substrate thickness has a significant effect on the steady-state energy release rate for channel cracks. This is so over a wide range of elastic mismatch between film and substrate, but is especially important if the substrate is more compliant than the film. Relaxation of the film stress due to elastic deformation of the substrate also plays an important role. If the substrate is clamped around the edge, as would be the case for a coated membrane, the stress in the coating cannot relax and the energy release rate for channel cracking increases significantly with decreasing substrate thickness. If the film stress is allowed to relax, however, the driving force for cracking is reduced as the substrate thickness decreases. The results from this study are used to evaluate the change in curvature of a film/substrate assembly due to channel cracking, a quantity that is of interest for the experimental determination of stresses in thin films. An expression for the elastic extension of the substrate due to channel cracking is derived making it possible to evaluate the effect of cracking on the mechanical behavior of bilayer membranes. It is expected that the present study may lead to the development of new experimental techniques for measuring the fracture toughness of thin coatings.     

Elasto-plastic properties of gold thin films deposited onto polymeric substrates

This work examines mechanical properties of 50–300 nm gold thin films deposited onto micrometer-thick flexible polymer substrates by means of tensile testing of the film–substrate system and modeling. The film properties are extracted from mechanical testing of the film–substrate system and modeling of the bimaterial. Unlike materials in bulk geometry, the film elastic modulus and yield strength present an important dependence with film thickness, with modulus and yield strength of about 520 and 30 GPa, respectively, for the thinner films and decreasing toward the bulk value as the film thickness increases. The relation between grain size, film thickness, and yield strength is examined. Finite element analysis provides further insight into the stress distribution in the film–substrate system. L. Llanes—MS student at ITM, Merida, Mexico.     

Anisotropy driven interrupted coarsening of the Asaro-Tiller-Grinfeld instability

We investigate the effects of surface energy anisotropy on the coarsening dynamics of the Asaro-Tiller-Grinfeld instability at stake in thin semiconductor films. We consider a continuum model which accounts for wetting interactions between the film and its substrate, elasticity driven mass currents and surface energy anisotropy. We derive an explicit non-linear, non-local evolution equation for the film height that we solve numerically. Anisotropy, which dictates the island shapes, impacts the growth kinetics by weakening the possible elastic relaxation, which can lead during annealing to an interruption of Ostwald ripening. The resulting stationary state is characterized by square-based pyramids separated by a wetting layer. It is found that the instability onset is delayed when the film thickness decreases above the critical thickness for the instability to occur. We characterize the influence of the growing flux used for the film deposition on the stationary state reached during subsequent annealing, and find that the density of the resulting self-organized islands increases with the flux.     

Mechanical properties of HfB<Subscript>2.7</Subscript> nanocrystalline thin films

The paper describes comparative nanoindentation tests of an HfB₂ single crystal and an HfB_2.7 nanocrystalline thin film deposited on a steel substrate by magnetron sputtering. The boron superstoichiometry and small grain size are shown to result in a significant increase in hardness and decrease of elastic modulus of the thin HfB_2.7 film in comparison to the bulk single crystal. The abnormally high (for inorganic materials) value (87%) of elastic recovery of the impression depth in the thin HfB_2.7 film upon the indenter unloading suggests that the film can be considered as a promising wear-resistant coating.     

Artificial Soft Elastic Media with Periodic Hard Inclusions for Tailoring Strain‐Sensitive Thin‐Film Responses

Engineering the coupling behavior between a functional thin film and a soft substrate provides an attractive pathway for controlling various properties of thin‐film materials. However, existing studies mostly rely on uniform deformation of the substrate, and the effect of well‐regulated and nonuniform strain distributions on strain‐sensitive thin‐film responses still remains elusive. Herein, artificially strain‐regulated elastic media are presented as a novel platform for tailoring strain‐sensitive thin‐film responses. The proposed artificial soft elastic media are composed of embedded arrays of inkjet‐printed polymeric strain modulators that exhibit a high modulus contrast with respect to that of the soft matrix. This strain‐modulating lattice induces spatially regulated strain distributions based on localized strain‐coupling. Controlling the structural parameters and lattice configurations of the media leads to spatial modulation of the microscopically localized as well as macroscopically accumulated strain profiles. Uniform thin films coupled to these media undergo artificially tailored deformation through lattice‐like strain‐coupled pathways. The resulting phenomena yield programmable strain‐sensitive responses such as spatial arrangement of ternary‐state surface wrinkles and stepwise tuning of piezoresistive responses. This work will open a new avenue for addressing the issue of controlling strain‐sensitive thin‐film properties through structural engineering of artificial soft elastic media.     

Study of electrical and microstructure properties of high dielectric hafnium oxide thin film for MOS devices

Hafnium oxide (HfO₂) has emerged as the most promising highkdielectric for MOS devices. As-deposited sputtered HfO₂ thin films have large number of defects resulting in increased oxide charge and leakage current. In this paper the effect of sputtering voltage, bias sputtering and post deposition thermal annealing is investigated. The I–V and C–V characteristics of the dielectric film are studied employing Al–HfO₂–Si MOS capacitor structure. It is found that oxide charge increases with increasing sputtering voltage. Thermal annealing in oxygen reduces the interface/oxide charges and leakage current. It is shown that applying substrate bias during film deposition leakage current is further reduced by an order of magnitude. The microstructure of thin film is examined by AFM. The reduction in surface roughness with bias sputtering is shown. The experimental results are presented and discussed for device application.