Indentation Of Thin Films Research Articles

Optimizing the Indirect Indentation Method for brittle material property measurements

This work reports on optimizing the Indirect Indentation Method for measuring the elastic properties of brittle materials by indentation. The method employs a thin metallic film that protects the brittle material by absorbing the inelastic damage causes by the penetrating indenter. It applies hyperbolic identities to the Zhou-Prorok Model for thin film indentation that approach an asymptote as the indenter advances toward the film/substrate interface. The slope of this asymptote has been shown to be directly related to the elastic modulus of the brittle material being tested. A parameter study was conducted and revealed that the method can be optimized when the film Poisson’s ratio is lower than the brittle material tested. This more directly transfers the indenter load to the substrate, enabling it to participate in the composite elastic response earlier in the indentation process. The result is an expanded range of fit of the experimental data to the models linear asymptote, providing more accurate elastic property measurements. Chromium was identified as an ideal film material due to its low Poisson’s ratio, ductility and ability to be deposited onto most ceramics with a strong interface. The improvement was demonstrated on 5 brittle materials with a wide variety of elastic properties; SiC, Al2O3, MgO, SiO2, CaCO3.

Examination of Prestressed Coating/Substrate Systems Using Spherical Indentation—Determination of Film Prestress, Film Modulus, and Substrate Modulus

There have been many studies performed with respect to the indentation of thin films affixed to a corresponding substrate base. These studies have primarily focused on determining the mechanical properties of the film. It is the goal of this paper to further understand the role that the film plays and how a potential prestressing of this film has on both the film and substrate base. It is equally important to be able to understand the material properties of the substrate since during manufacturing or long-term use, the substrate properties may change. In this study, we establish through spherical indentation a framework to characterize the material properties of both the substrate and film as well as a method to determine the prestress of the film. It is proposed that through an initial forward analysis, a set of relationships are developed. A single spherical indentation test can then be performed, measuring the indentation force at two prescribed depths, and with the relationships developed from the forward analysis, the material properties of both the film and substrate can be determined. The problem is further enhanced by also developing the capability of determining any equibiaxial stress state that may exist in the film. A generalized error sensitivity analysis of this formulation is also performed systematically. This study will enhance the present knowledge of a typical prestressed film/substrate system as is commonly used in many of today’s engineering and technical applications.

Molecular dynamics simulation of the indentation of nanoscale films on a substrate

It is shown that atomistic modeling of the indentation of thin films using the method of molecular dynamics (MD) has some advantages on the nanoscale level in comparison to the traditional method of finite elements. Effects revealed by the MD simulations, including delamination and cracking of the film under indenter and the formation and propagation of dislocations are considered. Elastic properties of a nanoscale film on substrate have been studied using the Tersoff potential in application to the silicon carbide film on silicon (SiC/Si). The results of MD simulation qualitatively agree with recent experimental data for indentation in the SiC/Si system. The influence of parameters of the Tersoff potential on the Young’s modulus of simulated materials has been studied for silicon.

Evaluating indent pile-up with metallic films on ceramic-like substrates

Abstract

Identification and design of novel polymer-based mechanical transducers: A nano-structural model for thin film indentation

Mechanical characterization is important for understanding small-scale systems and developing devices, particularly at the interface of biology, medicine, and nanotechnology. Yet, monitoring sub-surface forces is challenging with current technologies like atomic force microscopes (AFMs) or optical tweezers due to their probe sizes and sophisticated feedback mechanisms. An alternative transducer design relying on the indentation mechanics of a compressible thin polymer would be an ideal system for more compact and versatile probes, facilitating measurements in situ or in vivo. However, application-specific tuning of a polymer's mechanical properties can be burdensome via experimental optimization. Therefore, efficient transducer design requires a fundamental understanding of how synthetic parameters such as the molecular weight and grafting density influence the bulk material properties that determine the force response. In this work, we apply molecular-level polymer scaling laws to a first order elastic foundation model, relating the conformational state of individual polymer chains to the macroscopic compression of thin film systems. A parameter sweep analysis was conducted to observe predicted model trends under various system conditions and to understand how nano-structural elements influence the material stiffness. We validate the model by comparing predicted force profiles to experimental AFM curves for a real polymer system and show that it has reasonable predictive power for initial estimates of the force response, displaying excellent agreement with experimental force curves. We also present an analysis of the force sensitivity of an example transducer system to demonstrate identification of synthetic protocols based on desired mechanical properties. These results highlight the usefulness of this simple model as an aid for the design of a new class of compact and tunable nanomechanical force transducers.

Collective Mechanical Behavior of Multilayer Colloidal Arrays of Hollow Nanoparticles

The collective mechanical behavior of multilayer colloidal arrays of hollow silica nanoparticles (HSNP) is explored under spherical nanoindentation through a combination of experimental, numerical, and theoretical approaches. The effective indentation modulus E(ind) is found to decrease with an increasing number of layers in a nonlinear manner. The indentation force versus penetration depth behavior for multilayer hollow particle arrays is predicted by an approximate analytical model based on the spring stiffness of the individual particles and the multipoint, multiparticle interactions as well as force transmission between the layers. The model is in good agreement with experiments and with detailed finite element simulations. The ability to tune the effective indentation modulus, E(ind), of the multilayer arrays by manipulating particle geometry and layering is revealed through the model, where E(ind) = (0.725m(-3/2) + 0.275)E(mon) and E(mon) is the monolayer modulus and m is number of layers. E(ind) is seen to plateau with increasing m to E(ind_plateau) = 0.275E(mon) and E(mon) scales with (t/R)(2), t being the particle shell thickness and R being the particle radius. The scaling law governing the nonlinear decrease in indentation modulus with an increase in layer number (E(ind) scaling with m(-3/2)) is found to be similar to that governing the indentation modulus of thin solid films E(ind_solid) on a stiff substrate (where E(ind_solid) scales with h(-1.4) and also decreases until reaching a plateau value) which also decreases with an increase in film thickness h. However, the mechanisms underlying this trend for the colloidal array are clearly different, where discrete particle-to-particle interactions govern the colloidal array behavior in contrast to the substrate constraint on deformation, which governs the thickness dependence of the continuous thin film indentation modulus.

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.

Multiple 3D inhomogeneous inclusions in a half space under contact loading

A semi-analytic solution is given for multiple three-dimensional inhomogeneous inclusions of arbitrary shape in an isotropic half space under contact loading. The solution takes into account interactions between all the inhomogeneous inclusions as well as the interaction between the inhomogeneous inclusions and the loading indenter. In formulating the governing equations for the inhomogeneous inclusion problem, the inhomogeneous inclusions are treated as homogenous inclusions with initial eigenstrains plus unknown equivalent eigenstrains, according to Eshelby’s equivalent inclusion method. Such a treatment converts the original contact problem concerning an inhomogeneous half space into a homogeneous half-space contact problem, for which governing equations with unknown contact load distribution can be conveniently formulated. All the governing equations are solved iteratively using the Conjugate Gradient Method. The iterative process is performed until the convergence of the half-space surface displacements, which are the sum of the displacements due to the contact load and the inhomogeneous inclusions, is achieved. Finally, the obtained solution is applied to two example cases: a single inhomogeneity in a half space subjected to indentation and a stringer of inhomogeneities in an indented half-space. The validation of the solution is done by modeling a layer of film as an inhomogeneity and comparing the present solution with the analytic solution for elastic indentation of thin films. This general solution is expected to have wide applications in addressing engineering problems concerning inelastic deformation and material dissimilarity as well as contact loading.

A new paradigm in thin film indentation

A new method to accurately and reliably extract the actual Young's modulus of a thin film on a substrate by indentation was developed. The method involved modifying the discontinuous elastic interface transfer model to account for substrate effects that were found to influence behavior a few nanometers into a film several hundred nanometers thick. The method was shown to work exceptionally well for all 25 different combinations of five films on five substrates that encompassed a wide range of compliant films on stiff substrates to stiff films on compliant substrates. A predictive formula was determined that enables the film modulus to be calculated as long as one knows the film thickness, substrate modulus, and bulk Poisson's ratio of the film and the substrate. The calculated values of the film modulus were verified with prior results that used the membrane deflection experiment and resonance-based methods. The greatest advantages of the method are that the standard Oliver and Pharr analysis can be used, and that it does not require the continuous stiffness method, enabling any indenter to be used. The film modulus then can be accurately determined by simply averaging a handful of indents on a film/substrate composite.

A Discontinuous Elastic Interface Transfer Model of Thin Film Nanoindentation

A new model of thin film indentation that accounted for an apparent discontinuity in elastic strain transfer at the film/substrate interface was developed. Finite element analysis suggested that numerical values of strain were not directly continuous across the interface; the values in the film were higher when a soft film was deposited on a hard substrate. The new model was constructed based on this discontinuity; whereby, separate weighting factors were applied to account for the influence of the substrate in strain developed in the film and vice-versa. By comparing the model to experimental data from thirteen different amorphous thin film materials on a silicon substrate, constants in each weighting factor were found to have physical significance in being numerically similar to the bulk scale Poisson’s ratios of the materials involved. When employing these material properties in the new model it was found to provide an improved match to the experimental data over the existing Doerner and Nix and Gao models. Finally, the model was found to be capable of assessing the Young’s modulus of thin films that do not exhibit a flat region as long as the bulk Poisson’s ratio is known.

Molecular dynamics study of crystal plasticity during nanoindentation in Ni nanowires

Molecular dynamics simulations were performed to gain fundamental insight into crystal plasticity, and its size effects in nanowires deformed by spherical indentation. This work focused on <111>-oriented single-crystal, defect-free Ni nanowires of cylindrical shape with diameters of 12 and 30 nm. The indentation of thin films was also comparatively studied to characterize the influence of free surfaces in the emission and absorption of lattice dislocations in single-crystal Ni. All of the simulations were conducted at 300 K by using a virtual spherical indenter of 18 nm in diameter with a displacement rate of 1 m·s−1. No significant effect of sample size was observed on the elastic response and mean contact pressure at yield point in both thin films and nanowires. In the plastic regime, a constant hardness of 21 GPa was found in thin films for penetration depths larger than 0.8 nm, irrespective of variations in film thickness. The major finding of this work is that the hardness of the nanowires decreases as the sample diameter decreases, causing important softening effects in the smaller nanowire during indentation. The interactions of prismatic loops and dislocations, which are emitted beneath the contact tip, with free boundaries are shown to be the main factor for the size dependence of hardness in single-crystal Ni nanowires during indentation.

Wedge indentation of thin films modelled by strain gradient plasticity

A plane strain study of wedge indentation of a thin film on a substrate is performed. The film is modelled with the strain gradient plasticity theory by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379–1406] and analysed using finite element simulations. Several trends that have been experimentally observed elsewhere are captured in the predictions of the mechanical behaviour of the thin film. Such trends include increased hardness at shallow depths due to gradient effects as well as increased hardness at larger depths due to the influence of the substrate. In between, a plateau is found which is observed to scale linearly with the material length scale parameter. It is shown that the degree of hardening of the material has a strong influence on the substrate effect, where a high hardening modulus gives a larger impact on this effect. Furthermore, pile-up deformation dominated by plasticity at small values of the internal length scale parameter is turned into sink-in deformation where plasticity is suppressed for larger values of the length scale parameter. Finally, it is demonstrated that the effect of substrate compliance has a significant effect on the hardness predictions if the effective stiffness of the substrate is of the same order as the stiffness of the film.

An Improvement of the Doerner-Nix Function for Substrate Effects in Ultrathin Films

AbstractSubstrate effects continue to be the key issue in interrogating thin films by nanoindentation. In this study, we studies amorphous thin films of several different materials deposited onto a silicon wafer. These materials span from being considerable softer than the substrate to films significantly harder than the substrate. The thin film Young's modulusEfwas measured with a MTS Nanoindenter XP system using the continuous stiffness measurement (CSM). The so-called “flat region” was observed in the early stage of nearly every CSM modulus-displacement curve for all materials studied. The depth of this region (hcr) was found to vary with the material. Based on the experimental data, we were able to modify the Doerner & Nix model for thin film indentation on a substrate, particularly their parameter alpha (α). The modified relation was found to be adept at closely matching all experimental data collected, which spanned both soft films on hard substrates and hard films on soft substrates.

Variable temperature thin film indentation with a flat punch

We present modifications to conventional nanoindentation that realize variable temperature, flat punch indentation of ultrathin films. The technique provides generation of large strain, thin film extrusion of precise geometries that idealize the essential flows of nanoimprint lithography, and approximate constant area squeeze flow rheometry performed on thin, macroscopic soft matter samples. Punch radii as small as 185 nm have been realized in ten-to-one confinement ratio testing of 36 nm thick polymer films controllably squeezed in the melt state to a gap width of a few nanometers. Self-consistent, compressive stress versus strain measurements of a wide variety of mechanical testing conditions are provided by using a single die-sample system with temperatures ranging from 20 to 125 degrees C and loading rates spanning two decades. Low roughness, well aligned flat punch dies with large contact areas provide precise detection of soft surfaces with standard nanoindenter stiffness sensitivity. Independent heating and thermometry with heaters and thermocouples attached to the die and sample allow introduction of a novel directional heat flux measurement method to ensure isothermal contact conditions. This is a crucial requirement for interpreting the mechanical response in temperature sensitive soft matter systems. Instrumented imprint is a new nanomechanics material testing platform that enables measurements of polymer and soft matter properties during large strains in confined, thin film geometries and extends materials testing capabilities of nanoindentation into low modulus, low strength glassy, and viscoelastic materials.

박막 물성평가 압입시험의 수치접근법

In this work, the prior indentation theory for a bulk material is extended to an indentation theory for evaluation of thin-film material properties. We first select the optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to the thin-film indentation technique is then proposed by examining the finite element solutions at the optimal point. With this new approach, from the load-depth curve, we obtain the values of Young's modulus, yield strength, strainhardening exponent. The average errors of those values are less than 3, 5, 8% respectively.

Indentation of a hard film on a soft substrate: Strain gradient hardening effects

The strain gradient work hardening is important in micro-indentation of bulk metals and thin metallic films, though the indentation of thin films may display very different behavior from that of bulk metals. We use the conventional theory of mechanism-based strain gradient plasticity (CMSG) to study the indentation of a hard tungsten film on soft aluminum substrate, and find good agreement with experiments. The effect of friction stress (intrinsic lattice resistance), which is important in body-center-cubic tungsten, is accounted for. We also extend CMSG to a finite deformation theory since the indentation depth in experiments can be as large as the film thickness. Contrary to indentation of bulk metals or soft metallic films on hard substrate, the micro-indentation hardness of a hard tungsten film on soft aluminum substrate decreases monotonically with the increasing depth of indentation, and it never approaches a constant (macroscopic hardness). It is also shown that the strain gradient effect in the soft aluminum substrate is insignificant, but that in the hard tungsten thin film is important in shallow indentation. The strain gradient effect in tungsten, however, disappears rapidly as the indentation depth increases because the intrinsic material length in tungsten is rather small.

Nanoindentation of plasma-deposited nitrogen-rich silicon nitride thin films

Nanoindentation was performed on plasma-deposited nitrogen-rich silicon nitride thin films deposited on various substrates between 150 and 300°C. A very simple and effective depth-profiling method is introduced, which involves indentation of thin films deposited on substrates with different mechanical properties. The primary advantage of this method is that it avoids the complications associated with many of the complex mathematical models available to deconvolve thin film mechanical properties, while nevertheless allowing the user to visually identify thin film properties. This method is demonstrated on our thin films, which have a hardness between 14 and 21GPa, and reduced modulus between 120 and 160GPa. The initial rise in hardness at low contact depths, commonly attributed to an indentation-size effect, is shown to be due to elastic contact between the indenter and thin film surface. This demonstrates the perils of blindly following the 10% rule for hardness calculation. The contribution of elastic and plastic deformations from nanoindentation is used to clarify the physical meaning of hardness and reduced modulus.

Reply to ‘Comment on “Axisymmetric indentation of an incompressible elastic thin film”’

In this reply, it is shown that the solution suggested by Chadwick is a solution for a particularly simple set of conditions for indentation of thin films with a frictionless contact condition on both contact interfaces. A simple method is used to obtain the relation between the average indentation stress and the indentation displacement for indentation of compressible elastic thin films by a flat-ended cylindrical indenter. It turns out that the relation reduces to the previous result when the Poisson ratio is equal to 0.5.

Comment on ‘Axisymmetric indentation of an incompressible elastic thin film’

It is shown that a recent method based on the asymptotic inversion of Hankel transforms for indentation of thin films (Yang F Q 2003 J. Phys. D: Appl. Phys. 36 50) provides a non-unique solution for the case of frictionless contact between the film and the substrate. In addition to the solution given by Yang, another one exists having zero hydrostatic stress that results in half the force acting on the indenter for the same indentation. A more rigorous asymptotic method (Chadwick R S 2002 SIAM J. Appl. Math. 62 1520) singles out the smaller force solution as the correct one.

The Mechanics of Nanoimprint Forming

ABSTRACTNanoimprint and a number of other related techniques are a collection of surface patterning technologies that involve direct contact of a master template with the target surface. As such, they are governed by the laws of contacting bodies, and the mechanics involved can readily be investigated by existing indentation methods or close variants thereof. Among the many demonstrated applications of nanoimprint, lithographic resist processing has generated considerable interest due to its combination of high resolution with rapid throughput over wide areas. Pattern transfer can be achieved by the application of heat and pressure to the stamp (hot embossing), or solely by the generation of shear stress at the contact (cold forming.) In both cases we have found that elastic and viscoplastic strains are present during the forming process, the former of which can considerably alter the characteristics of the pattern transfer. The use of depth sensing instrumented indentation in conjunction with specially designed stamps and a variety of microscopy techniques has allowed us to isolate, control, and measure many of the stresses and strains directly during the imprint process. Further, in a more standard role, the indenter can be used to characterize the mechanical properties of imprinted structures. In this paper we summarize our experimental findings and conclusions on the role of important factors influencing the fidelity of the imprint process including elastic stresses, plastic deformation mechanisms, complexities in the confined deformation rheology, and choices in the form of applied stress. These are illustrated by a series of idealized experiments ranging from the squeeze flow of prepared coupons to the flat punch indentation of thin films and back extrusion into isolated cavities. A connection between these more localized experiments and the established findings and requirements of applications such as wide area lithography and functional polymer patterning will be made to establish the concept of “instrumented imprint”.