Yield Strength Of Thin Films Research Articles

Estimating the Modulus and Yield Strength of the Top-Layer Film on Multilayer BEOL Stacks

The manufacturing process-caused variation in the modulus and the yield strength of individual layers in passivated metal stacks critically impacts the reliability of back-end-of-line (BEOL) structures. However, experimentally characterizing the elastic modulus and yield strength of thin films as fabricated, with sufficient sensitivity to distinguish process-induced property variations, remains a significant challenge. Towards this end, we utilize nanoindentation experiments to estimate the elastic modulus and yield strength of top-layer films in multilayer stacks. To address the challenge of extracting individual layer modulus from the composite modulus, in the present paper, we propose a depth-dependent mathematical model (dominant regime theory) by which the modulus of the top-layer can be estimated accurately. Additionally, we employ optimization-based inverse finite element analysis (IFEA) to numerically estimate the modulus and the yield strength of the top-layer film. The uniqueness of the properties estimated by IFEA is investigated through a full-factorial statistically designed numerical experiment. The developed techniques are demonstrated by estimating the modulus as well as the yield strength of tetraethylorthosilicate (TEOS) film on a two-layer stack (TEOS, Silicon) and the same film deposited on a multilayer stack (TEOS, Aluminum, Silicon Nitride, Silicon).

Estimating the Yield Strength of Thin Metal Films Through Elastic–Plastic Buckling-Induced Debonding

In this correspondence, we propose a procedure to estimate the yield strength of thin films by debonding films from their substrate by elastic-plastic buckling under thermally induced compressive loading. The out-of-plane displacement of the metal lines under conditions of elastic-plastic buckling is dependent on the yield strength of the film. Thus, an inverse estimate of the yield strength is made from measurements of the out-of-plane displacements of the buckled metal lines. The procedure is demonstrated to estimate the yield strength of aluminum lines consistent with the measurements by other techniques.

Distribution of dislocation source length and the size dependent yield strength in freestanding thin films

A method is proposed to estimate the size-dependent yield strength of columnar-grained freestanding thin films. The estimate relies on assuming a distribution of the size of Frank–Read sources, which is then translated into a log-normal distribution of the source strength, depending on film thickness, grain size and theoretical strength of the material, augmented with a single fit parameter. Two-dimensional discrete dislocation plasticity (DDP) simulations are carried out for two sets of Cu films and the fit parameter is determined from independent experiments. Subsequent DDP predictions of the stress–strain curves in comparison with the corresponding experimental data show excellent agreement of initial yield strength and hardening rate for films of varying film thickness and grain size. Having thus demonstrated the power of the proposed strength distribution, it is shown that the mode of this distribution governs the most effective source strength. This is then used to suggest a method to estimate the yield strength of thin films as a function of film thickness and grain size. Simple maps are presented that are in very good agreement with recent experimental results for Cu thin films.

Size-dependent yield strength of thin films

Biaxial strain and pure shear of a thin film are analysed using a strain gradient plasticity theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379–1406]. Constitutive equations are formulated based on the assumption that the free energy only depends on the elastic strain and that the dissipation is influenced by the plastic strain gradients. The three material length scale parameters controlling the gradient effects in a general case are here represented by a single one. Boundary conditions for plastic strains are formulated in terms of a surface energy that represents dislocation buildup at an elastic/plastic interface. This implies constrained plastic flow at the interface and it enables the simulation of interfaces with different constitutive properties. The surface energy is also controlled by a single length scale parameter, which together with the material length scale defines a particular material. Numerical results reveal that a boundary layer is developed in the film for both biaxial and shear loading, giving rise to size effects. The size effects are strongly connected to the buildup of surface energy at the interface. If the interface length scale is small, the size effect vanishes. For a stiffer interface, corresponding to a non-vanishing surface energy at the interface, the yield strength is found to scale with the inverse of film thickness. Numerical predictions by the theory are compared to different experimental data and to dislocation dynamics simulations. Estimates of material length scale parameters are presented.

Yield strengths and stress induced crackles in copper films: effects of substrate and passivated layer

Yield strengths in unpassivated and 530 nm TiN passivated Cu films deposited on Ti, high-speed steel and Ni substrates have been measured by x-ray diffraction (XRD) in combination with the four-point bending method. The results show that, although the texture and average grain size, investigated by XRD and transmission electron microscopy respectively, do not vary with different substrate, the yield strength of the Cu film increases obviously when a thin passivated layer is present and varies slightly with substrates. Many crackles appear in the passivated Cu film on Ti substrate but do not appear in other samples. The experimental results have been explained satisfactorily with an expression for the yield strength of thin films given previously.

A simple technique for determining yield strength of thin films

A technique to measure the yield strength of thin films has been developed which combines experimental observations of deflection and plastic deformation with finite element predictions of stress. This technique relies on integrated circuit technology to build bridge and cross beam test structures with a range of dimensions. Each structure is deflected in increments of 1 μm until the structure no longer elastically recovers upon release. In tandem with experimentally verified numerical predictions of force and stress, the yield strength of the thin film can be bounded between the highest elastic stress result and the lowest plastic stress result. For our test material of copper, this method provides a yield strength between 2.80 and 3.09 GPa, a value significantly larger than that for bulk copper, but consistent with thin film theory.

A Simple Technique for Determining Yield Strength of Thin Films

A Simple Technique for Determining Yield Strength of Thin Films

A technique for the determination of stress in thin films

Intrinsic stress, elastic bulk modulus, and yield strength of thin films has been determined by measuring the deformation versus pressure of circular membranes of the materials. Low pressure chemical vapor deposited (LPCVD) silicon-rich silicon nitride (SiNx) has been extensively characterized and found to have an intrinsic stress of ∼1×109 dyn/cm2 and a bulk modulus of ∼1.9×1012 dyn/cm2. A SiNx membrane 1.0 cm in diameter and 1.0 μm thick has been found to survive a differential pressure of 470 Torr with no measurable plastic deformation. Experimental data for several different types of silicon nitride membranes is given. It is shown that the stress measurement technique can be extended to measure accurately the intrinsic stress of thin films deposited onto SiNx membranes.